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%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "2.23",
%%%     date            = "30 October 2017",
%%%     time            = "06:25:46 MDT",
%%%     filename        = "issac.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "09179 38216 189780 1948736",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography, ISSAC, International
%%%                        Symposium on Symbolic and Algebraic
%%%                        Computation",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of papers presented
%%%                        at the annual ISSAC (International Symposia
%%%                        on Symbolic and Algebraic Computation)
%%%                        conferences.  These conferences have been
%%%                        held most years since 1966, with the 23th on
%%%                        August 13--15, 1998 at the University of
%%%                        Rostock, Germany.
%%%
%%%                        It also includes papers from the PASCO
%%%                        (Parallel Symbolic Computation)
%%%                        conferences, the SYMSAC (Symbolic and
%%%                        Algebraic Computation) conferences, and a
%%%                        few papers on symbolic algebra from other
%%%                        conferences not specifically devoted to
%%%                        that subject.
%%%
%%%                        Companion bibliographies sigsam.bib and
%%%                        jsymcomp.bib cover papers in the area of
%%%                        symbolic and algebraic computation
%%%                        published in SIGSAM Bulletin and the
%%%                        Journal of Symbolic Computation.
%%%
%%%                        At version 2.23, the year coverage looked
%%%                        like this:
%%%
%%%                             1976 (   1)    1989 ( 106)    2002 (  36)
%%%                             1977 (   0)    1990 (  64)    2003 (  40)
%%%                             1978 (   0)    1991 (  86)    2004 (  47)
%%%                             1979 (   1)    1992 (  50)    2005 (  52)
%%%                             1980 (   0)    1993 (  58)    2006 (  55)
%%%                             1981 (   2)    1994 ( 103)    2007 (  54)
%%%                             1982 (   1)    1995 (  52)    2008 (  47)
%%%                             1983 (   0)    1996 (  50)    2009 (  54)
%%%                             1984 (   0)    1997 (  88)    2010 (  52)
%%%                             1985 (   0)    1998 (  49)    2011 (  50)
%%%                             1986 (  50)    1999 (  41)    2012 (  53)
%%%                             1987 (   0)    2000 (  44)    2013 (  55)
%%%                             1988 (   0)    2001 (  48)
%%%
%%%                             Article:          3
%%%                             Book:             1
%%%                             InProceedings: 1441
%%%                             Proceedings:     44
%%%
%%%                             Total entries: 1489
%%%
%%%                        Regrettably, bibliographic data for most of
%%%                        these conferences prior to 1989 are
%%%                        inaccessible electronically.  With an
%%%                        estimated 60 papers at each conference, a
%%%                        complete bibliography would have about 1800
%%%                        entries, so the coverage is only about 25%.
%%%
%%%                        This bibliography has been collected from
%%%                        bibliographies in the author's personal
%%%                        files, from the OCLC and IEEE INSPEC
%%%                        (1989--1995) databases, and from the
%%%                        computer science bibliography collection on
%%%                        ftp.ira.uka.de in /pub/bibliography to
%%%                        which many people of have contributed.  The
%%%                        snapshot of this collection was taken on
%%%                        5-May-1994, and it consists of 441 BibTeX
%%%                        files, 2,672,675 lines, 205,289 entries,
%%%                        and 6,375 <at>String{} abbreviations,
%%%                        occupying 94.8MB of disk space.
%%%
%%%                        Numerous errors have been corrected, and TeX
%%%                        mathematics mode markup has been added
%%%                        manually to more than 1000 text fragments in
%%%                        the key values.
%%%
%%%                        BibTeX citation tags are uniformly chosen
%%%                        as name:year:abbrev, where name is the
%%%                        family name of the first author or editor,
%%%                        year is a 4-digit number, and abbrev is a
%%%                        3-letter condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        In this bibliography, entries are sorted
%%%                        first by ascending year, and within each
%%%                        year, alphabetically by author or editor,
%%%                        and then, if necessary, by the 3-letter
%%%                        abbreviation at the end of the BibTeX
%%%                        citation tag, using the bibsort -byyear
%%%                        utility.  Year order has been chosen to
%%%                        make it easier to identify the most recent
%%%                        work.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
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%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-SIGNUM                = "ACM SIGNUM Newsletter"}

@String{j-SIGSAM                = "SIGSAM Bulletin (ACM Special
                                  Interest Group on Symbolic and
                                  Algebraic Manipulation)"}

%%% ====================================================================
%%% Publisher abbreviations:
@String{pub-ACM                 = "ACM Press"}

@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}

@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}

@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-IEEE                = "IEEE Computer Society Press"}

@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300, Silver
                                    Spring, MD 20910, USA"}

@String{pub-SIAM                = "SIAM Press"}

@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-SV                  = "Springer-Verlag"}

@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg, Germany~/
                                    London, UK~/ etc."}

@String{pub-WORLD-SCI           = "World Scientific Publishing Co."}

@String{pub-WORLD-SCI:adr       = "Singapore; Philadelphia, PA, USA; River
                                  Edge, NJ, USA"}

%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNCS                = "Lecture Notes in Computer Science"}

%%% ====================================================================
%%% Bibliography entries:
@InProceedings{Fateman:1981:CAN,
  author =       "Richard J. Fateman",
  title =        "Computer Algebra and Numerical Integration",
  crossref =     "Wang:1981:SPA",
  pages =        "228--232",
  year =         "1981",
  bibdate =      "Mon Apr 25 07:01:52 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Algebraic manipulation systems such as MACSYMA include
                 algorithms and heuristic procedures for indefinite and
                 definite integration, yet these system facilities are
                 not as generally useful as might be thought. Most
                 isolated definite integration problems are more
                 efficiently tackled with numerical programs.
                 Unfortunately, the answers obtained are sometimes
                 incorrect, in spite of assurances of accuracy;
                 furthermore, large classes of problems can sometimes be
                 solved more rapidly by preliminary algebraic
                 transformations. In this paper we indicate various
                 directions for improving the usefulness of integration
                 programs given closed form integrands, via algebraic
                 manipulation techniques. These include expansions in
                 partial fractions or Taylor series, detection and
                 removal of singularities and symmetries, and various
                 approximation techniques for troublesome problems.",
  acknowledgement = ack-nhfb,
}

@Book{Buchberger:1982:CAS,
  author =       "Bruno Buchberger and George Edward Collins and Rudiger
                 Loos and R. Albrecht",
  title =        "Computer algebra: symbolic and algebraic computation",
  volume =       "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 283",
  year =         "1982",
  ISBN =         "0-387-81684-4",
  ISBN-13 =      "978-0-387-81684-5",
  LCCN =         "QA155.7.E4 C65 1982",
  bibdate =      "Thu Dec 28 13:48:31 1995",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       "Computing. Supplementum",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; measurement; theory",
  subject =      "S1 Algebra --- Data processing; S2 Machine theory",
}

@InProceedings{Abbott:1986:BAN,
  author =       "J. A. Abbott and R. J. Bradford and J. H. Davenport",
  title =        "The {Bath} algebraic number package",
  crossref =     "Char:1986:PSS",
  pages =        "250--253",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p250-abbott/",
  acknowledgement = ack-nhfb,
  keywords =     "design; measurement; performance",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Simplification of expressions.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE.",
}

@InProceedings{Abdali:1986:OOA,
  author =       "S. K. Abdali and Guy W. Cherry and Neil Soiffer",
  title =        "An object-oriented approach to algebra system design",
  crossref =     "Char:1986:PSS",
  pages =        "24--30",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p24-abdali/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 D.3.3} Software, PROGRAMMING LANGUAGES, Language
                 Constructs and Features, Abstract data types. {\bf
                 D.3.4} Software, PROGRAMMING LANGUAGES, Processors,
                 Run-time environments. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Specialized application languages. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Very high-level languages.",
}

@InProceedings{Akritis:1986:TNU,
  author =       "Alkiviadis G. Akritis",
  title =        "There is no ``{Uspensky}'s method''",
  crossref =     "Char:1986:PSS",
  pages =        "88--90",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p88-akritis/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf G.1.5} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Polynomials, methods for. {\bf K.2} Computing Milieux,
                 HISTORY OF COMPUTING, Systems. {\bf G.1.5} Mathematics
                 of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Iterative methods. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Arnborg:1986:ADR,
  author =       "S. Arnborg and H. Feng",
  title =        "Algebraic decomposition of regular curves",
  crossref =     "Char:1986:PSS",
  pages =        "53--55",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p53-arnborg/",
  acknowledgement = ack-nhfb,
  keywords =     "theory",
  subject =      "{\bf I.1.m} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Miscellaneous.",
}

@InProceedings{Bachmair:1986:CPC,
  author =       "Leo Bachmair and Nachum Dershowitz",
  title =        "Critical-pair criteria for the {Knuth--Bendix}
                 completion procedure",
  crossref =     "Char:1986:PSS",
  pages =        "215--217",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p215-bachmair/",
  acknowledgement = ack-nhfb,
  keywords =     "languages; theory; verification",
  subject =      "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Grammars and Other Rewriting
                 Systems, Parallel rewriting systems. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf I.1.1}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Simplification of expressions. {\bf F.2.3} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Tradeoffs between Complexity Measures. {\bf
                 F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Complexity of proof procedures.",
}

@InProceedings{Bajaj:1986:LAS,
  author =       "Chanderjit Bajaj",
  title =        "Limitations to algorithm solvability: {Galois} methods
                 and models of computation",
  crossref =     "Char:1986:PSS",
  pages =        "71--76",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p71-bajaj/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf G.2.m} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Miscellaneous. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm design and analysis.",
}

@InProceedings{Bayer:1986:DMS,
  author =       "D. Bayer and M. Stillman",
  title =        "The design of {Macaulay}: a system for computing in
                 algebraic geometry and commutative algebra",
  crossref =     "Char:1986:PSS",
  pages =        "157--162",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p157-bayer/",
  acknowledgement = ack-nhfb,
  keywords =     "design; performance; theory",
  subject =      "{\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems.",
}

@InProceedings{Beck:1986:SAL,
  author =       "Robert E. Beck and Bernard Kolman",
  title =        "Symbolic algorithms for {Lie} algebra computation",
  crossref =     "Char:1986:PSS",
  pages =        "85--87",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p85-beck/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; performance; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.2.2} Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Automatic Programming. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, MACSYMA. {\bf K.2}
                 Computing Milieux, HISTORY OF COMPUTING, Systems.",
}

@InProceedings{Bradford:1986:ERD,
  author =       "R. J. Bradford and A. C. Hearn and J. A. Padget and E.
                 Schr{\"u}fer",
  title =        "Enlarging the {REDUCE} domain of computation",
  crossref =     "Char:1986:PSS",
  pages =        "100--106",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p100-bradford/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms.",
}

@InProceedings{Bronstein:1986:GFA,
  author =       "Manuel Bronstein",
  title =        "Gsolve: a faster algorithm for solving systems of
                 algebraic equations",
  crossref =     "Char:1986:PSS",
  pages =        "247--249",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p247-bronstein/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; performance; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Efficiency. {\bf G.1.5}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Systems of equations. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@InProceedings{Butler:1986:DCC,
  author =       "Greg Butler",
  title =        "Divide-and-conquer in computational group theory",
  crossref =     "Char:1986:PSS",
  pages =        "59--64",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p59-butler/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf G.2.0} Mathematics of Computing, DISCRETE
                 MATHEMATICS, General. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
}

@InProceedings{Chaffy:1986:HCM,
  author =       "C. Chaffy",
  title =        "How to compute multivariate {Pad{\'e}} approximants",
  crossref =     "Char:1986:PSS",
  pages =        "56--58",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p56-chaffy/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.2} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@InProceedings{Char:1986:CAU,
  author =       "B. W. Char and K. O. Geddes and G. H. Gonnet and B. J.
                 Marshman and P. J. Ponzo",
  title =        "Computer algebra in the undergraduate mathematics
                 classroom",
  crossref =     "Char:1986:PSS",
  pages =        "135--140",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p135-char/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; documentation; experimentation;
                 human factors; performance",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION,
                 Computer Uses in Education, Computer-assisted
                 instruction (CAI).",
}

@InProceedings{Cooperman:1986:SMC,
  author =       "Gene Cooperman",
  title =        "A semantic matcher for computer algebra",
  crossref =     "Char:1986:PSS",
  pages =        "132--134",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p132-cooperman/",
  acknowledgement = ack-nhfb,
  keywords =     "experimentation; human factors; languages",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf F.4.1} Theory
                 of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Evaluation strategies. {\bf
                 F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Pattern matching. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Representations
                 (general and polynomial). {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA.",
}

@InProceedings{Czapor:1986:IBA,
  author =       "S. R. Czapor and K. O. Geddes",
  title =        "On implementing {Buchberger}'s algorithm for
                 {Gr{\"o}bner} bases",
  crossref =     "Char:1986:PSS",
  pages =        "233--238",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p233-czapor/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
}

@InProceedings{Davenport:1986:PSM,
  author =       "J. H. Davenport and C. E. Roth",
  title =        "{PowerMath}: a system for the {Macintosh}",
  crossref =     "Char:1986:PSS",
  pages =        "13--15",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p13-davenport/",
  acknowledgement = ack-nhfb,
  keywords =     "design; theory",
  subject =      "{\bf K.8} Computing Milieux, PERSONAL COMPUTING,
                 Apple. {\bf I.1.3} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems.",
}

@InProceedings{Dora:1986:FSL,
  author =       "J. Della Dora and E. Tournier",
  title =        "Formal solutions of linear difference equations:
                 method of {Pincherle--Ramis}",
  crossref =     "Char:1986:PSS",
  pages =        "192--196",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p192-della_dora/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.m} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Miscellaneous. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computation of transforms.",
}

@InProceedings{Fitch:1986:AIA,
  author =       "J. Fitch and A. Norman and M. A. Moore",
  title =        "Alkahest {III}: automatic analysis of periodic weakly
                 nonlinear {ODEs}",
  crossref =     "Char:1986:PSS",
  pages =        "34--38",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p34-fitch/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; human factors; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf D.2.2}
                 Software, SOFTWARE ENGINEERING, Design Tools and
                 Techniques, User interfaces.",
}

@InProceedings{Freeman:1986:SMP,
  author =       "T. Freeman and G. Imirzian and E. Kaltofen",
  title =        "A system for manipulating polynomials given by
                 straight-line programs",
  crossref =     "Char:1986:PSS",
  pages =        "169--175",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p169-freeman/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; performance; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Roots of Nonlinear Equations, Polynomials, methods
                 for.",
}

@InProceedings{Furukawa:1986:GBM,
  author =       "A. Furukawa and T. Sasaki and H. Kobayashi",
  title =        "The {Gr{\"o}bner} basis of a module over
                 {KUX1,\ldots{},Xne} and polynomial solutions of a
                 system of linear equations",
  crossref =     "Char:1986:PSS",
  pages =        "222--224",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p222-furukawa/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods).",
}

@InProceedings{Gates:1986:NCG,
  author =       "Barbara L. Gates",
  title =        "A numerical code generation facility for {REDUCE}",
  crossref =     "Char:1986:PSS",
  pages =        "94--99",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p94-gates/",
  acknowledgement = ack-nhfb,
  keywords =     "design; languages; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Code generation.",
}

@InProceedings{Gebauer:1986:BAS,
  author =       "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
  title =        "{Buchberger}'s algorithm and staggered linear bases",
  crossref =     "Char:1986:PSS",
  pages =        "218--221",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p218-gebauer/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; measurement; performance; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.1}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Simplification of expressions.",
}

@InProceedings{Geddes:1986:NIS,
  author =       "K. O. Geddes",
  title =        "Numerical integration in a symbolic context",
  crossref =     "Char:1986:PSS",
  pages =        "185--191",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p185-geddes/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design",
  subject =      "{\bf G.1.4} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms.",
}

@InProceedings{Golden:1986:OAM,
  author =       "J. P. Golden",
  title =        "An operator algebra for {Macsyma}",
  crossref =     "Char:1986:PSS",
  pages =        "244--246",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p244-golden/",
  acknowledgement = ack-nhfb,
  keywords =     "design; theory; verification",
  subject =      "{\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, MACSYMA. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA.",
}

@InProceedings{Gonnet:1986:IOS,
  author =       "G. H. Gonnet",
  title =        "An implementation of operators for symbolic algebra
                 systems",
  crossref =     "Char:1986:PSS",
  pages =        "239--243",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p239-gonnet/",
  acknowledgement = ack-nhfb,
  keywords =     "design; languages; theory",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Representations (general and
                 polynomial). {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems.",
}

@InProceedings{Gonnet:1986:NRR,
  author =       "Gaston H. Gonnet",
  title =        "New results for random determination of equivalence of
                 expressions",
  crossref =     "Char:1986:PSS",
  pages =        "127--131",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p127-gonnet/",
  acknowledgement = ack-nhfb,
  keywords =     "theory",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials. {\bf G.2.m} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Miscellaneous.",
}

@InProceedings{Hadzikadic:1986:AKB,
  author =       "M. Hadzikadic and F. Lichtenberger and D. Y. Y. Yun",
  title =        "An application of knowledge-base technology in
                 education: a geometry theorem prover",
  crossref =     "Char:1986:PSS",
  pages =        "141--147",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p141-hadzikadic/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; human factors; languages;
                 performance; verification",
  subject =      "{\bf K.3.1} Computing Milieux, COMPUTERS AND
                 EDUCATION, Computer Uses in Education,
                 Computer-assisted instruction (CAI). {\bf F.2.2} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations. {\bf F.4.1}
                 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic, Mechanical theorem
                 proving. {\bf I.2.3} Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Deduction and Theorem
                 Proving.",
}

@InProceedings{Hayden:1986:SBC,
  author =       "Michael B. Hayden and Edmund A. Lamagna",
  title =        "Summation of binomial coefficients using
                 hypergeometric functions",
  crossref =     "Char:1986:PSS",
  pages =        "77--81",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p77-hayden/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf F.1.2} Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Parallelism and
                 concurrency. {\bf I.2.2} Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Automatic Programming,
                 Automatic analysis of algorithms. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf G.1.4} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Iterative methods.",
}

@InProceedings{Hilali:1986:ACF,
  author =       "A. Hilali and A. Wazner",
  title =        "Algorithm for computing formal invariants of linear
                 differential systems",
  crossref =     "Char:1986:PSS",
  pages =        "197--201",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p197-hilali/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues and
                 eigenvectors (direct and iterative methods). {\bf
                 G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions.",
}

@InProceedings{Jurkovic:1986:EES,
  author =       "N. Jurkovic",
  title =        "Edusym --- educational symbolic manipulator on a
                 microcomputer",
  crossref =     "Char:1986:PSS",
  pages =        "154--156",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p154-jurkovic/",
  acknowledgement = ack-nhfb,
  keywords =     "human factors; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, MuMATH.
                 {\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION,
                 Computer Uses in Education, Computer-assisted
                 instruction (CAI).",
}

@InProceedings{Kaltofen:1986:FPA,
  author =       "E. Kaltofen and M. Krishnamoorthy and B. D. Saunders",
  title =        "Fast parallel algorithms for similarity of matrices",
  crossref =     "Char:1986:PSS",
  pages =        "65--70",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p65-kaltofen/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
}

@InProceedings{Kapur:1986:GTP,
  author =       "Deepak Kapur",
  title =        "Geometry theorem proving using {Hilbert}'s
                 {Nullstellensatz}",
  crossref =     "Char:1986:PSS",
  pages =        "202--208",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p202-kapur/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Logic and
                 constraint programming. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations. {\bf I.2.3}
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Deduction and Theorem Proving. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions.",
}

@InProceedings{Knowles:1986:ILF,
  author =       "P. H. Knowles",
  title =        "Integration of {Liouvillian} functions with special
                 functions",
  crossref =     "Char:1986:PSS",
  pages =        "179--184",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p179-knowles/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.m} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Miscellaneous.",
}

@InProceedings{Kobayashi:1986:GBI,
  author =       "H. Kobayashi and A. Furukawa and T. Sasaki",
  title =        "Gr{\"o}bner bases of ideals of convergent power
                 series",
  crossref =     "Char:1986:PSS",
  pages =        "225--227",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p225-kobayashi/",
  acknowledgement = ack-nhfb,
  keywords =     "theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf G.m}
                 Mathematics of Computing, MISCELLANEOUS.",
}

@InProceedings{Kryukov:1986:CRA,
  author =       "A. P. Kryukov and Y. Rodionov and G. L. Litvinov",
  title =        "Construction of rational approximations by means of
                 {REDUCE}",
  crossref =     "Char:1986:PSS",
  pages =        "31--33",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p31-kryukov/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf G.1.2} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation. {\bf
                 I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Simplification of expressions.",
}

@InProceedings{Kryukov:1986:DRE,
  author =       "A. P. Kryukov",
  title =        "Dialogue in {REDUCE}: experience and development",
  crossref =     "Char:1986:PSS",
  pages =        "107--109",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p107-kryukov/",
  acknowledgement = ack-nhfb,
  keywords =     "design; human factors; performance; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design
                 Tools and Techniques, User interfaces.",
}

@InProceedings{Kryukov:1986:URC,
  author =       "A. P. Kryukov and A. Y. Rodionov",
  title =        "Usage of {REDUCE} for computations of
                 group-theoretical weight of {Feynman} diagrams in
                 {non-Abelian} gauge theories",
  crossref =     "Char:1986:PSS",
  pages =        "91--93",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p91-kryukov/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf G.2.m} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Miscellaneous.",
}

@InProceedings{Kutzler:1986:AGT,
  author =       "B. Kutzler and S. Stifter",
  title =        "Automated geometry theorem proving using
                 {Buchberger}'s algorithm",
  crossref =     "Char:1986:PSS",
  pages =        "209--214",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p209-kutzler/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Logic and
                 constraint programming. {\bf I.2.3} Computing
                 Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and
                 Theorem Proving. {\bf F.2.2} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Geometrical
                 problems and computations. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions.",
}

@InProceedings{Leff:1986:CSG,
  author =       "L. Leff and D. Y. Y. Yun",
  title =        "Constructive solid geometry: a symbolic computation
                 approach",
  crossref =     "Char:1986:PSS",
  pages =        "121--126",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p121-leff/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf J.6} Computer Applications, COMPUTER-AIDED
                 ENGINEERING. {\bf F.2.2} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Geometrical
                 problems and computations. {\bf I.1.m} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Miscellaneous.",
}

@InProceedings{Leong:1986:IDU,
  author =       "B. L. Leong",
  title =        "{Iris}: design of an user interface program for
                 symbolic algebra",
  crossref =     "Char:1986:PSS",
  pages =        "1--6",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p1-leong/",
  acknowledgement = ack-nhfb,
  keywords =     "design; human factors; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf D.2.2} Software, SOFTWARE ENGINEERING,
                 Design Tools and Techniques, User interfaces. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple. {\bf H.1.2}
                 Information Systems, MODELS AND PRINCIPLES,
                 User/Machine Systems, Human factors.",
}

@InProceedings{Lucks:1986:FIP,
  author =       "Michael Lucks",
  title =        "A fast implementation of polynomial factorization",
  crossref =     "Char:1986:PSS",
  pages =        "228--232",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p228-lucks/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; experimentation; performance;
                 theory",
  subject =      "{\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Polynomials,
                 methods for. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations.",
}

@InProceedings{Mawata:1986:SDR,
  author =       "C. P. Mawata",
  title =        "A sparse distributed representation using prime
                 numbers",
  crossref =     "Char:1986:PSS",
  pages =        "110--114",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p110-mawata/",
  acknowledgement = ack-nhfb,
  keywords =     "experimentation; performance; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Representations (general and polynomial). {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm design and analysis.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms.",
}

@InProceedings{Purtilo:1986:ASI,
  author =       "J. Purtilo",
  title =        "Applications of a software interconnection system in
                 mathematical problem solving environments",
  crossref =     "Char:1986:PSS",
  pages =        "16--23",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p16-purtilo/",
  acknowledgement = ack-nhfb,
  keywords =     "design; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 G.m} Mathematics of Computing, MISCELLANEOUS. {\bf
                 D.2.m} Software, SOFTWARE ENGINEERING, Miscellaneous.",
}

@InProceedings{Renbao:1986:CAS,
  author =       "Z. Renbao and X. Ling and R. Zhaoyang",
  title =        "The computer algebra system {CAS1} for the {IBM-PC}",
  crossref =     "Char:1986:PSS",
  pages =        "176--178",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p176-renbao/",
  acknowledgement = ack-nhfb,
  keywords =     "design; theory",
  subject =      "{\bf K.8} Computing Milieux, PERSONAL COMPUTING, IBM
                 PC. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.1}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Simplification of expressions.",
}

@InProceedings{Sasaki:1986:SAE,
  author =       "Tateaki Sasaki",
  title =        "Simplification of algebraic expression by multiterm
                 rewriting rules",
  crossref =     "Char:1986:PSS",
  pages =        "115--120",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p115-sasaki/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; languages",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Simplification of expressions. {\bf
                 F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES, Grammars and Other Rewriting Systems,
                 Parallel rewriting systems.",
}

@InProceedings{Seymour:1986:CCM,
  author =       "Harlan R. Seymour",
  title =        "Conform: a conformal mapping system",
  crossref =     "Char:1986:PSS",
  pages =        "163--168",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p163-seymour/",
  acknowledgement = ack-nhfb,
  keywords =     "design; languages; performance; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, LISP. {\bf D.3.3} Software,
                 PROGRAMMING LANGUAGES, Language Constructs and
                 Features.",
}

@InProceedings{Shavlik:1986:CUG,
  author =       "Jude W. Shavlik and Gerald F. DeJong",
  title =        "Computer understanding and generalization of symbolic
                 mathematical calculations: a case study in physics
                 problem solving",
  crossref =     "Char:1986:PSS",
  pages =        "148--153",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p148-shavlik/",
  acknowledgement = ack-nhfb,
  keywords =     "design; human factors; languages; performance; theory;
                 verification",
  subject =      "{\bf I.2.6} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Learning. {\bf K.3.1} Computing Milieux,
                 COMPUTERS AND EDUCATION, Computer Uses in Education,
                 Computer-assisted instruction (CAI). {\bf I.1.1}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation.
                 {\bf I.2.1} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Applications and Expert Systems. {\bf
                 J.2} Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Substitution mechanisms**. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Evaluation
                 strategies. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms.",
}

@InProceedings{Smith:1986:MUI,
  author =       "C. J. Smith and N. Soiffer",
  title =        "{MathScribe}: a user interface for computer algebra
                 systems",
  crossref =     "Char:1986:PSS",
  pages =        "7--12",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p7-smith/",
  acknowledgement = ack-nhfb,
  keywords =     "design; human factors; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and
                 Techniques, User interfaces.",
}

@InProceedings{Yun:1986:FCF,
  author =       "D. Y. Y. Yun and C. N. Zhang",
  title =        "A fast carry-free algorithm and hardware design for
                 extended integer {GCD} computation",
  crossref =     "Char:1986:PSS",
  pages =        "82--84",
  year =         "1986",
  bibdate =      "Thu Mar 12 07:38:29 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p82-yun/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm design and analysis. {\bf B.7.1} Hardware,
                 INTEGRATED CIRCUITS, Types and Design Styles,
                 Algorithms implemented in hardware.",
}

@InProceedings{A:1989:SSG,
  author =       "R. A. and J. r. Ravenscroft and E. A. Lamagna",
  title =        "Symbolic summation with generating functions",
  crossref =     "Gonnet:1989:PAI",
  pages =        "228--233",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p228-ravenscroft/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.2.1} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms. {\bf
                 G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Linear systems (direct and
                 iterative methods).",
}

@InProceedings{Abbot:1989:RAN,
  author =       "J. Abbot",
  title =        "Recovery of algebraic numbers from their $p$-adic
                 approximations",
  crossref =     "Gonnet:1989:PAI",
  pages =        "112--120",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author describes three ways to generalize
                 Lenstra's algebraic integer recovery method. One
                 direction adapts the algorithm so that rational numbers
                 are automatically produced given only upper bounds on
                 the sizes of the numerators and denominators. Another
                 direction produces a variant which recovers algebraic
                 numbers as elements of multiple generator algebraic
                 number fields. The third direction explains how the
                 method can work if a reducible minimal polynomial had
                 been given for an algebraic generator. Any two or all
                 three of the generalisations may be employed
                 simultaneously.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory)",
  keywords =     "Algebraic generator; Algebraic integer recovery
                 method; Algebraic numbers; Computer algebra;
                 Denominators; Factorisation; Lenstra; Multiple
                 generator algebraic number fields; Numerators; P-adic
                 approximations; Rational numbers; Reducible minimal
                 polynomial; Upper bounds",
  thesaurus =    "Computation theory; Number theory; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Abbott:1989:RAN,
  author =       "John Abbott",
  title =        "Recovery of algebraic numbers from their $p$-adic
                 approximations",
  crossref =     "Gonnet:1989:PAI",
  pages =        "112--120",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p112-abbott/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.2} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Abdali:1989:EQR,
  author =       "S. K. Abdali and D. S. Wiset",
  title =        "Experiments with quadtree representation of matrices",
  crossref =     "Gianni:1989:SAC",
  pages =        "96--108",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The quadtrees matrix representation has been recently
                 proposed as an alternative to the conventional linear
                 storage of matrices. If all elements of a matrix are
                 zero, then the matrix is represented by an empty tree;
                 otherwise it is represented by a tree consisting of
                 four subtrees, each representing, recursively, a
                 quadrant of the matrix. Using four-way block
                 decomposition, algorithms on quadtrees accelerate on
                 blocks entirely of zeros, and thereby offer improved
                 performance on sparse matrices. The paper reports the
                 results of experiments done with a quadtree matrix
                 package implemented in REDUCE to compare the
                 performance of quadtree representation with REDUCE's
                 built-in sequential representation of matrices. Tests
                 on addition, multiplication, and inversion of dense,
                 triangular, tridiagonal, and diagonal matrices (both
                 symbolic and numeric) of sizes up to 100*100 show that
                 the quadtree algorithms perform well in a broad range
                 of circumstances, sometimes running orders of magnitude
                 faster than their sequential counterparts.",
  acknowledgement = ack-nhfb,
  affiliation =  "Tektronix Labs., Beaverton, OR, USA",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4140 (Linear algebra); C6120 (File organisation);
                 C7310 (Mathematics)",
  keywords =     "Addition; Dense matrices; Diagonal matrices; Empty
                 tree; Four-way block decomposition; Inversion;
                 Multiplication; Performance comparison; Quadrant;
                 Quadtree algorithms; Quadtree matrix package; Quadtrees
                 matrix representation; REDUCE; Sparse matrices;
                 Subtrees; Triangular matrices; Tridiagonal matrices;
                 Zero elements",
  thesaurus =    "Data structures; Mathematics computing; Matrix
                 algebra; Trees [mathematics]",
}

@InProceedings{Abdulrab:1989:EW,
  author =       "H. Abdulrab",
  title =        "Equations in words",
  crossref =     "Gianni:1989:SAC",
  pages =        "508--520",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The study of equations in words was introduced by
                 Lentin (1972). There is always a solution for any
                 equation with no constant. Makanin (1977) showed that
                 solving equations with constants is decidable. Pecuchet
                 (1981) unified the two theories of equations with or
                 without constants and gave a new description of
                 Makanin's algorithm. This paper describes some new
                 results in the field of solving equations in words.",
  acknowledgement = ack-nhfb,
  affiliation =  "LITP, Fac. des Sci., Mont Saint Aignan, France",
  classification = "C4210 (Formal logic)",
  keywords =     "Decidable; Equations in words",
  thesaurus =    "Decidability",
}

@InProceedings{Abhyankar:1989:CAC,
  author =       "S. S. Abhyankar and C. L. Bajaj",
  title =        "Computations with algebraic curves",
  crossref =     "Gianni:1989:SAC",
  pages =        "274--284",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors present a variety of computational
                 techniques dealing with algebraic curves both in the
                 plane and in space. The main results are polynomial
                 time algorithms: (1) to compute the genus of plane
                 algebraic curves; (2) to compute the rational
                 parametric equations for implicitly defined rational
                 plane algebraic curves of arbitrary degree; (3) to
                 compute birational mappings between points on
                 irreducible space curves and points on projected plane
                 curves and thereby to compute the genus and rational
                 parametric equations for implicitly defined rational
                 space curves of arbitrary degree; and (4) to check for
                 the faithfulness (one to one) of parameterizations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Purdue Univ., West Lafayette, IN, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4190 (Other numerical methods)",
  keywords =     "Algebraic curves; Birational mappings; Computational
                 techniques; Irreducible space curves; Polynomial time
                 algorithms; Rational parametric equations",
  thesaurus =    "Computational geometry; Polynomials",
}

@InProceedings{Alonso:1989:CAS,
  author =       "M. E. Alonso and T. Mora and M. Raimondo",
  title =        "Computing with algebraic series",
  crossref =     "Gonnet:1989:PAI",
  pages =        "101--111",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p101-alonso/",
  abstract =     "The authors develop a computational model for
                 algebraic formal power series, based on a symbolic
                 codification of the series by means of the implicit
                 function theorem: i.e. they consider algebraic series
                 as the unique solutions of suitable functional
                 equations. They show that most of the usual local
                 commutative algebra can be effectively performed on
                 algebraic series, since they can reduce to the
                 polynomial case, where the tangent cone algorithm can
                 be used to effectively perform local algebra. The main
                 result to the paper is an effective version of
                 Weierstrass theorems, which allows effective
                 elimination theory for algebraic series and an
                 effective noether normalization lemma.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Complutense, Madrid, Spain",
  classification = "C1110 (Algebra); C1120 (Analysis); C4150 (Nonlinear
                 and functional equations); C4240 (Programming and
                 algorithm theory)",
  keywords =     "Algebraic formal power series; Algebraic series;
                 algorithms; Computational model; Elimination theory;
                 Functional equations; Implicit function theorem; Local
                 commutative algebra; Noether normalization lemma;
                 Polynomial; Symbolic codification; Tangent cone
                 algorithm; theory; Weierstrass theorems",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Computational logic.",
  thesaurus =    "Computability; Functional equations; Polynomials;
                 Series [mathematics]; Symbol manipulation",
}

@InProceedings{Arnborg:1989:EPO,
  author =       "S. Arnborg",
  title =        "Experiments with a projection operator for algebraic
                 decomposition",
  crossref =     "Gianni:1989:SAC",
  pages =        "177--182",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Reports an experiment with the projection phase of an
                 algebraic decomposition problem. The decomposition
                 asked for is a collection of rational sample points, at
                 least one in each full-dimensional region of a
                 decomposition, sign-invariant with respect to a set of
                 polynomials and with a cylindrical structure. Such a
                 decomposition is less general than a cylindrical
                 algebraic decomposition, but still useful for purposes
                 such as solving collision and motion planning problems
                 in theoretical robotics. Specifically, there is no
                 information about the structure of less than
                 full-dimensional regions and intersections between
                 projections of regions. This makes quantifier
                 elimination with alternating quantifiers difficult or
                 impossible.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Numer. Anal. and Comput. Sci., R. Inst. of
                 Technol., Stockholm, Sweden",
  classification = "C1110 (Algebra)",
  keywords =     "Algebraic decomposition; Cylindrical structure;
                 Full-dimensional region; Polynomials; Projection
                 operator; Projection phase; Rational sample points;
                 Sign-invariant",
  thesaurus =    "Algebra; Polynomials",
}

@InProceedings{Ausiello:1989:DMP,
  author =       "G. Ausiello and A. Marchetti Spaccamela and U. Nanni",
  title =        "Dynamic maintenance of paths and path expressions on
                 graphs",
  crossref =     "Gianni:1989:SAC",
  pages =        "1--12",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In several applications it is necessary to deal with
                 data structures that may dynamically change during a
                 sequence of operations. In these cases the classical
                 worst case analysis of the cost of a single operation
                 may not adequately describe the behaviour of the
                 structure but it is rather more meaningful to analyze
                 the cost of the whole sequence of operations. The paper
                 first discusses some results on maintaining paths in
                 dynamic graphs. Besides, it considers paths problems on
                 dynamic labeled graphs and shows how to maintain path
                 expressions in the acyclic case when insertions of new
                 arcs are allowed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Inf. e Sistemistica, Rome Univ.,
                 Italy",
  classification = "C1160 (Combinatorial mathematics); C4240
                 (Programming and algorithm theory); C6120 (File
                 organisation)",
  keywords =     "Acyclic case; Data structures; Dynamic graphs; Dynamic
                 labeled graphs; Dynamic maintenance; Insertions; New
                 arcs; Path expressions; Paths problems",
  thesaurus =    "Computational complexity; Data structures; Graph
                 theory",
}

@InProceedings{Avenhaus:1989:URT,
  author =       "J. Avenhaus and D. Wi{\ss}mann",
  title =        "Using rewriting techniques to solve the generalized
                 word problem in polycyclic groups",
  crossref =     "Gonnet:1989:PAI",
  pages =        "322--337",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p322-avenhaus/",
  abstract =     "The authors apply rewriting techniques to the
                 generalized word problem GWP in polycyclic groups. They
                 assume the group $G$ to be given by a canonical
                 polycyclic string-rewriting system $R$ and consider GWP
                 in $G$ which is defined by $GWP(w,U)$ iff $w$ in $<U>$
                 for $w$ in $G$, finite $U$ contained in $G$, where
                 $<U>$ is the subgroup of $G$ generated by $U$. They
                 describe $<U>$ also by a rewrite system $S$ and define
                 a rewrite relation $\mbox{implies}_{S,R}$ in such a way
                 that $w$ implied by * $\mbox{implies}_{S,R} \lambda$
                 iff $w$ in $<U>$ ($\lambda$ the empty word). For this
                 rewrite relation the authors develop different critical
                 pair criteria for $\mbox{implies}_{S,R}$ to be
                 $\lambda$-confluent, i.e. confluent on the
                 left-congruence class $(\lambda )$ of implied by *
                 $\mbox{implies}_{S,R}$. Using any of these
                 $\lambda$-confluence criteria they construct a
                 completion procedure which stops for every input $S$
                 and computes a $\lambda$-confluent rewrite system
                 equivalent to $S$. This leads to a decision procedure
                 for GWP in G. Thus the authors give an explicit uniform
                 algorithm for deciding GWP in polycyclic groups and a
                 new proof based almost only on rewriting techniques for
                 the decidability of this problem. Further, they define
                 a rewrite relation $\mbox{implies}_{LM,U}$ which is
                 stronger than $\mbox{implies}_{S,R}$. They show that if
                 $G$ is given by a nilpotent string-rewriting system,
                 then by a completion procedure the input $U$ can be
                 transformed into $V$ such that $\mbox{implies}_{LM,V}$
                 is even confluent, not just $\lambda$-confluent.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Inf., Kaiserslautern Univ., West Germany",
  classification = "C1110 (Algebra); C4210 (Formal logic)",
  keywords =     "$\Lambda$-confluent; algorithms; Canonical polycyclic
                 string-rewriting system; Completion procedure; Critical
                 pair criteria; Decidability; design; Explicit uniform
                 algorithm; Generalized word problem; Group theory;
                 Nilpotent string-rewriting system; Polycyclic groups;
                 Rewrite relation; Rewriting techniques; theory",
  subject =      "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Grammars and Other Rewriting
                 Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Decidability; Group theory; Rewriting systems; Symbol
                 manipulation",
}

@InProceedings{Bajaj:1989:FRP,
  author =       "C. Bajaj and J. Canny and T. Garrity and J. Warren",
  title =        "Factoring rational polynomials over the complexes",
  crossref =     "Gonnet:1989:PAI",
  pages =        "81--90",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p81-bajaj/",
  abstract =     "The authors give NC algorithms for determining the
                 number and degrees of the absolute factors (factors
                 irreducible over the complex numbers $C$) of a
                 multivariate polynomial with rational coefficients. NC
                 is the class of functions computable by
                 logspace-uniform boolean circuits of polynomial size
                 and polylogarithmic dept. The measures of size of the
                 input polynomial are its degree $d$, coefficient length
                 $c$, number of variables $n$, and for sparse
                 polynomials, the number of nonzero coefficients $s$.
                 For the general case, the authors give a random
                 (Monte-Carlo) NC algorithm in these input measures. If
                 $n$ is fixed, or if the polynomial is dense, they give
                 a deterministic NC algorithm. The algorithm also works
                 in random NC for polynomial represented by
                 straight-line programs, provided the polynomial can be
                 evaluated at integer points in NC. The authors discuss
                 a method for obtaining an approximation to the
                 coefficients of each factor whose running time is
                 polynomial in the size of the original (dense)
                 polynomial. These methods rely on the fact that the
                 connected components of a complex hypersurface
                 $P(z_1,\ldots{},z_n)=0$ minus its singular points
                 correspond to the absolute factors of $P$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Purdue Univ., Lafayette, IN,
                 USA",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4240 (Programming and algorithm theory)",
  keywords =     "Absolute factors; algorithms; Complex numbers;
                 Factorisation; Functions; Logspace-uniform boolean
                 circuits; measurement; Monte-Carlo; Multivariate
                 polynomial; NC algorithms; Rational coefficients;
                 Rational polynomials; Set theory; theory;
                 verification",
  subject =      "{\bf G.1.2} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic, Mechanical theorem proving.",
  thesaurus =    "Approximation theory; Computability; Computational
                 complexity; Monte Carlo methods; Polynomials; Set
                 theory; Symbol manipulation",
  xxauthor =     "C. Bajaj and J. Canny and R. Garrity and J. Warren",
}

@InProceedings{Barkatou:1989:RLS,
  author =       "M. A. Barkatou",
  title =        "On the reduction of linear systems of difference
                 equations",
  crossref =     "Gonnet:1989:PAI",
  pages =        "1--6",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p1-barkatou/",
  abstract =     "The author deals with linear systems of difference
                 equations whose coefficients admit generalized
                 factorial series representations at $z=\infty$. He
                 gives a criterion by which a given system is determined
                 to have a regular singularity. He gives an algorithm,
                 implementable in a computer algebra system, which
                 reduces in a finite number of steps the system of
                 difference equations on an irreducible form.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. TIM3-IMAG, Grenoble, France",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C7310 (Mathematics)",
  keywords =     "algorithms; Computer algebra system; Convergence;
                 Generalized factorial series; Irreducible form; Linear
                 difference equations; Regular singularity; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods).",
  thesaurus =    "Convergence; Difference equations; Linear differential
                 equations; Mathematics computing; Matrix algebra;
                 Series [mathematics]; Symbol manipulation",
}

@InProceedings{Barkatou:1989:RNA,
  author =       "M. A. Barkatou",
  title =        "Rational {Newton} algorithm for computing formal
                 solutions of linear differential equations",
  crossref =     "Gianni:1989:SAC",
  pages =        "183--195",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Presents a new algorithm for solving linear
                 differential equations in the neighbourhood of an
                 irregular singular point. This algorithm is based upon
                 the same principles as the Newton algorithm, however it
                 has a lower cost and is more suitable for computing
                 algebra.",
  acknowledgement = ack-nhfb,
  affiliation =  "CNRS, INPG, IMAG, Grenoble, France",
  classification = "C1120 (Analysis); C4170 (Differential equations)",
  keywords =     "Formal solutions; Irregular singular point; Linear
                 differential equations; Neighbourhood; Rational Newton
                 algorithm",
  thesaurus =    "Linear differential equations",
}

@InProceedings{BoydelaTour:1989:FAS,
  author =       "T. {Boy de la Tour} and R. Caferra",
  title =        "A formal approach to some usually informal techniques
                 used in mathematical reasoning",
  crossref =     "Gianni:1989:SAC",
  pages =        "402--406",
  year =         "1989",
  bibdate =      "Mon Dec 01 16:57:16 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "One of the striking characteristics of mathematical
                 reasoning is the contrast between the formal aspects of
                 mathematical truth and the informal character of the
                 ways to that truth. Among the many important and
                 usually informal mathematical activities the authors
                 are interested in proof analogy (i.e. common pattern
                 between proofs of different theorems) in the context of
                 interactive theorem proving.",
  acknowledgement = ack-nhfb,
  affiliation =  "LIFIA-INPG, Grenoble, France",
  classification = "C4210 (Formal logic)",
  keywords =     "Formal approach; Informal character; Interactive
                 theorem proving; Mathematical reasoning; Mathematical
                 truth; Usually informal techniques",
  thesaurus =    "Theorem proving",
}

@InProceedings{Bradford:1989:ETC,
  author =       "R. J. Bradford and J. H. Davenport",
  title =        "Effective tests for cyclotomic polynomials",
  crossref =     "Gianni:1989:SAC",
  pages =        "244--251",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors present two efficient tests that determine
                 if a given polynomial is cyclotomic, or is a product of
                 cyclotomics. The first method uses the fact that all
                 the roots of a cyclotomic polynomial are roots of
                 unity, and the second the fact that the degree of a
                 cyclotomic polynomial is a value of $\phi (n)$, for
                 some $n$. The authors also find the cyclotomic factors
                 of any polynomial.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "Cyclotomic polynomials; Roots",
  thesaurus =    "Polynomials",
}

@InProceedings{Bradford:1989:SRD,
  author =       "R. Bradford",
  title =        "Some results on the defect",
  crossref =     "Gonnet:1989:PAI",
  pages =        "129--135",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p129-bradford/",
  abstract =     "The defect of an algebraic number field (or, more
                 correctly, of a presentation of the field) is the
                 largest rational integer that divides the denominator
                 of any algebraic integer in the field when written
                 using that presentation. Knowing the defect, or
                 estimating it accurately is extremely valuable in many
                 algorithms, the factorization of polynomials over
                 algebraic number fields being a prime example. The
                 author presents a few results that are a move in the
                 right direction.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4130 (Interpolation and function approximation); C4240
                 (Programming and algorithm theory)",
  keywords =     "Algebraic integer; Algebraic number field; algorithms;
                 Defect; Factorization; Polynomials; Rational integer;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation. {\bf G.1.4} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation. {\bf G.1.9} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Integral Equations.",
  thesaurus =    "Computation theory; Number theory; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Bronstein:1989:FRR,
  author =       "M. Bronstein",
  title =        "Fast reduction of the {Risch} differential equation",
  crossref =     "Gianni:1989:SAC",
  pages =        "64--72",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Presents a weaker definition of weak-normality which:
                 can always be obtained in a tower of transcendental
                 elementary extensions, and gives an explicit formula
                 for the denominator of $y$, so the equation $y'+fy=g$
                 can be reduced to a polynomial equation in one
                 reduction step. As a consequence, a new algorithm is
                 obtained for solving y'+fy=g. The algorithm is very
                 similar to the one described by Rothstein (1976),
                 except that the present one uses weak normality to
                 prevent finite cancellation, rather than having to find
                 integer roots of polynomials over the constant field of
                 $K$ in order to detect it.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C1120 (Analysis); C4170 (Differential equations)",
  keywords =     "Denominator; Explicit formula; Fast reduction;
                 Polynomial equation; Reduction step; Risch differential
                 equation; Transcendental elementary extensions;
                 Weak-normality",
  thesaurus =    "Differential equations",
}

@InProceedings{Bronstein:1989:SRE,
  author =       "M. Bronstein",
  title =        "Simplification of real elementary functions",
  crossref =     "Gonnet:1989:PAI",
  pages =        "207--211",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p207-bronstein/",
  abstract =     "The author describes an algorithm, based on Risch's
                 real structure theorem, that determines explicitly all
                 the algebraic relations among a given set of real
                 elementary functions. He provides examples from its
                 implementation in the scratchpad computer algebra
                 system that illustrate the advantages over the use of
                 complex logarithms and exponentials.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., T. J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "algorithms; Computer algebra system; Real elementary
                 functions; Real structure theorem; Scratchpad; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations.",
  thesaurus =    "Functions; Mathematics computing; Symbol
                 manipulation",
}

@InProceedings{Brown:1989:SPP,
  author =       "C. Brown and G. Cooperman and L. Finkelstein",
  title =        "Solving permutation problems using rewriting systems",
  crossref =     "Gianni:1989:SAC",
  pages =        "364--377",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A new approach is described for finding short
                 expressions for arbitrary elements of a permutation
                 group in terms of the original generators which uses
                 rewriting methods. This forms an important component in
                 a long term plan to find short solutions for `large'
                 permutation problems (such as Rubik's cube), which are
                 difficult to solve by existing search techniques. In
                 order for this methodology to be successful, it is
                 important to start with a short presentation for a
                 finite permutation group. A new method is described for
                 giving a presentation for an arbitrary permutation
                 group acting on $n$ letters. This can be used to show
                 that any such permutation group has a presentation with
                 at most $n-1$ generators and $(n-1)^2$ relations. As an
                 application of this method, an $O(n^4)$ algorithm is
                 described for determining if a set of generators for a
                 permutation group of $n$ letters is a strong generating
                 set (in the sense of Sims). The `back end' includes a
                 novel implementation of the Knuth--Bendix technique on
                 symmetrization classes for groups.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
                 USA",
  classification = "C4210 (Formal logic)",
  keywords =     "Knuth--Bendix technique; Permutation problems;
                 Rewriting systems",
  thesaurus =    "Rewriting systems",
}

@InProceedings{Butler:1989:CVU,
  author =       "G. Butler and J. Cannon",
  title =        "{Cayley}, version 4: the user language",
  crossref =     "Gianni:1989:SAC",
  pages =        "456--466",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Cayley, version 4, is a proposed knowledge-based
                 system for modern algebra. The proposal integrates the
                 existing powerful algorithm base of Cayley with modest
                 deductive facilities and large sophisticated databases
                 of groups and related algebraic structures. The outcome
                 will be a revolutionary computer algebra system. The
                 user language of Cayley, version 4, is the first stage
                 of the project to develop a computer algebra system
                 which integrates algorithmic, deductive, and factual
                 knowledge. The language plays an important role in
                 shaping the users' communication of their knowledge to
                 the system, and in presenting the results to the user.
                 The very survival of a system depends upon its
                 acceptance by the users, so the language must be
                 natural, extensible, and powerful. The major changes in
                 the language (over version 3) are the definitions of
                 algebraic structures, set constructors and associated
                 control structures, the definitions of maps and
                 homomorphisms, the provision of packages for procedural
                 abstraction and encapsulation, database facilities, and
                 other input/output. The motivation for these changes
                 has been the need to provide facilities for a
                 knowledge-based system; to allow sets to be defined by
                 properties; and to remove semantic ambiguities of
                 structure definitions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sydney Univ., NSW, Australia",
  classification = "C6170 (Expert systems); C7310 (Mathematics)",
  keywords =     "Algebra; Algebraic structures; Associated control
                 structures; Cayley; Computer algebra system; Deductive
                 facilities; Encapsulation; Factual knowledge;
                 Homomorphisms; Knowledge-based system; Procedural
                 abstraction; Set constructors; Sophisticated databases;
                 User language; Version 4",
  thesaurus =    "Knowledge based systems; Symbol manipulation",
}

@InProceedings{Cabay:1989:FRA,
  author =       "S. Cabay and G. Labahn",
  title =        "A fast, reliable algorithm for calculating
                 {Pad{\'e}--Hermite} forms",
  crossref =     "Gonnet:1989:PAI",
  pages =        "95--100",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p95-cabay/",
  abstract =     "The authors present a new fast algorithm for the
                 calculation of a Pad{\'e}--Hermite form for a vector of
                 power series. When the vector of power series is
                 normal, the algorithm is shown to calculate a
                 Pad{\'e}--Hermite form of type $(n_0, \ldots{}, n_k)$
                 in $O(k.(n_0^2+\ldots{} +n_k^2))$ operations. This
                 complexity is the same as that of other fast algorithms
                 for computing Pad{\'e}--Hermite approximants. However,
                 unlike other algorithms, the new algorithm also
                 succeeds in the nonnormal case, usually with only a
                 moderate increase in cost.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Alberta Univ., Edmonton, Alta.,
                 Canada",
  classification = "C1120 (Analysis); C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory)",
  keywords =     "algorithms; Complexity; Iterative methods; Nonnormal
                 case; Pad{\'e}--Hermite approximants; Pad{\'e}--Hermite
                 forms; theory; Vector of power series",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations. {\bf G.1.9} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Integral Equations.",
  thesaurus =    "Computational complexity; Iterative methods; Linear
                 differential equations; Series [mathematics]; Vectors",
}

@InProceedings{Canny:1989:GCP,
  author =       "J. Canny",
  title =        "Generalized characteristic polynomials",
  crossref =     "Gianni:1989:SAC",
  pages =        "293--299",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author generalises the notion of characteristic
                 polynomial for a system of linear equations to systems
                 of multivariate polynomial equations. The
                 generalization is natural in the sense that it reduces
                 to the usual definition when all the polynomials are
                 linear. Whereas the constant coefficient of the
                 characteristic polynomial of a linear system is the
                 determinant, the constant coefficient of the general
                 characteristic polynomial is the resultant of the
                 system. This construction is applied to solve a
                 traditional problem with efficient methods for solving
                 systems of polynomial equations: the presence of
                 infinitely many solutions `at infinity'. The author
                 gives a single-exponential time method for finding all
                 the isolated solution points of a system of
                 polynomials, even in the presence of infinitely many
                 solutions at infinity or elsewhere.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Comput. Sci., California Univ., Berkeley, CA,
                 USA",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "Generalised characteristic polynomials; Multivariate
                 polynomial equations; Single-exponential time method;
                 System of linear equations",
  thesaurus =    "Polynomials",
}

@InProceedings{Canny:1989:SSN,
  author =       "J. F. Canny and E. Kaltofen and L. Yagati",
  title =        "Solving systems of non-linear polynomial equations
                 faster",
  crossref =     "Gonnet:1989:PAI",
  pages =        "121--128",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p121-canny/",
  abstract =     "Finding the solution to a system of $n$ non-linear
                 polynomial equations in $n$ unknowns over a given
                 field, say the algebraic closure of the coefficient
                 field, is a classical and fundamental problem in
                 computational algebra. The authors give a method that
                 allows the computation of resultants and $u$-resultants
                 of polynomial systems in essentially linear space and
                 quadratic time. The algorithm constitutes the first
                 improvement over Gaussian elimination-based methods for
                 computing these fundamental invariants.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Comp. Sci., California Univ., Berkeley, CA,
                 USA",
  classification = "C1110 (Algebra); C1120 (Analysis); C4130
                 (Interpolation and function approximation); C4150
                 (Nonlinear and functional equations); C4240
                 (Programming and algorithm theory)",
  keywords =     "Algebraic closure; algorithms; Coefficient field;
                 Computational algebra; Computational complexity; Linear
                 space; Nonlinear polynomial equations; Quadratic time;
                 Resultants; theory; U-resultants",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.1.5}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Systems of equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms. {\bf G.1.1} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation.",
  thesaurus =    "Computational complexity; Nonlinear equations;
                 Polynomials; Symbol manipulation",
}

@InProceedings{Cantone:1989:DPE,
  author =       "D. Cantone and V. Cutello and A. Ferro",
  title =        "Decision procedures for elementary sublanguages of set
                 theory. {XIV}. {Three} languages involving rank related
                 constructs",
  crossref =     "Gianni:1989:SAC",
  pages =        "407--422",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors present three decidability results for
                 some quantifier-free and quantified theories of sets
                 involving rank related constructs.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Courant Inst. of Math. Sci.,
                 New York Univ., NY, USA",
  classification = "C1160 (Combinatorial mathematics); C4210 (Formal
                 logic)",
  keywords =     "Decidability results; Decision procedures; Elementary
                 sublanguages; Quantified theories; Quantifier-free;
                 Rank related constructs; Set theory",
  thesaurus =    "Decidability; Formal logic; Set theory",
}

@InProceedings{Caprasse:1989:CEB,
  author =       "H. Caprasse and J. Demaret and E. Schrufer",
  title =        "Can {EXCALC} be used to investigate high-dimensional
                 cosmological models with nonlinear {Lagrangians}?",
  crossref =     "Gianni:1989:SAC",
  pages =        "116--124",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Recent work in cosmology is characterized by the
                 extension of the traditional four-dimensional general
                 relativity models in two directions: Kaluza--Klein type
                 models which have more than four dimensions, and models
                 with Lagrangians containing nonlinear terms in the
                 Riemann curvature tensor and its contractions. The
                 package EXCALC 2 seems particularly well suited to
                 investigate these models further. The implementation of
                 all operations of EXTERIOR CALCULUS opens the way to
                 perform these calculations efficiently. The article
                 presents the current stage of investigation in this
                 direction.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. de Phys., Liege Univ., Belgium",
  classification = "A9575P (Mathematical and computer techniques);
                 A9880D (Theoretical cosmology); C7350 (Astronomy and
                 astrophysics)",
  keywords =     "Contractions; Cosmology; EXCALC 2; Four-dimensional
                 general relativity models; High-dimensional
                 cosmological models; Kaluza--Klein type models;
                 Nonlinear Lagrangians; Package; Riemann curvature
                 tensor",
  thesaurus =    "Astronomy computing; Astrophysics computing;
                 Cosmology; Software packages",
}

@InProceedings{ChaffyCamus:1989:ARA,
  author =       "C. Chaffy-Camus",
  title =        "An application of {REDUCE} to the approximation of
                 $f(x,y)$",
  crossref =     "Gianni:1989:SAC",
  pages =        "73--84",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Pad{\'e} approximants are an important tool in
                 numerical analysis, to evaluate $f(x)$ from its power
                 series even outside the disk of convergence, or to
                 locate its singularities. The paper generalizes this
                 process to the multivariate case and presents two
                 applications of this method: the approximation of
                 implicit curves and the approximation of double power
                 series. Computations are carried out on a computer
                 algebra system REDUCE.",
  acknowledgement = ack-nhfb,
  affiliation =  "TIM3-INPG, Grenoble, France",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics)",
  keywords =     "Approximation; Computer algebra system; Convergence;
                 Double power series; Implicit curves; Multivariate
                 case; Numerical analysis; Pad{\'e} approximants;
                 Reduce; Singularities",
  thesaurus =    "Approximation theory; Convergence of numerical
                 methods; Mathematics computing; Software packages",
}

@InProceedings{Char:1989:ARA,
  author =       "B. W. Char",
  title =        "Automatic reasoning about numerical stability of
                 rational expressions",
  crossref =     "Gonnet:1989:PAI",
  pages =        "234--241",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p234-char/",
  abstract =     "While numerical (e.g. Fortran) code generation from
                 computer algebra is nowadays relatively easy to do, the
                 expressions as they are produced via computer algebra
                 typically benefit from nontrivial reformulation for
                 efficiency and numerical stability. To assist in
                 automatic `expert reformulation', we desire good
                 automated tools to assess the stability of a particular
                 form of an expression. The author discusses an approach
                 to proofs of numerical stability (with respect to
                 roundoff error) of rational expressions. The proof
                 technique is based upon the ability to propagate
                 properties such as sign, exact representability, or a
                 certain kind of numerical stability, to floating point
                 results from properties of their antecedents. The
                 qualitative approach to numerical stability lends
                 itself to implementation as a backwards-chaining
                 theorem prover. While it is not a replacement for
                 alternative forms of stability analysis, it can
                 sometimes discover stability and explain it
                 straightforwardly.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
                 USA",
  classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
  keywords =     "algorithms; Backwards-chaining theorem prover; Code
                 generation; Computer algebra; Floating point; Numerical
                 stability; Rational expressions; Roundoff error;
                 theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Code generation.
                 {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
                 theorem proving. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic.",
  thesaurus =    "Automatic programming; Convergence of numerical
                 methods; Mathematics computing; Symbol manipulation",
}

@InProceedings{Char:1989:DIC,
  author =       "B. W. Char and A. R. Macnaughton and P. A. Strooper",
  title =        "Discovering inequality conditions in the analytical
                 solutions of optimization problems",
  crossref =     "Gianni:1989:SAC",
  pages =        "109--115",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The Kuhn--Tucker conditions can provide an analytic
                 solution to the problem of maximizing or minimizing a
                 function subject to inequality constraints, if the
                 artificial variables known as Lagrange multipliers can
                 be eliminated. The paper describes an automated
                 reasoning program that assists in the solution process.
                 The program may also be useful for other problems
                 involving algebraic reasoning with inequalities.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
                 USA",
  classification = "C1180 (Optimisation techniques); C1230 (Artificial
                 intelligence); C7310 (Mathematics)",
  keywords =     "Algebraic reasoning; Analytic solution; Artificial
                 variables; Automated reasoning program; Function
                 maximization; Function minimization; Inequality
                 conditions; Inequality constraints; Kuhn--Tucker
                 conditions; Lagrange multipliers; Optimization
                 problems",
  thesaurus =    "Inference mechanisms; Mathematics computing;
                 Optimisation",
}

@InProceedings{Chen:1989:CNF,
  author =       "Guoting Chen",
  title =        "Computing the normal forms of matrices depending on
                 parameters",
  crossref =     "Gonnet:1989:PAI",
  pages =        "242--249",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p242-chen/",
  abstract =     "The author considers an algorithm for the exact
                 computation of the Frobenius, Jordan and Arnold's form
                 of matrices depending holomorphically on parameters.
                 The problem originates from the problem of formal
                 resolution of a first order system of differential
                 equations depending on parameter. This algorithm has
                 been implemented in Macsyma.",
  acknowledgement = ack-nhfb,
  affiliation =  "Equipe de Calcul Formel et Algorithmique Parallele,
                 Laboratoire TIM3-IMAG, Grenoble, France",
  classification = "C1110 (Algebra); C1120 (Analysis); C4140 (Linear
                 algebra); C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "algorithms; design; Differential equations; Formal
                 resolution; Macsyma; Matrices; Normal forms; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations.",
  thesaurus =    "Differential equations; Mathematics computing; Matrix
                 algebra; Symbol manipulation",
}

@InProceedings{Collins:1989:PRP,
  author =       "G. E. Collins and J. R. Johnson",
  title =        "The probability of relative primality of {Gaussian}
                 integers",
  crossref =     "Gianni:1989:SAC",
  pages =        "252--258",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors generalize, to an arbitrary number field,
                 the theorem which gives the probability that two
                 integers are relatively prime. The probability that two
                 integers are relatively prime is $ 1/ \zeta (2)$, where
                 $\zeta$ is the Riemann $\zeta$ function and
                 $1/\zeta(2)=6/\pi^2$. The theorem for an arbitrary
                 number field states that the probability that two
                 ideals are relatively prime is the reciprocal of the
                 $\zeta$ function of the number field evaluated at two.
                 In particular, since the Gaussian integers are a unique
                 factorization domain, the authors get the probability
                 that two Gaussian integers are relatively prime is
                 $1/\zeta_G(2)$ where $\zeta_G$ is the $\zeta$ function
                 associated with the Gaussian integers. In order to
                 calculate the Gaussian probability, they use a theorem
                 that enables them to factor the $\zeta$ function into a
                 product of the Riemann $\zeta$ function and a Dirichlet
                 series called an L-series.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
                 Columbus, OH, USA",
  classification = "C1140 (Probability and statistics); C1160
                 (Combinatorial mathematics)",
  keywords =     "Arbitrary number field; Dirichlet series; Gaussian
                 integers; L-series; Probability; Relative primality;
                 Riemann $\zeta$ function",
  thesaurus =    "Number theory; Probability",
}

@InProceedings{Collins:1989:QES,
  author =       "G. E. Collins and J. R. Johnson",
  title =        "Quantifier elimination and the sign variation method
                 for real root isolation",
  crossref =     "Gonnet:1989:PAI",
  pages =        "264--271",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p264-collins/",
  abstract =     "An important aspect of the construction of a
                 cylindrical algebraic decomposition (CAD) is real root
                 isolation. Root isolation involves finding disjoint
                 intervals, each containing a single root, for all of
                 the real roots of a given polynomial. Root isolation is
                 used to construct a CAD of the real line, which serves
                 as the base case in the construction of higher
                 dimensional CAD's. It is also an essential part of the
                 extension phase, which lifts an induced CAD to the next
                 higher dimension. The authors reexamine the sign
                 variation method of root isolation devised by Collins
                 and Akritas (1976). A new proof of termination is
                 given, which more accurately describes the behavior of
                 the algorithm. This theorem is then sharpened for the
                 special case of cubic polynomials. The result for cubic
                 polynomials is obtained with the aid of Collins's CAD
                 based quantifier elimination algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
                 Columbus, OH, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation)",
  keywords =     "algorithms; Cubic polynomials; Cylindrical algebraic
                 decomposition; design; Disjoint intervals; Polynomial;
                 Quantifier elimination; Real root isolation; Sign
                 variation method; Symbol manipulation; theory",
  subject =      "{\bf J.6} Computer Applications, COMPUTER-AIDED
                 ENGINEERING. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Cooperman:1989:RGC,
  author =       "G. Cooperman and L. Finkelstein and E. Luks",
  title =        "Reduction of group constructions to point
                 stabilizers",
  crossref =     "Gonnet:1989:PAI",
  pages =        "351--356",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p351-cooperman/",
  abstract =     "The construction of point stabilizer subgroups is a
                 problem which has been studied intensively. This work
                 describes a general reduction of certain group
                 constructions to the point stabilizer problem. Examples
                 are given for the centralizer, the normal closure, and
                 a restricted group intersection problem. For the normal
                 closure problem, this work provides an alternative to
                 current algorithms, which are limited by the need for
                 repeated closures under conjugation. For the
                 centralizer and restricted group intersection problems,
                 one can use an existing point stabilizer sequence along
                 with a recent base change algorithm to avoid generating
                 a new point stabilizer sequence. This reduces the time
                 complexity by at least an order of magnitude.
                 Algorithms and theoretical time estimates for the
                 special case of a small base are also summarized. An
                 implementation is in progress.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
                 USA",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory)",
  keywords =     "algorithms; Base change algorithm; Centralizer; Group
                 constructions; Group intersection; Group theory; Normal
                 closure; Point stabilizers; theory; Time complexity",
  subject =      "{\bf G.2.1} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Permutations and
                 combinations. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Number-theoretic
                 computations. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Mechanical theorem proving.",
  thesaurus =    "Computational complexity; Group theory; Symbol
                 manipulation",
}

@InProceedings{Deprit:1989:MPS,
  author =       "A. Deprit and E. Deprit",
  title =        "Massively parallel symbolic computation",
  crossref =     "Gonnet:1989:PAI",
  pages =        "308--316",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p308-deprit/",
  abstract =     "A massively parallel processor proves to be a powerful
                 tool for manipulating the very large Poisson series
                 encountered in nonlinear dynamics. Exploiting the
                 algebraic structure of Poisson series leads quite
                 naturally to parallel data structures and algorithms
                 for symbolic manipulation. Exercising the parallel
                 symbolic processor on the solution of Kepler's equation
                 reveals the need to reexamine the serial computational
                 methods traditionally applied to problems in
                 dynamics.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
                 USA",
  classification = "C1120 (Analysis); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "Algebraic structure; algorithms; design; Massively
                 parallel processor; Nonlinear dynamics; Parallel data
                 structures; Symbolic manipulation; theory; Very large
                 Poisson series",
  subject =      "{\bf F.1.2} Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Parallelism and
                 concurrency. {\bf E.1} Data, DATA STRUCTURES. {\bf
                 G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Roots of Nonlinear Equations. {\bf C.1.3} Computer
                 Systems Organization, PROCESSOR ARCHITECTURES, Other
                 Architecture Styles, Stack-oriented processors**.",
  thesaurus =    "Data structures; Mathematics computing; Nonlinear
                 equations; Parallel algorithms; Series [mathematics];
                 Symbol manipulation",
}

@InProceedings{Devitt:1989:UCA,
  author =       "J. S. Devitt",
  title =        "Unleashing computer algebra on the mathematics
                 curriculum",
  crossref =     "Gonnet:1989:PAI",
  pages =        "218--227",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author presents examples of the actual use of a
                 computer algebra system in the mathematics classroom.
                 These methods and observations are based on the daily
                 use of symbolic algebra during lectures. The potential
                 for focusing student energies on the concepts and ideas
                 of mathematical instead of just mimicking routine
                 computations is enormous. Considerable work remains to
                 make such tools widely accessible but the observations
                 presented will help to make others aware of the great
                 potential which exists for these and similar methods.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Saskatchewan Univ., Saskatoon, Sask.,
                 Canada",
  classification = "C7310 (Mathematics); C7810C (Computer-aided
                 instruction)",
  keywords =     "Computer algebra; Educational computing; Mathematics
                 curriculum; Symbolic algebra",
  thesaurus =    "Educational computing; Mathematics computing; Symbol
                 manipulation",
}

@InProceedings{Dewar:1989:IIS,
  author =       "M. C. Dewar",
  title =        "{IRENA}: an integrated symbolic and numerical
                 computation environment",
  crossref =     "Gonnet:1989:PAI",
  pages =        "171--179",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Computer algebra systems provide an extremely
                 user-friendly and natural problem-solving environment,
                 but are comparatively slow and limited in the scope of
                 problems they can treat. Programs which call routines
                 from numerical software libraries are fast, but require
                 longer development and testing time, as well as forcing
                 potential users to describe their problems in what is,
                 to them, an unnatural form. Both approaches have
                 advantages and disadvantages, but until now it has been
                 rather difficult to mix the two. The author describes
                 IRENA, an interface between the computer algebra system
                 REDUCE and the NAG numerical subroutine library, which
                 provides the NAG user with the advantages of a computer
                 algebra system and the REDUCE user with the facilities
                 of an extensive library of numerical software. He
                 discusses how the two methods could be used
                 side-by-side to solve problems in definite
                 integration.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C4160 (Numerical integration and differentiation);
                 C6130 (Data handling techniques); C7310 (Mathematics)",
  keywords =     "Computer algebra system; Definite integration; IRENA;
                 NAG; Numerical software; Numerical subroutine library;
                 REDUCE",
  thesaurus =    "Integration; Mathematics computing; Symbol
                 manipulation; User interfaces",
}

@InProceedings{Dicrescenzo:1989:AEA,
  author =       "C. Dicrescenzo and D. Duval",
  title =        "Algebraic extensions and algebraic closure in
                 {Scratchpad II}",
  crossref =     "Gianni:1989:SAC",
  pages =        "440--446",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Many problems in computer algebra, as well as in
                 high-school exercises, are such that their statement
                 only involves integers but their solution involves
                 complex numbers. For example, the complex numbers
                 $\sqrt{2}$ and $-\sqrt{2}$ appear in the solutions of
                 elementary problems in various domains. The authors
                 describe an implementation of an algebraic closure
                 domain constructor in the language Scratchpad II. In
                 the first part they analyze the problem, and in the
                 second part they describe a solution based on the D5
                 system.",
  acknowledgement = ack-nhfb,
  affiliation =  "TIM3, INPG, Grenoble, France",
  classification = "C7310 (Mathematics)",
  keywords =     "Algebraic closure domain constructor; D5 system;
                 Language Scratchpad II",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Edelsbrunner:1989:TPS,
  author =       "H. Edelsbrunner and F. P. Preparata and D. B. West",
  title =        "Tetrahedrizing point sets in three dimensions",
  crossref =     "Gianni:1989:SAC",
  pages =        "315--331",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper offers combinatorial results on extremum
                 problems concerning the number of tetrahedra in a
                 tetrahedrization of $n$ points in general position in
                 three dimensions, i.e. such that no four points are
                 coplanar. It also presents an algorithm that in
                 $O(n\log{}n)$ time constructs a tetrahedrization of a
                 set of $n$ points consisting of at most $3n-11$
                 tetrahedra.",
  acknowledgement = ack-nhfb,
  affiliation =  "Illinois Univ., Urbana, IL, USA",
  classification = "C4190 (Other numerical methods)",
  keywords =     "Combinatorial results; Extremum problems; Tetrahedra;
                 Tetrahedrization",
  thesaurus =    "Computational geometry",
}

@InProceedings{Einwohner:1989:MPG,
  author =       "T. H. Einwohner and R. J. Fateman",
  title =        "A {MACSYMA} package for the generation and
                 manipulation of {Chebyshev} series",
  crossref =     "Gonnet:1989:PAI",
  pages =        "180--185",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p180-einwohner/",
  abstract =     "Techniques for a MACSYMA package for expanding an
                 arbitrary univariate expression as a truncated series
                 in Chebyshev polynomials and manipulating such
                 expansions are described. A data structure is
                 introduced to represent a truncated expansion in a set
                 of orthogonal polynomials which contains the
                 independent variable, the name of the orthogonal
                 polynomial set, the number of terms retained, and a
                 list of the expansion coefficients. The package
                 converts a given expression into the aforementioned
                 data structure. Special cases are the conversion of
                 sums, products, the ratio, or the composition of
                 truncated Chebyshev expansions. Another special case is
                 converting an expression free of truncated Chebyshev
                 expansions. The package generates exact expansion
                 coefficients whenever possible. In addition to
                 well-known Chebyshev expansions, such as for
                 polynomials, the authors provide new methods for
                 getting exact Chebyshev expansions for reciprocals of
                 polynomials of degree one or two, meromorphic
                 functions, arbitrary powers of a first-degree
                 polynomial, the error-function, and generalized
                 hypergeometric functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lawrence Livermore Lab., California Univ., CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C6120 (File organisation); C6130 (Data handling
                 techniques); C7310 (Mathematics)",
  keywords =     "algorithms; Chebyshev polynomials; Chebyshev series;
                 Data structure; MACSYMA; Orthogonal polynomials;
                 theory; Univariate expression",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 E.1} Data, DATA STRUCTURES. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Chebyshev approximation; Data structures; Mathematics
                 computing; Polynomials; Series [mathematics]; Software
                 packages; Symbol manipulation",
}

@InProceedings{Fateman:1989:LTR,
  author =       "R. J. Fateman",
  title =        "Lookup tables, recurrences and complexity",
  crossref =     "Gonnet:1989:PAI",
  pages =        "68--73",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p68-fateman/",
  abstract =     "The use of lookup tables can reduce the complexity of
                 calculation of functions defined typically by
                 mathematical recurrence relations. Although this
                 technique has been adopted by several algebraic
                 manipulation systems, it has not been examined
                 critically in the literature. While the use of
                 tabulation or `memoization' seems to be particularly
                 simple and worthwhile technique in some areas, there
                 are some negative consequences. Furthermore, the
                 expansion of this technique to other areas (other than
                 recurrences) has not been subjected to analysis. The
                 paper examines some of the assumptions.",
  acknowledgement = ack-nhfb,
  affiliation =  "California Univ., Berkeley, CA, USA",
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory)",
  keywords =     "Algebraic manipulation; algorithms; Complexity;
                 Functions; Lookup tables; Mathematical recurrence
                 relations; theory",
  subject =      "{\bf F.1.3} Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Complexity Measures and Classes. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Computational complexity; Number theory; Recursive
                 functions; Symbol manipulation; Table lookup",
}

@InProceedings{Fateman:1989:SSA,
  author =       "R. J. Fateman",
  title =        "Series solutions of algebraic and differential
                 equations: a comparison of linear and quadratic
                 algebraic convergence",
  crossref =     "Gonnet:1989:PAI",
  pages =        "11--16",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p11-fateman/",
  abstract =     "Speed of convergence of Newton-like iterations in an
                 algebraic domain can be affected heavily by the
                 increasing cost of each step, so much so that a
                 quadratically convergent algorithm with complex steps
                 may be comparable to a slower one with simple steps.
                 The author gives two examples: solving algebraic and
                 first-order ordinary differential equations using the
                 MACSYMA algebraic manipulation system, demonstrating
                 this phenomenon. The relevant programs are exhibited in
                 the hope that they might give rise to more widespread
                 application of these techniques.",
  acknowledgement = ack-nhfb,
  affiliation =  "California Univ., Berkeley, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations); C7310 (Mathematics)",
  keywords =     "Algebraic equations; Algebraic manipulation system;
                 algorithms; Convergence; Differential equations; Linear
                 algebraic convergence; MACSYMA; Newton-like iterations;
                 Polynomials; Quadratic algebraic convergence; Series
                 solutions; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems. {\bf G.1.4} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Iterative methods. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Convergence of numerical methods; Differential
                 equations; Iterative methods; Mathematics computing;
                 Polynomials; Series [mathematics]; Symbol
                 manipulation",
}

@InProceedings{Fitch:1989:CRB,
  author =       "J. Fitch",
  title =        "Can {REDUCE} be run in parallel?",
  crossref =     "Gonnet:1989:PAI",
  pages =        "155--162",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p155-fitch/",
  abstract =     "In order to make a substantial improvement in the
                 performance of algebra systems it will eventually be
                 necessary to use a parallel execution system. This
                 paper considers one approach to detecting parallelism,
                 an automatic method related to compilation, and applies
                 it to REDUCE, and to the factoriser in particular.",
  acknowledgement = ack-nhfb,
  classification = "C6130 (Data handling techniques); C6150C (Compilers,
                 interpreters and other processors); C7310
                 (Mathematics)",
  keywords =     "Algebra systems; algorithms; Automatic method;
                 Compilation; Factoriser; measurement; Parallel
                 execution system; Parallelism; REDUCE",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf F.1.2} Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Parallelism and
                 concurrency. {\bf F.3.2} Theory of Computation, LOGICS
                 AND MEANINGS OF PROGRAMS, Semantics of Programming
                 Languages.",
  thesaurus =    "Mathematics computing; Parallel programming; Program
                 compilers; Symbol manipulation",
}

@InProceedings{Freire:1989:ASC,
  author =       "E. Freire and E. Gamero and E. Ponce and L. G.
                 Franquelo",
  title =        "An algorithm for symbolic computation of center
                 manifolds",
  crossref =     "Gianni:1989:SAC",
  pages =        "218--230",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A useful technique for the study of local bifurcations
                 is part of the center manifold theory because a
                 dimensional reduction is achieved. The computation of
                 Taylor series approximations of center manifolds gives
                 rise to several difficulties regarding the operational
                 complexity and the computational effort. Previous works
                 proceed in such a way that the computational effort is
                 not optimized. In the paper an algorithm for center
                 manifolds well suited to symbolic computation is
                 presented. The algorithm is organized according to an
                 iterative scheme making good use of the previous steps,
                 thereby minimizing the number of operations. The
                 results of two examples obtained through a REDUCE 3.2
                 implementation of the algorithm are included.",
  acknowledgement = ack-nhfb,
  affiliation =  "Escuela Superior Ingenieros Ind., Sevilla, Spain",
  classification = "C1120 (Analysis); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "Algorithm; Center manifold theory; Computational
                 effort; Dimensional reduction; Iterative scheme; Local
                 bifurcations; Operational complexity; REDUCE 3.2;
                 Symbolic computation; Taylor series approximations",
  thesaurus =    "Approximation theory; Differential equations;
                 Mathematics computing; Symbol manipulation",
}

@InProceedings{Galligo:1989:GEC,
  author =       "Andr\'e Galligo and Lo{\"\i}c Pottier and Carlo
                 Traverso",
  title =        "Greater easy common divisor and standard basis
                 completion algorithms",
  crossref =     "Gianni:1989:SAC",
  pages =        "162--176",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The paper considers arithmetic complexity problems;
                 the main problem is how to limit the growth of the
                 coefficients in the algorithms and the complexity of
                 the field operations involved. The problem is important
                 with every ground field, with the obvious exception of
                 finite fields.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nice Univ., France",
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory)",
  keywords =     "Algorithms; Arithmetic complexity problems;
                 Coefficients; Field operations; Greater easy common
                 divisor; Standard basis completion algorithms",
  thesaurus =    "Computational complexity; Rewriting systems",
}

@InProceedings{Gaonzalez:1989:SS,
  author =       "L. Gaonzalez and H. Lombardi and T. Recio and M.-F.
                 Roy",
  title =        "{Sturm--Habicht} sequence",
  crossref =     "Gonnet:1989:PAI",
  pages =        "136--146",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p136-gaonzalez/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.9} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations. {\bf F.1.3} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Measures and Classes. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic.",
}

@InProceedings{Geddes:1989:HMO,
  author =       "K. O. Geddes and G. H. Gonnet and T. J. Smedley",
  title =        "Heuristic methods for operations with algebraic
                 numbers",
  crossref =     "Gianni:1989:SAC",
  pages =        "475--480",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Algorithms for doing computations involving algebraic
                 numbers have been known for quite some time and
                 implementations now exist in many computer algebra
                 systems. Many of these algorithms have been analysed
                 and shown to run in polynomial time and space, but in
                 spite of this many real problems take large amounts of
                 time and space to solve. The authors describe a
                 heuristic method which can be used for many operations
                 involving algebraic numbers. They give specifics for
                 doing algebraic number inverses, and algebraic number
                 polynomial exact division and greatest common divisor
                 calculation. The heuristic will not solve all instances
                 of these problems, but it returns either the correct
                 result or with failure very quickly, and succeeds for a
                 very large number of problems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics)",
  keywords =     "Algebraic numbers; Heuristic methods; Polynomial",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Geddes:1989:NAC,
  author =       "K. O. Geddes and G. H. Gonnet",
  title =        "A new algorithm for computing symbolic limits using
                 hierarchical series",
  crossref =     "Gianni:1989:SAC",
  pages =        "490--495",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors describe an algorithm for computing
                 symbolic limits, i.e. limits of expressions in symbolic
                 form, using hierarchical series. A hierarchical series
                 consists of two levels: an inner level which uses a
                 simple generalization of Laurent series with finite
                 principal part and which captures the behaviour of
                 subexpressions without essential singularities, and an
                 outer level which captures the essential singularities.
                 Once such a series has been computed for an expression
                 at a given point, the limit of the expression at the
                 point is determined by looking at the most significant
                 term of the series. This algorithm solves the limit
                 problem for a large class of expressions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
  classification = "C6130 (Data handling techniques); C7310
                 (Mathematics)",
  keywords =     "Algorithm; Finite principal part; Hierarchical series;
                 Laurent series; Limit problem; Singularities; Symbolic
                 form; Symbolic limits",
  thesaurus =    "Series [mathematics]; Symbol manipulation",
}

@InProceedings{Geddes:1989:RIM,
  author =       "K. O. Geddes and L. Y. Stefanus",
  title =        "On the {Risch--Norman} integration method and its
                 implementation in {MAPLE}",
  crossref =     "Gonnet:1989:PAI",
  pages =        "212--217",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p212-geddes/",
  abstract =     "Unlike the recursive Risch algorithm for the
                 integration of transcendental elementary functions, the
                 Risch--Norman method processes the tower of field
                 extensions directly in one step. In addition to
                 logarithmic and exponential field extensions, this
                 method can handle extensions in terms of tangents.
                 Consequently, it allows trigonometric functions to be
                 treated without converting them to complex exponential
                 form. The authors review this method and describe its
                 implementation in MAPLE. A heuristic enhancement to
                 this method is also presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
  classification = "C1110 (Algebra); C1120 (Analysis); C4160 (Numerical
                 integration and differentiation); C7310 (Mathematics)",
  keywords =     "algorithms; Exponential field extensions; Logarithmic
                 field extensions; MAPLE; Risch--Norman integration;
                 Tangents; theory; Transcendental elementary functions;
                 Trigonometric functions",
  subject =      "{\bf G.1.9} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations. {\bf F.1.3} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Measures and Classes. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative
                 methods).",
  thesaurus =    "Functions; Integration; Mathematics computing; Symbol
                 manipulation",
}

@InProceedings{Gianni:1989:DA,
  author =       "P. Gianni and V. Miller and B. Trager",
  title =        "Decomposition of algebras",
  crossref =     "Gianni:1989:SAC",
  pages =        "300--308",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors deal with the problem of decomposing
                 finite commutative Q-algebras as a direct product of
                 local Q-algebras. They solve this problem by reducing
                 it to the problem of finding a decomposition of finite
                 algebras over finite field. They show that it is
                 possible to define a lifting process that allows to
                 reconstruct the answer over the rational numbers. This
                 lifting appears to be very efficient since it is a
                 quadratic lifting that doesn't require stepwise
                 inversions. It is easy to see that the
                 Berlekamp--Hensel algorithm for the factorization of
                 polynomials is a special case of this argument.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C1110 (Algebra); C4190 (Other numerical methods)",
  keywords =     "Berlekamp--Hensel algorithm; Decomposing finite
                 commutative Q-algebras; Lifting process",
  thesaurus =    "Algebra; Computational geometry",
}

@InProceedings{Giusti:1989:ATP,
  author =       "M. Giusti and D. Lazard and A. Valibouze",
  title =        "Algebraic transformations of polynomial equations,
                 symmetric polynomials and elimination",
  crossref =     "Gianni:1989:SAC",
  pages =        "309--314",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors define a general transformation of
                 polynomials and study the following concrete problem:
                 how to perform such a transformation using a standard
                 system of computer algebra, providing the usual
                 algebraic tools.",
  acknowledgement = ack-nhfb,
  affiliation =  "Centre de Math., Ecole Polytech., Palaiseau, France",
  classification = "C4130 (Interpolation and function approximation);
                 C6130 (Data handling techniques); C7310 (Mathematics)",
  keywords =     "Algebraic tools; Algebraic transformations of
                 polynomial equations; Computer algebra; Elimination;
                 Symmetric polynomials",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Giusti:1989:CRC,
  author =       "M. Giusti",
  title =        "On the {Castelnuovo} regularity for curves",
  crossref =     "Gonnet:1989:PAI",
  pages =        "250--253",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p250-giusti/",
  abstract =     "Let $k$ be a field of characteristic zero; let us
                 consider an algebraic subvariety of the projective
                 space $P_k^n$, defined by a homogeneous ideal I of the
                 polynomial algebra $R=k(x_o,\ldots{},x_n)$. There
                 exists different objects measuring the complexity of
                 this subvariety. Some invariants are naturally
                 intrinsic: the dimension and the degree of the
                 subvariety, the Hilbert function and its regularity,
                 and the Castelnuovo regularity. A natural question is
                 to study the relationships between the integers, at
                 least when the dimension is small (less or equal to
                 one). The author gives a slightly different version of
                 the Castelnuovo--Gruson--Lazarsfeld--Peskine theorem
                 (1983), which relates the Castelnuovo regularity and
                 the degree in the case of curves with more general
                 hypotheses but unfortunately slightly weaker
                 conclusion.",
  acknowledgement = ack-nhfb,
  affiliation =  "Centre de Mathematiques, CNRS, Ecole Polytechnique,
                 Palaiseau, France",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation)",
  keywords =     "algorithms; Castelnuovo regularity; Complexity;
                 Curves; design; Hilbert function; measurement;
                 Polynomial algebra; Polynomials; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Complexity Measures and Classes.",
  thesaurus =    "Computational complexity; Curve fitting; Polynomials",
}

@InProceedings{Gonzalez:1989:SS,
  author =       "L. Gonzalez and H. Lombardi and T. Recio and M.-F.
                 Roy",
  title =        "{Sturm--Habicht} sequence",
  crossref =     "Gonnet:1989:PAI",
  pages =        "136--146",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Formal computations with inequalities is a subject of
                 general interest in computer algebra. In particular it
                 is fundamental in the parallelisation of basic
                 algorithms and quantifier elimination for real closed
                 fields. The authors give a generalisation of the Sturm
                 theorem essentially due to Sylvester, which is the key
                 for formal computations with inequalities. They study
                 the subresultant sequence, precise some of the
                 classical definitions in order to avoid problems and
                 study specialisation properties. They introduce the
                 Sturm--Habicht sequence, which generalizes Habicht's
                 work (1948). This new sequence, obtained automatically
                 from a subresultant sequence, has some remarkable
                 properties: it gives the same information as the Sturm
                 sequence, recovered by looking only at its principal
                 coefficients; it can be computed by ring operations and
                 exact divisions only, in polynomial time in case of
                 integer coefficients, eventually by modular methods; it
                 has good specialisation properties. Some information
                 about applications and implementation of the
                 Sturm--Habicht sequence is given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. de Matematicas, Cantabria Univ., Spain",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory)",
  keywords =     "Computational complexity; Computer algebra;
                 Inequalities; Integer coefficients; Modular methods;
                 Parallelisation; Polynomial time; Quantifier
                 elimination; Ring operations; Sturm theorem;
                 Sturm--Habicht sequence",
  thesaurus =    "Computational complexity; Parallel algorithms;
                 Polynomials; Series [mathematics]; Symbol
                 manipulation",
}

@InProceedings{Grigorev:1989:CCC,
  author =       "D. Yu. Grigor'ev",
  title =        "Complexity of computing the characters and the genre
                 of a system of exterior differential equations",
  crossref =     "Gianni:1989:SAC",
  pages =        "534--543",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let a system
                 $(\sum_JA_{J,i}(dX_{j1},\ldots{},dX_{jm})=0)_{m,i}$ of
                 exterior differential equations be given, where
                 $A_{J,i}$ are polynomials in $n$ variables
                 $X_1,\ldots{}, X_n$ of degrees less than $d$ and
                 skew-symmetric relatively to multiindices
                 $J=(j_1,\ldots{}, j_m)$, the square brackets denote the
                 exterior product of the differentials
                 $dX_{j1},\ldots{}, dX_{jm}$. E. Cartan (1945)
                 introduced the characters and the genre $h$ of the
                 system. Cauchy--Kovalevski theorem guarantees the
                 existence of an integral manifold (and even of the
                 general form) with the dimension less or equal to $h$
                 satisfying the given system. An algorithm for computing
                 the characters and the genre is designed with the
                 running time polynomial in $L$, $(dn)^n$, herein $L$
                 denotes the bit-size of the system. The algorithm
                 involves the subexponential-time procedures for finding
                 the irreducible components of an algebraic variety.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., V. A. Steklov Inst., Acad. of Sci.,
                 Leningrad, USSR",
  classification = "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  keywords =     "Algebraic variety; Cauchy--Kovalevski theorem;
                 Characters; Exterior differential equations; Integral
                 manifold; Irreducible components; Polynomials",
  thesaurus =    "Differential equations; Polynomials",
}

@InProceedings{Grossman:1989:LTE,
  author =       "R. Grossman and R. G. Larson",
  title =        "Labeled trees and the efficient computation of
                 derivations",
  crossref =     "Gonnet:1989:PAI",
  pages =        "74--80",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p74-grossman/",
  abstract =     "The paper is concerned with the effective parallel
                 symbolic computation of operators under composition.
                 Examples include differential operators under
                 composition and vector fields under the Lie bracket. In
                 general, such operators do not commute. An important
                 problem is to find efficient algorithms to write
                 expressions involving noncommuting operators in terms
                 of operators which do commute. If the original
                 expression enjoys a certain symmetry, then naive
                 rewriting requires the computation of terms which in
                 the end cancel. Previously, the authors gave an
                 algorithm which in some cases is exponentially faster
                 than the naive expansion of the noncommutating
                 operators (1989). In this paper they show how that
                 algorithm can be naturally parallelized.",
  acknowledgement = ack-nhfb,
  affiliation =  "Illinois Univ., Chicago, IL, USA",
  classification = "C1120 (Analysis); C1160 (Combinatorial mathematics);
                 C4210 (Formal logic); C4240 (Programming and algorithm
                 theory)",
  keywords =     "algorithms; Computational complexity; Data structures;
                 Derivations; Differential operators; Labeled trees; Lie
                 bracket; Noncommuting operators; Operators; Parallel
                 algorithms; Parallel symbolic computation; theory;
                 Vector fields",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.1.2} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Modes of Computation,
                 Parallelism and concurrency.",
  thesaurus =    "Computational complexity; Data structures;
                 Differentiation; Parallel algorithms; Symbol
                 manipulation; Trees [mathematics]",
}

@InProceedings{Hentzel:1989:VNA,
  author =       "I. R. Hentzel and D. J. Pokrass",
  title =        "Verification of non-identities in algebras",
  crossref =     "Gianni:1989:SAC",
  pages =        "496--507",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors present a computer assisted algorithm
                 which establishes whether or not a proposed identity is
                 a consequence of the defining identities of a variety
                 of nonassociative algebras. When the nonassociative
                 polynomial is not an identity, the algorithm produces a
                 proof called a characteristic function. Like an
                 ordinary counterexample, the characteristic function
                 can be used to convince a verifier that the polynomial
                 is not identically zero. However the characteristic
                 function appears to be computationally easier to
                 verify. Also, it reduces or eliminates problems with
                 characteristic. The authors used this method to obtain
                 and verify a new result in the theory of nonassociative
                 algebras. Namely, in a free right alternative algebra
                 $(a,a,b)^3 \ne 0$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  classification = "C7310 (Mathematics)",
  keywords =     "Algebras; Characteristic function; Computer assisted
                 algorithm; Nonassociative polynomial; Nonidentities
                 verification",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Juozapavicius:1989:SCW,
  author =       "A. Juozapavicius",
  title =        "Symbolic computation for {Witt} rings",
  crossref =     "Gianni:1989:SAC",
  pages =        "271--273",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author considers bilinear and quadratic forms over
                 polynomial rings, such that they can carry linear
                 discrete orderings. The author defines the notion of
                 reduced form and presents theorems concerning
                 equivalence of forms to their reduced presentation. The
                 proofs of these statements are based on the
                 Buchberger's algorithms and their modifications to
                 Gr{\"o}bner bases.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Vilnius State Univ., Lithuanian SSR,
                 USSR",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics)",
  keywords =     "Bilinear forms; Symbolic computation; Witt rings;
                 Quadratic forms; Polynomial rings; Linear discrete
                 orderings; Reduced form; Gr{\"o}bner bases",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Kaltofen:1989:ISM,
  author =       "E. Kaltofen and L. Yagati",
  title =        "Improved sparse multivariate polynomial interpolation
                 algorithms",
  crossref =     "Gianni:1989:SAC",
  pages =        "467--474",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The authors consider the problem of interpolating
                 sparse multivariate polynomials from their values. They
                 discuss two algorithms for sparse interpolation, one
                 due to Ben-Or and Tiwari (1988) and the other due to
                 Zippel (1988). They present efficient algorithms for
                 finding the rank of certain special Toeplitz systems
                 arising in the Ben-Or and Tiwari algorithm and for
                 solving transposed Vandermonde systems of equations,
                 the use of which greatly improves the time complexities
                 of the two interpolation algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "Sparse multivariate polynomial interpolation
                 algorithms; Time complexities; Toeplitz systems;
                 Transposed Vandermonde systems of equations",
  thesaurus =    "Interpolation; Polynomials",
}

@InProceedings{Kaltofen:1989:IVP,
  author =       "E. Kaltofen and T. Valente and N. Yui",
  title =        "An improved {Las Vegas} primality test",
  crossref =     "Gonnet:1989:PAI",
  pages =        "26--33",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p26-kaltofen/",
  abstract =     "The authors present a modification of the
                 Goldwasser--Kilian--Atkin primality test, which, when
                 given an input $n$, outputs either prime or composite,
                 along with a certificate of correctness which may be
                 verified in polynomial time. Atkin's method computes
                 the order of an elliptic curve whose endomorphism ring
                 is isomorphic to the ring of integers of a given
                 imaginary quadratic field $Q(\sqrt{-D})$. Once an
                 appropriate order is found, the parameters of the curve
                 are computed as a function of a root modulo $n$ of the
                 Hilbert class equation for the Hilbert class field of
                 $Q(\sqrt{-D})$. The modification proposed determines
                 instead a root of the Watson class equation for
                 $Q(\sqrt{-D})$ and applies a transformation to get a
                 root of the corresponding Hilbert equation. This is a
                 substantial improvement, in that the Watson equations
                 have much smaller coefficients than do the Hilbert
                 equations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C1160 (Combinatorial mathematics); C4240
                 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "algorithms; Certificate of correctness; Elliptic
                 curve; Endomorphism ring; Goldwasser--Kilian--Atkin
                 primality test; Hilbert equation; Imaginary quadratic
                 field; Las Vegas primality test; Number theory;
                 Polynomial time; Prime number; Programming theory;
                 theory; Watson class equation",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Hyperbolic
                 equations. {\bf G.3} Mathematics of Computing,
                 PROBABILITY AND STATISTICS. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation.",
  thesaurus =    "Computational complexity; Mathematics computing;
                 Number theory; Program verification; Programming
                 theory",
}

@InProceedings{Kirchner:1989:CER,
  author =       "C. Kirchner and H. Kirchner",
  title =        "Constrained equational reasoning",
  crossref =     "Gonnet:1989:PAI",
  pages =        "382--389",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p382-kirchner/",
  abstract =     "The theory of constrained equational reasoning is
                 outlined. Many questions and prolongations of this work
                 arise.",
  acknowledgement = ack-nhfb,
  classification = "C4210 (Formal logic)",
  keywords =     "algorithms; Constrained equational reasoning; Formal
                 logic; Theorem proving; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES, Mathematical Logic, Logic and
                 constraint programming. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic, Computational logic.",
  thesaurus =    "Formal logic; Theorem proving",
}

@InProceedings{Kobayashi:1989:SSA,
  author =       "H. Kobayashi and S. Moritsugu and R. W. Hogan",
  title =        "Solving systems of algebraic equations",
  crossref =     "Gianni:1989:SAC",
  pages =        "139--149",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Shows an algorithm for computing all the solutions
                 with their multiplicities of a system of algebraic
                 equations. The algorithm previously proposed by the
                 authors for the case where the ideal is
                 zero-dimensional and radical seems to have practical
                 efficiency. The authors present a new method for
                 solving systems which are not necessarily radical. The
                 set of all solutions is partitioned into subsets each
                 of which consists of mutually conjugate solutions
                 having the same multiplicity.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Coll. of Sci. and Technol., Nihon
                 Univ., Tokyo, Japan",
  classification = "C1110 (Algebra); C4210 (Formal logic)",
  keywords =     "Algebraic equations; Algorithm; Ideal; Multiplicities;
                 Mutually conjugate solutions; Radical; Subsets;
                 Zero-dimensional",
  thesaurus =    "Algebra; Problem solving; Theorem proving",
}

@InProceedings{Kredel:1989:SDC,
  author =       "H. Kredel",
  title =        "Software development for computer algebra or from
                 {ALDES\slash SAC-2} to {WEB\slash Modula-2}",
  crossref =     "Gianni:1989:SAC",
  pages =        "447--455",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author defines a new concept for developing
                 computer algebra software. The development system will
                 integrate a documentation system, a programming
                 language, algorithm libraries, and an interactive
                 calculation facility. The author exemplifies the
                 workability of this concept by applying it to the well
                 known ALDES/SAC-2 system. The ALDES Translator is
                 modified to help in converting ALDES/SAC-2 Code to
                 Modula-2. The implementation and module setup of the
                 SAC-2 basic system, list processing system and
                 arithmetic system in Modula-2 are discussed. An example
                 gives a first idea of the performance of the system.
                 The WEB System of Structured Documentation is used to
                 generate documentation with {\TeX}.",
  acknowledgement = ack-nhfb,
  affiliation =  "Passau Univ., West Germany",
  classification = "C6110B (Software engineering techniques); C7310
                 (Mathematics)",
  keywords =     "ALDES/SAC-2 system; Algorithm libraries; Computer
                 algebra software; Documentation system; Interactive
                 calculation facility; Performance; Programming
                 language; WEB/Modula-2",
  thesaurus =    "Mathematics computing; Software engineering; Symbol
                 manipulation",
}

@InProceedings{Kuhn:1989:MEC,
  author =       "N. Kuhn and K. Madlener",
  title =        "A method for enumerating cosets of a group presented
                 by a canonical system",
  crossref =     "Gonnet:1989:PAI",
  pages =        "338--350",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p338-kuhn/",
  abstract =     "The application of rewriting techniques to enumerate
                 cosets of subgroups in groups is investigated. Given a
                 class of groups $G$ having canonical string rewriting
                 presentations the authors consider the GWP for this
                 class which is defined by $GWP(w,U)$ iff $w$ in $<U>$
                 for $w$ in finite $U$ contained in $G$, $G \in G$,
                 where $<U>$ is the subgroup of $G$ generated by $U$.
                 They show how to associate to $U$ two rewriting
                 relations to $-{}_U$ and implies $-{}_U$ on strings
                 such that $w$ in $<U>$ iff $w$ from $*$ to
                 $-{}_U\lambda$ iff $w$ implied by
                 $*\mbox{implies}-_U\lambda$ ($\lambda$ the empty word),
                 both representing the left congruence generated by
                 $<U>$. They derive general critical pair criteria for
                 confluence and $\lambda$-confluence for these
                 relations. Using these criteria completion procedures
                 can be constructed which enumerate cosets like the
                 Todd--Coxeter algorithm without explicit definition of
                 all cosets. The procedures are shown to be terminating
                 if the index of the subgroup is finite or for groups
                 with finite canonical monadic group presentations. If
                 the completion procedure terminates it returns a prefix
                 rewriting system which is confluent on $\Sigma *$, thus
                 deciding the GWP and the index problem for this class
                 of groups. The normal forms of the rewriting relations
                 form a minimal Schreier-representative system of $<U>$
                 in $G$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Inf., Kaiserslautern Univ., West Germany",
  classification = "C1110 (Algebra); C4210 (Formal logic)",
  keywords =     "$\Lambda$-confluence; algorithms; Canonical string
                 rewriting presentations; Completion procedures;
                 Confluence; Cosets; Critical pair criteria;
                 Decidability; Finite canonical monadic group
                 presentations; Generalized word problem; Group theory;
                 Minimal Schreier-representative system; Rewriting
                 relations; Rewriting techniques; Subgroups; theory;
                 Todd--Coxeter algorithm",
  subject =      "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Grammars and Other Rewriting
                 Systems. {\bf F.4.2} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
                 Other Rewriting Systems, Decision problems. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Decidability; Group theory; Rewriting systems; Symbol
                 manipulation",
}

@InProceedings{Kutzler:1989:CAT,
  author =       "B. Kutzler",
  title =        "Careful algebraic translations of geometry theorems",
  crossref =     "Gonnet:1989:PAI",
  pages =        "254--263",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p254-kutzler/",
  abstract =     "Modern application areas like computer-aided design
                 and robotics have revived interest in geometry. The
                 algorithmic techniques of computer algebra are
                 important tools for solving large classes of nonlinear
                 geometric problems. However, their application requires
                 a translation of geometric problems into algebraic
                 form. So far, this algebraization process has not
                 gained special attention, since it was considered
                 `obvious'. In the context of automated geometry theorem
                 proving, the use of algebraic deduction techniques led
                 to very promising results, but it seemed to change the
                 nature of proof problems from deciding the validity of
                 a theorem to finding nondegeneracy conditions under
                 which the theorem holds. A careful analysis shows, that
                 this is mainly due to the `careless' translation
                 method. A careful translation technique is presented
                 that resolves this defect. The usefulness of the new
                 algebraization method is demonstrated on concrete
                 examples. A practical comparison with the former
                 `careless' translation is done.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1160 (Combinatorial mathematics); C4190 (Other
                 numerical methods); C4210 (Formal logic); C4290 (Other
                 computer theory); C7310 (Mathematics)",
  keywords =     "Algebraic deduction; algorithms; Automated geometry
                 theorem proving; Computer algebra; experimentation;
                 Geometry theorems; Nonlinear geometric problems;
                 theory",
  subject =      "{\bf I.2.0} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, General. {\bf G.2.1} Mathematics of
                 Computing, DISCRETE MATHEMATICS, Combinatorics.",
  thesaurus =    "Computational geometry; Symbol manipulation; Theorem
                 proving",
}

@InProceedings{MacCallum:1989:ODE,
  author =       "M. A. H. MacCallum",
  title =        "An ordinary differential equation solver for
                 {REDUCE}",
  crossref =     "Gianni:1989:SAC",
  pages =        "196--205",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Progress and plans for the implementation of an
                 ordinary differential equation solver in REDUCE 3.3 are
                 reported; the aim is to incorporate the best available
                 methods for obtaining closed-form solutions, and to aim
                 at the `best possible' alternative when this fails. It
                 is hoped that this will become a part of the standard
                 REDUCE program library. Elementary capabilities have
                 already been implemented, i.e. methods for first order
                 differential equations of simple types and linear
                 equations of any order with constant coefficients. The
                 further methods to be used include: for first-order
                 equations, an adaptation of Shtokhamer's MACSYMA
                 program; for higher-order linear equations,
                 factorisation of the operator where possible; and for
                 nonlinear equations, the exploitation of Lie
                 symmetries.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Queen Mary Coll., London, UK",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C7310 (Mathematics)",
  keywords =     "Closed-form solutions; Factorisation; First-order
                 equations; Lie symmetries; MACSYMA program; Nonlinear
                 equations; Ordinary differential equation solver;
                 REDUCE 3.3; REDUCE program library",
  thesaurus =    "Differential equations; Mathematics computing;
                 Software packages; Subroutines",
}

@InProceedings{Menezes:1989:SCA,
  author =       "A. J. Menezes and P. C. {van Oorschot} and S. A.
                 Vanstone",
  title =        "Some computational aspects of root finding in
                 ${GF}(q^m)$",
  crossref =     "Gianni:1989:SAC",
  pages =        "259--270",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper is an implementation report comparing
                 several variations of a deterministic algorithm for
                 finding roots of polynomials in finite extension
                 fields. Running times for problem instances in fields
                 $\mbox{GF}(2^m)$, including $m>1000$, are given.
                 Comparisons are made between the variations, and
                 improvements achieved in running times are discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Waterloo Univ., Ont., Canada",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "Computational aspects; Root finding; Roots of
                 polynomials",
  thesaurus =    "Polynomials",
}

@InProceedings{Miller:1989:PGE,
  author =       "B. R. Miller",
  title =        "A program generator for efficient evaluation of
                 {Fourier} series",
  crossref =     "Gonnet:1989:PAI",
  pages =        "199--206",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p199-miller/",
  abstract =     "Many fields require the evaluation of large
                 multi-variate Fourier series, but the naive method of
                 calling sine and cosine for each term can be
                 prohibitive where computing resources are constrained
                 or the series are extremely large (30000 terms).
                 Although the number of such calls can be reduced by
                 using trigonometric identities, such a reduction is
                 usually not possible by hand. Indeed, even when it is
                 carried out by computer, care must be taken to generate
                 compact programs and avoid generating large numbers of
                 intermediate terms. The author describes an algorithm
                 for automatically generating very efficient Fortran
                 programs directly from the mathematical description of
                 the series to be evaluated. The resulting Fortran
                 programs are 5-7 times faster than the naive version
                 and sometimes significantly more compact.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Inst. of Stand. and Technol., Gaithersbury, MD,
                 USA",
  classification = "C6115 (Programming support); C7310 (Mathematics)",
  keywords =     "algorithms; design; Fortran programs; Fourier series;
                 languages; Program generator",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Computability
                 theory. {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Code generation. {\bf D.3.3} Software,
                 PROGRAMMING LANGUAGES, Language Constructs and
                 Features, Procedures, functions, and subroutines.",
  thesaurus =    "Automatic programming; Mathematics computing; Series
                 [mathematics]; Symbol manipulation",
}

@InProceedings{Mora:1989:GBN,
  author =       "T. Mora",
  title =        "{Gr{\"o}bner} bases in noncommutative algebras",
  crossref =     "Gianni:1989:SAC",
  pages =        "150--161",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author has studied, in 1988, the concept of
                 standard and Gr{\"o}bner bases and algorithms for their
                 computation in a very wide algebraic context (graded
                 structures). It is easy to show that if
                 $R=k<X_1,\ldots{}, X_n>/H$, where $H$ is the ideal
                 generated by $(X_jX_j-c_{ij}X_iX_j-p_{ij})$ and
                 $\deg(p_{ij})<\deg(X_iX_j)$ for each $i,j$, then $R$ is
                 such a graded structure; so his previous techniques can
                 be applied to it in order to define a concept of
                 Gr{\"o}bner basis and to produce an algorithm for their
                 computation, provided that if $J$ is the ideal
                 generated by $(X_jX_i-c_{ij}X_iX_j:i<j)$, it holds
                 that: (1) Each ideal in $k<X_1, \ldots{}, X_n>$,
                 homogeneous for the graduation defined above and
                 containing J, is finitely generated; (2) For each
                 homogeneous ideal $(h_1, \ldots{}, h_s)$ in
                 $k<X_1,\ldots{},X_n>/J$, it is possible to compute a
                 finite set of syzygies, which together with the trivial
                 ones, generate the module of syzygies; and (3) For each
                 homogeneous ideal $(h_1, \ldots{}, h_s)$ and each
                 homogeneous element $h$ in $k<X_1,\ldots{}, X_n>/J$, it
                 is possible to decide whether $h$ in
                 $(h_1,\ldots{},h_s)$, in which case it is possible to
                 compute a representation of $h$ in terms of
                 $(h_1,\ldots{},h_s)$. It turns out that the above
                 conditions hold whenever for no
                 $i<j<k,c_{ij}=c_{jk}=0$. The author shows how to solve
                 problems (2) and (3) in case for no
                 $i<j<k,C_{ij}=c_{jk}=0$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Genova Univ., Italy",
  classification = "C4210 (Formal logic)",
  keywords =     "Gr{\"o}bner bases; Noncommutative algebras; Graded
                 structures; Ideal; Homogeneous; Set of syzygies;
                 Decide",
  thesaurus =    "Algebra; Decidability; Theorem proving",
}

@InProceedings{Murray:1989:EPD,
  author =       "N. V. Murray and E. Rosenthal",
  title =        "Employing path dissolution to shorten tableaux
                 proofs",
  crossref =     "Gonnet:1989:PAI",
  pages =        "373--381",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p373-murray/",
  abstract =     "Path dissolution is an inferencing mechanism that
                 generalizes the method of analytic tableaux. The main
                 result presented is that every nontrivial step in any
                 tableau proof can be speeded up with the application of
                 dissolution techniques.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., State Univ. of New York,
                 Albany, NY, USA",
  classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
                 intelligence); C4210 (Formal logic)",
  keywords =     "algorithms; Analytic tableaux; Formal logic; Graph
                 theory; Inferencing mechanism; Path dissolution;
                 Rewrite operations; Tableau proof; Tableaux proofs;
                 theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES, Mathematical Logic.",
  thesaurus =    "Graph theory; Inference mechanisms; Rewriting systems;
                 Theorem proving",
}

@InProceedings{Musser:1989:GP,
  author =       "D. R. Musser and A. A. Stepanov",
  title =        "Generic programming",
  crossref =     "Gianni:1989:SAC",
  pages =        "13--25",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Generic programming centers around the idea of
                 abstracting from concrete, efficient algorithms to
                 obtain generic algorithms that can be combined with
                 different data representations to produce a wide
                 variety of useful software. Four kinds of
                 abstraction-data, algorithmic, structural, and
                 representational-are discussed, with examples of their
                 use in building an Ada library of software components.
                 The main topic discussed is generic algorithms and an
                 approach to their formal specification and
                 verification, with illustration in terms of a
                 partitioning algorithm such as is used in the quicksort
                 algorithm. It is argued that generically programmed
                 software component libraries offer important advantages
                 for achieving software productivity and reliability.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C6110 (Systems analysis and programming); C6120
                 (File organisation)",
  keywords =     "Abstracting; Ada library; Algorithmic abstraction;
                 Data abstraction; Data representations; Formal
                 specification; Formal verification; Generic algorithms;
                 Generic programming; Generically programmed software
                 component libraries; Partitioning algorithm; Quicksort
                 algorithm; Representational abstraction; Software
                 productivity; Software reliability; Structural
                 abstraction",
  thesaurus =    "Data structures; Programming",
}

@InProceedings{OHearn:1989:NTP,
  author =       "P. O'Hearn and Z. Stachniak",
  title =        "Note on theorem proving strategies for resolution
                 counterparts of nonclassical logics",
  crossref =     "Gonnet:1989:PAI",
  pages =        "364--372",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p364-o_hearn/",
  abstract =     "The paper shows that two of the more powerful speed-up
                 techniques available for the classical first-order
                 logic, namely the set of support and the polarity
                 strategies, can be formulated and applied to resolution
                 proof systems for nonclassical logics. The authors
                 review background information on propositional logics
                 and propositional resolution proof systems. They
                 introduce the set of support and polarity strategies.
                 They show that resolution counterparts of most
                 structural propositional logics admit both strategies
                 preserving their refutational completeness.",
  acknowledgement = ack-nhfb,
  affiliation =  "Queen's Univ., Kingston, Ont., Canada",
  classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
                 intelligence); C4210 (Formal logic)",
  keywords =     "algorithms; Deductive systems; First-order logic;
                 Inference rules; Nonclassical logics; Polarity;
                 Propositional logics; Propositional resolution proof
                 systems; Resolution counterparts; Resolution proof
                 systems; Speed-up techniques; Support; Theorem proving;
                 theory; Trees",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
                 theorem proving. {\bf G.2.2} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory.",
  thesaurus =    "Formal logic; Inference mechanisms; Theorem proving;
                 Trees [mathematics]",
}

@InProceedings{Okada:1989:SNC,
  author =       "M. Okada",
  title =        "Strong normalizability for the combined system of the
                 typed $\lambda$ calculus and an arbitrary convergent
                 term rewrite system",
  crossref =     "Gonnet:1989:PAI",
  pages =        "357--363",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p357-okada/",
  abstract =     "The author gives a proof of strong normalizability of
                 the typed $\lambda$-calculus extended by an arbitrary
                 convergent term rewriting system, which provides the
                 affirmative answer to the open problem proposed in
                 Breazu-Tannen (1988). Klop (1980) showed that a
                 combined system of the untyped $\lambda$-calculus and
                 convergent term rewriting system is not Church--Rosser
                 in general, though both are Church--Rosser. It is
                 well-known that the typed $\lambda$-calculus is
                 convergent (Church--Rosser and terminating).
                 Breazu-Tannen showed that a combined system of the
                 typed $\lambda$-calculus and an arbitrary
                 Church--Rosser term rewriting system is again
                 Church--Rosser. The strong normalization result in this
                 paper shows that the combined system of the typed
                 $\lambda$-calculus and an arbitrary convergent term
                 rewriting system is again convergent. The strong
                 normalizability proof is easily extended to the case of
                 the second order (polymorphically) typed $\lambda$
                 calculus and the case in which $\mu$-reduction rule is
                 added.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Concordia Univ., Montreal,
                 Que., Canada",
  classification = "C4210 (Formal logic)",
  keywords =     "algorithms; Church--Rosser; Convergent term rewrite
                 system; design; Polymorphically; Rewriting system;
                 Strong normalizability; theory; Typed $\lambda$
                 calculus; Typed $\lambda$-calculus",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Lambda
                 calculus and related systems. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic, Computational logic.",
  thesaurus =    "Convergence; Rewriting systems; Symbol manipulation",
}

@InProceedings{Ollivier:1989:IRM,
  author =       "F. Ollivier",
  title =        "Inversibility of rational mappings and structural
                 identifiability in automatics",
  crossref =     "Gonnet:1989:PAI",
  pages =        "43--54",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p43-ollivier/",
  abstract =     "The author investigates different methods for testing
                 whether a rational mapping $f$ from $k^n$ to $k^m$
                 admits a rational inverse, or whether a polynomial
                 mapping admits a polynomial one. He gives a new
                 solution, which seems much more efficient in practice
                 than previously known ones using `tag' variables and
                 standard basis, and a majoration for the degree of the
                 standard basis calculations which is valid for both
                 methods in the case of a polynomial map which is
                 birational. He shows that a better bound can be given
                 for the method, under some assumption on the form of
                 $f$. The method can also extend to check whether a
                 given polynomial belongs to the subfield generated by a
                 finite set of fractions. The author illustrates the
                 algorithm with an application to structural
                 identifiability. The implementation has been done in
                 the IBM computer algebra system Scratchpad II.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. d'Inf. de l'X, Ecole Polytech., Palaiseau,
                 France",
  classification = "C1110 (Algebra); C1120 (Analysis); C7310
                 (Mathematics)",
  keywords =     "algorithms; Computer algebra system; experimentation;
                 Fractions; IBM; Inversibility; Polynomial inverse;
                 Polynomial mapping; Rational inverse; Rational
                 mappings; Scratchpad II; Structural identifiability;
                 theory",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Inverse problems; Mathematics computing; Polynomials;
                 Set theory; Symbol manipulation",
}

@InProceedings{Pan:1989:SCD,
  author =       "Victor Pan",
  title =        "On some computations with dense structured matrices",
  crossref =     "Gonnet:1989:PAI",
  pages =        "34--42",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p34-pan/",
  abstract =     "The author reduces several computations with Hilbert
                 and Vandermonde type matrices to matrix computations of
                 the Hankel--Toeplitz type (and vice versa). This
                 unifies various known algorithms for computations with
                 dense structured matrices and allows the extension of
                 any progress in computations with matrices of one class
                 to the computations with other classes. This allows the
                 computation of the inverses and the determinants of
                 $n*n$ matrices of Vandermonde and Hilbert types for the
                 cost of $O(n \log^2n)$ arithmetic operations.
                 Previously, such results were only known for the more
                 narrow class of Vandermonde and generalized Hilbert
                 matrices.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., City Univ. of New York, Bronx, NY,
                 USA",
  classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
                 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "algorithms; Computational complexity; Dense structured
                 matrices; Determinants; Hankel--Toeplitz type; Hilbert;
                 Inverses; theory; Vandermonde",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Matrix inversion.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
  thesaurus =    "Computational complexity; Determinants; Inverse
                 problems; Mathematics computing; Matrix algebra",
}

@InProceedings{Porter:1989:DRA,
  author =       "S. C. Porter",
  title =        "Dense representation of affine coordinate rings of
                 curves with one point at infinity",
  crossref =     "Gonnet:1989:PAI",
  pages =        "287--297",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p287-porter/",
  abstract =     "Traditional methods of representing rational functions
                 on curves are unwieldy and unsuitable for solution of
                 many problems. This paper describes a simple and
                 elegant representation of elements of the affine
                 coordinate ring of an algebraic curve and describes
                 efficient, easy to implement algorithms to perform
                 addition, subtraction, multiplication and polynomial
                 evaluation. This data structure overcomes many of the
                 disadvantages of more unwieldy traditional
                 representations. Elements are represented as vectors of
                 elements of the ground field in a manner similar to the
                 representation of polynomials of one variable as an
                 array of coefficients. This data structure is a
                 fundamental ingredient in the author's decoding method
                 for algebraic geometry codes. The rational function
                 approximation techniques used for decoding could not
                 have been described with multivariate polynomials or
                 truncated infinite series.",
  acknowledgement = ack-nhfb,
  affiliation =  "Baise State Univ., ID, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "Affine coordinate rings; Algebraic curve; Algebraic
                 geometry codes; algorithms; Curves; Data structure;
                 Decoding; Polynomial; Rational function approximation;
                 Rational functions; theory; Vectors",
  subject =      "{\bf E.1} Data, DATA STRUCTURES. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf E.4}
                 Data, CODING AND INFORMATION THEORY.",
  thesaurus =    "Computational geometry; Data structures; Functions;
                 Mathematics computing; Polynomials; Programming theory;
                 Symbol manipulation; Vectors",
  xxpages =      "288--297",
}

@InProceedings{Purtilo:1989:MEO,
  author =       "J. M. Purtilo",
  title =        "Minion: an environment to organize mathematical
                 problem solving",
  crossref =     "Gonnet:1989:PAI",
  pages =        "147--154",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p147-purtilo/",
  abstract =     "Maryland University are constructing a management
                 assistant that works in conjunction with existing
                 symbolic computation systems. Called Minion, it allows
                 users to express simple plans for solving large
                 problems in the interactive environment, and then
                 guides the user's interaction according to that plan.
                 Key features are that plans are easy to construct; the
                 assistant helps a user visualize progress towards
                 solving the global problem; and individual steps within
                 a plan can be executed by arbitrary software tools,
                 whether symbolic-, numeric- or logic-based in their
                 implementation. The author briefly portrays the
                 organizational problem that must be treated, and
                 motivates the need for structure management tools in
                 mathematical problem solving environments. He details
                 features of the Minion prototype. After a brief update
                 on the status of the existing Polylith system, he
                 describes how Minion is implemented using an
                 interconnection resource.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Maryland Univ., College Park,
                 MD, USA",
  classification = "C6130 (Data handling techniques); C6180 (User
                 interfaces); C7310 (Mathematics)",
  keywords =     "algorithms; Interactive environment; Interconnection
                 resource; Management assistant; Maryland University;
                 Mathematical problem solving; Minion; Polylith;
                 Structure management tools; Symbolic computation
                 systems; theory; User interfaces",
  subject =      "{\bf I.3.1} Computing Methodologies, COMPUTER
                 GRAPHICS, Hardware Architecture. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms.",
  thesaurus =    "Interactive systems; Mathematics computing; Symbol
                 manipulation; User interfaces",
}

@InProceedings{Rabinowitz:1989:CSS,
  author =       "S. Rabinowitz",
  title =        "On the computer solution of symmetric homogeneous
                 triangle inequalities",
  crossref =     "Gonnet:1989:PAI",
  pages =        "272--286",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p272-rabinowitz/",
  abstract =     "The article presents an effective systematic algorithm
                 that one can use to prove inequalities. A computer
                 algorithm that can prove many inequalities is
                 presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Alliant Comput. Syst. Corp., Littleton, MA, USA",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "algorithms; Computer algorithm; Symmetric homogeneous
                 triangle inequalities; theory",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
                 theorem proving. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems.",
  thesaurus =    "Equations; Mathematics computing; Programming theory;
                 Symbol manipulation",
}

@InProceedings{Ravenscroft:1989:SSG,
  author =       "R. A. {Ravenscroft, Jr.} and E. A. Lamagna",
  title =        "Symbolic summation with generating functions",
  crossref =     "Gonnet:1989:PAI",
  pages =        "228--233",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The generating function technique presented is an
                 important addition to the area of summation algorithms.
                 With it, many summations that cannot be evaluated by
                 existing algorithms can be solved. Among these are
                 hybrid sums and sums involving special classes of
                 functions including binomial coefficients, Fibonacci
                 numbers, and harmonic numbers. However, the method is
                 not viable for hand calculation since the algebraic
                 manipulation gets very complex. Fortunately, the steps
                 used in the procedure are consistent regardless of the
                 particular generating functions that are involved.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Brown Univ., Providence, RI,
                 USA",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "Generating functions; Hybrid sums; Summation
                 algorithms; Symbolic summation",
  thesaurus =    "Computation theory; Functions; Series [mathematics];
                 Symbol manipulation",
}

@InProceedings{Roch:1989:CAM,
  author =       "J.-L. Roch and P. Senechaud and F. Siebert-Roch and G.
                 Villard",
  title =        "Computer algebra on {MIMD} machine",
  crossref =     "Gianni:1989:SAC",
  pages =        "423--439",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "PAC is a computer algebra system, based on MIMD type
                 parallelism. It uses parallelism as a tool for
                 processing problems which are too complex for a
                 sequential treatment. Basic fundamentals of the system
                 are firstly discussed. Then, different problems are
                 studied, particularly the implementation of
                 infinite-precision arithmetic, the solution of linear
                 systems and of Diophantine equations, the
                 parallelization of Buchberger's algorithm for
                 Gr{\"o}bner bases. A prototype of PAC is implemented on
                 the Floating Point System hypercube Tesseract 20 (16
                 nodes), and different timing results obtained on this
                 machine are given.",
  acknowledgement = ack-nhfb,
  affiliation =  "TIM3, INPG, Grenoble, France",
  classification = "C7310 (Mathematics)",
  keywords =     "MIMD machine; PAC; Computer algebra system;
                 Infinite-precision arithmetic; Solution of linear
                 systems; Diophantine equations; Parallelization;
                 Gr{\"o}bner bases; Floating Point System hypercube
                 Tesseract 20; Timing results",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Rolletschek:1989:SDC,
  author =       "H. Rolletschek",
  title =        "Shortest division chains in imaginary quadratic number
                 fields",
  crossref =     "Gianni:1989:SAC",
  pages =        "231--243",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $O_d$ be the set of algebraic integers in an
                 imaginary quadratic number field $Q(\sqrt{d})$, $d<0$,
                 where $d$ is the discriminant of $O_d$. Consider the
                 Euclidean Algorithm (EA), applied to algebraic integers
                 $\xi$, $\eta$ in $O_d$. It consists in computing a
                 sequence of remainders
                 $\rho_0=\xi,\rho_1=\eta,\rho_2,\ldots{},\rho_{n+1}=0$,
                 where $\rho_{i+1}=\rho_{i-1}-\gamma_i\rho_i$ for
                 algebraic integers $\gamma _i \in K, i=1, \ldots{}, n$.
                 It is shown that except for $d=-11$ the number of
                 divisions to be carried out is always minimized by
                 choosing each $\gamma_i$ such that
                 $N(\rho_{i-1}-\gamma_i\rho_i)$, the norm of
                 $\rho_{i-1}-\gamma_i\rho_i$, is minimal. This result
                 has been proven previously in special cases. It also
                 applies to those imaginary quadratic number rings which
                 are not Euclidean; in this case the division chains may
                 be infinite. For $d=-7,-8$ the methods applied so far
                 must be modified somewhat, and for $d=-11$ a
                 counterexample is provided and a theorem which
                 partially answers the question, how shortest division
                 chains can be obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Kent State Univ., OH, USA",
  classification = "C1160 (Combinatorial mathematics)",
  keywords =     "Algebraic integers; Discriminant; Divisions; EA;
                 Euclidean Algorithm; Imaginary quadratic number fields;
                 Norm; Remainders; Set; Shortest division chains",
  thesaurus =    "Number theory",
}

@InProceedings{Saunders:1989:PIC,
  author =       "B. D. Saunders and H. R. Lee and S. K. Abdali",
  title =        "A parallel implementation of the cylindrical algebraic
                 decomposition algorithm",
  crossref =     "Gonnet:1989:PAI",
  pages =        "298--307",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p298-saunders/",
  abstract =     "The authors describe a parallelization scheme for
                 Collins's cylindrical algebraic decomposition algorithm
                 for quantifier elimination in the theory of real closed
                 fields. They discuss a parallel implementation of the
                 computer algebra system SAC2 in which a complete
                 sequential implementation of Collins's algorithm
                 already exists. They report some initial results on the
                 speedup obtained, drawing on a suite of examples
                 previously given by Arnon.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. and Inf. Sci., Delaware Univ.,
                 Newark, DE, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "algorithms; Computer algebra system; Cylindrical
                 algebraic decomposition algorithm; Parallel
                 implementation; Parallelization; Polynomials;
                 Quantifier elimination; Real closed fields; SAC2;
                 theory",
  subject =      "{\bf F.1.2} Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Parallelism and
                 concurrency. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems.",
  thesaurus =    "Mathematics computing; Parallel algorithms;
                 Polynomials; Programming theory; Symbol manipulation",
}

@InProceedings{Schwarz:1989:FAL,
  author =       "F. Schwarz",
  title =        "A factorization algorithm for linear ordinary
                 differential equations",
  crossref =     "Gonnet:1989:PAI",
  pages =        "17--25",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p17-schwarz/",
  abstract =     "The reducibility and factorization of linear
                 homogeneous differential equations are of great
                 theoretical and practical importance in mathematics.
                 Although it has been known for a long time that
                 factorization is in principle a decision procedure, its
                 use in an automatic differential equation solver
                 requires a more detailed analysis of the various steps
                 involved. Especially important are certain auxiliary
                 equations, the so-called associated equations. An upper
                 bound for the degree of its coefficients is derived.
                 Another important ingredient is the computation of
                 optimal estimates for the size of polynomial and
                 rational solutions of certain differential equations
                 with rotational coefficients. Applying these results,
                 the design of the factorization algorithm LODEF and its
                 implementation in the Scratchpad II Computer Algebra
                 System is described.",
  acknowledgement = ack-nhfb,
  affiliation =  "GMD, Inst. F1, St. Augustin, West Germany",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C7310 (Mathematics)",
  keywords =     "algorithms; Associated equations; Automatic
                 differential equation solver; Factorization algorithm;
                 Linear ordinary differential equations; LODEF; Optimal
                 estimates; Polynomial solutions; Rational solutions;
                 Rotational coefficients; Scratchpad II Computer Algebra
                 System; theory; Upper bound",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods). {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  thesaurus =    "Linear differential equations; Mathematics computing;
                 Polynomials; Symbol manipulation",
}

@InProceedings{Sergeraert:1989:NRN,
  author =       "F. Sergeraert",
  title =        "From a noncomputability result to new interesting
                 definitions and computability results",
  crossref =     "Gianni:1989:SAC",
  pages =        "26--32",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Examines the strange situation encountered in
                 algebraic topology: on one hand no general algorithm is
                 able to decide whether some topological space is simply
                 connected; this is an easy consequence of the
                 undecidability of the word problem. On the other hand
                 most of the important results in algebraic topology
                 assume that the spaces under consideration are simply
                 connected. So that one can ask for algorithms that use
                 some method or other, and always compute something, in
                 such a way that if the space given is simply connected,
                 then the result obtained is the good one. The problem
                 is to explain what is something in general. The paper
                 explains that a solution can be found for the computing
                 problems of the homotopy groups. Then something is a
                 K-theory group. It obtains in this way a new
                 understanding of the algebraic K-theory groups and
                 positive results about their computability.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. Fourier, St. Martin d'Heres, France",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
  keywords =     "Algebraic K-theory groups; Algebraic topology;
                 Computability; Homotopy groups; Simply connected;
                 Topological space; Undecidability; Word problem",
  thesaurus =    "Group theory; Topology",
}

@InProceedings{Shackell:1989:AEO,
  author =       "J. Shackell",
  title =        "Asymptotic estimation of oscillating functions using
                 an interval calculus",
  crossref =     "Gianni:1989:SAC",
  pages =        "481--489",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author considers the problem of estimating the
                 asymptotic growth of functions defined by expressions
                 involving exponentials, logarithms, algebraic
                 operations and also sine functions. Modulo the
                 assumption that zero-equivalence can be decided on the
                 set of constant terms, an algorithm exists for the case
                 when there are no trigonometric functions in the
                 expression.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Math., Kent Univ., Canterbury, UK",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics)",
  keywords =     "Algebraic operations; Asymptotic estimation;
                 Asymptotic growth; Exponentials; Interval calculus;
                 Logarithms; Oscillating functions; Sine functions;
                 Zero-equivalence",
  thesaurus =    "Approximation theory; Estimation theory; Symbol
                 manipulation",
}

@InProceedings{Shackell:1989:DAF,
  author =       "J. Shackell",
  title =        "A differential-equations approach to functional
                 equivalence",
  crossref =     "Gonnet:1989:PAI",
  pages =        "7--10",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "To seek algebraic dependencies between functions is to
                 ask whether there exists a polynomial in them which is
                 functionally equivalent to zero. The methods outlined
                 work directly with the given expression, which is
                 regarded as a polynomial in a top-level basic function
                 with coefficients in a function field containing the
                 other basic functions. The top-level function is
                 defined by a differential equation over the coefficient
                 field. The techniques are entirely elementary and
                 involve differentiation, substitution and calculation
                 of GCDs. The methods decide zero-equivalence in fields
                 built using arithmetic operations and functional
                 composition with functions defined as solutions of
                 algebraic differential equations. The paper treats only
                 first-order, first-degree equations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Kent Univ., Canterbury, UK",
  classification = "C1110 (Algebra); C1120 (Analysis); C4130
                 (Interpolation and function approximation); C4170
                 (Differential equations)",
  keywords =     "Algebraic dependencies; Differential-equations;
                 Differentiation; Functional equivalence; Functions;
                 Polynomial; Substitution; Zero-equivalence",
  thesaurus =    "Differential equations; Functions; Polynomials",
}

@InProceedings{Shackle:1989:DAF,
  author =       "J. Shackle",
  title =        "A differential-equations approach to functional
                 equivalence",
  crossref =     "Gonnet:1989:PAI",
  pages =        "7--10",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p7-shackle/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General. {\bf G.1.7} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
}

@InProceedings{Sharma:1989:SDA,
  author =       "N. Sharma and P. S. Wang",
  title =        "Symbolic derivation and automatic generation of
                 parallel routines for finite element analysis",
  crossref =     "Gianni:1989:SAC",
  pages =        "33--56",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Describes some initial results of a joint research
                 project involving engineering and computer science.
                 Based on earlier work on the automatic derivation and
                 generation of numeric code for finite element analysis,
                 the authors are conducting research into the mapping of
                 finite element computations on parallel architectures.
                 Software is being developed to automatically derive and
                 generate parallel code that can be used with existing
                 sequential code to improve speed. They are developing
                 techniques to derive parallel procedures, based on
                 high-level user input, to exploit parallel computer
                 architectures. An experimental software system called
                 P-FINGER is under development to derive key finite
                 element routines for the Warp systolic array computer.
                 A separate parallel code generation package is used to
                 render the symbolically derived parallel procedures
                 into code for the Warp parallel computer.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. Sci., Kent State Univ., OH, USA",
  classification = "C4100 (Numerical analysis); C7400 (Engineering)",
  keywords =     "Automatic derivation; Automatic generation; Computer
                 science; Engineering; Experimental software system;
                 Finite element analysis; Finite element computations;
                 Finite element routines; P-FINGER; Parallel
                 architectures; Parallel code; Parallel code generation
                 package; Parallel computer architectures; Parallel
                 procedures; Parallel routines; Symbolic derivation;
                 Symbolically derived parallel procedures; Warp parallel
                 computer; Warp systolic array computer",
  thesaurus =    "Engineering computing; Finite element analysis;
                 Parallel processing",
}

@InProceedings{Siebert-Roch:1989:PAH,
  author =       "F. Siebert-Roch",
  title =        "Parallel algorithms for {Hermite} normal form of an
                 integer matrix",
  crossref =     "Gonnet:1989:PAI",
  pages =        "317--321",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p317-siebert-roch/",
  abstract =     "The main problem in integral matrices
                 triangularization is the `intermediate coefficients
                 swell'. This aspect limits the dimension of treated
                 matrices. The lliopoulos algorithm computes the Hermite
                 normal form of an integer matrix controlling the
                 coefficients growth by means of the determinant. The
                 author presents two parallelizations of this algorithm
                 and their implementations on a MIMD machine, with 16
                 processors.",
  acknowledgement = ack-nhfb,
  affiliation =  "Laboratoire TIM3-IMAG, Grenoble, France",
  classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
                 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "algorithms; Determinant; Hermite normal form; Integer
                 matrix; Integral matrices triangularization;
                 Intermediate coefficients swell; Lliopoulos algorithm;
                 MIMD; Parallel algorithms; Parallelizations; theory",
  subject =      "{\bf G.1.9} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Computational complexity; Determinants; Mathematics
                 computing; Matrix algebra; Parallel algorithms; Symbol
                 manipulation",
}

@InProceedings{Singer:1989:LFI,
  author =       "M. F. Singer",
  title =        "{Liouvillian} first integrals of differential
                 equations",
  crossref =     "Gianni:1989:SAC",
  pages =        "57--63",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The system of differential equations
                 $x=P(x,y),y=Q(x,y)$ has a Liouvillian first integral if
                 and only if the differential form $Q(x,y)dx-P(x,y)dy$
                 has an integrating factor of the form
                 $R(x,y)=exp(\int{}U(x,y)dx+V(x,y)dy)$ where $U$ and $V$
                 are rational functions and $U_y=V_x$. This theorem
                 shows that if a Liouvillian first integral exists, then
                 there is a Liouvillian first integral of a very special
                 form, but it does not show how to find one. Before
                 turning to this latter question, the author discusses
                 how this theorem is placed in the setting of
                 differential algebra and the tools used to prove it.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., North Carolina State Univ., Raleigh,
                 NC, USA",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C4180 (Integral equations)",
  keywords =     "Differential algebra; Differential equations;
                 Differential form; Integrating factor; Liouvillian
                 first integrals; Rational functions",
  thesaurus =    "Differential equations; Integral equations",
}

@InProceedings{Smedley:1989:NMA,
  author =       "T. J. Smedley",
  title =        "A new modular algorithm for computation of algebraic
                 number polynomial gcds",
  crossref =     "Gonnet:1989:PAI",
  pages =        "91--94",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p91-smedley/",
  abstract =     "Euclid's algorithm for finding the greatest common
                 divisor of two polynominals when applied to polynomials
                 over an algebraic extension field, tends to be very
                 slow. In the case of polynomials with integer
                 coefficients, one approach to solving this problem is
                 to use a modular algorithm. This approach has been
                 extended to algebraic number fields by Langemyr and
                 McCallum (1987). Another approach for algebraic numbers
                 is to use a heuristic method (Geddes, Gonnett and
                 Smedley, 1988). The paper shows that this heuristic
                 method can be made into an algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci. Waterloo Univ., Ont., Canada",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory)",
  keywords =     "Algebraic number polynomial gcds; algorithms; Euclid;
                 Heuristic method; Integer coefficients; Modular
                 algorithm; Symbol manipulation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Computation theory; Polynomials; Symbol manipulation",
}

@InProceedings{Stifter:1989:GRM,
  author =       "S. Stifter",
  title =        "A generalization of the {Roider} method to solve the
                 robot collision problem in {3D}",
  crossref =     "Gianni:1989:SAC",
  pages =        "332--343",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The Roider method is a method to test by means of
                 computational geometry whether two convex, compact
                 objects, say $A$ and $B$, in two dimensions intersect.
                 Roughly, this iterative method constructs a witness to
                 disjointness (a wedge formed by a pair of
                 touching-lines from some $P(\in A)$ to $B$ that
                 separates $A$ and $B$) if the objects are disjoint. If
                 the objects intersect then a witness to intersection,
                 i.e. a point in common to both objects, is constructed.
                 The author generalizes the Roider method in two
                 aspects: Firstly, he generalizes the algorithm such
                 that it is also applicable to convex, compact objects
                 in three dimensions. Secondly, he generalizes the
                 method such that it can be used to test whether a
                 non-moving object A collides with a moving object
                 $B$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Keples
                 Univ., Linz, Austria",
  classification = "C3120C (Spatial variables); C4190 (Other numerical
                 methods)",
  keywords =     "3D; Computational geometry; Disjointness; Iterative
                 method; Robot collision problem; Roider method",
  thesaurus =    "Computational geometry; Position control",
}

@InProceedings{Teitelbaum:1989:CCR,
  author =       "J. Teitelbaum",
  title =        "On the computational complexity of the resolution of
                 plane curve singularities",
  crossref =     "Gianni:1989:SAC",
  pages =        "285--292",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author describes an algorithm which computes the
                 resolution of a plane curve singularity-that is, a
                 singularity at the origin defined by a formal power
                 series $F$ in two variables $x$ and $y$ over a field
                 $k$. The algorithm requires that $k$ be of
                 characteristic zero (or at least of `large'
                 characteristic) but this hypothesis can certainly be
                 removed at the expense of some complications. The
                 algorithm obtains explicit equations for the blowing-up
                 of the singularity, and therefore yields all of the
                 interesting invariants of the singularity, such as its
                 conductor and its Milnor number. The author also
                 provides upper bounds for the number of $k$-operations
                 needed for the operation of the algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Michigan Univ., Ann Arbor, MI, USA",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "Computational complexity; Formal power series;
                 Resolution of plane curve singularities",
  thesaurus =    "Computational complexity; Series [mathematics]",
}

@InProceedings{Todd:1989:SAP,
  author =       "P. H. Todd and G. W. Cherry",
  title =        "Symbolic analysis of planar drawings",
  crossref =     "Gianni:1989:SAC",
  pages =        "344--355",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A method is described for performing a symbolic
                 analysis of planar drawings. The method takes input in
                 the form of a dimensioned (i.e. labeled) drawing and
                 determines whether the coordinates of all of the points
                 in the drawing can be uniquely written in terms of the
                 specified labels. If it is possible to determine the
                 coordinates of the points (i.e. the drawing is
                 consistently dimensioned), then they are calculated.
                 Otherwise the algorithm returns a flag specifying
                 whether the drawing is underdimensioned or
                 overdimensioned. The method employs standard
                 constructions from geometry such as the construction of
                 a line from two distinct points or the construction of
                 a line from a given line, a point and an angle. In
                 order to determine whether some sequence of given
                 constructions can be used to calculate the coordinates
                 of each point the authors construct and analyse an
                 undirected graph called the dimension graph of the
                 drawing. If such a sequence exists, then the
                 calculations are performed by calling symbolic routines
                 which correspond to the various constructions. An
                 implementation is described and examples are given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Tektronix Labs., Beaverton, OR, USA",
  classification = "C1160 (Combinatorial mathematics); C4190 (Other
                 numerical methods); C6130 (Data handling techniques)",
  keywords =     "Coordinates; Dimension graph; Geometry; Labeled
                 drawing; Planar drawings; Symbolic analysis; Symbolic
                 routines; Undirected graph",
  thesaurus =    "Computational geometry; Graph theory; Symbol
                 manipulation",
}

@InProceedings{Traverso:1989:EGB,
  author =       "C. Traverso and L. Donati",
  title =        "Experimenting the {Gr{\"o}bner} basis algorithm with
                 the {A1PI} system",
  crossref =     "Gonnet:1989:PAI",
  pages =        "192--198",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p192-traverso/",
  abstract =     "The AlPI (Algoritmi Pisa) system is a small polynomial
                 algebra system. It was designed and implemented by the
                 first author in MuLISP-86. It is now (almost) ported by
                 the second author in lucid COMMON-LISP, in such a way
                 that only a few macros are needed to transport it in
                 any COMMON-LISP dialect (MuLISP included). Its main aim
                 is the experimentation on the Buchberger Gr{\"o}bner
                 basis completion algorithm with its different versions,
                 and on the Mora tangent cone algorithm. It is driven by
                 a menu, and has a series of facilities to manipulate
                 lists of polynomials. After a description of the system
                 and of the versions of the algorithms presently
                 implemented, the authors give a series of experimental
                 results (for the MuLISP version). These results, and
                 results of the same kind to obtain with further
                 experimentation, can give suggestions on the versions
                 of the algorithm to choose as default for other
                 implementations of the algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartmento di Matematica, Pisa Univ., Italy",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics)",
  keywords =     "algorithms; experimentation; theory; User interfaces;
                 Gr{\"o}bner basis algorithm; AlPI system; Algoritmi
                 Pisa; Polynomial algebra system; MuLISP-86; Macros;
                 Buchberger Gr{\"o}bner basis; Completion algorithm;
                 Mora tangent cone algorithm",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Mathematics computing; Polynomials; Symbol
                 manipulation",
  xxtitle =      "Experimenting the {Gr{\"o}bner} basis algorithm with
                 the {AlPI} system",
}

@InProceedings{Traverso:1989:GTA,
  author =       "C. Traverso",
  title =        "{Gr{\"o}bner} trace algorithms",
  crossref =     "Gianni:1989:SAC",
  pages =        "125--138",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Practical computing experience on Gr{\"o}bner bases
                 has shown that computing with rational numbers or
                 integers, very frequently one has very large
                 coefficients in the intermediate computations, and that
                 often the final result is of more moderate size.
                 Sometimes it happens that the size of these numbers,
                 which have to be kept up to the end, is such that
                 memory overflow or excessive paging occurs. The
                 author's approach gives a series of algorithms, based
                 on the concept of Gr{\"o}bner trace; these algorithms
                 are mainly probabilistic (Monte Carlo); they include a
                 series of tests (still probabilistic) to check the
                 probable correctness; he also describes deterministic
                 tests that unfortunately are sometimes as costly as a
                 direct Gr{\"o}bner basis computation, but sometimes
                 instead very rapid.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Pisa Univ., Italy",
  classification = "C1140G (Monte Carlo methods); C4210 (Formal logic)",
  keywords =     "Gr{\"o}bner trace algorithms; Gr{\"o}bner bases;
                 Rational numbers; Integers; Probabilistic; Monte Carlo;
                 Probable correctness; Deterministic tests",
  thesaurus =    "Monte Carlo methods; Rewriting systems",
}

@InProceedings{Valibouze:1989:RSF,
  author =       "A. Valibouze",
  title =        "Resolvents and symmetric functions",
  crossref =     "Gonnet:1989:PAI",
  pages =        "390--399",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p390-valibouze/",
  abstract =     "A model of transformations of polynomial equations
                 (direct image model) is studied. The model expresses
                 some minimal polynomials and some resolvents relative
                 to the Galois group of a polynomial in order to use a
                 general algorithm of resolution. This algorithm can be
                 effectively computed in MACSYMA with the extension SYM
                 that manipulates symmetric polynomials. Examples
                 obtained by specializing the general algorithm for the
                 Galois resolvent are given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Pierre et Marie Curie, Paris, France",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C7310 (Mathematics)",
  keywords =     "algorithms; Direct image model; Galois group; MACSYMA;
                 Minimal polynomials; Polynomial equations; Resolution;
                 Resolvents; SYM; Symmetric polynomials; theory;
                 Transformations",
  language =     "French",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Functions; Mathematics computing; Polynomials; Symbol
                 manipulation",
}

@InProceedings{vanHulzen:1989:COP,
  author =       "J. A. {van Hulzen} and B. J. A. Hulshof and B. L.
                 Gates and M. C. {van Heerwaarden}",
  title =        "A code optimization package for {REDUCE}",
  crossref =     "Gonnet:1989:PAI",
  pages =        "163--170",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p163-van_hulzen/",
  abstract =     "A survey of the strategy behind and the facilities of
                 a code optimization package for REDUCE are given. The
                 authors avoid a detailed discussion of the different
                 algorithms and concentrate on the user aspects of the
                 package. Examples of straightforward and more advanced
                 usage are shown.",
  acknowledgement = ack-nhfb,
  affiliation =  "Twente Univ., Dept. of Comput. Sci., Enschede,
                 Netherlands",
  classification = "C6130 (Data handling techniques); C6150C (Compilers,
                 interpreters and other processors); C7310
                 (Mathematics)",
  keywords =     "algorithms; Code optimization package; Compilers;
                 REDUCE; theory; User aspects",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 I.2.2} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Automatic Programming. {\bf D.3.4}
                 Software, PROGRAMMING LANGUAGES, Processors,
                 Compilers.",
  thesaurus =    "Mathematics computing; Optimisation; Program
                 compilers; Symbol manipulation",
}

@InProceedings{Vinette:1989:USC,
  author =       "F. Vinette and J. Cizek",
  title =        "The use of symbolic computation in solving some
                 nonrelativistic quantum mechanical problems",
  crossref =     "Gianni:1989:SAC",
  pages =        "85--95",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Stresses the importance of symbolic computation
                 languages as a new research tool in applied
                 mathematics. The treatment of some non-relativistic
                 quantum mechanical problems are presented as
                 illustrations of the use of the symbolic computation
                 language MAPLE developed at the University of Waterloo.
                 Emphasis is given on the possibility to manipulate
                 expressions symbolically, to perform rapidly tedious
                 operations as well as to work in rational arithmetic.
                 Another important feature will consist in the interface
                 of MAPLE and FORTRAN.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Appl. Math., Waterloo Univ., Ont., Canada",
  classification = "A0365D (Functional analytical methods); C7320
                 (Physics and Chemistry)",
  keywords =     "Applied mathematics; Expression manipulation; FORTRAN;
                 Interface; MAPLE; Nonrelativistic quantum mechanical
                 problems; Symbolic computation languages; Symbolic
                 manipulation",
  thesaurus =    "High level languages; Physics computing; Quantum
                 theory; Symbol manipulation",
}

@InProceedings{Watt:1989:FPM,
  author =       "S. M. Watt",
  title =        "A fixed point method for power series computation",
  crossref =     "Gianni:1989:SAC",
  pages =        "206--217",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Presents a novel technique for manipulating structures
                 which represent infinite power series. The technique
                 described allows a power series to be defined in a very
                 natural but computationally inefficient way and
                 transforms it to an equivalent, efficient form. This is
                 achieved by using a fixed point operator on the delayed
                 part to remove redundant calculations. The paper
                 describes this fixed point method and the class of
                 problems to which it is applicable. It has been used in
                 Scratchpad II to improve the performance of a number of
                 operations on infinite series, including division,
                 reversion, special functions and the solution of linear
                 and non-linear ordinary differential equations. A few
                 examples are given of the method and of the speed up
                 obtained. To illustrate, the computation of the first
                 $n$ terms of $\exp(u)$ for a dense, infinite series $u$
                 is reduced from $O(n^4)$ to $O(n^2)$ coefficient
                 operations, the same as required by the standard
                 on-line algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C4240 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "Delayed part; Fixed point method; Fixed point
                 operator; Infinite power series; Power series
                 computation; Redundant calculations; Scratchpad II",
  thesaurus =    "Computational complexity; Mathematics computing",
}

@InProceedings{Weerawarana:1989:GPC,
  author =       "S. Weerawarana and P. S. Wang",
  title =        "{GENCRAY}: a portable code generator for {Cray}
                 {Fortran}",
  crossref =     "Gonnet:1989:PAI",
  pages =        "186--191",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p186-weerawarana/",
  abstract =     "The authors have applied these concepts to finite
                 element analysis. Their research resulted in the
                 software systems FINGER and GENTRAN, both written in
                 Franz LISP. FINGER, derives element strain-displacement
                 matrices and stiffness matrices based on user-supplied
                 parameters. The derived codes involve declarations,
                 expressions, arrays, functions and subroutines. These
                 quantities are represented by LISP internal data
                 structures that must be generated into numerical code
                 by a code translation process. This is the function of
                 GENTRAN which can translate MACSYMA representations
                 into f77, ratfor, or C. GENCRAY is a code generation
                 package similar to GENTRAN but different in many
                 respects. The output of GENCRAY is f77 or Cray
                 Fortran-77 (CFT77) code. CFT77 is a superset of f77 and
                 is the standard Fortran used on Cray supercomputers.
                 The authors present the design of GENCRAY, the steps of
                 code translation, its implementation, features for
                 generating vectorizable and parallel code for the Cray,
                 and how a user can customize GENCRAY to suite different
                 purposes.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. Sci., Kent State Univ., OH, USA",
  classification = "C6115 (Programming support); C6130 (Data handling
                 techniques); C6150C (Compilers, interpreters and other
                 processors); C7310 (Mathematics)",
  keywords =     "algorithms; Code generation package; Code translation;
                 Cray Fortran; Data structures; FINGER; Finite element
                 analysis; GENCRAY; GENTRAN; Portable code generator;
                 Supercomputers; theory",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Finite
                 element methods. {\bf D.3.4} Software, PROGRAMMING
                 LANGUAGES, Processors, Code generation. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Automatic programming; Finite element analysis;
                 Mathematics computing; Parallel programming; Program
                 interpreters; Software portability; Symbol
                 manipulation",
}

@InProceedings{Weispfenning:1989:EDP,
  author =       "V. Weispfenning",
  title =        "Efficient decision procedures for locally finite
                 theories. {II}",
  crossref =     "Gianni:1989:SAC",
  pages =        "262--273",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "For pt. I, see AECC-3, Grenoble, Springer LNCS, vol.
                 229.",
  abstract =     "Let $T$ be a finitely axiomatized, universal theory in
                 a finite, first-order language $L$, and suppose $T$ has
                 a model companion $T'$ with only finitely many
                 countable models. $T$ is uniformly locally finite, say
                 with generating function $g: N$ to $N$. The author
                 shows the existence of a further function $am: N$ to
                 $N$ measuring the extent to which $\mbox{Mod(T)}$ fails
                 to satisfy the amalgamation property. The main result
                 is as follows: There exist explicitly described uniform
                 decision and quantifier elimination procedures for
                 $T'$, whose asymptotic complexity can be bounded from
                 above by an elementary recursive function in $g$ and
                 am, without any further reference to $T$ or $T'$. A
                 corresponding result (with $g$ replaced by $d$) holds,
                 if $T$ is not finitely axiomatized, provided there is a
                 function $d: N$ to $N$ bounding the size of suitable
                 descriptions of $n$-generated $T$-models.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lehrstuhl fur Math., Passau Univ., West Germany",
  classification = "C1140E (Game theory); C4210 (Formal logic)",
  keywords =     "Asymptotic complexity; Decision procedures;
                 First-order language; Generating function; Locally
                 finite theories; Quantifier elimination procedures",
  thesaurus =    "Decision theory; Formal logic",
}

@InProceedings{White:1989:CF,
  author =       "N. L. White and T. McMillan",
  title =        "{Cayley} factorization",
  crossref =     "Gianni:1989:SAC",
  pages =        "521--533",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An important problem in computer-aided geometric
                 reasoning is to automatically find geometric
                 interpretations for algebraic expressions. For
                 projective geometry this question can be reduced to the
                 Cayley factorization problem. A Cayley factorization of
                 a homogeneous bracket polynomial $P$ is a Cayley
                 algebra expression (using only the join and meet
                 operations) which evaluates to P. The authors give an
                 introduction to both Cayley algebra and bracket
                 algebra. The main result of the paper is an algorithm
                 which solves the Cayley factorization problem in the
                 important special case that $P$ is multilinear.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Florida Univ., Gainesville, FL, USA",
  classification = "C4210 (Formal logic); C7310 (Mathematics)",
  keywords =     "Algebraic expressions; Bracket algebra; Cayley
                 factorization; Computer-aided geometric reasoning;
                 Homogeneous bracket polynomial; Projective geometry",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Winkler:1989:GDA,
  author =       "F. Winkler",
  title =        "A geometrical decision algorithm based on the
                 {Gr{\"o}bner} bases algorithm",
  crossref =     "Gianni:1989:SAC",
  pages =        "356--363",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Gr{\"o}bner bases have been used in various ways for
                 dealing with the problem of geometry theorem proving as
                 posed by Wu (1978). Kutzler and Stifter (1986) have
                 proposed a procedure centered around the computation of
                 a basis for the module of syzygies of the geometrical
                 hypotheses. The author elaborates this approach and
                 extends it to a complete decision procedure. Also, in
                 geometry theorem proving the problem of constructing
                 subsidiary (or degeneracy) conditions arises. Such
                 subsidiary conditions usually are not uniquely
                 determined and obviously one wants to keep them as
                 simple as possible. This problem, however, has not
                 received enough attention in the geometry theorem
                 proving literature. The author's algorithm is able to
                 construct the simplest subsidiary conditions with
                 respect to certain predefined criteria, such as lowest
                 degree or dependence on a given set of variables.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C4190 (Other numerical methods); C4210 (Formal
                 logic)",
  keywords =     "Geometrical decision algorithm; Gr{\"o}bner bases
                 algorithm; Geometry theorem proving; Complete decision
                 procedure; Subsidiary conditions",
  thesaurus =    "Computational geometry; Theorem proving",
}

@InProceedings{Winkler:1989:KPB,
  author =       "F. Winkler",
  title =        "{Knuth--Bendix} procedure and {Buchberger} algorithm
                 --- a synthesis",
  crossref =     "Gonnet:1989:PAI",
  pages =        "55--67",
  year =         "1989",
  bibdate =      "Thu Mar 12 08:33:50 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p55-winkler/",
  abstract =     "The Knuth--Bendix procedure for the completion of a
                 rewrite rule system and the Buchberger algorithm for
                 computing a Gr{\"o}bner basis of a polynomial ideal are
                 very similar in two respects: they both start with an
                 arbitrary specification of an algebraic structure
                 (axioms for an equational theory and a basis for a
                 polynomial ideal, respectively) which is transformed to
                 a very special specification of this algebraic
                 structure (a complete rewrite rule system and a
                 Gr{\"o}bner basis of the polynomial ideal,
                 respectively). This special specification allows many
                 problems concerning the given algebraic structure to be
                 decided. Moreover, both algorithms achieve their goals
                 by employing the same basic concepts: formation of
                 critical pairs and completion. Although the two methods
                 are obviously related, the exact nature of this
                 relation remains to be clarified. The author shows how
                 the Knuth--Bendix procedure and the Buchberger
                 algorithm can be seen as special cases of a more
                 general completion procedure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4210 (Formal logic); C4240 (Programming and algorithm
                 theory)",
  keywords =     "algorithms; theory; Decidability; Programming theory;
                 Knuth--Bendix procedure; Rewrite rule system;
                 Buchberger algorithm; Gr{\"o}bner basis; Polynomial;
                 Algebraic structure; Equational theory",
  subject =      "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Grammars and Other Rewriting
                 Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Mechanical theorem proving.",
  thesaurus =    "Decidability; Polynomials; Programming theory;
                 Rewriting systems; Set theory",
}

@InProceedings{Wissmann:1989:ART,
  author =       "D. Wissmann",
  title =        "Applying rewriting techniques to groups with
                 power-commutation-presentations",
  crossref =     "Gianni:1989:SAC",
  pages =        "378--389",
  year =         "1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author applies rewriting techniques to certain
                 types of string-rewriting systems related to
                 power-commutation-presentations for finitely generated
                 (f.g.) abelian groups, f.g. nilpotent groups, f.g.
                 supersolvable groups and f.g. polycyclic groups. The
                 author develops a modified version of the Knuth--Bendix
                 completion procedure which transforms such a
                 string-rewriting system into an equivalent canonical
                 system of the same type. This completion procedure
                 terminates on all admissible inputs and works with a
                 fixed reduction ordering on strings. Since canonical
                 string-rewriting systems have decidable word problem
                 this procedure shows that the systems above have
                 uniformly decidable word problem. In addition, this
                 result yields a new purely combinatorial proof for the
                 well-known uniform decidability of the work problem for
                 the corresponding groups.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Kaiserslautern Univ., West
                 Germany",
  classification = "C1160 (Combinatorial mathematics); C4210 (Formal
                 logic)",
  keywords =     "Abelian groups; Combinatorial proof; Decidable word
                 problem; Knuth--Bendix completion; Nilpotent groups;
                 Polycyclic groups; Power-commutation-presentations;
                 Rewriting techniques; String-rewriting systems;
                 Supersolvable groups; Uniform decidability",
  thesaurus =    "Decidability; Group theory; Rewriting systems",
}

@InProceedings{Aberer:1990:NFF,
  author =       "K. Aberer",
  title =        "Normal forms in function fields",
  crossref =     "Watanabe:1990:IPI",
  pages =        "1--7",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p1-aberer/",
  abstract =     "Considers function fields of functions of one variable
                 augmented by the binary operation of composition of
                 functions. It is shown that the straightforward
                 axiomatization of this concept allows the introduction
                 of a normal form for expressions denoting elements in
                 such fields. While the description of this normal form
                 seems relatively intuitive, it is surprisingly
                 difficult to prove this fact. The author presents an
                 algorithm for the normalization of expressions,
                 formulated in the symbolic computer algebra language
                 Mathematica. This allows us to effectively decide
                 compositional identities in such fields. Examples are
                 given.",
  acknowledgement = ack-nhfb,
  affiliation =  "ETH, Zurich, Switzerland",
  classification = "C1100 (Mathematical techniques); C4240 (Programming
                 and algorithm theory); C7310 (Mathematics)",
  keywords =     "algorithms; Axiomatization; Binary operation;
                 Compositional identities; Function fields; languages;
                 Mathematica; Symbolic computer algebra language",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Simplification of expressions. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Algebra; Functions; Symbol manipulation",
}

@InProceedings{Adamchik:1990:ACI,
  author =       "V. S. Adamchik and O. I. Marichev",
  title =        "The algorithm for calculating integrals of
                 hypergeometric type functions and its realization in
                 {REDUCE} system",
  crossref =     "Watanabe:1990:IPI",
  pages =        "212--224",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p212-adamchik/",
  abstract =     "The most effective and the simplest algorithm for
                 analytical integration was made by O. I. Marichev
                 (1983). This algorithm allows one to calculate definite
                 and indefinite integrals of the products of elementary
                 and special functions of hypergeometric type. It
                 embraces about 70 per cent of integrals which are
                 included in the world reference-literature. It allows
                 one to calculate many other integrals too. The article
                 contains a short description of this algorithm and its
                 realization in the REDUCE system during the process of
                 creation of the INTEGRATOR system.",
  acknowledgement = ack-nhfb,
  affiliation =  "Byelorussian Univ., Minsk, Byelorussian SSR, USSR",
  classification = "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  keywords =     "algorithms; Analytical integration; Convergence;
                 Hypergeometric type functions; INTEGRATOR system;
                 languages; Pascal; REDUCE system; Residue number
                 theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Pascal.",
  thesaurus =    "Convergence of numerical methods; Integration",
}

@InProceedings{Baaz:1990:SPR,
  author =       "M. Baaz and A. Leitsch",
  title =        "A strong problem reduction method based on function
                 introduction",
  crossref =     "Watanabe:1990:IPI",
  pages =        "30--37",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p30-baaz/",
  abstract =     "Although problem reduction is a very important tool in
                 mathematical practice, relatively little attention has
                 been paid to problem reduction in automated theorem
                 proving. The authors propose problem reduction based on
                 a splitting rule of the form $C$ implies $C'$, where
                 $C\approx{}C_1vC_2,C'\approx{}C_1vC_2',C_2'\approx{}C_2$
                 $(x\mbox{from}f(y_1,\ldots{},y_n)),(x,y_1,\ldots{},y_n)$
                 is the set of variables both in $C_1$ and $C_2$ and $f$
                 is a new function symbol up to this point not occurring
                 in any clause. Finally the authors construct a sequence
                 of clause sets $C_n$ having resolution proofs
                 exponential in $n$ only, but application of the new
                 reduction rule reduces the problem to two problems
                 linear in $n$. Thus it turns out that the introduction
                 of (elementary) quantificational rules into clause
                 logic can strongly influence the structure of proofs
                 and the performance of theorem provers",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Algebra und Diskrete Math., Tech. Univ.
                 Wien, Austria",
  classification = "C4210 (Formal logic)",
  keywords =     "algorithms; Automated theorem proving; Clause logic;
                 Problem reduction; Quantificational rules; Theorem
                 provers; theory",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic. {\bf I.2.3}
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Deduction and Theorem Proving. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Functions; Theorem proving",
  xxauthor =     "M. Baaz and A. Leitsh",
}

@InProceedings{Belmesk:1990:EME,
  author =       "M. Belmesk",
  title =        "An execution model for exploiting and-or parallelism
                 in logic programs (abstract)",
  crossref =     "Watanabe:1990:IPI",
  pages =        "288--288",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p288-belmesk/",
  abstract =     "Several models have been developed for parallel
                 execution of logic programming languages. Most of them
                 involve variations of two basic mechanisms: and
                 parallelism and or parallelism. The model developed
                 exploits both the and -and or- parallelism using a
                 compile-time program-level and clause-level data
                 dependence analysis to generate an execution graph that
                 embodies the possible parallel executions. The
                 execution graph is a directed acyclic graph, containing
                 one node per atom of the clause body and two nodes for
                 the head clause. Simple tests on the terms provided at
                 run-time determine which of the different possible
                 executions graph is to be used.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lifia-Inst. IMAG, Grenoble, France",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; And-or parallelism; Execution graph;
                 Execution model; Logic programming languages; Parallel
                 execution",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Logic and
                 constraint programming. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures. {\bf F.1.2} Theory
                 of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes
                 of Computation, Parallelism and concurrency.",
  thesaurus =    "Logic programming; Parallel programming",
}

@InProceedings{Bini:1990:PPC,
  author =       "D. Bini and V. Pan",
  title =        "Parallel polynomial computations by recursive
                 processes",
  crossref =     "Watanabe:1990:IPI",
  pages =        "294--294",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p294-bini/",
  abstract =     "Let $\lg$ stand for $\log_2$, $\lg^{(0)}n=n$,
                 $\lg^{(h)}n=\lg\lg^{(h-1)}n,h=1,\ldots{},\lg*n,\lg*n=\min(h,\lg^{(h)}n<=1)$.
                 Given natural $N$, $h$, $1<=h<=\lg*N$, and polynomial
                 $p(x), p(0) \ne 0$, the authors compute
                 $r(x)=p(x)^{-1}\bmod{}x^N$ for the cost
                 $O_A(t,P),t=h\lg{}N, P=(N/h)\lg^{(h)}N$, under the PRAM
                 arithmetic model, that is, the authors need $O(t)$
                 steps and $O(P)$ processors (with $t$ and $P$ as
                 above), provided $DFT(m)$ costs $O_A(\lg{}m,m)$. For
                 $h=\lg*N$, the cost bounds turn into
                 $O_A(\lg{}N\lg*N,N/\lg*N)$. The results apply to
                 various related computations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Pisa Univ., Italy",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Computational complexity; Parallel
                 computations; Polynomial computations; PRAM arithmetic
                 model; Recursive processes",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms.",
  thesaurus =    "Computational complexity; Parallel algorithms;
                 Polynomials; Recursive functions",
}

@InProceedings{Bradford:1990:PBA,
  author =       "R. Bradford",
  title =        "A parallelization of the {Buchberger} algorithm",
  crossref =     "Watanabe:1990:IPI",
  pages =        "296--296",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p296-bradford/",
  abstract =     "Describes experiments with a little elementary
                 parallelism applied to Buchberger's algorithm. This is
                 in contrast to Ponder (1988) and Vidal (1990) as gains
                 can be achieved by using the method even on a single
                 processor.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory)",
  keywords =     "algorithms; Buchberger's algorithm; experimentation;
                 languages; Parallelism",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE.",
  thesaurus =    "Parallel algorithms; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Cantone:1990:DFE,
  author =       "D. Cantone and V. Cutello",
  title =        "A decidable fragment of the elementary theory of
                 relations and some applications",
  crossref =     "Watanabe:1990:IPI",
  pages =        "24--29",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p24-cantone/",
  abstract =     "The class of purely universal formulae of the
                 elementary theory of relations with equality is shown
                 to have an NP-complete satisfiability problem, under
                 the assumption that there is an a priori bound on the
                 length of quantifier prefixes and the arities of
                 relation variables. In the second part of the paper the
                 authors discuss possible applications in the field of
                 theorem proving in set and graph theory and of
                 consistency checking for queries in relational
                 databases.",
  acknowledgement = ack-nhfb,
  affiliation =  "Archimedes SRL, Catania, Italy",
  classification = "C4210 (Formal logic); C4250 (Database theory)",
  keywords =     "algorithms; Consistency checking; Decidable;
                 Elementary theory of relations; Graph theory;
                 Relational databases; Satisfiability; Theorem proving;
                 theory",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Computability
                 theory. {\bf G.2.2} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures.",
  thesaurus =    "Database theory; Decidability; Relational databases;
                 Theorem proving",
}

@InProceedings{Char:1990:PRS,
  author =       "B. W. Char",
  title =        "Progress report on a system for general-purpose
                 parallel symbolic algebraic computation",
  crossref =     "Watanabe:1990:IPI",
  pages =        "96--103",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p96-char/",
  abstract =     "Discusses on-going work on large-grained parallel
                 symbolic computation using a system based on Maple and
                 Linda. The prototype runs on a Sequent Balance. The
                 approach can be used with most existing algebra/symbol
                 manipulation systems and provides the potential to
                 deliver of parallel symbolic computation on a variety
                 of architectures (e.g. shared memory, hypercubes,
                 networked workstations). Parallel speedup was achieved
                 on a variety of algebraic problems, although many
                 significant improvements in efficiency remain to be
                 achieved.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
                 USA",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "Algebraic computation; design; languages;
                 Large-grained; Linda; Maple; Parallel symbolic
                 computation; performance; Sequent Balance; Symbol
                 manipulation systems",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
                 Computation, Parallelism and concurrency. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Linda. {\bf D.1.3} Software,
                 PROGRAMMING TECHNIQUES, Concurrent Programming.",
  thesaurus =    "Parallel processing; Symbol manipulation",
}

@InProceedings{Chen:1990:ACF,
  author =       "Guoting Chen",
  title =        "An algorithm for computing the formal solutions of
                 differential systems in the neighborhood of an
                 irregular singular point",
  crossref =     "Watanabe:1990:IPI",
  pages =        "231--235",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p231-chen/",
  abstract =     "Discusses an algorithm for the computation of the
                 formal solutions of differential systems in the
                 neighborhood of an irregular singular point. In the
                 reduction of the differential systems, the author uses
                 its Arnold--Wasow's canonical form. He discusses also
                 an algorithm for the reduction of the differential
                 system to its Arnold--Wasow's canonical form. Then he
                 discusses the results of a shearing transformation on
                 this canonical form and gets the convergence of the
                 algorithm. This paper consists of a complete study of
                 the problem of computations of the formal solutions of
                 differential systems in the neighborhood of a singular
                 point (regular or irregular).",
  acknowledgement = ack-nhfb,
  affiliation =  "LMC, IMAG INPC CNRS, Grenoble, France",
  classification = "C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "algorithms; Computation; Convergence; Differential
                 systems; Formal solutions; Irregular singular point;
                 languages; Shearing transformation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA.",
  thesaurus =    "Convergence of numerical methods; Differential
                 equations; Symbol manipulation",
}

@InProceedings{Chen:1990:IAM,
  author =       "G. Chen and I. Gil",
  title =        "The implementation of an algorithm in {Macsyma}:
                 computing the formal solutions of differential systems
                 in the neighborhood of regular singular point",
  crossref =     "Watanabe:1990:IPI",
  pages =        "307--307",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p307-chen/",
  abstract =     "Discusses the problems arising in the implementation
                 in Macsyma of a direct algorithm for computing the
                 formal solutions of differential systems in the
                 neighborhood of regular singular point. The
                 differential system to be considered is of the form
                 $x^h dy/dx=A(x)y$ with $A(x)=A_0+A_1x+\ldots{}$ is an
                 $n$ by $n$ matrices of formal series.",
  acknowledgement = ack-nhfb,
  affiliation =  "Equipe de Calcul Parallele et Calcul Formel, Grenoble,
                 France",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Differential systems; Formal solutions;
                 Macsyma; Regular singular point",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms.",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Cherief:1990:AMP,
  author =       "F. Cherief",
  title =        "An algebraic model for the parallel interpretation of
                 equationally defined functions (abstract)",
  crossref =     "Watanabe:1990:IPI",
  pages =        "285--285",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p285-cherief/",
  abstract =     "Summary form only given. Algebraic Languages are well
                 suited for rapid prototyping. Their operational
                 semantics is given by means of term rewriting systems.
                 Here, the author proposes a new approach for the
                 parallel interpretation of term rewriting systems by
                 mapping every defined function into parallel processes.
                 The target language is HAL, a new process algebra where
                 parallel computations are described as a set of
                 interconnected processes which communicate through the
                 explicit sending and receiving of messages. HAL is
                 derived from LOTOS, FP2 and CCS. In HAL an event is a
                 set of simultaneous communications. Each communication
                 within an event transports one term along one
                 connector. When two connectors are linked, the
                 corresponding communication unifies the two terms. This
                 essential feature makes it possible to perform all
                 computations via communications
                 (computation=communication). In the case considered
                 here unification reduces to matching.",
  acknowledgement = ack-nhfb,
  affiliation =  "LIFIA-IMAG, Grenoble, France",
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory)",
  keywords =     "Algebraic model; algorithms; HAL; Interconnected
                 processes; languages; Operational semantics; Parallel
                 interpretation; Prototyping; Simultaneous
                 communications; Target language; Term rewriting
                 systems",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES, Grammars and Other Rewriting Systems.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.3.2} Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
                 of Programming Languages, Algebraic approaches to
                 semantics.",
  thesaurus =    "Formal languages; Parallel languages; Rewriting
                 systems",
}

@InProceedings{Chou:1990:ARG,
  author =       "Shang-Ching Chou",
  title =        "Automated reasoning in geometries using the
                 characteristic set method and {Gr{\"o}bner} basis
                 method",
  crossref =     "Watanabe:1990:IPI",
  pages =        "255--260",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p255-chou/",
  abstract =     "Presents an overview of the applications of the
                 characteristic set method and the Gr{\"o}bner basis
                 method to automated reasoning in elementary geometries,
                 differential geometries, and mechanics.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA",
  classification = "C4190 (Other numerical methods); C4290 (Other
                 computer theory); C7310 (Mathematics)",
  keywords =     "Characteristic set method; Gr{\"o}bner basis method;
                 Automated reasoning; Elementary geometries;
                 Differential geometries; algorithms; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems. {\bf
                 F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES, Mathematical Logic, Mechanical
                 theorem proving.",
  thesaurus =    "Computational geometry; Inference mechanisms; Symbol
                 manipulation",
}

@InProceedings{Chou:1990:MMG,
  author =       "Shang-Ching Chou and Xiao-Shan Gao",
  title =        "Methods for mechanical geometry formula deriving",
  crossref =     "Watanabe:1990:IPI",
  pages =        "265--270",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p265-chou/",
  abstract =     "A precise formulation for the relations among certain
                 variables under a set of polynomial equations and a set
                 of polynomial inequations (to exclude certain special
                 cases which cannot be excluded by the selection of
                 parameters alone) is given. Several methods are
                 presented to find such relations. The methods have been
                 implemented and used to find geometry formulas, to
                 discover geometry theorems, and to find geometry locus
                 equations. About 120 non-trivial problems have been
                 solved using the methods.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA",
  classification = "C1120 (Analysis); C7310 (Mathematics)",
  keywords =     "algorithms; Geometry formulas; Geometry locus
                 equations; Geometry theorems; Mechanical geometry;
                 Polynomial equations; Polynomial inequations",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms.",
  thesaurus =    "Computational geometry; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Codognet:1990:EDU,
  author =       "P. Codognet",
  title =        "Equations, disequations and unsolvable subsets
                 (abstract)",
  crossref =     "Watanabe:1990:IPI",
  pages =        "289--289",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p289-codognet/",
  abstract =     "Presents a framework for solving a system of equations
                 and disequations that allow to determine, upon
                 unsolvability, the `cause' of the failure, i.e. the
                 minimal unsolvable subsets of equations and
                 disequations responsible of it.",
  acknowledgement = ack-nhfb,
  affiliation =  "INRIA, Le Chesnay, France",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "algorithms; Disequations; Equations; Failure;
                 Unsolvability; Unsolvable subsets",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Computational
                 logic. {\bf I.1.0} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory
                 of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic, Computability theory.
                 {\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems.",
  thesaurus =    "Algebra; Symbol manipulation",
}

@InProceedings{Cooperman:1990:RBC,
  author =       "G. Cooperman and L. Finkelstein and N. Sarawagi",
  title =        "A random base change algorithm for permutation
                 groups",
  crossref =     "Watanabe:1990:IPI",
  pages =        "161--168",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p161-cooperman/",
  abstract =     "A new random base change algorithm is presented for a
                 permutation group $G$ acting on $n$ points whose worst
                 case asymptotic running time is better for groups with
                 a small to moderate size base than any known
                 deterministic algorithm. To achieve this time bound,
                 the algorithm requires a \mbox{Rand}om generator
                 $\mbox{Rand}(G)$ producing a Random element of $G$ with
                 the uniform distribution and so that each call to
                 $\mbox{Rand}(G)$ takes time
                 $O(\log(\bmod{}G\bmod{})n)$. The random base change
                 algorithm has probability $1-1/\bmod{}G\bmod{}^2$ of
                 completing in time $ O(\log^2(\bmod{}G\bmod{})n)$ and
                 outputting a data structure for representing the point
                 stabilizer sequence relative to the new ordering which
                 requires $O(\log(\bmod{}g\bmod{})n)$ space and which
                 can be used to test group membership in time
                 $O(\log(\bmod{}G\bmod{})n)$. The time to build a data
                 structure for computing a $\mbox{Rand}(G)$ with the
                 above properties from a strong generating set for $G$
                 is dominated by the time to construct the strong
                 generating set of from the original set of
                 generators.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
                 USA",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Asymptotic running time; Data structure;
                 Deterministic algorithm; Permutation groups; Point
                 stabilizer sequence; Random base change algorithm;
                 Random generator; Space complexity; Time complexity",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous. {\bf F.2.2} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Computations on
                 discrete structures.",
  thesaurus =    "Algorithm theory; Computational complexity; Data
                 structures; Group theory; Random functions",
}

@InProceedings{Doleh:1990:SSI,
  author =       "Y. Doleh and P. S. Wang",
  title =        "{SUI}: a system independent user interface for an
                 integrated scientific computing environment",
  crossref =     "Watanabe:1990:IPI",
  pages =        "88--95",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p88-doleh/",
  abstract =     "The design and implementation of a Scientific User
                 Interface is presented. Written in the C language, SUI
                 is a window-menu-mouse oriented graphical user
                 interface that is designed to provide a modern and
                 integrated computing environment for scientific work.
                 SUI can serve multiple client systems in parallel
                 including symbolic, numeric, graphics and document
                 formatting systems. SUI achieves hardware and operating
                 system independence as well as network transparency by
                 employing the X11 protocols and achieves client system
                 independence by defining a client-SUI protocol that is
                 simple and effective. Features of SUI includes input
                 editing, history, 2-D mathematical expression display,
                 interactive selection of subexpressions, interactive
                 display and manipulation of 2-D and 3-D plots of
                 mathematical functions, cut and paste with syntax
                 translation, command templates, incremental 2-D display
                 of mathematical input, and interactive configuration.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
                 USA",
  classification = "C6180 (User interfaces)",
  keywords =     "2-D display; 3-D plots; C language; Command templates;
                 Cut and paste; Document formatting; Graphical user
                 interface; Graphics; History; Input editing; Integrated
                 computing environment; Integrated scientific computing
                 environment; Interactive display; languages;
                 Mathematical expression display; Mathematical
                 functions; Network transparency; Numeric; Scientific
                 User Interface; SUI; Symbolic; Syntax translation;
                 Window-menu-mouse oriented",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C. {\bf I.3.6} Computing
                 Methodologies, COMPUTER GRAPHICS, Methodology and
                 Techniques, Interaction techniques. {\bf I.3.1}
                 Computing Methodologies, COMPUTER GRAPHICS, Hardware
                 Architecture, Input devices. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Graphical user interfaces; Symbol manipulation",
}

@InProceedings{Fateman:1990:ATD,
  author =       "R. J. Fateman",
  title =        "Advances and trends in the design and construction of
                 algebraic manipulation systems",
  crossref =     "Watanabe:1990:IPI",
  pages =        "60--67",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p60-fateman/",
  abstract =     "Compares and contrast several techniques for the
                 implementation of components of an algebraic
                 manipulation system. On one hand is the mathematical
                 algebraic approach which characterizes (for example)
                 IBM's Scratchpad II. On the other hand is the more ad
                 hoc approach which characterizes many other popular
                 systems (for example, Macsyma, Reduce, Maple, and
                 Mathematica). While the algebraic approach has
                 generally positive results, careful examination
                 suggests that there are significant remaining problems,
                 especially in the representation and manipulation of
                 analytical, as opposed to algebraic mathematics. The
                 author describes some of these problems, and some
                 general approaches for solutions.",
  acknowledgement = ack-nhfb,
  affiliation =  "California Univ., Berkeley, CA, USA",
  classification = "C4240 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "Algebraic manipulation systems; Algebraic mathematics;
                 design; languages; Macsyma; Maple; Mathematica;
                 Mathematical algebraic; Reduce; Scratchpad II",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA.",
  thesaurus =    "Algebra; Symbol manipulation",
}

@InProceedings{Faure:1990:MS,
  author =       "C. Faure",
  title =        "A {Meta} simplifier",
  crossref =     "Watanabe:1990:IPI",
  pages =        "290--290",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p290-faure/",
  abstract =     "The simplification process is a key point in computer
                 algebra systems. The author presents a model of a
                 simplifier based on two ideas: homogenizing the
                 computation over numerical and formal expressions, and
                 building a simplifier completely reachable by the user.
                 In order to evaluate numerical expressions, the
                 simplifier calls functions which compute the result or
                 raise a runtime type error. Formal expressions are
                 transformed modulo the properties of the operators. For
                 homogenizing those two processes, three basic
                 mechanisms come out: simplification by properties, type
                 checking, evaluation. Moreover a fourth mechanism using
                 rewriting rules is necessary to compute nonstandard
                 transformations needed by the user.",
  acknowledgement = ack-nhfb,
  affiliation =  "INRIA, Centre de Sophia-Antipolis, Valbonne, France",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "Computer algebra systems; design; Evaluation;
                 Homogenization; Meta amplifier; Nonstandard
                 transformations; Rewriting rules; Run-time error;
                 Runtime type error; Simplification; Type checking",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Simplification of expressions.",
  thesaurus =    "Algebra; Rewriting systems; Symbol manipulation",
}

@InProceedings{Fee:1990:CCC,
  author =       "G. J. Fee",
  title =        "Computation of {Catalan}'s constant using
                 {Ramanujan}'s formula",
  crossref =     "Watanabe:1990:IPI",
  pages =        "157--160",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p157-fee/",
  abstract =     "The author uses some formulas due to Ramanujan for the
                 multiple precision computation of Catalan's constant
                 $C=0.915\ldots{}$. The algorithm has been implemented
                 in Maple and $C$ has been computed to 20000 decimal
                 places. The resulting program is very simple yet
                 efficient. It computes $N$ digits of $C$ in $O(N^2)$
                 time and $O(N)$ space.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
  classification = "B0290D (Functional analysis); C4120 (Functional
                 analysis); C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; C; Catalan constant; Function evaluation;
                 languages; Maple; Ramanujan formula",
  subject =      "{\bf G.2.1} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications, C.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms.",
  thesaurus =    "Computational complexity; Function evaluation",
}

@InProceedings{Fitch:1990:DSR,
  author =       "J. Fitch",
  title =        "A delivery system for {REDUCE}",
  crossref =     "Watanabe:1990:IPI",
  pages =        "76--81",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p76-fitch/",
  abstract =     "A nonLISP delivery system for REDUCE is described and
                 compared with other implementations of REDUCE for speed
                 and size, as well as ease of porting. The mechanism for
                 this delivery system is direct compilation of the
                 REDUCE sources into ANSI C, which is then compiled and
                 linked together with some support code for arithmetic
                 and space administration. The resulting system is
                 compared with a number of other implementations of true
                 REDUCE, and is shown to be similar in size, but faster.
                 The time to port the system is measured in hours. Also
                 considered are the difficulties in this method of
                 delivering LISP code, and an assessment of the loss of
                 flexibility.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C7310 (Mathematics)",
  keywords =     "algorithms; Delivery system; languages; LISP code;
                 REDUCE",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications, LISP.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C. {\bf D.3.4} Software, PROGRAMMING
                 LANGUAGES, Processors, Compilers.",
  thesaurus =    "Algebra; Symbol manipulation",
}

@InProceedings{Franova:1990:PIC,
  author =       "M. Franov{\'a}",
  title =        "{PRECOMAS}. {An} implementation of constructive
                 matching methodology",
  crossref =     "Watanabe:1990:IPI",
  pages =        "16--23",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p16-franova/",
  abstract =     "The system PRECOMAS (PRoofs Educed by COnstructive
                 MATching of Synthesis) implements the Constructive
                 Matching methodology for automatic constructions of
                 programs from formal specifications. The author
                 describes briefly the goal of PRECOMAS, its logical
                 background and the CM method applied to proving atomic
                 formulae. She shows how the user of the system is
                 involved in solving a program synthesis problem. She
                 shows that this interaction does not concern the
                 problem of guiding the program synthesis process, this
                 being solved by CM. The experimental version serves to
                 confirm that the system is worth being developed.",
  acknowledgement = ack-nhfb,
  affiliation =  "CNRS, Univ. Paris Sud, Orsay, France",
  classification = "C4240 (Programming and algorithm theory); C6115
                 (Programming support)",
  keywords =     "algorithms; Atomic formulae; Constructive Matching;
                 design; Formal specifications; PRECOMAS; Program
                 synthesis; theory",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf D.1.2}
                 Software, PROGRAMMING TECHNIQUES, Automatic
                 Programming.",
  thesaurus =    "Formal logic; Programming environments",
}

@InProceedings{Ganzha:1990:ARS,
  author =       "V. G. Ganzha and S. V. Meleshko and V. P. Shelest",
  title =        "Application of {REDUCE} system for analyzing
                 consistency of systems of {PDE}'s",
  crossref =     "Watanabe:1990:IPI",
  pages =        "301--301",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p301-ganzha/",
  abstract =     "Summary form only given. A consistency analysis of
                 differential equation systems involves a sequence of
                 differential-algebraic operations. At present there are
                 known two methods: the Cartan's and the
                 Riquier--Janet--Kuranishi (RJK) method which are
                 equivalent. The implementation of the both of the
                 methods with the purpose of their practical application
                 leads to large symbolic computations which often cannot
                 be performed without a computer.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR",
  classification = "C4170 (Differential equations); C4240 (Programming
                 and algorithm theory); C7310 (Mathematics)",
  keywords =     "algorithms; Consistency; Consistency analysis;
                 Differential equation systems; Partial differential
                 equations; Riquier--Janet--Kuranishi method; RJK
                 method",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms.",
  thesaurus =    "Computational complexity; Partial differential
                 equations; Symbol manipulation",
}

@InProceedings{Ganzha:1990:LAS,
  author =       "V. G. Ganzha and M. Yu. Shashkov",
  title =        "Local approximation study of difference operators by
                 means of {REDUCE} system",
  crossref =     "Watanabe:1990:IPI",
  pages =        "185--192",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p185-ganzha/",
  abstract =     "Describes new algorithms and programs in the REDUCE
                 system for the automated study of a local order of the
                 approximation of difference operator written on
                 non-orthogonal meshes. The performance of the program
                 is demonstrated by local approximation of several
                 difference operators in one and two-dimensional
                 cases.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C4170
                 (Differential equations)",
  keywords =     "algorithms; Approximation; Difference operators;
                 languages; Local order; Nonorthogonal meshes; Numerical
                 methods; performance; REDUCE system",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Difference equations; Function approximation",
}

@InProceedings{Gatemann:1990:SSP,
  author =       "K. Gatemann",
  title =        "Symbolic solution polynomial equation systems with
                 symmetry",
  crossref =     "Watanabe:1990:IPI",
  pages =        "112--119",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p112-gatemann/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Gatermann:1990:SSP,
  author =       "K. Gatermann",
  title =        "Symbolic solution of polynomial equation systems with
                 symmetry",
  crossref =     "Watanabe:1990:IPI",
  pages =        "112--119",
  year =         "1990",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Systems of polynomial equations often have symmetry.
                 The Buchberger algorithm which may be used for the
                 solution ignores this symmetry. It is restricted to
                 moderate problems unless factorizing polynomials are
                 found leading to several smaller systems. Therefore two
                 methods are presented which use the symmetry to find
                 factorizing polynomials, decompose the ideal and thus
                 decrease the complexity of the system a lot. In a first
                 approach projections determine factorizing polynomials
                 as input for the solution process, if the group
                 contains reflections with respect to a hyperplane. Two
                 different ways are described for the symmetric group
                 $S_m$ and the dihedral group $D_m$. While for $S_m$
                 subsystems are ignored if they have the same zeros
                 modulo $G$ as another subsystem, for the dihedral group
                 $D_m$ polynomials with more than two factors are
                 generated with the help of the theory of linear
                 representations and restrictions are used as well.
                 These decomposition algorithms are independent of the
                 finally used solution technique. The author uses the
                 REDUCE package Gr{\"o}bner to solve examples which
                 illustrate the efficiency of the REDUCE program. A
                 short introduction to the theory of linear
                 representations is given. In a second approach problems
                 of another class are transformed such that more factors
                 are found during the computation; these transformations
                 are based on the theory of linear representations.
                 Examples illustrate these approaches. The range of
                 solvable problems is enlarged significantly.",
  acknowledgement = ack-nhfb,
  affiliation =  "Konrad Zuse Zentrum fur Inf. Berlin, Germany",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  keywords =     "Symbolic solution; Polynomial equation systems;
                 Buchberger algorithm; Factorizing polynomials;
                 Symmetry; Complexity; Symmetric group; Dihedral group;
                 Linear representations; REDUCE package; Gr{\"o}bner;
                 Solvable problems",
  thesaurus =    "Computational complexity; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Gerdt:1990:CGN,
  author =       "V. P. Gerdt and A. Yu. Zharkov",
  title =        "Computer generation of necessary integrability
                 conditions for polynomial nonlinear evolution systems",
  crossref =     "Watanabe:1990:IPI",
  pages =        "250--254",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p250-gerdt/",
  abstract =     "Uses the symmetry approach to establish an efficient
                 program in REDUCE for verifying necessary integrability
                 conditions for polynomial-nonlinear evolution equations
                 and systems in one-spatial and one-temporal dimensions.
                 These conditions follow from the existence of higher
                 infinitesimal symmetries and conservation law
                 densities. The authors briefly consider the
                 mathematical background of the symmetry approach to the
                 problem of integrability. In the description of the
                 algorithms and their implementation in REDUCE they
                 present in particular the basic algorithm for reversing
                 the operator of the total derivative with respect to
                 the spatial variable. One of the most interesting
                 applications of the present program is the problem of
                 classification when the complete list of integrable
                 equations from a given multiparametric family is
                 needed. In this case the program generates necessary
                 integrability conditions in form of a system of
                 nonlinear algebraic equations in the parameters present
                 in the initial equations. In spite of their often
                 complicated structure, there are systems for which the
                 solution can be found in exact form by applying the
                 technique of Gr{\"o}bner basis. The authors present
                 three examples of evolution equations for which this
                 system can in fact be solved.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C7310 (Mathematics)",
  keywords =     "Integrability; Polynomial nonlinear evolution systems;
                 REDUCE; Symmetry approach; Spatial variable; Nonlinear
                 algebraic equations; Gr{\"o}bner basis; algorithms;
                 languages; verification",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Gerdt:1990:SAS,
  author =       "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov",
  title =        "Solving algebraic systems which arise as necessary
                 integrability conditions for polynomial-nonlinear
                 evolution equations",
  crossref =     "Watanabe:1990:IPI",
  pages =        "299--299",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p299-gerdt/",
  abstract =     "The investigation of the problem of integrability of
                 polynomial-nonlinear evolution equations in particular,
                 verifying the existence of the higher symmetries and
                 conservation laws can often be reduced to the problem
                 of finding the exact solution of a complicated system
                 of nonlinear algebraic equations. It is remarkable that
                 these algebraic equations can be not only obtained
                 completely automatically by computer but also often not
                 only completely solved by computer, in spite of their
                 complicated structure and often infinitely many
                 solutions. The authors demonstrate this fact using the
                 Gr{\"o}bner basis method and obtain all (infinitely
                 many) solutions of the systems of algebraic equations
                 which are equivalent to integrability of three
                 different multiparametric families of NLEEs: the
                 seventh order scalar KdV-like equations, the seventh
                 order MKdV-like equations, and the third order coupled
                 KdV-like systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR",
  classification = "C4170 (Differential equations); C4240 (Programming
                 and algorithm theory); C7310 (Mathematics)",
  keywords =     "Algebraic systems; Integrability; Polynomial-nonlinear
                 evolution equations; Nonlinear algebraic equations;
                 Gr{\"o}bner basis; Algebraic equations; NLEEs;
                 verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE. {\bf K.8} Computing
                 Milieux, PERSONAL COMPUTING, IBM PC.",
  thesaurus =    "Differential equations; Nonlinear equations;
                 Polynomials; Symbol manipulation",
}

@InProceedings{Glueck:1990:AMT,
  author =       "R. Glueck and V. F. Turchin",
  title =        "Application of metasystem transition to function
                 inversion and transformation",
  crossref =     "Watanabe:1990:IPI",
  pages =        "286--287",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p286-glueck/",
  abstract =     "The authors prove by construction an application
                 considered theoretically by Turchin (1972) that
                 self-application of metacomputation will allow the
                 automatic construction of inverse algorithms, in
                 particular the algorithm of binary subtraction from the
                 algorithm of binary addition. Further, they present
                 results concerning the algorithmic construction of an
                 efficient pattern matcher, which leads to the Knuth,
                 Morris and Pratt algorithm. These results were achieved
                 with the first working model of a self-applicable
                 supercompiler system, implementing the concept of
                 metacomputation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Technol. Vienna, Austria",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "Algorithmic construction; algorithms; Function
                 inversion; Inverse algorithms; Metacomputation;
                 Metasystem transition; Pattern matcher; theory;
                 Transformation; verification",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors. {\bf F.2.2} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Pattern matching.",
  thesaurus =    "Algorithm theory; Computation theory; Symbol
                 manipulation",
}

@InProceedings{Grigoriev:1990:CIT,
  author =       "D. Yu. Grigoriev",
  title =        "Complexity of irreducibility testing for a system of
                 linear ordinary differential equations",
  crossref =     "Watanabe:1990:IPI",
  pages =        "225--230",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p225-grigoriev/",
  abstract =     "Let a system of linear ordinary differential equations
                 of the first order $Y'=AY$ be given, where $A$ is $n*n$
                 matrix over a field $F(X)$, assume that the degree
                 $deg_X(A)<d$ and the size of any coefficient occurring
                 in $A$ is at most $M$. The system $Y'=AY$ is called
                 reducible if it is equivalent (over the field $F(X)$)
                 to a system $Y'_1=A_1Y_1$. An algorithm is described
                 for testing irreducibility of the system, with an
                 expression for the time complexity.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., V. A. Steklov Inst., Acad. of Sci.,
                 Leningrad, USSR",
  classification = "C4170 (Differential equations); C4240 (Programming
                 and algorithm theory)",
  keywords =     "algorithms; Irreducibility; Irreducibility testing;
                 Linear ordinary differential equations; Time
                 complexity",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Computational complexity; Differential equations",
}

@InProceedings{Grigoriev:1990:HTS,
  author =       "D. Yu. Grigoriev",
  title =        "How to test in subexponential time whether two points
                 can be connected by a curve in a semialgebraic set",
  crossref =     "Watanabe:1990:IPI",
  pages =        "104--105",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p104-grigoriev/",
  abstract =     "A subexponential-time algorithm is designed which
                 finds the number of connected components of a
                 semialgebraic set given by a quantifier-free formula of
                 the first-order theory of real closed fields. Moreover,
                 the algorithm allows for any two points from the
                 semialgebraic set to test, whether they belong to the
                 same connected component. Decidability of the mentioned
                 problems follows from the quantifier elimination method
                 in the first-order theory of real closed fields.
                 However, complexity bound of this method is
                 nonelementary, in particular, one cannot estimate it by
                 any finite iteration of the exponential function. G.
                 Collins (1975) has proposed a construction of
                 cylindrical algebraic decomposition which allows to
                 solve these problems in exponential time.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. V.A Steklov, Inst. of Acad. of Sci.,
                 Leningrad, USSR",
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory)",
  keywords =     "algorithms; Complexity; Connected components;
                 Cylindrical algebraic decomposition; Decidability; Real
                 closed fields; Semialgebraic set; Subexponential time;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms.",
  thesaurus =    "Computational complexity; Computational geometry;
                 Decidability; Symbol manipulation",
}

@InProceedings{Hong:1990:IPO,
  author =       "Hooh Hong",
  title =        "An improvement of the projection operator in
                 cylindrical algebraic decomposition",
  crossref =     "Watanabe:1990:IPI",
  pages =        "261--264",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p261-hong/",
  abstract =     "The Cylindrical Algebraic Decomposition (CAD) method
                 of Collins (1975) decomposes $r$-dimensional Euclidean
                 space into regions over which a given set of
                 polynomials have constant signs. An important component
                 of the CAD method is the projection operation: given a
                 set A of $r$-variate polynomials, the projection
                 operation produces a set $P$ of $(r-1)$-variate
                 polynomials such that a CAD of $r$-dimensional space
                 for $A$ can be constructed from a CAD of
                 $(r-1)$-dimensional space for $P$. The author presents
                 an improvement to the projection operation. By
                 generalizing a lemma on which the proof of the original
                 projection operation is based, he is able to find
                 another projection operation which produces a smaller
                 number of polynomials.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Ohio State Univ., Columbus, OH,
                 USA",
  classification = "C4190 (Other numerical methods); C4290 (Other
                 computer theory); C7310 (Mathematics)",
  keywords =     "algorithms; CAD; Cylindrical Algebraic Decomposition;
                 Euclidean space; Polynomials; Projection operator",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Computational geometry; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Kalkbrener:1990:SSB,
  author =       "M. Kalkbrener",
  title =        "Solving systems of bivariate algebraic equations by
                 using primitive polynomial remainder sequences",
  crossref =     "Watanabe:1990:IPI",
  pages =        "295--295",
  year =         "1990",
  bibdate =      "Sat Apr 25 12:58:10 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p295-kalkbrener/",
  abstract =     "Let $K$ be a field, $K$ the algebraic closure of $K$
                 and $f=q_m(x)y^m+ \cdots{} +q_o(x)$ a polynomial in
                 $K(x,y)$ with $q_m \ne 0$. The polynomial $q_m$ is
                 called the leading coefficient of $f$, abbreviated
                 $lc(f)$. The degree of $f$ in $y$ is denoted by
                 $\deg(f)$. Let $f_1, f_2,\ldots{}, f_k$ be the
                 primitive polynomial remainder sequence of the
                 primitive polynomials $f_1$ and $f_2$ in $K(x,y)$,
                 abbreviated $pprs(f_1,f_2)$. For every $i$ in
                 $(2,\ldots{},k-1)$ let $c_i$ be the content of the
                 pseudoremainder of $f_{i-}1$ and
                 $f_i,l_i:=lc(f_i)^{deg(fi-1)-deg(fi)+1},M_i:=(p\in{}K(x)-K\bmod{}p)$
                 is irreducible, monic and there exists a $j$ in $N$
                 such that $p^j$ divides $c_2\ldots{}c_i$ but not
                 $l_2\ldots{}l_i$,
                 $(\pi,1,\ldots{},\pi,s_i):=(p\in{}Mi\bmod{}p\in{}M_r
                 {\rm for } r=2,\ldots{},i-1)$ and
                 $e_i:=\pi,1\ldots{}pis_i.e_2,\ldots{},e_k-1$ is called
                 the elimination sequence of $f_1$ and $f_2$,
                 abbreviated $\mbox{elimseq}(f_1, f_2)$. Theorem 1 Let
                 $a=(a_1,a_2)$ be an element of $K^2$. $f_1(a)=f_2(a)=0$
                 iff $f_k(a)=0$ or there exists an $i$ in
                 $(2,\ldots{},k-1)$ with $(f_i/f_k)(a)=e_i(a)=0$. The
                 correctness of bsolve is based on this result. By using
                 this algorithm arbitrary systems of bivariate algebraic
                 equations can be solved.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "Algebraic closure; Algorithm correctness; algorithms;
                 Bivariate algebraic equations; Bsolve; Primitive
                 polynomial remainder sequences",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Algebra; Program verification; Symbol manipulation",
}

@InProceedings{Kaltofen:1990:MRS,
  author =       "E. Kaltofen and {Lakshman Y. N.} and J.-M. Wiley",
  title =        "Modular rational sparse multivariate polynomial
                 interpolation",
  crossref =     "Watanabe:1990:IPI",
  pages =        "135--139",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p135-kaltofen/",
  abstract =     "The problem of interpolating multivariate polynomials
                 whose coefficient domain is the rational numbers is
                 considered. The effect of intermediate number growth on
                 a speeded Ben-Or and Tiwari algorithm (1988) is
                 studied. Then the newly developed modular algorithm is
                 presented. The computing times for the speeded Ben-Or
                 and Tiwari and the modular algorithm are compared, and
                 it is shown that the modular algorithm is markedly
                 superior.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Computing times; Modular algorithm;
                 Multivariate polynomials; Polynomial interpolation;
                 Rational numbers; Rational sparse polynomials; Symbolic
                 expressions; Time complexity",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Computational complexity; Interpolation; Polynomials",
}

@InProceedings{Kapur:1990:RPG,
  author =       "D. Kapur and H. K. Wan",
  title =        "Refutational proofs of geometry theorems via
                 characteristic set computation",
  crossref =     "Watanabe:1990:IPI",
  pages =        "277--284",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p277-kapur/",
  abstract =     "A refutational approach to geometry theorem proving
                 using Ritt--Wu's algorithm for computing a
                 characteristic set is discussed. A geometry problem is
                 specified as a quantifier-free formula consisting of a
                 finite set of hypotheses implying a conclusion, where
                 each hypothesis is either a geometry relation or a
                 subsidiary condition ruling out degenerate cases, and
                 the conclusion is another geometry relation. The
                 conclusion is negated, and each of the hypotheses
                 (including the subsidiary conditions) and the negated
                 conclusion is converted to a polynomial equation.
                 Characteristic set computation is used for checking the
                 inconsistency of a finite set of polynomial equations
                 over an algebraic closed field. The method is
                 contrasted with a related refutational method that used
                 Buchberger's Gr{\"o}bner basis algorithm for the
                 inconsistency check.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., State Univ. of New York,
                 Albany, NY, USA",
  classification = "C1110 (Algebra); C4210 (Formal logic); C7310
                 (Mathematics)",
  keywords =     "Algebraic closed field; algorithms; Characteristic set
                 computation; Geometry theorem proving; Polynomial
                 equations; Refutational approach; Ritt--Wu's algorithm;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf I.1.4} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Applications.",
  thesaurus =    "Computational geometry; Polynomials; Theorem proving",
}

@InProceedings{Kohno:1990:RPT,
  author =       "M. Kohno",
  title =        "Reduction problems in the theory of differential
                 equations",
  crossref =     "Watanabe:1990:IPI",
  pages =        "244--249",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p244-kohno/",
  abstract =     "In studying the theory of differential equations, it
                 seems to be better to treat systems of differential
                 equations rather than single differential equations,
                 since the latter are included in a class of the former
                 and the theory can be made clear through full use of
                 matrix calculus. Even some specialists of numerical
                 analysis of differential equations recommend to deal
                 with systems rather than single equations in practical
                 calculation of approximate solutions. The objective of
                 this report is to show an attempt to solve the
                 reduction problems, illustrating some algorithms to be
                 applied by algebraic manipulation system.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Kumamoto Univ., Japan",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C7310 (Mathematics)",
  keywords =     "Algebraic manipulation system; algorithms;
                 Differential equations; Matrix calculus; Reduction
                 problems; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices.",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Kolyada:1990:SSC,
  author =       "S. V. Kolyada",
  title =        "Systems for symbolic computations in {Boolean}
                 algebra",
  crossref =     "Watanabe:1990:IPI",
  pages =        "291--291",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p291-kolyada/",
  abstract =     "Boolean algebra as scientific discipline has a few
                 features. It is a pure mathematical theory and, on the
                 other hand, an applied mathematical theory too. Boolean
                 algebra is applied, for instance, to improve
                 intelligence of software, to automate integrated
                 circuit design and theorem proving as it can be used to
                 model situation analysis and decision making. Computer
                 algebra system for boolean algebra (APAL-PC) allows one
                 to write and process logical formulae in usual manner.
                 The system APAL-PC is developed for IBM PC personal
                 computers on the basis of the programming language C
                 and universal formula processing tools implemented at
                 Glushkov Institute of Cybernetics. The experience of
                 development of a similar system APAL-ES (implemented in
                 OS/360 environment) is taken into consideration in
                 designing of the APAL-PC.",
  acknowledgement = ack-nhfb,
  affiliation =  "Glushkov Inst. of Cybernetics, Kiev, USSR",
  classification = "C4210 (Formal logic); C7310 (Mathematics)",
  keywords =     "APAL-PC; Boolean algebra; design; IBM PC; languages;
                 Symbolic computations",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic.",
  thesaurus =    "Boolean algebra; IBM computers; Symbol manipulation",
}

@InProceedings{Kuhn:1990:TLC,
  author =       "N. Kuhn and K. Madlener and F. Otto",
  title =        "A test for $\lambda$-confluence for certain prefix
                 rewriting systems with applications to the generalized
                 word problem",
  crossref =     "Watanabe:1990:IPI",
  pages =        "8--15",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p8-kuhn/",
  abstract =     "Applies rewriting techniques to the generalized word
                 problem for groups. Let $R$ be a finite
                 string-rewriting system on an alphabet $\Sigma$ such
                 that the monoid $M_R$ presented by $(\Sigma:R)$ is a
                 group, and let $U$ contained in $\Sigma ^+$ be a finite
                 set. The generalized word problem GWP is defined by
                 $GWP(w,U)$ iff $w \in (U)$, where $(U)$ is the subgroup
                 of $M_R$ generated by $U$. With $U$ we associate a
                 prefix rewriting relation $\mbox{implies}_P$ on
                 $\Sigma*$ such that $w$ implies/implied by $-{}_P$
                 $\lambda$ iff $GWP(w,U)$ holds. If $\mbox{implies} _P$
                 is $\lambda$-confluent then $w\mbox{implies}_P\lambda$
                 iff $w \in (U)$. Then $\mbox{implies} _P$ yields a
                 decision procedure for GWP. For groups given through
                 confluent string-rewriting systems $R$ the authors
                 develop a necessary and sufficient condition for
                 $\mbox{implies}_P$ being $\lambda$-confluent and show
                 that this condition becomes decidable in case of $R$
                 being length-reducing, in addition.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Inf., Kaiserslautern Univ., Germany",
  classification = "C4210 (Formal logic)",
  keywords =     "$\Lambda$-confluence; algorithms; Decidable;
                 Generalized word problem; languages; Length-reducing;
                 Prefix rewriting systems; Rewriting; String-rewriting
                 system; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Grammars and Other Rewriting Systems. {\bf F.2.2}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems.",
  thesaurus =    "Decidability; Rewriting systems",
}

@InProceedings{Letichevsky:1990:APA,
  author =       "A. A. Letichevsky and J. V. Kapitonova",
  title =        "Algebraic programming in the {APS} system",
  crossref =     "Watanabe:1990:IPI",
  pages =        "68--75",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p68-letichevsky/",
  abstract =     "System APS (algebraic programming system) which was
                 developed in the Glushkov Institute of Cybernetics of
                 the Ukrainian Acadamy of Sciences is an instrumental
                 tool for designing applied systems by means of
                 algebraic programming. Systems of rewriting rules may
                 be interpreted in APS by means of different
                 computational strategies. This approach allows the use
                 of not only canonical (confluent and noetherian) but
                 any other systems of equalities, and algebraic programs
                 may be designed by combining rewriting rules with
                 different strategies of their applications. Another
                 peculiarity of APS is the possibility to combine
                 procedural and algebraic methods of programming.",
  acknowledgement = ack-nhfb,
  affiliation =  "Glushkov Inst. of Cybernetics, Acad. of Sci., Kiev,
                 Ukrainian SSR, USSR",
  classification = "C6115 (Programming support)",
  keywords =     "Algebraic programming; algorithms; APS system;
                 Computational strategies; languages; Rewriting rules",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Grammars and Other Rewriting Systems. {\bf F.3.2}
                 Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
                 Semantics of Programming Languages, Algebraic
                 approaches to semantics.",
  thesaurus =    "Programming environments; Symbol manipulation",
}

@InProceedings{Liska:1990:FRP,
  author =       "R. Liska and L. Drska",
  title =        "{FIDE}: a {REDUCE} package for automation of {FInite}
                 difference method for solving {pDE}",
  crossref =     "Watanabe:1990:IPI",
  pages =        "169--176",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p169-liska/",
  abstract =     "Discusses the automation of the process of numerical
                 solving of partial differential equations systems
                 (PDES) by means of computer algebra. For solving PDES
                 the finite difference method is applied. The computer
                 algebra system REDUCE and the numerical programming
                 language FORTRAN are used in the methodology presented,
                 its main aim being to speed up the process of preparing
                 numerical programs for solving PDES. Quite often,
                 especially for complicated systems, this process is a
                 tedious and time consuming task. In the process several
                 stages can be found in which computer algebra can be
                 used for performing routine analytical calculations,
                 namely: transformation of differential equations into
                 different coordinate systems, discretization of
                 differential equations, analysis of difference schemes,
                 and generation of numerical programs. The FIDE package
                 is applied to two physical problems. The first one is
                 the nonlinear Schr{\"o}dinger equation. The second one
                 is the Fokker--Planck equation. The numerical programs
                 have been tested and compared with similar published
                 calculations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fac. of Nucl. Sci. and Phys. Eng., Tech. Univ. of
                 Prague, Czechoslovakia",
  classification = "C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "algorithms; Computer algebra; Coordinate systems;
                 Discretization; FIDE; FInite difference method;
                 Fokker--Planck equation; FORTRAN;
                 Integro-interpolation; languages; Nonlinear
                 Schr{\"o}dinger equation; Numerical solving; Partial
                 differential equations; PDE; REDUCE package",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Finite
                 difference methods. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
                 Language Classifications, FORTRAN.",
  thesaurus =    "Difference equations; Partial differential equations;
                 Software packages; Symbol manipulation",
  xxauthor =     "R. Liska and L. Drsda",
}

@InProceedings{Liu:1990:AFA,
  author =       "Zhuo-jun Liu",
  title =        "An algorithm for finding all isolated zeros of
                 polynomial systems",
  crossref =     "Watanabe:1990:IPI",
  pages =        "300--300",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p300-liu/",
  abstract =     "Solving algebraic equations is desired for many
                 problems appearing in applied science. Sometimes,
                 finding all isolated solutions is enough. Suppose a set
                 of polynomials (abbr. polset), denoted by PS, to be
                 given. As a usual convention, by Zero(PS) and
                 ISZero(PS), we respectively denote the zeros and
                 isolated zeros defined by PS. Recently, the homotopy
                 continuation method was widely used to find all
                 isolated zeros of polset. However, that method is not
                 good enough to find the isolated zeros of any polset.
                 Here, based on Wu's method, the author introduces a new
                 algorithm to solve this problem.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Algorithm; algorithms; Isolated zeros; Polset;
                 Polynomial systems; Polynomials; Wu's method",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Poles and zeros; Polynomials; Symbol manipulation",
}

@InProceedings{Llovet:1990:MAC,
  author =       "J. Llovet and J. R. Sendra",
  title =        "A modular approach to the computation of the number of
                 real roots",
  crossref =     "Watanabe:1990:IPI",
  pages =        "298--298",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p298-llovet/",
  abstract =     "The problem of computing the number of distinct real
                 roots of a real polynomial can be solved analyzing the
                 sign variations of the sequence of principal minors of
                 the Hankel matrix associated with the given polynomial.
                 In this paper, the authors present a modular algorithm
                 to achieve this goal. In this approach, the principal
                 minors sequence of the associated Hankel matrix is
                 computed using modular methods. The computing time
                 analysis shows that the maximum computing time function
                 of the modular algorithm is $O(n^5l^2)$, where $n$ is
                 the degree of the polynomial and $l$ its length.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Alcala Univ., Madrid, Spain",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  keywords =     "algorithms; Associated Hankel matrix; Computing time;
                 Distinct real roots; Hankel matrix; Modular algorithm;
                 Principal minors; Real polynomial",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Computational complexity; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Manocha:1990:RCP,
  author =       "D. Manocha",
  title =        "Regular curves and proper parametrizations",
  crossref =     "Watanabe:1990:IPI",
  pages =        "271--276",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p271-manocha/",
  abstract =     "Presents an algorithm for determining whether a given
                 rational parametric curve, defined as vector valued
                 function over a finite domain, has a regular
                 parametrization. A curve has a regular parametrization
                 if it has no cusps in its defining interval. It has
                 been known that the vanishing of the derivative vector
                 is a necessary condition for the existence of cusps.
                 The author shows that if a curve is properly
                 parametrized, then the vanishing of the derivative
                 vector is a necessary and sufficient condition for the
                 existence of cusps. If a curve has no cusps in its
                 defining interval, its proper parametrization is a
                 regular parametrization. He presents a simple algorithm
                 to compute the proper parametrization of a polynomial
                 parametric curve which is used to analyze for cusps and
                 later on reduce the problem of detecting cusps in a
                 rational curve to that of a polynomial curve.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Sci. Div., California Univ., Berkeley, CA,
                 USA",
  classification = "C1160 (Combinatorial mathematics); C7310
                 (Mathematics)",
  keywords =     "algorithms; Cusps; Polynomial curve; Polynomial
                 parametric curve; Proper parametrization; Rational
                 parametric curve; Vector valued function",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.3.5} Computing
                 Methodologies, COMPUTER GRAPHICS, Computational
                 Geometry and Object Modeling, Geometric algorithms,
                 languages, and systems.",
  thesaurus =    "Computational geometry; Symbol manipulation",
}

@InProceedings{Mazurik:1990:SCS,
  author =       "S. I. Mazurik and E. V. Vorozhtsov",
  title =        "Symbolic-numerical computations in the stability
                 analyses of difference schemes",
  crossref =     "Watanabe:1990:IPI",
  pages =        "177--184",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p177-mazurik/",
  abstract =     "The authors propose a number of symbolic-numeric
                 approaches to the computer-aided construction of the
                 stability domains of difference schemes approximating
                 the partial differential equations with constant
                 coefficients. They use the Fourier method, the
                 algebraic methods of the Routh--Hurwitz and Schur--Cohn
                 theories for the localization of the polynomial zeros,
                 the methods of optimization theory as well as the means
                 of computer algebra, digital image processing and
                 computer graphics. The efficiency of the approaches is
                 demonstrated at the practical examples of difference
                 schemes for fluid dynamics problems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
                 Novosibirsk, USSR",
  classification = "C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "Algebraic methods; algorithms; Computer algebra;
                 Computer graphics; Difference schemes; Digital image
                 processing; Fluid dynamics problems; Fourier method;
                 Optimization theory; Partial differential equations;
                 Polynomial zeros; Routh--Hurwitz; Schur--Cohn theories;
                 Stability analyses; Symbolic-numeric approaches;
                 theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.8}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Finite difference methods. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Convergence of numerical methods; Difference
                 equations; Mathematics computing; Partial differential
                 equations; Symbol manipulation",
}

@InProceedings{Mishra:1990:ARA,
  author =       "B. Mishra and P. Pedersen",
  title =        "Arithmetic with real algebraic numbers is in {NC}",
  crossref =     "Watanabe:1990:IPI",
  pages =        "120--126",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p120-mishra/",
  abstract =     "The authors describe NC algorithms for doing exact
                 arithmetic with real algebraic numbers in the
                 sign-coded representation introduced by Coste and Roy
                 (1988). They present polynomial sized circuits of depth
                 $O(\log^3N)$ for the monadic operations
                 $-\alpha,1/\alpha$, as well as $\alpha +r$,
                 $\alpha\cdot{}r$, and $\mbox{sgn} (\alpha -r)$, where
                 $r$ is rational and $\alpha$ is real algebraic. They
                 also present polynomial sized circuits of depth
                 $O(\log^7N)$ for the dyadic operations $\alpha+\beta$,
                 $\alpha\cdot\beta$, and $\mbox{sgn}(\alpha-\beta)$,
                 where $\alpha$ and $\beta$ are both real algebraic. The
                 algorithms employ a strengthened form of the NC
                 polynomial-consistency algorithm of Ben-Or, Kozen, and
                 Reif (1986).",
  acknowledgement = ack-nhfb,
  affiliation =  "New York Univ., NY, USA",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; Dyadic operations; Exact arithmetic; Fast
                 parallel algorithms; Monadic operations; NC algorithms;
                 NC polynomial-consistency algorithm; Polynomial sized
                 circuits; Real algebraic numbers; Sign-coded
                 representation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Parallel algorithms; Polynomials",
}

@InProceedings{Murray:1990:RIT,
  author =       "N. V. Murray and E. Rosenthal",
  title =        "Reexamining intractability of tableau methods",
  crossref =     "Watanabe:1990:IPI",
  pages =        "52--59",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p52-murray/",
  abstract =     "Considers the class of formulas on which the method of
                 analytic tableaux was first shown to be intractable,
                 and shows that the applications of the ordinary
                 distributive law tableau methods admit linear time
                 proofs for this class. The authors introduce a new
                 class of formulas that are intractable for tableaux
                 (even with the distributive law), and demonstrate that
                 path dissolution admits linear proofs of these
                 formulas. Modifications of the tableau method are
                 described that would render this class tractable. Since
                 dissolution is linear on this class, these results
                 demonstrate that dissolution cannot be $p$-simulated by
                 the method of analytic tableau.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., State Univ. of New York,
                 Albany, NY, USA",
  classification = "C4210 (Formal logic)",
  keywords =     "algorithms; Analytic tableaux; Dissolution; Linear
                 proofs; Linear time proofs; Path dissolution; Tableau
                 methods; theory; verification",
  subject =      "{\bf G.2.2} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory, Graph algorithms. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 I.2.3} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Deduction and Theorem Proving,
                 Deduction.",
  thesaurus =    "Formal logic",
}

@InProceedings{Noda:1990:SHI,
  author =       "Matu-Tarow T. Noda and E. Miyahiro",
  title =        "On the symbolic\slash numeric hybrid integration",
  crossref =     "Watanabe:1990:IPI",
  pages =        "304--304",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p304-noda/",
  abstract =     "Integrating a given function is one of the most
                 important areas in the mathematical computing. Both
                 numerical and symbolic integration methods have been
                 developed and widely used. Numerical methods, however,
                 have some defects such as (1) formal integrals are not
                 obtained, (2) wrong answers are given for pathological
                 integrand and (3) error estimates depend on types of
                 integrands. Symbolic methods have also difficulties on
                 (1) restrictions on an integrand and (2) uses of
                 wasteful big-number computation. To avoid difficulties,
                 some attempts in which both methods are combined have
                 been proposed, called hybrid methods. The authors
                 propose new hybrid integration method for a rational
                 function, (say $q/r$, $q$ and $r$ are polynomials) with
                 floating point but real coefficients.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Ehime Univ., Matsuyama, Japan",
  classification = "C4160 (Numerical integration and differentiation)",
  keywords =     "algorithms; Floating point; Hybrid integration;
                 Numerical; Numerical integration; Rational function;
                 Symbolic integration",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Nonalgebraic algorithms. {\bf G.1.4}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation.",
  thesaurus =    "Integration; Numerical methods; Symbol manipulation",
}

@InProceedings{Norman:1990:CBI,
  author =       "A. C. Norman",
  title =        "A critical-pair\slash completion based integration
                 algorithm",
  crossref =     "Watanabe:1990:IPI",
  pages =        "201--205",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p201-norman/",
  abstract =     "The presentation re-expresses the 1976 Risch method in
                 terms of rewrite rules, and thus exposes the major
                 problem it suffers from as a manifestation of the fact
                 that in certain circumstances the set of rewrites
                 generated is not confluent. This difficulty is then
                 attacked using a critical-pair/completion (CPC)
                 approach. For very many integrands it is then easy to
                 see that the initial set of rewrites used in the early
                 implementations do not need any extension, and this
                 fact explains the high level of competence of the
                 programs involved despite their shaky theoretical
                 foundations. For a further large collection of problems
                 even a simple CPC scheme converges rapidly; when the
                 techniques are applied to the REDUCE integration test
                 suite in all applicable cases a short computation
                 succeeds in completing the set of rewrites and hence
                 gives a secure basis for testing for integrability.
                 This paper describes the implementation of the CPC
                 process and discusses current limitations to and
                 possible future extended applications of it.",
  acknowledgement = ack-nhfb,
  affiliation =  "Trinity Coll., Cambridge, UK",
  classification = "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  keywords =     "algorithms; Convergence; CPC scheme;
                 Critical-pair/completion based integration algorithm;
                 experimentation; Integrability; REDUCE integration test
                 suite; Rewrite rules; Transcendental functions",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, REDUCE. {\bf F.2.2} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Computations on
                 discrete structures.",
  thesaurus =    "Convergence of numerical methods; Integration;
                 Rewriting systems",
}

@InProceedings{Okubo:1990:GTO,
  author =       "K. Okubo",
  title =        "Global theory of ordinary differential equations and
                 formula manipulation",
  crossref =     "Watanabe:1990:IPI",
  pages =        "193--200",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p193-okubo/",
  abstract =     "The author discusses the fundamental domain of the
                 monodromy group for hypergeometric equations. One can
                 classify these triangles formed by circular arcs with
                 the sum of inner angles greater, equal or less than
                 $\pi$. The domains have been classified into three
                 classes, those on the unit sphere, those on the open
                 complex plane and those on the unit disk. Any
                 algebraically integrable solution of a hypergeometric
                 equation is expressed by invariants of the groups of
                 five platonic solids or dipyramids. One can express the
                 key in terms of non-Euclidean expression by the sum of
                 inner angles of triangles. The authors rephrases this
                 into quadratic invariant of definite, degenerate or
                 indefinite sign. The quadratic invariants may be of
                 help as the key to the classification in higher
                 dimensions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Electro-Commun., Chofu, Tokyo, Japan",
  classification = "B0290P (Differential equations); C4170 (Differential
                 equations)",
  keywords =     "Algebraically integrable solution; Circular arcs;
                 Dipyramids; Five platonic solids; Formula manipulation;
                 Gauss equation; Hypergeometric equations; Inner angles;
                 Monodromy group; Open complex plane; Ordinary
                 differential equations; Quadratic invariant; Unit disk;
                 Unit sphere",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Padget:1990:UPS,
  author =       "J. Padget and A. Barnes",
  title =        "Univariate power series expansions in {Reduce}",
  crossref =     "Watanabe:1990:IPI",
  pages =        "82--87",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p82-padget/",
  abstract =     "Describes the development of a formal power series
                 expansion package for Reduce which takes advantage of
                 Reduce's domain mechanism to make for a seamless
                 integration of series values with the rest of the
                 Reduce system. Consequently, series values may be
                 manipulated with the same algebraic operators as other
                 algebraic objects. To create the illusion of infinite
                 power series a simulated lazy-evaluation mechanism has
                 been used. The paper reports experience of using the
                 Reduce domain mechanism and documents the algorithms
                 and data structures that can be used to implement and
                 to represent power series.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C7310 (Mathematics)",
  keywords =     "Algebraic operators; Algorithms; algorithms; Data
                 structures; Domain mechanism; languages;
                 Lazy-evaluation mechanism; Power series expansions;
                 Reduce; Series values",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA.",
  thesaurus =    "Series [mathematics]; Symbol manipulation",
}

@InProceedings{Scott:1990:SAM,
  author =       "T. C. Scott and G. J. Fee",
  title =        "Some applications of {Maple} symbolic computation to
                 scientific and engineering problems",
  crossref =     "Watanabe:1990:IPI",
  pages =        "302--303",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p302-scott/",
  abstract =     "Presents a survey of use of the Maple symbolic
                 computation system at the University of Waterloo. This
                 represents only a sample of what has and can be done
                 with symbolic computation. However, these examples have
                 been chosen from a broad spectrum of areas which
                 includes: Quantum theory, general and special
                 relativity, audio engineering and asbestos fiber
                 analysis (an application of fluid and
                 magneto-dynamics). They represent new avenues of
                 research and illustrate the large untapped potential of
                 symbolic computation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Maple Symbolic Comput. Group, Waterloo Univ., Ont.,
                 Canada",
  classification = "C7300 (Natural sciences); C7400 (Engineering)",
  keywords =     "Asbestos fiber analysis; Audio engineering; design;
                 General relativity; Maple; Quantum theory; Special
                 relativity; Symbolic computation; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple.",
  thesaurus =    "Engineering computing; Natural sciences computing;
                 Symbol manipulation",
}

@InProceedings{Shirayanagi:1990:IPF,
  author =       "K. Shirayanagi",
  title =        "On the isomorphism problem for finite-dimensional
                 binomial algebras",
  crossref =     "Watanabe:1990:IPI",
  pages =        "106--111",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p106-shirayanagi/",
  abstract =     "Binomial algebras are finitely presented algebras
                 defined by monomials or binomials. Given two binomial
                 algebras, one important problem is to decide whether or
                 not they are isomorphic as algebras. The author studies
                 an algorithm for solving this problem, when both
                 algebras are finite-dimensional over a field. In
                 particular, when they are monomial algebras (i.e
                 binomial algebras defined by monomials only), the
                 problem has already been completely solved by the
                 presentation uniqueness. The author provides some
                 necessary conditions in terms of partially ordered sets
                 for two certain binomial algebras to be isomorphic. In
                 other words, invariants of the binomial algebras are
                 presented. These conditions together serve as an
                 effective procedure for solving the isomorphism
                 problem.",
  acknowledgement = ack-nhfb,
  affiliation =  "NTT Software Lab., Tokyo, Japan",
  classification = "C1160 (Combinatorial mathematics); C7310
                 (Mathematics)",
  keywords =     "algorithms; Binomial algebras; Binomials; Finitely
                 presented algebras; Monomials; Partially ordered sets;
                 Presentation uniqueness; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms.",
  thesaurus =    "Algebra; Set theory; Symbol manipulation",
}

@InProceedings{Smedley:1990:DAD,
  author =       "T. J. Smedley",
  title =        "Detecting algebraic dependencies between unnested
                 radicals (abstract)",
  crossref =     "Watanabe:1990:IPI",
  pages =        "292--293",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p292-smedley/",
  abstract =     "There are a number of known methods for checking for
                 dependencies between unnested radicals. However, these
                 methods usually have one or both of the following
                 disadvantages: 1. They rely on integer factorisation,
                 or 2. They generate an algebraic extension field of
                 degree higher than is necessary to express the input.
                 The first disadvantage is not generally too important,
                 as the integers involved are usually quite small and
                 can be easily factored. However, the second
                 disadvantage can cause real problems. Since the degree
                 of the algebraic extension has a large influence on the
                 cost of algorithms involving algebraic numbers, the
                 author wants a method which detects dependencies but
                 keeps the degree of the extension field as low as
                 possible.",
  acknowledgement = ack-nhfb,
  affiliation =  "Delaware Univ., Newark, DE, USA",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "Algebraic dependencies; Algebraic extension; Algebraic
                 numbers; Unnested radicals; verification",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Representations (general and
                 polynomial). {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Simplification of expressions.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
  thesaurus =    "Computational complexity; Symbol manipulation",
}

@InProceedings{Stachniak:1990:RPS,
  author =       "Z. Stachniak",
  title =        "Resolution proof systems with weak transformation
                 rules",
  crossref =     "Watanabe:1990:IPI",
  pages =        "38--43",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p38-stachniak/",
  abstract =     "In previous papers the author defined and explored a
                 formal methodological framework on the basis of which
                 resolution proof systems for strongly-finite logics can
                 be introduced and studied. In the present paper he
                 extends this approach to a wider class of so-called
                 resolution logics.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., York Univ., North York, Ont.,
                 Canada",
  classification = "C4210 (Formal logic)",
  keywords =     "algorithms; Formal methodological framework;
                 Resolution logics; Resolution proof systems;
                 Strongly-finite logics; theory; verification; Weak
                 transformation rules",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Computational
                 logic. {\bf I.2.3} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Deduction and Theorem Proving, Deduction.
                 {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic.",
  thesaurus =    "Formal logic",
}

@InProceedings{Takayama:1990:ACI,
  author =       "N. Takayama",
  title =        "An algorithm of constructing the integral of a module
                 --- an infinite dimensional analog of {Gr{\"o}bner}
                 basis",
  crossref =     "Watanabe:1990:IPI",
  pages =        "206--211",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p206-takayama/",
  abstract =     "Let $U$ be a left ideal of Weyl algebra:
                 $A_n=K(x_1,\ldots{},x_n,\delta_1,\ldots{},\delta_n)$.
                 Put $M=A_n/U$. M is a left $A_n$ module. The paper
                 presents an explicit construction of the left $A_{n-1}$
                 module by introducing an analog of Gr{\"o}bner basis of
                 a submodule of a kind of infinite dimensional free
                 module. The author gives a complete algorithm. The
                 algorithm is an answer to the research problem of the
                 paper (AZ).",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Kobe Univ., Japan",
  classification = "B0290R (Integral equations); C4180 (Integral
                 equations)",
  keywords =     "algorithms; Integral; Gr{\"o}bner basis; Left ideal;
                 Weyl algebra",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Integral equations; Symbol manipulation",
}

@InProceedings{Takayama:1990:GBI,
  author =       "N. Takayama",
  title =        "{Gr{\"o}bner} basis, integration and transcendental
                 functions",
  crossref =     "Watanabe:1990:IPI",
  pages =        "152--156",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p152-takayama/",
  abstract =     "It is well known that Gr{\"o}bner basis is a
                 fundamental and powerful tool to solve problems of
                 polynomials. One can use the Gr{\"o}bner basis of Weyl
                 algebra to solve the problems of integration and
                 formula verification of transcendental functions. The
                 paper surveys the theory of the Gr{\"o}bner basis of
                 the ring of differential operators and its applications
                 to the following problems: computation of differential
                 equations for a definite integral with parameters; zero
                 recognition of an expression that contains special
                 functions or binomial coefficients etc., i.e. formula
                 verification by a computer; derivations of some of
                 special function identities; solving a definite
                 integral or obtaining an asymptotic expansion of a
                 definite integral with parameters.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Kobe Univ., Japan",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  keywords =     "Transcendental functions; Gr{\"o}bner basis;
                 Polynomials; Weyl algebra; Integration; Formula
                 verification; Differential operators; Differential
                 equations; Definite integral; Zero recognition;
                 Binomial coefficients; Special function identities;
                 Asymptotic expansion; algorithms; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Differential equations; Function approximation;
                 Integration; Polynomials; Symbol manipulation",
}

@InProceedings{Tan:1990:OTS,
  author =       "H. Q. Tan and X. Dong",
  title =        "Optimization techniques for symbolic equation solver
                 in engineering applications",
  crossref =     "Watanabe:1990:IPI",
  pages =        "305--305",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p305-tan/",
  abstract =     "In MACSYMA, there are procedures for solving systems
                 of equations, such as solve and linsolve. Because the
                 systems of equations we are dealing with are mostly
                 sparse, the application of Gaussian elimination which
                 is used in linsolve produces results that are usually
                 lengthy and inefficient. The authors have implemented a
                 new derivation procedure to solve the problem of
                 expression growth and increase the computational
                 efficiency. The underlying concept is the
                 identification of the smallest full subsystems
                 contained within the original and then subsequent
                 remaining systems, labeling common terms by
                 intermediate variables. Gaussian elimination is
                 employed to solve these subsystems independently and
                 sequentially instead of the complete system.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. Sci., Akron Univ., OH, USA",
  classification = "C7310 (Mathematics)",
  keywords =     "algorithms; Derivation procedure; Gaussian
                 elimination; Symbolic equation solver",
  subject =      "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
  thesaurus =    "Algebra; Symbol manipulation",
}

@InProceedings{Tao:1990:SAM,
  author =       "Qingsheng Tao",
  title =        "Symbolic and algebraic manipulation for formulae of
                 interpolation and quadrature",
  crossref =     "Watanabe:1990:IPI",
  pages =        "306--306",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p306-tao/",
  abstract =     "Computer algebra has been used for construction and
                 analysis of algorithms of numerical computation. In the
                 paper, an attempt has been made to derive the formulae
                 of interpolation and quadrature with Computer Algebra.
                 In REDUCE language, the formula manipulation system for
                 interpolation INTEP and for quadrature QUADRAT are
                 developed. The two formula manipulators can be used to
                 derive Lagrange, Hermite and Birkhoff interpolation
                 formulae with any degree of polynomials and to derive
                 Newton--Cotes quadrature formulae and the quadrature
                 formulae involving the derivatives of the integrand.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Mech., Zhejiang Univ., Hangzhou, China",
  classification = "C4130 (Interpolation and function approximation);
                 C4160 (Numerical integration and differentiation)",
  keywords =     "Algebraic manipulation; algorithms; Birkhoff; Computer
                 Algebra; Formula manipulators; Hermite; INTEP;
                 Interpolation; Interpolation formulae; Lagrange;
                 languages; Newton--Cotes quadrature formulae; QUADRAT;
                 Quadrature; Symbolic manipulation",
  subject =      "{\bf G.1.4} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms.",
  thesaurus =    "Integration; Interpolation; Symbol manipulation",
}

@InProceedings{Ulmer:1990:LSH,
  author =       "F. Ulmer and J. Calmet",
  title =        "On {Liouvillian} solutions of homogeneous linear
                 differential equations",
  crossref =     "Watanabe:1990:IPI",
  pages =        "236--243",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p236-ulmer/",
  abstract =     "Deals with the problem of finding Liouvillian
                 solutions of an $n$-th order homogeneous linear
                 differential equation $L(y)=0$ with coefficients in a
                 differential field $k$ whose field of constants is $C$.
                 For second order linear differential equations such an
                 algorithm has been given by J. Kovacic (1986) and
                 implemented. A general decision procedure for finding
                 Liouvillian solutions of $n$-th order equations has
                 been given by M. F. Singer (1981), but the resulting
                 algorithm, although constructive, is not in
                 implementable form even for second order equations. The
                 algorithm uses the fact that, if $L(y)=0$ has a
                 Liouvillian solution, then, $L(y)=0$ has a solution $z$
                 such that $u=z'/z$ is algebraic over $k$, which means
                 that $L(y)$ has a solution $z$ of the form
                 $e^{\int{}u}$, where $u$ is algebraic over $k$. Since
                 the logarithmic derivative $u=z'/z$ of a solution $z$
                 is a solution of the Riccati equation $R(y)=0$
                 associated to $L(y)=0$, the problem thus reduces to
                 find an algebraic solution $u$ of $R(y)=0$. This task
                 is now split into two parts: (i) to find the set DEG(n)
                 of possible degrees $N$ for the minimal polynomial
                 $P(x)=0$ of $u$ over $k$, (ii) to compute, for each
                 possible degree of $P(x)$, the possible coefficients of
                 $P(x)$. If we donate $c(ii)$ the complexity of the
                 second step and Hash DEG($n$) the size of the set
                 DEG($n$), one sees that the complexity of the whole
                 procedure is of the form $c(ii)^{Hash DEG(n)}$ and thus
                 exponential in Hash DEG($n$). This shows that the only
                 way to make the procedure effective is to get sharp
                 bounds on the size of the set DEG($n$), which is the
                 scope of this paper.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
                 Univ., Germany",
  classification = "C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "Algebraic solution; algorithms; Complexity;
                 Homogeneous; Linear differential equations; Liouvillian
                 solutions; Sharp bounds",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Nonalgebraic algorithms. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Computational complexity; Differential equations;
                 Symbol manipulation",
}

@InProceedings{vonzurGathen:1990:PFF,
  author =       "J. {von zur Gathen}",
  title =        "Polynomials over finite fields with large images",
  crossref =     "Watanabe:1990:IPI",
  pages =        "140--144",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p140-von_zur_gathen/",
  abstract =     "A polynomial $f$ in $F_q(x)$, over a finite field
                 $F_q$ with $q$ elements, is $\rho$-large if its image
                 in $F_q$ contains at least $q-\rho$ elements. The
                 article presents an efficient probabilistic test for
                 this property, using expected time polynomial in
                 $\deg{}f$, $\log{}q$, and $\rho$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Toronto Univ., Ont., Canada",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Expected time polynomial; Finite fields;
                 Large images; Polynomial; Probabilistic test; Time
                 complexity",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.1.2} Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Probabilistic
                 computation.",
  thesaurus =    "Computational complexity; Polynomials",
}

@InProceedings{Wang:1990:PUP,
  author =       "P. S. Wang",
  title =        "Parallel univariate polynomial factorization on
                 shared-memory multiprocessors",
  crossref =     "Watanabe:1990:IPI",
  pages =        "145--151",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p145-wang/",
  abstract =     "Using parallelism afforded by shared-memory
                 multiprocessors to speed up systems for polynomial
                 factorization is discussed. The approach is to take the
                 fastest known factoring algorithm for practical
                 purposes and parallelize key parts of it. The
                 univariate factoring algorithm consists of two major
                 tasks (a) factoring modulo small integer primes and (b)
                 EEZ lifting and recovery of true factors. A C coded
                 system PFACTOR that implements (a) in parallel is
                 described in detail. PFACTOR is a stand-alone parallel
                 factorizer that can take input from a file, a pipe or a
                 socket connection over a network. It can also be used
                 interactively as a UNIX command. PFACTOR consists of
                 parallel selection of primes, automatic balancing of
                 work, parallel Berlekamp algorithm, and parallel
                 reconciliation of degrees of factors modulo different
                 primes. Actual timings on the Encore Multimax show the
                 effectiveness of the approach.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
                 USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; C coded system; EEZ lifting; Encore
                 Multimax; Modulo small integer primes; Parallel
                 Berlekamp algorithm; Parallel reconciliation;
                 Parallelism; performance; PFACTOR; Polynomial
                 factorization; Shared-memory multiprocessors; Time
                 complexity; Univariate factoring algorithm; UNIX
                 command",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Modes of Computation, Parallelism and
                 concurrency.",
  thesaurus =    "Computational complexity; Parallel algorithms;
                 Polynomials",
}

@InProceedings{Yamasaki:1990:DLP,
  author =       "S. Yamasaki",
  title =        "Dataflow for logic program as substitution
                 manipulator",
  crossref =     "Watanabe:1990:IPI",
  pages =        "44--51",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p44-yamasaki/",
  abstract =     "Shows a method of constructing a dataflow, which
                 denotes the deductions of a logic program, by means of
                 a sequence domain based on equivalence classes of
                 substitutions. The dataflow involves fair merge
                 functions to represent unions of atom subsets over a
                 sequence domain, as well as functions as manipulations
                 of unifiers for the deductions of clauses. A continuous
                 functional is associated with the dataflow on condition
                 that the dataflow completely and soundly denotes the
                 atom generation in terms of equivalent substitutions
                 sets. Its least fixpoint is interpreted as denoting the
                 whole atom generation based on manipulations of
                 equivalent substitutions sets.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Technol., Okayama Univ., Japan",
  classification = "C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Continuous functional; Dataflow;
                 Equivalence classes; Fair merge functions; Logic
                 program; Sequence domain; Substitution manipulator;
                 theory",
  subject =      "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Logic and
                 constraint programming. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic, Computational logic.",
  thesaurus =    "Logic programming; Programming theory",
}

@InProceedings{Yokoyama:1990:DSP,
  author =       "K. Yokoyama and M. Noro and T. Takeshima",
  title =        "On determining the solvability of polynomials",
  crossref =     "Watanabe:1990:IPI",
  pages =        "127--134",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p127-yokoyama/",
  abstract =     "Landau and Miller (1985) presented a method for
                 determining the solvability of a monic irreducible
                 polynomial over integers in polynomial time. In their
                 method, a series of polynomials is constructed so that
                 the original problem is reduced to determining the
                 solvability of new polynomials. The authors present an
                 improved method for finding such a series of
                 polynomials efficiently. More precisely, they introduce
                 a new notion on a series of blocks in the set of all
                 roots of the original polynomial under the action of
                 its Galois group, and then present an efficient method
                 for finding such a series of blocks by modifying Landau
                 and Miller's method for finding minimal imprimitive
                 blocks.",
  acknowledgement = ack-nhfb,
  affiliation =  "IIAS-SIS, Fujitsu Ltd., Numazu, Japan",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Galois group; Minimal imprimitive blocks;
                 Monic irreducible polynomial; Polynomials; Problem
                 complexity; Solvability; Time complexity",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS,
                 Graph Theory, Graph algorithms.",
  thesaurus =    "Computability; Computational complexity; Polynomials",
}

@InProceedings{Yokoyama:1990:FMP,
  author =       "Kazuhiro Yokoyama and Masayuki Noro and Taku
                 Takeshima",
  title =        "On factoring multi-variate polynomials over
                 algebraically closed fields (abstract)",
  crossref =     "Watanabe:1990:IPI",
  pages =        "297--297",
  year =         "1990",
  bibdate =      "Thu Mar 12 08:36:58 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p297-yokoyama/",
  abstract =     "For a problem how to find an extension field over
                 which we can obtain an absolutely irreducible factor,
                 Kaltofen gave an answer in 1983 and explicitly in 1985
                 by employing analytic argument for showing his answer,
                 and Chistov and Grigor'ev also gave the same answer in
                 1983 by algebraic arguments. Here the authors give an
                 alternative proof for Kaltofen's answer in algebraic
                 way, independently to Chistov and Grigor'ev, and by the
                 benefit of new way, they also give several extensions
                 of his answer and properties of absolutely irreducible
                 factors. They also discuss usage of their results for
                 actual computation of absolutely irreducible factors.
                 They restrict themselves to bi-variate polynomials with
                 integer (or rational) coefficients.",
  acknowledgement = ack-nhfb,
  affiliation =  "IIAS-SIS, Fujitsu Ltd., Japan",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Actual computation; Algebraic arguments; Algebraically
                 closed fields; Bi-variate polynomials; Irreducible
                 factor; Multi-variate polynomials; theory;
                 verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Abramov:1991:FAS,
  author =       "S. A. Abramov and K. Yu. Kvashenko",
  title =        "Fast algorithms to search for the rational solutions
                 of linear differential equations with polynomial
                 coefficients",
  crossref =     "Watt:1991:IPI",
  pages =        "267--270",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p267-abramov/",
  abstract =     "The paper is concerned with some ways for an
                 improvement with regard to solving the linear ordinary
                 differential equations of the form
                 $\sum_0^na_i(x)y^{(i)}(x)=b(x)$ where
                 $a_0(x),\ldots{},a_n(x),b(x)$ in $K(x)$ ($K$ is the
                 constant field), $a_n(x) \neq 0$. The authors consider
                 one after another of the problems of finding all the
                 polynomial and rational solutions of equation. They
                 consider the simplest approach and then its
                 improvement.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, USSR",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Linear differential equations; Polynomial
                 coefficients; Rational solutions; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.7} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
  thesaurus =    "Linear differential equations; Symbol manipulation",
}

@InProceedings{Amirkhanov:1991:BOV,
  author =       "I. V. Amirkhanov and E. P. Zhidkov and I. E.
                 Zhidkova",
  title =        "The betatron oscillations in the vicinity of nonlinear
                 resonance in cyclic accelerator investigation",
  crossref =     "Watt:1991:IPI",
  pages =        "452--453",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p452-amirkhanov/",
  abstract =     "Motion of charged particle in given fields in a cyclic
                 accelerator has been investigated. The nonlinear
                 problem of finding stable trajectories in the vicinity
                 of a resonance has been solved. The equations of motion
                 for charged particle deviation from ideal orbit or the
                 betatron oscillations equations (which are lateral to
                 the closed orbit oscillations with the frequencies
                 $\nu_x, \nu_z$) are studied using REDUCE-3.2. The study
                 of the equations formed by computer is applied to two
                 types of accelerators: (1) the averaged equations in
                 the vicinity of 19 resonances for a weakly focusing
                 accelerator (WFA) and (2) those in the vicinity of 24
                 resonances-for a strong focusing accelerator (SFA).",
  acknowledgement = ack-nhfb,
  affiliation =  "JINR, Moscow, USSR",
  classification = "A2920F (Betatrons); B7410 (Accelerators); C7320
                 (Physics and Chemistry)",
  keywords =     "algorithms; Betatron oscillations; Charged particle
                 deviation; Cyclic accelerator; Nonlinear resonance;
                 REDUCE-3.2; Strong focusing accelerator; Weakly
                 focusing accelerator",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf J.2}
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics.",
  thesaurus =    "Betatrons; Physics computing",
}

@InProceedings{Apel:1991:FAA,
  author =       "Joachim Apel and Uwe Klaus",
  title =        "{FELIX}: an assistant for algebraists",
  crossref =     "Watt:1991:IPI",
  pages =        "382--389",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p382-apel/",
  abstract =     "FELIX is a special computer algebra system designed
                 for calculations with elements of algebraic structures
                 as well as with substructures and homomorphisms. It
                 covers both commutative polynomial rings and modules
                 and non-commutative structures. Buchberger's algorithm
                 for the computation of Gr{\"o}bner bases is fundamental
                 for many of the included operations. The articles
                 contains a short description of the system FELIX and
                 illustrates the sensitivity of Buchberger's algorithm
                 against changes of selection strategies.",
  acknowledgement = ack-nhfb,
  affiliation =  "Leipzig Univ., Germany",
  classification = "C7310 (Mathematics)",
  keywords =     "algorithms; design; FELIX; Computer algebra system;
                 Algebraic structures; Substructures; Homomorphisms;
                 Commutative polynomial rings; Modules; Non-commutative
                 structures; Buchberger's algorithm; Gr{\"o}bner bases",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Astrelin:1991:BDI,
  author =       "A. V. Astrelin",
  title =        "A bound of degree of irreducible eigenpolynomial of
                 some differential operator",
  crossref =     "Watt:1991:IPI",
  pages =        "265--266",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p265-astrelin/",
  abstract =     "Consider the following problem: for the differential
                 operator $D=P \delta / \delta x+Q \delta / \delta y$
                 find an integer $K$, such that any irreducible
                 polynomial $f$ dividing $Df$ has degree $\deg{}f<=K$.
                 This problem arises when one wants to find the symbolic
                 solution of a differential equation $dy/dx=R(x,y)$
                 where $R$ is a rational function. A solution when $P$
                 and $Q$ are homogeneous polynomials of equal degrees
                 i.e. $P(x,y)=x^mp(x/y),Q(x,y)=x^mq(x,y)$ for some $m$
                 is proposed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Mech. and Math., Moscow State Univ., USSR",
  classification = "C1110 (Algebra); C1120 (Analysis); C4170
                 (Differential equations)",
  keywords =     "algorithms; Differential equation; Differential
                 operator; Homogeneous polynomials; Irreducible
                 eigenpolynomial; Irreducible polynomial; Rational
                 function; Symbolic solution",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Differential equations; Polynomials",
}

@InProceedings{Babai:1991:NLT,
  author =       "L{\'a}szl{\'o} Babai and Gene Cooperman and Larry
                 Finkelstein and {\'A}kos Seress",
  title =        "Nearly linear time algorithms for permutation groups
                 with a small base",
  crossref =     "Watt:1991:IPI",
  pages =        "200--209",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p200-babai/",
  abstract =     "A base of a permutation group $G$ is a subset $B$ of
                 the permutation domain such that only the identity of
                 $G$ fixes $B$ pointwise. The permutation
                 representations of important classes of groups,
                 including all finite simple groups other than the
                 alternating groups, admit $O(\log{}n)$ size bases,
                 where $n$ is the size of the permutation domain. Groups
                 with very small bases dominate the work on permutation
                 groups in much of computational group theory. A series
                 of new combinatorial results allows us to present Monte
                 Carlo algorithms achieving $O(n \log^cn)$ ($c$ a
                 constant) time and space performance for such groups
                 with respect to the fundamental operations of finding
                 order and testing membership. (The input is a list of
                 generators of the group). Previous methods have
                 achieved similar space performance only at the expense
                 of increased time performance. Adaptations of a
                 `cube-doubling' technique (L. Babai, E. Szemeredi,
                 1984) and a local expansion property of groups (L.
                 Babai, 1991) are the key to theoretically reducing the
                 time complexity to $O(n \log^c n)$. The shared
                 principal novelty of the new ideas is in their ability
                 to build and manipulate certain chains of subsets of a
                 group, which are not themselves subgroups, in order to
                 build the point stabilizer subgroup chain. Further
                 combinatorial ideas are used to lower the constant $c$.
                 Comparative timing estimates, based on asymptotic
                 worst-case analysis, lead us to expect a new
                 implementation to be faster than previous
                 implementations for groups of high degree.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comp. Sci. Chicago Univ., IL, USA",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Alternating groups; Asymptotic worst-case
                 analysis; Computational group theory; Cube-doubling;
                 Finite simple groups; Fundamental operations; Group
                 order determination; Local expansion property;
                 Membership testing; Monte Carlo algorithms; Permutation
                 domain; Permutation group; Point stabilizer subgroup
                 chain; Shared principal novelty; theory; Time
                 complexity",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.3} Mathematics
                 of Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo). {\bf G.2.1}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Combinatorial algorithms.",
  thesaurus =    "Computational complexity; Group theory",
}

@InProceedings{Backelin:1991:HWP,
  author =       "J{\"o}rgen Backelin and Ralf Fr{\"o}berg",
  title =        "How we proved that there are exactly 924 cyclic
                 7-roots",
  crossref =     "Watt:1991:IPI",
  pages =        "103--111",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p103-backelin/",
  abstract =     "The following problem has become some sort of test
                 problem for Gr{\"o}bner bases techniques: find all
                 solutions to $Sn=z_1+z_2+\ldots{}+z_{n-1}+z_n=0$,
                 $z_1z_2+z_2z_3+\ldots{}+z_{n-1}z_n+z_nz_1=0$, \ldots{}
                 $z_1z_2\ldots{}z_{n-1}+z_2z_3\ldots{}z_n+\ldots{}+z_{n-1}z_n\ldots{}z_{n-3}+z_nz_1\ldots{}z_{n-2}=0$,
                 $z_1z_2\ldots{}z_n=1$. The solutions are called cyclic
                 $n$-roots. In order to solve the problem one of the
                 authors constructed a new characteristic 0 Gr{\"o}bner
                 basis programme, Bergman. The authors describe some
                 features of Bergman, in particular its graph component
                 algorithm. They make some theoretical analysis and
                 practical tests of the differences in performance
                 between Bergman and some other Buchberger based
                 algorithms, mainly the Gebauer--Moller algorithm. With
                 the help of Bergman and some commutative algebra they
                 succeeded to prove: there are exactly 924 cyclic
                 7-roots. Each of them has multiplicity 1.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Stockholm Univ., Sweden",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; verification; Exact proof; Cyclic 7-roots;
                 Cyclic $n$-roots; Characteristic 0 Gr{\"o}bner basis
                 programme; Bergman; Graph component algorithm;
                 Gebauer--Moller algorithm; Multiplicity",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Polynomials",
}

@InProceedings{Becker:1991:CRP,
  author =       "Thomas Becker and Volker Weispfenning",
  title =        "The {Chinese} remainder problem, multivariate
                 interpolation, and {Gr{\"o}bner} bases",
  crossref =     "Watt:1991:IPI",
  pages =        "64--69",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p64-becker/",
  abstract =     "Let $K(X)$ be a multivariate polynomial ring over a
                 field $K, I_1, \ldots{}, I_m$ ideals in $K(X)$, $U$
                 contained in $X$. Using a single Gr{\"o}bner basis in
                 an extension ring of $K(X)$, the authors solve the
                 following problems effectively. Given
                 $f_1,\ldots{},f_m$ in $K(X)$, put
                 $A_f=\cap_{k=1}^m(I_k+f_k)$. (1) Decide whether
                 $A_f\cap{}K(U)\ne0$ and if so, construct some element
                 of $A_f\cap{}K(U)$. (2) For given $g$ in $K(U)$, decide
                 whether $g\in{}A_f$. (3) Construct all elements of
                 $A_f\cap{}K(U)$. Taking for $I^k$ a suitable vanishing
                 ideal of some parametrized hypersurface in
                 $K^n(1<=k<=m)$, this solves a generalized Hermite and
                 spline interpolation problem.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fakultat fur Math. und Inf., Passau Univ., Germany",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; theory; Hermite problem; Chinese remainder
                 problem; Multivariate interpolation; Gr{\"o}bner bases;
                 Multivariate polynomial ring; Extension ring; Vanishing
                 ideal; Parametrized hypersurface; Spline
                 interpolation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf G.2.m} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Miscellaneous. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations.",
  thesaurus =    "Interpolation; Polynomials; Splines [mathematics]",
}

@InProceedings{Belkov:1991:RUC,
  author =       "Alexander A. Bel'kov and Alexander V. Lanyov",
  title =        "{REDUCE} usage for calculation of low-energy process
                 amplitudes in chiral {QCD} model",
  crossref =     "Watt:1991:IPI",
  pages =        "454--455",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p454-bel_kov/",
  abstract =     "Describes the extension of REDUCE capabilities for the
                 calculations of strong and weak meson processes within
                 the chiral Lagrangians with higher derivatives. The
                 main non-trivial difficulty is to obtain the process
                 amplitude from the Lagrangian, describing these
                 interactions. Another one is to overcome some REDUCE
                 deficiencies such as the lack of arguments in the
                 matrix data type as well as of some physical operations
                 with the particle operators. This package of procedures
                 allows one to calculate the amplitudes of the strong
                 and weak processes by simple specifying the particles
                 involved and their momenta.",
  acknowledgement = ack-nhfb,
  affiliation =  "Particle Phys. Lab., JINR, Moscow, USSR",
  classification = "A0270 (Computational techniques); A1110 (Field
                 theory); A1130R (Chiral symmetries); A1235C (General
                 properties of quantum chromodynamics (dynamics,
                 confinement, etc.)); C7320 (Physics and Chemistry)",
  keywords =     "algorithms; Chiral Lagrangians; Meson processes;
                 REDUCE capabilities",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General. {\bf I.1.0} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Chiral symmetries; Colour model; Meson field theory;
                 Physics computing; Symbol manipulation",
}

@InProceedings{Berndt:1991:ACA,
  author =       "R. Berndt and A. Lock and G. Witte and C. h.
                 W{\"o}ll",
  title =        "Application of computer algebra to surface lattice
                 dynamics",
  crossref =     "Watt:1991:IPI",
  pages =        "433--438",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p433-berndt/",
  abstract =     "Lattice dynamical calculations for surfaces and in
                 particular for stepped and absorbed covered surfaces
                 are commonly hampered by the complexity of the
                 dynamical matrix for these systems. The authors propose
                 the use of computer algebra programs to set up the
                 dynamical matrix. In the present implementation the
                 dynamical matrix is calculated fully analytically
                 within the framework of a force constant-mode and
                 partially analytically for other interaction models
                 such as the shell model or the bond charge model.",
  acknowledgement = ack-nhfb,
  affiliation =  "Max-Planck Inst. fur Stromungsforschung, Gottingen,
                 Germany",
  classification = "A6830 (Dynamics of solid surfaces and interface
                 vibrations); A6845 (Solid-fluid interface processes);
                 C4140 (Linear algebra); C7320 (Physics and Chemistry)",
  keywords =     "Absorbed covered surfaces; algorithms; Bond charge
                 model; Computer algebra; Dynamical matrix; Force
                 constant-mode; Interaction models; languages; Shell
                 model; Surface lattice dynamics",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf G.2.m} Mathematics of
                 Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN.",
  thesaurus =    "Adsorbed layers; Crystal surface and interface
                 vibrations; Matrix algebra; Phonon dispersion
                 relations; Physics computing; Symbol manipulation",
}

@InProceedings{Beth:1991:FGN,
  author =       "T. Beth and W. Geiselmann and F. Meyer",
  title =        "Finding (good) normal bases in finite fields",
  crossref =     "Watt:1991:IPI",
  pages =        "173--178",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p173-beth/",
  abstract =     "An algorithm to generate low complexity normal bases
                 in finite fields is presented. This algorithm
                 generalizes the method of Ash et al. to fields of
                 arbitrary characteristic. It can be applied to most
                 finite fields and produces (under certain conditions)
                 the multiplication matrix for the normal basis
                 multiplication of $\mbox{GF}(q^n):\mbox{GF}(q)$ in
                 $O(n^2 \log^2 n \log{}q)$ bit-operations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
                 Univ., Germany",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C4240
                 (Programming and algorithm theory)",
  keywords =     "algorithms; Finite fields; Low complexity normal
                 bases; Multiplication matrix; Normal basis
                 multiplication",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations in finite fields. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Computational complexity; Number theory",
}

@InProceedings{Bosma:1991:CFG,
  author =       "Wieb Bosma and Michael Pohst",
  title =        "Computations with finitely generated modules over
                 {Dedekind} rings",
  crossref =     "Watt:1991:IPI",
  pages =        "151--156",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p151-bosma/",
  abstract =     "In computer algebra the use of normal forms for
                 matrices is of eminent importance. Especially, Hermite
                 and Smith normal form techniques are frequently used
                 for various computational problems over Euclidean
                 rings. The paper discusses a generalization of these
                 concepts to Dedekind rings. It considers the problem of
                 normal forms for matrices in the context of basis
                 transformations for finitely generated modules.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Pure Math., Sydney Univ., NSW, Australia",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
  keywords =     "algorithms; Basis transformations; Computer algebra;
                 Dedekind rings; Euclidean rings; Finitely generated
                 modules; Hermite normal form; Matrices; Smith normal
                 form; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Matrix algebra; Number theory",
}

@InProceedings{Bronstein:1991:RDE,
  author =       "Manuel Bronstein",
  title =        "The {Risch} differential equation on an algebraic
                 curve",
  crossref =     "Watt:1991:IPI",
  pages =        "241--246",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p241-bronstein/",
  abstract =     "The author presents a new rational algorithm for
                 solving Risch differential equations over algebraic
                 curves. This algorithm can also be used to solve
                 $n^{\mbox{th}}$-order linear ordinary differential
                 equations with coefficients in an algebraic extension
                 of the rational functions. In the general (`mixed
                 function') case, this algorithm finds the denominator
                 of any solution of the equation. The algorithm has been
                 implemented in the Maple and Scratchpad computer
                 algebra systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inf. ETH-Zentrum, Zurich, Switzerland",
  classification = "C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "$N^{th}$-order linear ordinary differential equations;
                 Algebraic curve; algorithms; Computer algebra systems;
                 Maple; Rational algorithm; Rational functions; Risch
                 differential equation; Scratchpad",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
                 systems (direct and iterative methods). {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, SCRATCHPAD. {\bf
                 G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple.",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Buchmann:1991:CNP,
  author =       "Johannes Buchmann and Volker M{\"u}ller",
  title =        "Computing the number of points of elliptic curves over
                 finite fields",
  crossref =     "Watt:1991:IPI",
  pages =        "179--182",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p179-buchmann/",
  abstract =     "The authors study the problem of counting the points
                 on an elliptic curve over a prime field. Although
                 Schoof (1985) proves that the cardinality of an
                 elliptic curve group over a finite field can be
                 computed in polynomial time, his algorithm is extremely
                 inefficient in practice. On the other hand, the
                 application of Shanks' babystep giantstep idea (1970)
                 to the problem yields an algorithm which is efficient
                 for medium size prime numbers but of exponential
                 complexity. So far no experimental results concerning
                 those algorithms have been published. The authors
                 present a practical improvement of the algorithm of
                 Shanks which is based on the ideas of Schoof. It turns
                 out to be very efficient.",
  acknowledgement = ack-nhfb,
  affiliation =  "FB 14 Inf., Saarlandes Univ., Saarbrucken, Germany",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C4240
                 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "algorithms; Cardinality; Elliptic curves; Finite
                 fields; Medium size prime numbers; Prime field",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Computational complexity; Number theory",
}

@InProceedings{Bundgen:1991:CIP,
  author =       "Reinhard B{\"u}ndgen",
  title =        "Completion of integral polynomials by {AC-term}
                 completion",
  crossref =     "Watt:1991:IPI",
  pages =        "70--78",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p70-bundgen/",
  abstract =     "The article presents a canonical term rewriting system
                 RX whose ground normal forms can directly be mapped to
                 integral polynomials in distributive normal form.
                 Completing RX and a set of ground equations simulates
                 the Gr{\"o}bner base computation for the ideal
                 presented by the ground equations. With this approach,
                 it clearly shows the correspondence of the key features
                 of algebraic completion procedures for integral
                 polynomial ideals and their simulation in a term
                 rewriting environment.",
  acknowledgement = ack-nhfb,
  affiliation =  "Wilhelm-Schickard-Inst., Tubingen Univ., Germany",
  classification = "C4130 (Interpolation and function approximation);
                 C4210 (Formal logic)",
  keywords =     "algorithms; AC-term completion; Canonical term
                 rewriting system; Ground normal forms; Distributive
                 normal form; Ground equations; Gr{\"o}bner base
                 computation; Algebraic completion procedures; Integral
                 polynomial ideals",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Polynomials; Rewriting systems",
}

@InProceedings{Burge:1991:SRI,
  author =       "William H. Burge",
  title =        "{Scratchpad} and the {Rogers--Ramanujan} identities",
  crossref =     "Watt:1991:IPI",
  pages =        "189--190",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p189-burge/",
  abstract =     "This note sketches the part played by Scratchpad in
                 obtaining new proofs of Euler's theorem and the
                 Rogers--Ramanujan Identities.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C1160 (Combinatorial mathematics); C7310
                 (Mathematics)",
  keywords =     "algorithms; Euler theorem; Infinite series; Restricted
                 partition pairs; Rogers--Ramanujan identities;
                 Scratchpad",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, SCRATCHPAD.",
  thesaurus =    "Mathematics computing; Number theory; Symbol
                 manipulation",
}

@InProceedings{Butler:1991:DDG,
  author =       "Greg Butler and Sridhar S. Iyer and Susan H. Ley",
  title =        "A deductive database of the groups of order dividing
                 128",
  crossref =     "Watt:1991:IPI",
  pages =        "210--218",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p210-butler/",
  abstract =     "The paper describes the design and implementation of a
                 deductive database for the 2668 groups of order $2^n$,
                 ($n<=7$). The system was implemented in NU-Prolog, a
                 Prolog system with built-in functions for creating and
                 using deductive databases. In addition to the database,
                 a simple query language was written. This enables
                 database users to assess the data using a simpler and
                 more familiar set-theoretic syntax than that provided
                 by the Prolog interpreter.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Sydney Univ., NSW, Australia",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C6160Z (Other DBMS); C6170 (Expert systems); C7310
                 (Mathematics)",
  keywords =     "Built-in functions; Deductive database; design;
                 languages; NU-Prolog; Query language; Set-theoretic
                 syntax",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Special-purpose algebraic
                 systems. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
                 Language Classifications, Prolog.",
  thesaurus =    "Deductive databases; Group theory; Knowledge based
                 systems; Mathematics computing; Set theory",
}

@InProceedings{Canny:1991:OCD,
  author =       "John Canny and J. Maurice Rojas",
  title =        "An optimal condition for determining the exact number
                 of roots of a polynomial system",
  crossref =     "Watt:1991:IPI",
  pages =        "96--102",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p96-canny/",
  abstract =     "It was shown by Bernshtein (1975) that the number of
                 roots in $(C*)^n$ of a polynomial system depends only
                 on the Newton polytopes of the system, for almost all
                 specializations of the coefficients. This result,
                 referred to as the BKK bound, gives an upper bound on
                 the number of roots of a polynomial system. The BKK
                 bound is often much better than the Bezout bound for
                 the same system, but the original theorem gives an
                 exact bound only if all the coefficients corresponding
                 to Newton polytope boundaries are generically chosen.
                 The current paper shows that the BKK bound is exact
                 under much weaker assumptions: only coefficients
                 corresponding to certain vertices of the Newton
                 polytopes need be generic. This result allows
                 application of the BKK bound to many practical
                 problems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Sci. Div., California Univ., Berkeley, CA,
                 USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; BKK bound; Newton polytopes; Optimal
                 condition; Polynomial system; Roots; theory; Upper
                 bound; verification; Vertices",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Computational complexity; Polynomials",
}

@InProceedings{Chen:1991:NNF,
  author =       "Guoting Chen and Jean Della Dora and Laurent
                 Stolovitch",
  title =        "Nilpotent normal form via {Carleman} linearization
                 (for systems of ordinary differential equations)",
  crossref =     "Watt:1991:IPI",
  pages =        "281--288",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p281-chen/",
  abstract =     "Considers in this paper the normal formal problem for
                 systems of nonlinear ordinary differential equations
                 with singularity at the origin. The problem has its
                 origin in the classical work of Poincare. The authors
                 define a normal form for differential systems whose
                 linear part is nilpotent which is called nilpotent
                 normal form. They give an algorithm for the computation
                 of the normal form and the transformation that leads a
                 system to its normal form. The elementary notations and
                 methods used in the paper are the Carleman
                 linearizations of differential systems and formal
                 diffeomorphisms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. de Math., Univ. Louis Pasteur, Strasbourg,
                 France",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Carleman linearizations; Formal
                 diffeomorphisms; Nilpotent normal form; Nonlinear
                 ordinary differential equations; Normal form;
                 Singularity; Transformation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.7} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
  thesaurus =    "Nonlinear differential equations",
}

@InProceedings{Cohen:1991:OES,
  author =       "Ian Cohen and Karl-Erik E. Thylwe",
  title =        "Obtaining exact steady-state responses in driven
                 undamped oscillators",
  crossref =     "Watt:1991:IPI",
  pages =        "319--320",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p319-cohen/",
  abstract =     "Exact solutions are very scarce in non-linear applied
                 mathematics. However, exact solutions can be an
                 invaluable aid to understanding how well an approximate
                 method is working. It can also be used as a `stepping
                 off' solution into parameter regions where no exact
                 solutions exist. Most importantly however, each exact
                 solution is a potential candidate for a new area of
                 research as it can contain new insights into the
                 physics of the equation under investigation or may be
                 used to replace numerical methods in an investigation.
                 Another important motivation is the synthesis in this
                 project of Gr{\"o}bner bases with dynamical systems
                 research, two areas at the forefront of modern
                 research.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Mech., R. Inst. of Technol., Stockholm,
                 Sweden",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Steady-state responses; Undamped
                 oscillators; Gr{\"o}bner bases; Dynamical systems",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms.",
  thesaurus =    "Differential equations; Nonlinear systems",
}

@InProceedings{Crouch:1991:CID,
  author =       "Peter Crouch and Robert Grossman and Richard Larson",
  title =        "Computations involving differential operators and
                 their actions on functions",
  crossref =     "Watt:1991:IPI",
  pages =        "301--307",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p301-crouch/",
  abstract =     "Further develops the authors algorithms for rewriting
                 expressions involving differential operators. The
                 differential operators considered arise in the local
                 analysis of nonlinear dynamical systems. The authors
                 extend these algorithms in two different directions:
                 they generalize the algorithms so that they apply to
                 differential operators on groups and develop the data
                 structures and algorithms to compute symbolically the
                 action of differential operators on functions. Both of
                 these generalizations are needed for applications. The
                 paper is preliminary: a final paper containing proofs
                 and a further analysis of the algorithm will appear
                 elsewhere.",
  acknowledgement = ack-nhfb,
  affiliation =  "Arizona State Univ., Tempe, AZ, USA",
  classification = "C6120 (File organisation); C7310 (Mathematics)",
  keywords =     "algorithms; Data structures; Differential operators;
                 Nonlinear dynamical systems; Rewriting expressions;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures.",
  thesaurus =    "Rewriting systems; Symbol manipulation",
}

@InProceedings{Czapor:1991:HSS,
  author =       "S. R. Czapor",
  title =        "A heuristic selection strategy for lexicographic
                 {Gr{\"o}bner} bases?",
  crossref =     "Watt:1991:IPI",
  pages =        "39--48",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p39-czapor/",
  abstract =     "It is well known that the computation of lexicographic
                 Gr{\"o}bner bases using the Buchberger's algorithm is
                 more difficult than the computation of Gr{\"o}bner
                 bases with respect to total degree orderings. The
                 lexicographic algorithm is particularly susceptible to
                 the problem of intermediate expression swell; that is,
                 intermediate polynomials may be far larger than those
                 which make up the final basis. To some extent, this is
                 a function of `selection strategy', i.e. the order in
                 which S-polynomials are used to extend a partial basis.
                 The paper argues and provides empirical evidence that
                 for the lexicographic ordering (in direct contrast to
                 the case of degree orderings), a simple heuristic
                 strategy will in practice control intermediate growth
                 more effectively than the normal strategy based on the
                 lexicographic term ordering alone. The results is
                 usually a much more efficient computation, even for
                 nonzero dimension ideals.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Stat. and Comput. Sci., Dalhousie
                 Univ., Halifax, NS, Canada",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; Heuristic selection strategy;
                 Lexicographic Gr{\"o}bner bases; Buchberger's
                 algorithm; Intermediate expression swell; Intermediate
                 polynomials; S-polynomials; Partial basis;
                 Lexicographic ordering; Intermediate growth; Nonzero
                 dimension ideals",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.0} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, General.",
  thesaurus =    "Polynomials",
}

@InProceedings{Davenport:1991:SVA,
  author =       "J. H. Davenport and P. Gianni and B. M. Trager",
  title =        "{Scratchpad}'s view of algebra. {II}. {A} categorical
                 view of factorization",
  crossref =     "Watt:1991:IPI",
  pages =        "32--38",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p32-davenport/",
  abstract =     "For pt.I see Proc. DISCO 1990 (p.40-54). The paper
                 explains how Scratchpad solves the problem of
                 presenting a categorical view of factorization in
                 unique factorization domains, i.e. a view which can be
                 propagated by functors such as
                 SparseUnivariatePolynomial or Fraction. This is not
                 easy, as the constructive version of the classical
                 concept of UniqueFactorizationdomain cannot be so
                 propagated. The solution adopted is based largely on
                 the Seidenberg conditions ($F$) and ($P$), but there
                 are several additional points that have to be borne in
                 mind to produce reasonably efficient algorithms in the
                 required generality. The consequence of the algorithms
                 and interfaces presented is that Scratchpad can
                 factorize in any extension of the integers or finite
                 fields by any combination of polynomial, fraction and
                 algebraic extensions: a capability far more general
                 than any other computer algebra system possesses.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math., Bath Univ., Claverton Down, UK",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics)",
  keywords =     "Algebraic extensions; algorithms; Categorical view;
                 Computer algebra system; Factorization; Finite fields;
                 Fraction; Integers; Polynomial; Scratchpad; Seidenberg
                 conditions",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations in finite fields.",
  thesaurus =    "Mathematics computing; Polynomials; Symbol
                 manipulation",
}

@InProceedings{deJager:1991:SCZ,
  author =       "Bram de Jager",
  title =        "Symbolic calculation of zero dynamics for nonlinear
                 control systems",
  crossref =     "Watt:1991:IPI",
  pages =        "321--322",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p321-de_jager/",
  abstract =     "The calculation of the zero dynamics of a nonlinear
                 system is of advantage in the design of controllers for
                 this system. Because the calculation is difficult to do
                 by hand, symbolic algebra programs are used. To access
                 the usefulness of these programs and to solve some
                 design problems, a MAPLE procedure, ZERODYN, is written
                 to calculate the zero dynamics symbolically. The
                 procedure can, however, not solve all problems, mainly
                 because general symbolic algebra programs have
                 insufficient capabilities to solve sets of nonlinear
                 equations and partial differential equations. A
                 realistic analysis problem shows this.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Mech. Eng., Eindhoven Univ. of Technol.,
                 Netherlands",
  classification = "C1340K (Nonlinear systems); C7310 (Mathematics)",
  keywords =     "algorithms; experimentation; MAPLE procedure;
                 Nonlinear control systems; Nonlinear system; Partial
                 differential equations; Symbolic algebra; Zero
                 dynamics; ZERODYN",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple.",
  thesaurus =    "Nonlinear control systems; Symbol manipulation",
}

@InProceedings{Diaz:1991:DSD,
  author =       "A. Diaz and E. Kaltofen and K. Schmitz and T. Valente
                 and M. Hitz and A. Lobo and P. Smyth",
  title =        "{DSC}: a system for distributed symbolic computation",
  crossref =     "Watt:1991:IPI",
  pages =        "323--332",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p323-diaz/",
  abstract =     "DSC is a general purpose tool that allows the
                 distribution of a computation over a network of Unix
                 workstations. Its control mechanisms automatically
                 start up daemon processes on the participating
                 workstations in order to communicate data by the
                 standard IP/TCP/UDP protocols. The user's program
                 distributes either remote procedure calls or source
                 code of programs and their corresponding input data
                 files by calling a DSC library function. The authors
                 have tested DSC with a primarily test for large
                 integers and with a factorization algorithm for
                 polynomials over large finite fields and observed
                 significant speed-ups over executing the best-known
                 methods on a single workstation computation. These
                 experiments have been carried out not only on our local
                 area network but also on off-site workstations at the
                 University of Delaware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C7310 (Mathematics)",
  keywords =     "algorithms; Distributed symbolic computation; DSC;
                 experimentation; Factorization algorithm; Large
                 integers; Polynomials; Primarily test; Unix
                 workstations",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf D.2.2} Software, SOFTWARE
                 ENGINEERING, Design Tools and Techniques, User
                 interfaces.",
  thesaurus =    "Distributed processing; Software packages; Symbol
                 manipulation",
}

@InProceedings{Faradzev:1991:CCC,
  author =       "I. A. Faradzev and M. H. Klin",
  title =        "For computations with coherent configurations",
  crossref =     "Watt:1991:IPI",
  pages =        "219--223",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p219-faradzev/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures. {\bf G.2.2}
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory. {\bf G.2.1} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Permutations and
                 combinations.",
}

@InProceedings{Faradzev:1991:CPC,
  author =       "I. A. Faradzev and M. H. Klin",
  title =        "Computer package for computations with coherent
                 configurations",
  crossref =     "Watt:1991:IPI",
  pages =        "219--223",
  year =         "1991",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A collection of computer programs based on the Galois
                 correspondence between coherent configurations and
                 permutation groups is described. A number of examples
                 of application of this package for construction of
                 combinatorial objects with interesting properties and
                 for solving some group theoretical problems (extension
                 of a permutation group and intersection of subgroups)
                 are presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "inst. for Syst. Studies, Acad. of Sci., Moscow, USSR",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C7310 (Mathematics)",
  keywords =     "Coherent configurations; Combinatorial objects;
                 Computer programs; Galois correspondence; Group
                 theoretical problems; Permutation groups",
  thesaurus =    "Group theory; Mathematics computing; Software
                 packages; Symbol manipulation",
}

@InProceedings{Fateman:1991:CRL,
  author =       "Richard J. Fateman",
  title =        "Canonical representations in {Lisp} and applications
                 to computer algebra systems",
  crossref =     "Watt:1991:IPI",
  pages =        "360--369",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p360-fateman/",
  abstract =     "Lisp, as well as many other programming languages,
                 provides for the creation of compound data-structures
                 or objects. What if one follows a discipline in which
                 any time one constructs an object which happens to be
                 isomorphic to one previously stored, the constructor
                 function simply returns the same location in memory as
                 the first? The author discusses some of the advantages
                 and show how an implementation fits neatly into Common
                 Lisp. Some of the results are especially relevant for
                 the design and implementation of efficient `general
                 representation' computer algebra systems. The author
                 gives some experimental results showing speedups of a
                 factor of ten or more in basic operations such as
                 simplification of sums.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electron. Eng. and Comput. Sci., California
                 Univ., Berkeley, CA, USA",
  classification = "C6120 (File organisation); C6140D (High level
                 languages); C7310 (Mathematics)",
  keywords =     "algorithms; Canonical representation; Computer algebra
                 systems; experimentation; languages; Lisp",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Common Lisp. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Data structures; LISP; Symbol manipulation",
}

@InProceedings{Gaal:1991:RIF,
  author =       "I. Ga{\'a}l and A. Peth{\"o} and M. Pohst",
  title =        "On the resolution of index form equations",
  crossref =     "Watt:1991:IPI",
  pages =        "185--186",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p185-gaal/",
  abstract =     "For practical applications it is very important to
                 know a power integral basis of the algebraic number
                 field $K$. The solutions of the index form equation,
                 $I(x_2,\ldots{},x_n)=\pm 1$ in $x_2,\ldots{},x_n$ in
                 $Z$ enable one to determine all power integral bases of
                 $K$. If there are no power integral bases, then the
                 best is to determine all integral elements of $K$,
                 having the least possible index, i.e. to determine the
                 least positive $m$ in $Z$ for which
                 $I(x_2,\ldots{},x_n)=\pm m$ in $x_2,\ldots{},x_n$ in
                 $Z$ is soluble and to compute all solutions of this
                 equation to find all integral elements with least
                 index. The authors discuss their attempts at
                 constructing algorithms to solve the equations and
                 results obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Kossuth Lajos Univ., Debrecen, Hungary",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
  keywords =     "algorithms; Index form equations; Power integral
                 basis",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms.",
  thesaurus =    "Algebra; Number theory",
}

@InProceedings{Ganzha:1991:SAD,
  author =       "V. G. Ganzha and B. Yu. Scobelev and E. V.
                 Vorozhtsov",
  title =        "Stability analysis of difference schemes by the
                 catastrophe theory methods and by means of computer
                 algebra",
  crossref =     "Watt:1991:IPI",
  pages =        "427--428",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p427-ganzha/",
  abstract =     "A new method for determining the stability domains of
                 difference schemes(d.s.) is based on the Fourier method
                 and the methods of catastrophe theory. In the paper the
                 authors propose a symbolic-numerical approach to a
                 realization of the method of the work.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
                 Novosibirsk, USSR",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Catastrophe theory; Computer algebra;
                 Difference schemes; Stability analysis; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Catastrophe theory; Convergence of numerical methods;
                 Difference equations; Symbol manipulation",
}

@InProceedings{Gao:1991:CPE,
  author =       "Xiao-Shan Gao and Shang-Ching Chou",
  title =        "Computations with parametric equations",
  crossref =     "Watt:1991:IPI",
  pages =        "122--127",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p122-gao/",
  abstract =     "The authors present a complete method of
                 implicitization for general rational parametric
                 equations. They also present a method to decide whether
                 the parameters of a set of parametric equations (PEs)
                 are independent, and if not, to reparameterize the PEs
                 so that the new PEs have independent parameters. They
                 give a method to compute the inversion maps of the PEs
                 with independent parameters, and as a consequence, they
                 can decide whether the PEs are proper. A new method to
                 find a proper reparameterization for a set of improper
                 PEs of algebraic curves is presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "Algebraic curves; algorithms; Implicitization;
                 Independent parameters; Inversion maps; Rational
                 parametric equations; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Polynomials",
}

@InProceedings{Gatermann:1991:MSS,
  author =       "Karin Gatermann",
  title =        "Mixed symbolic-numeric solution of symmetrical
                 nonlinear systems",
  crossref =     "Watt:1991:IPI",
  pages =        "431--432",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p431-gatermann/",
  abstract =     "The mixed symbolic-numeric algorithm SYMCON for the
                 fully automatic treatment of equivariant systems is
                 presented. The global aspects of the theory of
                 Vanderbauwhede (1982) for these systems are viewed with
                 regard to the full bifurcation scenario containing
                 solution paths with different isotropy groups and
                 symmetry preserving and symmetry breaking bifurcation
                 points. The advanced exploitation of symmetry in the
                 numerical computations causes a comprehensive symmetry
                 analysis and complicated organization of numerical work
                 which is done by the symbolic part of the algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Konrad-Zuse-Zentrum Berlin, Germany",
  classification = "C1340K (Nonlinear systems); C4150 (Nonlinear and
                 functional equations)",
  keywords =     "algorithms; Bifurcation points; Equivariant systems;
                 Symbolic-numeric algorithm; SYMCON; Symmetrical
                 nonlinear systems; Symmetry analysis; theory",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Nonlinear systems; Symbol manipulation",
}

@InProceedings{Gebauer:1991:CCA,
  author =       "R. Gebauer and M. Kalkbrener and B. Wall and F.
                 Winkler",
  title =        "{CASA}: a computer algebra package for constructive
                 algebraic geometry",
  crossref =     "Watt:1991:IPI",
  pages =        "403--410",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p403-gebauer/",
  abstract =     "The program package CASA is designed to enhance the
                 power of a traditional computer algebra system by
                 adding programs for constructive algebraic geometry.
                 The objects that CASA works with are algebraic sets in
                 affine or projective spaces over a field. The geometric
                 objects may be given in various different
                 representations. CASA is able to analyse properties of
                 algebraic sets, such as to compute their dimensions,
                 compute their irreducible components, determine
                 singular points, determine intersection properties and
                 the like. The user can also create 2- and 3-dimensional
                 pictures of curves and surfaces.",
  acknowledgement = ack-nhfb,
  affiliation =  "Johannes Kepler Univ., Linz, Austria",
  classification = "C4190 (Other numerical methods)",
  keywords =     "Algebraic geometry; Algebraic sets; algorithms; CASA;
                 Computer algebra; Computer algebra package;
                 Constructive algebraic geometry; Intersection
                 properties; Irreducible components; Singular points",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Computational geometry; Symbol manipulation",
}

@InProceedings{Gerdt:1991:LSC,
  author =       "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov",
  title =        "{Lie--B{\"a}cklund} symmetries of coupled nonlinear
                 {Schr{\"o}dinger} equations",
  crossref =     "Watt:1991:IPI",
  pages =        "313--314",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p313-gerdt/",
  abstract =     "Applies computer-aided symmetry approach to an
                 investigation of an eight-parametric system of two
                 coupled nonlinear Schr{\"o}dinger equations. Symmetry
                 approach allows one not only to verify the necessary
                 integrability conditions which follow from the
                 existence of a higher infinitesimal or
                 Lie--B{\"a}cklund symmetry but often to find an
                 explicit form of the latter. The corresponding
                 necessary conditions in the form of existence of the
                 series of the local conservation laws lead to the
                 system of nonlinear algebraic equations in numeric
                 parameters. As a result of the first two necessary
                 integrability conditions the REDUCE program provided
                 with some new additional facilities, generates the
                 three set of algebraic equations.",
  acknowledgement = ack-nhfb,
  affiliation =  "JINR, Moscow, USSR",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Lie--B{\"a}cklund symmetry; Nonlinear
                 Schr{\"o}dinger equations",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, REDUCE.",
  thesaurus =    "Schr{\"o}dinger equation; Symbol manipulation",
}

@InProceedings{Giovini:1991:OSC,
  author =       "Alessandro Giovini and Teo Mora and Gianfranco Niesi
                 and Lorenzo Robbiano and Carlo Traverso",
  title =        "`One sugar cube, please' or selection strategies in
                 the {Buchberger} algorithm",
  crossref =     "Watt:1991:IPI",
  pages =        "49--54",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p49-giovini/",
  abstract =     "The paper describes some experimental findings on
                 selection strategies for Gr{\"o}bner basis computation
                 with the Buchberger algorithm. In particular, the
                 results suggest that the sugar flavor of the normal
                 selection is the best choice for a selection strategy.
                 It has to be combined with the straightforward
                 simplification strategy and with a special form of the
                 Gebauer--Moller criteria to obtain the best results.
                 The idea of the sugar flavor is the following: the
                 Buchberger algorithm for homogeneous ideals, with
                 degree-compatible term ordering and normal selection
                 strategy, usually works fine. Homogenizing the basis of
                 the ideal is good for the strategy, but bad for the
                 basis to be computed. The sugar flavor computes, for
                 every polynomial in the course of the algorithm, `the
                 degree that it would have if computed with the
                 homogeneous algorithm', and uses this phantom degree
                 (the sugar) only for the selection strategy.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Genova Univ., Italy",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; experimentation; Selection strategies;
                 Buchberger algorithm; Gr{\"o}bner basis computation;
                 Sugar flavor; Normal selection; Straightforward
                 simplification strategy; Gebauer--Moller criteria;
                 Homogeneous ideals; Degree-compatible term ordering;
                 Polynomial; Homogeneous algorithm; Phantom degree",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Polynomials",
}

@InProceedings{Gonzalez-Vega:1991:STM,
  author =       "Laureano Gonz{\'a}lez-Vega",
  title =        "A subresultant theory for multivariate polynomials",
  crossref =     "Watt:1991:IPI",
  pages =        "79--85",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p79-gonzalez-vega/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
}

@InProceedings{Gonzalez-Vega:1991:WRA,
  author =       "Laureano Gonz{\'a}lez-Vega",
  title =        "Working with real algebraic plane curves in {REDUCE}
                 the {GCUR} package",
  crossref =     "Watt:1991:IPI",
  pages =        "397--402",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p397-gonzalez-vega/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.2.2}
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Graph algorithms.",
}

@InProceedings{GonzalezVega:1991:STM,
  author =       "L. {Gonzalez Vega}",
  title =        "A subresultant theory for multivariate polynomials",
  crossref =     "Watt:1991:IPI",
  pages =        "79--85",
  year =         "1991",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In computer algebra, subresultant theory provides a
                 powerful method to construct algorithms solving
                 problems for polynomials in one variable in an optimal
                 way. The paper extends the subresultant theory to the
                 multivariate case. In order to achieve this, first of
                 all, it introduces the definition of a subresultant
                 sequence associated to two polynomials in one variable
                 with coefficients in an integral domain, describing the
                 properties of this sequence that one would like to
                 extend to the multivariate case. In the second section
                 it generalizes the definition of a subresultant
                 polynomial to the multivariate case, showing that many
                 of the properties obtained in the one variable case
                 work also in the multivariate case. In this way it
                 shows how these subresultants can be used to get a
                 greatest common divisor of $n$ polynomials in
                 $D(x_1,\ldots{},x_{n-1})$ where $D$ is an integral
                 domain. The paper then applies this subresultant theory
                 to get a determinantal formula for the solution set of
                 almost all $0$-dimensional ideals defined by $n$
                 polynomials in $D(x_1, \ldots{}, x_n)$, with $D$ an
                 integral domain. Finally, some open problems related
                 with this construction are shown.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. de Matematicas, Cantabria Univ., Santander,
                 Spain",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "0-Dimensional ideals; Computer algebra; Determinantal
                 formula; Greatest common divisor; Integral domain;
                 Multivariate polynomials; Solution set; Subresultant
                 polynomial; Subresultant sequence; Subresultant
                 theory",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{GonzalezVega:1991:WRA,
  author =       "L. {Gonzalez Vega}",
  title =        "Working with real algebraic plane curves in {REDUCE}:
                 the {GCUR} package",
  crossref =     "Watt:1991:IPI",
  pages =        "397--402",
  year =         "1991",
  bibdate =      "Sat Apr 25 12:53:35 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Presents an implementation in Reduce of a package to
                 get topological and geometric information about real
                 algebraic plane curves defined as the real zeros of
                 polynomials in $Z(x, y)$. More precisely, if $P$ in
                 $Z(x,y)$ the output using the package GCUR will be a
                 plane graph homeomorphic to the set:
                 $C(P)=((\alpha,\beta) {\rm in }
                 R^2/P(\alpha,\beta)=0)$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. Mat., Cantabria Univ., Santander, Spain",
  classification = "C4190 (Other numerical methods)",
  keywords =     "Algebraic plane curves; GCUR; Geometric information;
                 Plane graph; REDUCE; Topological information",
  thesaurus =    "Computational geometry; Poles and zeros; Polynomials;
                 Symbol manipulation; Topology",
}

@InProceedings{Grigoriev:1991:ASR,
  author =       "Dima Yu. u. Grigoriev and Marek Karpinski",
  title =        "Algorithms for sparse rational interpolation",
  crossref =     "Watt:1991:IPI",
  pages =        "7--13",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p7-grigoriev/",
  abstract =     "Presents two algorithms for interpolating sparse
                 rational functions. The first is the interpolation
                 algorithm in a sense of sparse partial fraction
                 representation of rational functions. The second is the
                 algorithm for computing the entier and the remainder of
                 a rational function. The first algorithm works without
                 a priori known bound on the degree of a rational
                 function, the second one is in the parallel class NC
                 provided that the degree is known.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Bonn Univ., Germany",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Entier; Interpolation algorithm; NC;
                 Parallel class; Remainder; Sparse partial fraction
                 representation; Sparse rational functions",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
  thesaurus =    "Computational complexity; Interpolation; Parallel
                 algorithms",
}

@InProceedings{Grudtsin:1991:ISI,
  author =       "S. N. Grudtsin and V. N. Larin",
  title =        "Integrated system {INTERCOMP} and computer language
                 for physicists",
  crossref =     "Watt:1991:IPI",
  pages =        "377--381",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p377-grudtsin/",
  abstract =     "Contains a description of a general approach to
                 physics related integrated software elaborations. A
                 development history and modern stage of the INTERCOMP
                 system, containing a large set of language and program
                 means for a description and computer analysis of
                 physical models are also described. The system has a
                 high level interpreted language and includes a powerful
                 symbolic algebraic computation subsystem, a numeric
                 algorithms library, a relational DBMS, a graphic
                 package, editor and text processor.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for High Energy Phys., Protvino, USSR",
  classification = "C6140D (High level languages); C7320 (Physics and
                 Chemistry)",
  keywords =     "Algebraic; Computer analysis; Computer language;
                 Graphic package; Integrated software elaborations;
                 INTERCOMP; languages; Numeric algorithms; Physical
                 models; Relational DBMS; Symbolic computation",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 J.2} Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics. {\bf D.3.2} Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "High level languages; Physics computing; Symbol
                 manipulation",
}

@InProceedings{Havas:1991:CES,
  author =       "George Havas",
  title =        "Coset enumeration strategies",
  crossref =     "Watt:1991:IPI",
  pages =        "191--199",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p191-havas/",
  abstract =     "A primary reference on computer implementation of
                 coset enumeration procedures is a 1973 paper of Cannon,
                 Dimino, Havas and Watson. Programs and techniques
                 described there are updated in this paper. Improved
                 coset definition strategies, space saving techniques
                 and advice for obtaining improved performance are
                 included. New coset definition strategies for
                 Felsch-type methods give substantial reductions in
                 total cosets defined for some pathological
                 enumerations. Significant time savings are achieved for
                 coset enumeration procedures in general. Statistics on
                 performance are presented, both in terms of time and in
                 terms of maximum and total cosets defined for selected
                 enumerations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Queensland Univ., St. Lucia,
                 Qld., Australia",
  classification = "C1160 (Combinatorial mathematics); C7310
                 (Mathematics)",
  keywords =     "Coset definition strategies; Coset enumeration
                 procedures; Felsch-type methods; Pathological
                 enumerations; performance; Subgroups",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, CAYLEY.",
  thesaurus =    "Mathematics computing; Set theory",
}

@InProceedings{Hietarinta:1991:SIP,
  author =       "Jarmo Hietarinta",
  title =        "Searching for integrable {PDE}'s by testing {Hirota}'s
                 three-soliton condition",
  crossref =     "Watt:1991:IPI",
  pages =        "295--300",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p295-hietarinta/",
  abstract =     "The search for integrable PDE's has been an active
                 research subject with computer algebra as a necessary
                 tool. The author describes a search method based on the
                 requirement that standard type three- and four-soliton
                 solution exist in the bilinear formalism of Hirota. The
                 existence of $N$-soliton solutions can be formulated as
                 a requirement that a certain high degree polynomial in
                 $N*M$ variables vanishes on an affine manifold defined
                 by $N$ polynomials of $M$ variables each. An exhaustive
                 search has been carried out for certain classes of
                 typical equations and several new equations have been
                 found.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Phys., Turku Univ., Finland",
  classification = "A0230 (Function theory, analysis); A0340K (Waves and
                 wave propagation: general mathematical aspects)",
  keywords =     "algorithms; Bilinear formalism; Computer algebra;
                 Integrable PDE's; Search method; theory; Three-soliton
                 condition",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Partial differential equations; Search problems;
                 Solitons; Symbol manipulation",
}

@InProceedings{Ilyin:1991:PIF,
  author =       "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodionov and
                 A. Yu. Taranov",
  title =        "{PC} implementation of fast {Dirac} matrix trace
                 calculations",
  crossref =     "Watt:1991:IPI",
  pages =        "456--457",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p456-ilyin/",
  abstract =     "Presents an implementation of a fast algorithm for
                 Dirac matrix trace calculations. This implementation is
                 made for IBM compatible PC and works under REDUCE
                 3.3.1. Name of package is CVIT. The algorithm is based
                 on intense use of Fierz identities in N-dimensional
                 space ($N$ is arbitrary natural number or symbol) and
                 may be considered as an extension of well known Kahane
                 algorithm on higher space dimensions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Nucl. Phys., Moscow State Univ., USSR",
  classification = "C7320 (Physics and Chemistry)",
  keywords =     "algorithms; CVIT; Dirac matrix trace calculations;
                 Fierz identities; IBM compatible PC; Kahane algorithm;
                 N-dimensional space; REDUCE 3.3.1",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf J.2}
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics.",
  thesaurus =    "IBM computers; Matrix algebra; Physics computing;
                 Symbol manipulation",
}

@InProceedings{Ilyin:1991:SST,
  author =       "V. A. Ilyin and A. P. Kryukov",
  title =        "Symbolic simplification of tensor expressions using
                 symmetries, dummy indices and identities",
  crossref =     "Watt:1991:IPI",
  pages =        "224--228",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p224-ilyin/",
  abstract =     "The algorithm based on simple geometrical ideas is
                 suggested for simplification of tensor expressions
                 which takes into account symmetries, dummy indices, and
                 linear identities with many terms. The results of the
                 realization in REDUCE system are adduced. The Riemann
                 tensor is used as an example.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Nucl. Phys., Moscow State Univ., USSR",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C7310 (Mathematics)",
  keywords =     "algorithms; Dummy indices; Geometrical ideas; Linear
                 identities; REDUCE; Simplification; Symbolic
                 simplification; Symmetries; Tensor expressions",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms.",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Kleczka:1991:SCA,
  author =       "W. Kleczka and E. Kreuzer",
  title =        "Systematic computer-aided analysis of dynamic
                 systems",
  crossref =     "Watt:1991:IPI",
  pages =        "429--430",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p429-kleczka/",
  abstract =     "An automated numerical-symbolical analysis concept for
                 dynamic systems in engineering mechanics is outlined.
                 Besides the computerized generation of symbolic
                 equations of motion, the subsequent analysis is also
                 performed by means of computer algebra in combination
                 with well-established numerical methods.",
  acknowledgement = ack-nhfb,
  affiliation =  "Meerestech. II, Tech. Univ., Hamburg-Harburg,
                 Germany",
  classification = "C1210 (General system theory); C7440 (Civil and
                 mechanical engineering)",
  keywords =     "algorithms; Computer-aided analysis; Dynamic systems;
                 Engineering mechanics; Numerical-symbolical analysis;
                 Symbolic equations",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Engineering. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra,
                 Eigenvalues and eigenvectors (direct and iterative
                 methods).",
  thesaurus =    "Computer aided analysis; Convergence of numerical
                 methods; Mechanical engineering computing; Symbol
                 manipulation",
}

@InProceedings{Kornyak:1991:PSA,
  author =       "V. V. Kornyak and W. I. Fushchich",
  title =        "A program for symmetry analysis of differential
                 equations",
  crossref =     "Watt:1991:IPI",
  pages =        "315--316",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p315-kornyak/",
  abstract =     "Proposes in this work a program for determining
                 Lie--B{\"a}cklund (LB) symmetries of (partial or
                 ordinary) differential equations and for classification
                 of equations containing arbitrary functions and
                 parameters with respect to symmetries of this kind. The
                 program was implemented in Turbo C language and
                 designed in such a way to be more effective for systems
                 of equations with multidimensional spaces of
                 independent and dependent variables. The internal data
                 structures for representation of expressions are
                 right-threaded binary trees. The program reduces input
                 system of equations to the passive form, computes the
                 differential consequences of equations up to the needed
                 order, constructs the invariance conditions for a given
                 order LB symmetries, eliminates the dependencies
                 between the invariance conditions using differential
                 manifold, separates the determining equations and tries
                 to integrate them.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Appl. Res., Acad. of Sci., Kiev, Ukrainian
                 SSR, USSR",
  classification = "C4170 (Differential equations); C7310
                 (Mathematics)",
  keywords =     "algorithms; Differential equations; languages;
                 Lie--B{\"a}cklund symmetries; Symmetry analysis",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.7} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations.
                 {\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Turbo C.",
  thesaurus =    "Differential equations",
}

@InProceedings{Kuchlin:1991:MCI,
  author =       "Wolfgang K{\"u}chlin",
  title =        "On the multi-threaded computation of integral
                 polynomial greatest common divisors",
  crossref =     "Watt:1991:IPI",
  pages =        "333--342",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p333-kuchlin/",
  abstract =     "Reports experiences and practical results from
                 parallelizing the Brown--Collins polynomial g.c.d.
                 algorithm, starting from Collins' SAC-2 implementation
                 IPGCDC. The parallelization environment is PARSAC-2, a
                 multi-threaded version of SAC-2 programmed in C with
                 the parallelization constructs of the C Threads
                 library. IPGCDC computes the g.c.d. and its co-factors
                 of two polynomials in $Z(x_1,\ldots{},x_r)$, by first
                 reducing the problem to multiple calculations of
                 modular polynomial g.c.d.'s in $Z_p(x_1,\ldots{},x_r)$,
                 and then recovering the result by Chinese remaindering.
                 After studying timings of the SAC-2 algorithm, the
                 author first parallelizes the Chinese remainder
                 algorithm, and then parallelizes the main loop of
                 IPGCDC by executing the modular g.c.d. computations
                 concurrently. Finally, he determines speed-up's and
                 speed-up efficiencies of our parallel algorithms over a
                 wide range of polynomials. The experiments were
                 conducted on a 12 processor Encore Multimax under
                 Mach.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
                 Columbus, OH, USA",
  classification = "C4240 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "algorithms; Brown--Collins polynomial g.c.d.
                 algorithm; Chinese remaindering; Encore Multimax;
                 Multi-threaded computation; PARSAC-2; Polynomial
                 greatest common divisors",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General. {\bf I.1.3} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C.",
  thesaurus =    "Mathematics computing; Parallel algorithms; Symbol
                 manipulation",
}

@InProceedings{Langemyr:1991:ASA,
  author =       "Lars Langemyr",
  title =        "An analysis of the subresultant algorithm over an
                 algebraic number field",
  crossref =     "Watt:1991:IPI",
  pages =        "167--172",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p167-langemyr/",
  abstract =     "The author shows that one can compute the subresultant
                 polynomial remainder sequence over an algebraic number
                 field in $O((n^5m^3+n^4m^5) \log^2(nDE^m))$ binary
                 operations, where the generator of the field is given
                 by a monic irreducible polynomial of degree $m$ with
                 integer coefficients bounded by $E$ in absolute value,
                 and where the two input polynomials are of degree at
                 most $n$ and with integer coefficients bounded by $D$
                 in absolute value.",
  acknowledgement = ack-nhfb,
  affiliation =  "Numerical Anal. and Comput. Sci., R. Inst. of
                 Technol., Stockholm, Sweden",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4130 (Interpolation and function approximation); C4240
                 (Programming and algorithm theory); C7310
                 (Mathematics)",
  keywords =     "Algebraic number field; algorithms; Greatest common
                 division; Integer coefficients; Monic irreducible
                 polynomial; Subresultant polynomial remainder
                 sequence",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Number-theoretic computations.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
  thesaurus =    "Algebra; Computational complexity; Mathematics
                 computing; Number theory; Polynomials",
}

@InProceedings{Letichevsky:1991:APO,
  author =       "A. A. Letichevsky and J. V. Kapitonova and S. V.
                 Konozenko",
  title =        "Algebraic programs optimization",
  crossref =     "Watt:1991:IPI",
  pages =        "370--376",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p370-letichevsky/",
  abstract =     "Algebraic program is a system of relations (equalities
                 of data algebra) with a given strategy for applying
                 these relations as rewriting rules. An algebraic
                 program may be optimized by transforming a system of
                 relations or by transforming a strategy. Only second
                 case of optimization is considered in the paper. The
                 problem of algebraic program optimization is
                 investigated in the context of programming in the APS-1
                 system.",
  acknowledgement = ack-nhfb,
  affiliation =  "Glushkov Inst. of Cybern., Acad. of Sci., Kiev,
                 Ukrainian SSR, USSR",
  classification = "C6110 (Systems analysis and programming); C7310
                 (Mathematics)",
  keywords =     "Algebraic program optimization; algorithms; APS-1;
                 Data algebra; languages; Programming; Rewriting rules;
                 System of relations",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf G.1.6} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization. {\bf
                 F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Computations on discrete structures.",
  thesaurus =    "Optimisation; Programming; Symbol manipulation",
}

@InProceedings{Liska:1991:ADS,
  author =       "Richard Liska and Michail Yu. u. Shashkov",
  title =        "Algorithms for difference schemes construction on
                 non-orthogonal logically rectangular meshes",
  crossref =     "Watt:1991:IPI",
  pages =        "419--426",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p419-liska/",
  abstract =     "Deals with the formalization of the basic operator
                 method for construction of difference schemes for the
                 numerical solving of partial differential equations.
                 The strength of the basic operator method lies in the
                 fact that it produces fully conservative difference
                 schemes. The difference mesh can be non-orthogonal but
                 has to be logically orthogonal. Algorithms for working
                 with grid functions and grid operators in symbolic form
                 which are necessary in the basic operator method are
                 described. The algorithms have been implemented in the
                 computer algebra system REDUCE.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fac. of Nucl. Sci. and Phys. Eng., Czech Tech. Univ.,
                 Prague, Czechoslovakia",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Basic operator method; Computer algebra;
                 Difference mesh; Difference schemes; Grid functions;
                 Grid operators; Logically orthogonal; Numerical
                 solving; Partial differential equations; Rectangular
                 meshes; REDUCE",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Numerical methods; Partial differential equations;
                 Symbol manipulation",
}

@InProceedings{Manocha:1991:ETM,
  author =       "Dinesh Manocha and John Canny",
  title =        "Efficient techniques for multipolynomial resultant
                 algorithms",
  crossref =     "Watt:1991:IPI",
  pages =        "86--95",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p86-manocha/",
  abstract =     "The paper presents efficient techniques for applying
                 multipolynomial resultant algorithms and shows their
                 effectiveness for manipulating systems of polynomial
                 equations. In particular, it presents efficient
                 algorithms for computing the resultant of a system of
                 polynomial equations (whose coefficients may be
                 symbolic variables). These algorithms can be used for
                 interpolating polynomials from their values and
                 expanding symbolic determinants. Moreover, it uses
                 multipolynomial resultants for computing the real or
                 complex solutions of nonlinear polynomial equations. It
                 also discusses the implementation of these algorithms
                 in the context of certain applications.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Sci. Div., California Univ., Berkeley, CA,
                 USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Complex solutions; Efficient algorithms;
                 Multipolynomial resultant algorithms; Nonlinear
                 polynomial equations; Polynomial interpolation; Real
                 solutions; Symbolic determinants; Symbolic variables",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
  thesaurus =    "Algorithm theory; Interpolation; Polynomials",
}

@InProceedings{Marinari:1991:GBI,
  author =       "M. G. Marinari and H. M. M{\"o}ller and T. Mora",
  title =        "{Gr{\"o}bner} bases of ideals given by dual bases",
  crossref =     "Watt:1991:IPI",
  pages =        "55--63",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p55-marinari/",
  abstract =     "In 1982, Buchberger and Moller proposed an algorithm
                 which, given a finite number of rational points in the
                 affine $n$-dimensional space, computes a Gr{\"o}bner
                 basis for the ideal I of the polynomials vanishing at
                 the points. In 1988, Faugere, Gianni, Lazard and Mora
                 supplied an algorithm, which, given the reduced
                 Gr{\"o}bner basis w.r.t. some term-ordering $<_1$ of a
                 0-dim. ideal I, returns its reduced Gr{\"o}bner basis
                 w.r.t. some other term-ordering $<_2$. The paper
                 systematizes and generalizes the common properties of
                 the Buchberger--M{\"o}ller and the FGLM algorithms to
                 the frame of ideals defined by functionals. It gives
                 two algorithms to compute the Gr{\"o}bner basis of an
                 ideal defined by functionals, together with a set of
                 biorthogonal polynomials: the first one is a direct
                 generalization of the B-M and the FGLM algorithms; the
                 second one iteratively for each $i$ solves the question
                 for the ideals defined by $L_1,\ldots{}, L_i$. It then
                 measures the complexity of the algorithms in terms of
                 the number of additions+multiplications in $K$ which
                 they require and proves that both have a complexity of
                 $1/2 s^3+s^2 b+f s (s+b)<=O (n s^3+f n s^2)$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Genova Univ., Italy",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Gr{\"o}bner bases; Ideals; Dual bases;
                 Rational points; Affine $n$-dimensional space;
                 Term-ordering; Functionals; Biorthogonal polynomials;
                 Complexity",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms.",
  thesaurus =    "Computational complexity; Polynomials",
}

@InProceedings{Marzinkewitsch:1991:OCA,
  author =       "Reiner Marzinkewitsch",
  title =        "Operating computer algebra systems by handprinted
                 input",
  crossref =     "Watt:1991:IPI",
  pages =        "411--413",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p411-marzinkewitsch/",
  abstract =     "Nearly twenty years have passed since the first
                 computer algebra systems (CAS) came up in the beginning
                 of the seventies. Since then CAS have gained a lot of
                 computational power. In contrast to this fact CAS have
                 not experienced the deserved widespread use by
                 potential users. The main reason for this discrepancy
                 is the unnatural operation of CAS by artificial
                 linearized notations, which tend to give little
                 comprehensive survey of the problem under work.
                 Calculation with pencil and paper not only offers many
                 efficient techniques but also appeals to the user's
                 ease. Especially occasional users need a familiar i.e.
                 paperlike interface to CAS. In this paper an integrated
                 system is presented, which offers the demanded
                 facilities: Calculating by hand in a traditional, `two
                 dimensional' fashion with the computational support of
                 a CAS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich 14, Saarlandes Univ., Saarbrucken,
                 Germany",
  classification = "C5260B (Computer vision and picture processing);
                 C5530 (Pattern recognition and computer vision
                 equipment); C5540 (Terminals and graphic displays);
                 C7310 (Mathematics)",
  keywords =     "algorithms; CAS; Computer algebra systems; design;
                 Handprinted input",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 H.5.2} Information Systems, INFORMATION INTERFACES AND
                 PRESENTATION, User Interfaces, Interaction styles.",
  thesaurus =    "Character recognition; Neural nets; Symbol
                 manipulation; Workstations",
}

@InProceedings{Molenkamp:1991:IAA,
  author =       "J. H. J. Molenkamp and V. V. Goldman and J. A. {van
                 Hulzen}",
  title =        "An improved approach to automatic error cumulation
                 control",
  crossref =     "Watt:1991:IPI",
  pages =        "414--418",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p414-molenkamp/",
  abstract =     "For evaluation of arithmetical expressions using
                 multiple precision floating-point arithmetic, a method
                 is given to automatically perform error cumulation
                 control prior to the actual computations. Individual
                 errors and their effects are identified, and it is
                 shown how to compute these effects efficiently via
                 automatic differentiation. In the presented approach
                 these effects are used to determine which precisions
                 have to be chosen during the real computations, in
                 order to limit error cumulation to admissible, user
                 chosen error bounds.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Twente Univ., Enschede,
                 Netherlands",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  keywords =     "algorithms; Arithmetical expressions; Computations;
                 Error bounds; Error cumulation control; Multiple
                 precision floating-point arithmetic",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE.",
  thesaurus =    "Digital arithmetic; Error analysis",
}

@InProceedings{Oevel:1991:YES,
  author =       "Walter Oevel and Klaus Strack",
  title =        "The {Yang--Baxter} equation and a systematic search
                 for {Poisson} brackets on associative algebras",
  crossref =     "Watt:1991:IPI",
  pages =        "229--236",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p229-oevel/",
  abstract =     "Starting with an associative algebra equipped with a
                 linear map solving the Yang--Baxter equation three
                 Poisson brackets may be constructed admitting a common
                 hierarchy of functions in involution. Realizations of
                 the algebra lead to various integrable hierarchies
                 known to admit an infinite number of invariant Poisson
                 brackets. In all cases three of these brackets are
                 known to originate from the three abstract brackets
                 defined on the algebra. A systematic search for
                 abstract versions of the higher Poisson brackets is
                 performed using computer algebra. It is shown that
                 apart from the three known brackets no further relevant
                 abstract brackets of a certain `local' form may be
                 constructed from solutions of the Yang--Baxter
                 equations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. Sci., Univ. of Technol., Loubhborough,
                 UK",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Abstract brackets; algorithms; Associative algebras;
                 Computer algebra; Integrable hierarchies; Poisson
                 brackets; Yang--Baxter equation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Algebra; Mathematics computing",
}

@InProceedings{Pecelli:1991:FMD,
  author =       "Giampiero Pecelli",
  title =        "Formal methods in delay-differential equations",
  crossref =     "Watt:1991:IPI",
  pages =        "317--318",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p317-pecelli/",
  abstract =     "Studies formal methods in the solution of
                 delay-differential equations (DDEs). The motivation for
                 such study comes from the introduction of Hopf
                 bifurcation techniques and the method of averaging to
                 the study of stable oscillations in such systems. The
                 author concentrates on the formal aspects associated
                 with the construction of solutions required for an
                 application of the methods. These classes of solutions
                 are quite simple, being solutions to linear systems.
                 The paper concentrates on completing the formalization
                 and showing that an automated system is possible.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Lowell Univ., MA, USA",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; DDEs; Delay-differential equations; Formal
                 methods; Hopf bifurcation; Stable oscillations",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple.",
  thesaurus =    "Differential equations",
}

@InProceedings{Petho:1991:AGB,
  author =       "Attila Peth{\"o}",
  title =        "Application of {Gr{\"o}bner} bases to the resolution
                 of systems of norm equations",
  crossref =     "Watt:1991:IPI",
  pages =        "144--150",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p144-petho/",
  abstract =     "Let $K$ be a cubic extension of the rational number
                 field $Q$. Denote by $Z_K$ the ring of integers of $K$
                 and by $N_KQ/(\gamma )$ the norm of $\gamma$ in $K$.
                 Let $P(x)=x^2+cx+d$ in $Z(x)$ and $a,b,n_1,n_2,n_3$, in
                 $Z$. The paper gives necessary and sufficient
                 conditions for the existence of cubic number fields $K$
                 and elements $\eta$ in $Z_K$ such that
                 $N_KQ/(\eta)=n_1,N_KQ/(\eta-a)=n_2,N_KQ/(\eta-b)=n_3$;
                 or $N_KQ/(\eta)=n_1,N_KQ/(P(\eta))=n_2$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Kossuth Lajos Univ., Debrecen,
                 Hungary",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
  keywords =     "algorithms; theory; Gr{\"o}bner bases; Norm equations;
                 Cubic extension; Rational number field; Integers;
                 Necessary and sufficient conditions; Cubic number
                 fields",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Number theory; Polynomials",
}

@InProceedings{Reid:1991:RSD,
  author =       "G. J. Reid and A. Boulton",
  title =        "Reduction of systems of differential equations to
                 standard form and their integration using directed
                 graphs",
  crossref =     "Watt:1991:IPI",
  pages =        "308--312",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p308-reid/",
  abstract =     "Discusses an algorithm developed in earlier work which
                 has been implemented in MACSYMA that reduces systems of
                 partial differential equations to a simplified standard
                 form by eliminating redundances and including all
                 integrability conditions. Once a system has been put in
                 standard form the authors show how directed graphs
                 representing the dependencies amongst the system's
                 variables can be used to simplify the problem of
                 explicitly or numerically integrating the system.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., British Columbia Univ., Vancouver, BC,
                 Canada",
  classification = "C1160 (Combinatorial mathematics); C4160 (Numerical
                 integration and differentiation); C4170 (Differential
                 equations)",
  keywords =     "algorithms; Directed graphs; Integration; MACSYMA;
                 Partial differential equations; Standard form",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf G.2.2}
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory. {\bf I.1.2} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Computations on discrete structures. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, MACSYMA.",
  thesaurus =    "Directed graphs; Integration; Partial differential
                 equations",
}

@InProceedings{Renner:1991:NEE,
  author =       "Friedrich Renner",
  title =        "Nonlinear evolution equations and the {Painleve}
                 analysis: a constructive approach with {REDUCE}",
  crossref =     "Watt:1991:IPI",
  pages =        "289--294",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p289-renner/",
  abstract =     "A number of necessary conditions for a class of
                 nonlinear partial differential equations to pass the
                 Painleve test with the Kruskal ansatz is given. Using
                 these one can (theoretically) construct all evolution
                 equations of certain form and this property with a
                 computer algebra package based on REDUCE.",
  acknowledgement = ack-nhfb,
  affiliation =  "Kassel Univ., Germany",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; Computer algebra package; Evolution
                 equations; Kruskal ansatz; Nonlinear partial
                 differential equations; Painleve test; REDUCE; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Nonlinear differential equations; Partial differential
                 equations; Symbol manipulation",
}

@InProceedings{Richardson:1991:TCN,
  author =       "Daniel Richardson",
  title =        "Towards computing nonalgebraic cylindrical
                 decompositions",
  crossref =     "Watt:1991:IPI",
  pages =        "247--255",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p247-richardson/",
  abstract =     "Non algebraic cylindrical decompositions are
                 discussed. False derivatives and local Sturm sequences
                 are defined as tools for computing them. The crucial
                 fact in the algebraic case is that one can characterize
                 the number of distinct real roots of a polynomial
                 $p(y)$ by a condition on the coefficients. An attempt
                 is made to obtain an analogous characterization for
                 nonalgebraic functions such as polynomials in monomials
                 which are defined by algebraic differential equations.
                 An example would be an exponential polynomial
                 $p(y,e^y)$. The difficulties of applying this
                 characterization are described, using the example of
                 exponential polynomials in two variables,
                 $p(x,e^y,y,e^y)$. The characterization obtained does
                 not lead to quantifier elimination.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Bath Univ., UK",
  classification = "C1110 (Algebra); C1120 (Analysis); C7310
                 (Mathematics)",
  keywords =     "Algebraic differential equations; algorithms;
                 Cylindrical decompositions; Differential geometry;
                 Distinct real roots; Exponential polynomials; Local
                 Sturm sequences; Monomials; Nonalgebraic functions;
                 theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Nonalgebraic algorithms.",
  thesaurus =    "Algebra; Differential equations; Polynomials",
}

@InProceedings{Roch-Siebert:1991:PFE,
  author =       "Fran{\c{c}}oise Roch-Siebert and Gilles Villard",
  title =        "{PAC}: first experiments on a 128 transputers
                 m{\'e}ganode",
  crossref =     "Watt:1991:IPI",
  pages =        "343--351",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p343-roch-siebert/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; performance",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Parallel algorithms. {\bf G.1.3} Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf C.1.2}
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Multiple-instruction-stream, multiple-data-stream
                 processors (MIMD).",
}

@InProceedings{RochSiebert:1991:PFE,
  author =       "F. Roch-Siebert and G. Villard",
  title =        "{PAC}: first experiments on a 128 transputers
                 meganode",
  crossref =     "Watt:1991:IPI",
  pages =        "343--351",
  year =         "1991",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "From its beginning three years ago, the PAC project:
                 parallel algebraic computing, has been exploiting a 16
                 processors hypercube to validate some algebraic
                 computation algorithms, and to justify the use of
                 parallelism. Going further, the authors begin to
                 generalize the previous results and study new problems.
                 Experiments are now held on a more massively parallel
                 computer: a 128 Transputers network. The authors
                 present the first results have obtained: as an example,
                 they have been interested in applying the Chinese
                 remainder theorem in linear algebra. For a fixed number
                 of processors, they show how the behaviour of an
                 algorithm is influenced by the chosen network topology.
                 They point out the communication costs and the
                 constraints due to the storage requirements.",
  acknowledgement = ack-nhfb,
  affiliation =  "Equipe Calcul Parallele et Calcul Formel, CNRS,
                 Grenoble, France",
  classification = "C4140 (Linear algebra); C7310 (Mathematics)",
  keywords =     "Algebraic computation; Chinese remainder theorem;
                 Linear algebra; Network topology; PAC project; Parallel
                 algebraic computing; Parallelism",
  thesaurus =    "Linear algebra; Parallel algorithms; Symbol
                 manipulation",
}

@InProceedings{Roelofs:1991:IMO,
  author =       "Marcel Roelofs and Peter K. H. Gragert",
  title =        "Implementation of multilinear operators in {REDUCE}
                 and applications in mathematics",
  crossref =     "Watt:1991:IPI",
  pages =        "390--396",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p390-roelofs/",
  abstract =     "Introduces and implement a concept for dealing with
                 mathematical bases of linear spaces and mappings
                 (multi)linear with respect to such bases, in REDUCE
                 (cf. (1)). Using this concept the authors give some
                 examples how to implement some well known (multi)linear
                 mappings in mathematics with very little effort.
                 Moreover they implement a procedure operatorcoeff
                 similar to the standard REDUCE procedure coeff, but now
                 for linear spaces instead of polynomial rings.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Appl. Math., Twente Univ., Enschede,
                 Netherlands",
  classification = "C4140 (Linear algebra); C7310 (Mathematics)",
  keywords =     "algorithms; Linear spaces; Mappings; Multilinear
                 operators; REDUCE",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions.",
  thesaurus =    "Linear algebra; Symbol manipulation",
}

@InProceedings{Roque:1991:QRD,
  author =       "W. L. Roque and R. P. {dos Santos}",
  title =        "Qualitative reasoning, dimensional analysis and
                 computer algebra",
  crossref =     "Watt:1991:IPI",
  pages =        "460--461",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p460-roque/",
  abstract =     "In this short application report the authors discuss
                 qualitative reasoning about physical processes under
                 the framework of dimensional analysis. The symbolic
                 system QDR-Qualitative Dimensional Reasoner-has been
                 developed to automate the whole qualitative reasoning
                 analysis.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1230 (Artificial intelligence)",
  keywords =     "algorithms; Computer algebra; Dimensional analysis;
                 languages; Physical processes; Qualitative reasoning;
                 Reasoning; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics. {\bf I.1.4} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Special-purpose
                 algebraic systems.",
  thesaurus =    "Inference mechanisms; Symbol manipulation",
}

@InProceedings{Rudenko:1991:ACA,
  author =       "V. M. Rudenko and V. V. Leonov and A. F. Bragazin and
                 I. P. Shmyglevsky",
  title =        "Application of computer algebra to the investigation
                 of the orbital satellite motion",
  crossref =     "Watt:1991:IPI",
  pages =        "450--451",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p450-rudenko/",
  abstract =     "Presents the features of a program package
                 `Polymech-symbol' helping to solve some laborious
                 mechanical problems. The package was written by means
                 of the REDUCE system and contains several algorithms in
                 a form of REDUCE procedures. The authors consider the
                 problems of navigation and center of mass motion on
                 board a satellite.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Problems of Mech., Acad. of Sci., Moscow,
                 USSR",
  classification = "C7460 (Aerospace engineering)",
  keywords =     "algorithms; Center of mass motion; Computer algebra;
                 Navigation; Orbital satellite motion; Polymech-symbol;
                 REDUCE system",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf J.2}
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Aerospace.",
  thesaurus =    "Aerospace computing; Artificial satellites; Symbol
                 manipulation",
}

@InProceedings{Rybowicz:1991:ACI,
  author =       "Marc Rybowicz",
  title =        "An algorithm for computing integral bases of an
                 algebraic function field",
  crossref =     "Watt:1991:IPI",
  pages =        "157--166",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p157-rybowicz/",
  abstract =     "The author presents a new algorithm for function
                 fields which borrows techniques from previous methods
                 and works in any characteristic. Theorem 5 allows one
                 to reduce the problem to the factorization of rational
                 primes via some standard linear algebra techniques. He,
                 in turn, reduces this factorization problem to study
                 how two branches of the underlying curve intersect.
                 This latter task is achieved with the help of the
                 `Hamburger--Noether Development', a special type of
                 local parametrization. He expects the algorithm to be
                 more efficient than Zassenhaus' global approach and to
                 highlight the classical local approach. Moreover, the
                 techniques presented allow one to build a function with
                 specified zeros in any characteristic and could be
                 applied to other problems. Although the algorithm is
                 complete, some steps clearly need to be improved and
                 studied more carefully before attempting any
                 implementation. In particular, he assumes that the
                 constant field is algebraically closed, but a
                 `rational' extension of the algorithm would be
                 welcome.",
  acknowledgement = ack-nhfb,
  affiliation =  "Symbolic Comput. Group, Waterloo Univ., Ont., Canada",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C7310 (Mathematics)",
  keywords =     "Algebraic function field; algorithms; Factorization;
                 Hamburger--Noether Development; Integral bases; Linear
                 algebra; Local parametrization; Rational primes",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Group theory; Mathematics computing; Number theory;
                 Symbol manipulation",
}

@InProceedings{Schlegel:1991:DRS,
  author =       "H. Schlegel",
  title =        "Determination of the root system of semisimple {Lie}
                 algebras from the {Dynkin} diagram",
  crossref =     "Watt:1991:IPI",
  pages =        "239--240",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p239-schlegel/",
  abstract =     "One way to represent the properties of the Lie algebra
                 for calculations is by means of the commutation
                 relations, i.e. the structure constants. The paper
                 shows a way of the calculation of the Cartan--Weyl
                 basis for all simple Lie algebras starting from the
                 Dynkin diagram. The package DYNKIN written in REDUCE
                 implements the described relations and can as an
                 application be used to perform the calculations for a
                 specified Lie algebra.",
  acknowledgement = ack-nhfb,
  affiliation =  "Zentralinstitut fur Elektronenphys., Berlin, Germany",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "algorithms; Cartan--Weyl basis; Commutation relations;
                 Dynkin diagram; Root system; Semisimple Lie algebras;
                 Simple Lie algebras; Structure constants",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
  thesaurus =    "Algebra; Diagrams; Mathematics computing",
}

@InProceedings{Schmitt:1991:EAA,
  author =       "Joacheim Schmitt",
  title =        "An embedding algorithm for algebraic congruence
                 function fields",
  crossref =     "Watt:1991:IPI",
  pages =        "187--188",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p187-schmitt/",
  abstract =     "Provides an analogue of the Round 4 algorithm of
                 Ford/Zassenhaus (1978) for algebraic congruence
                 function fields. The reduction steps can also be used
                 in other embedding algorithms. The algorithm is
                 implemented within the computer algebra system SIMATH.
                 The corresponding programs are written in C. The
                 results can be used in integration and cryptography.",
  acknowledgement = ack-nhfb,
  affiliation =  "Saarlandes Univ., Saarbrucken, Germany",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
  keywords =     "Algebraic congruence function fields; algorithms;
                 Computer algebra system; Cryptography; Embedding
                 algorithms; Integration; Round 4 algorithm; SIMATH",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Number theory",
}

@InProceedings{Schonhage:1991:FRC,
  author =       "Arnold Sch{\"o}nhage",
  title =        "Fast reduction and composition of binary quadratic
                 forms",
  crossref =     "Watt:1991:IPI",
  pages =        "128--133",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p128-schonhage/",
  abstract =     "Similar to the fast computation of integer gcd's,
                 reduction of binary quadratic forms $ax^2+bxy+cy^2$
                 with integral coefficients $a, b, c$ bounded by $2^n$
                 is possible in time $O (\mu (n) \log{}n)$, where
                 $\mu(n)$ is a time bound for $n$-bit integer
                 multiplication. This result is obtained by a
                 corresponding algorithm for the monotone reduction of
                 positive forms. The same time bound holds for the
                 composition of forms. Moreover, finding a reduced form
                 is shown to be at least as difficult as extended gcd
                 computation, up to terms of order $\mu (n)$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Bonn Univ., Germany",
  classification = "C1160 (Combinatorial mathematics); C4240
                 (Programming and algorithm theory)",
  keywords =     "algorithms; Binary quadratic forms; Integer
                 multiplication; Integral coefficients; Monotone
                 reduction; Positive forms; Time bound",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation.",
  thesaurus =    "Computational complexity; Number theory",
}

@InProceedings{Schulze-Pillot:1991:ACG,
  author =       "Rainer Schulze-Pillot",
  title =        "An algorithm for computing genera of ternary and
                 quaternary quadratic forms",
  crossref =     "Watt:1991:IPI",
  pages =        "134--143",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p134-schulze-pillot/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms.",
}

@InProceedings{SchulzePillot:1991:ACG,
  author =       "R. Schulze-Pillot",
  title =        "An algorithm for computing genera of ternary and
                 quaternary quadratic forms",
  crossref =     "Watt:1991:IPI",
  pages =        "134--143",
  year =         "1991",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The paper reports on an algorithm for computing genera
                 of ternary and quaternary positive definite quadratic
                 forms over Z. It is well known that due to the simple
                 shape of the reduction conditions in these dimensions
                 it is in principle no problem to compute
                 representatives of all classes of such quadratic forms
                 whose discriminant is below a given bound. It is,
                 however, sometimes desirable to be able to quickly
                 determine representatives of all classes in some fixed
                 genus of quadratic forms of possibly high discriminant
                 without having to generate along the way all forms of
                 smaller discriminant. An obvious attempt in such a case
                 is to use Kneser's method of neighbouring or adjacent
                 lattices. The paper draws attention to the fact that it
                 is indeed not difficult to use this method in
                 dimensions 3 and 4 as the basis of an algorithm that
                 serves the purpose. With almost no extra work one
                 obtains at the same time the adjacency graph of the
                 classes determined; this has interesting arithmetic and
                 graph theoretic applications. It is intended to use the
                 algorithm for the experimental investigation of the
                 Fourier and Fourier--Jacobi coefficients of certain
                 linear combinations of Siegel $\theta$ series of
                 quaternary quadratic forms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fakultat fur Math., Bielefeld Univ., Germany",
  classification = "C1160 (Combinatorial mathematics)",
  keywords =     "Adjacency graph; Adjacent lattices; Discriminant;
                 Fourier--Jacobi coefficients; Genera; Linear
                 combinations; Neighbouring lattices; Quaternary
                 positive definite quadratic forms; Reduction
                 conditions; Siegel $\theta$ series; Ternary positive
                 definite quadratic forms",
  thesaurus =    "Number theory",
}

@InProceedings{Schwarz:1991:ETP,
  author =       "Fritz Schwarz",
  title =        "Existence theorems for polynomial first integrals",
  crossref =     "Watt:1991:IPI",
  pages =        "256--264",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p256-schwarz/",
  abstract =     "In various areas of applied mathematics there occur
                 autonomous systems of ordinary differential equations
                 of the form $x_i= \omega _i(x,c), i=1,\ldots{}n$ where
                 the right hand sides are polynomial in all arguments
                 $x=(x_1,\ldots{}x_n)$ and $c=(c_1,c_2,\ldots{})$; the
                 latter variables are parameters which are a priori
                 unspecified. There arises the following question: Do
                 first integrals of a certain type, e.g. polynomial
                 first integrals? The computer algebra package DYNSYS
                 allows one to find all polynomial first integrals up to
                 a given highest degree $D$ but does not provide any
                 information beyond $D$. To obtain a complete answer
                 these packages should be complemented by rigorous
                 results concerning the possible existence of first
                 integrals of any degree. Theorems of this kind are
                 obtained. The basic principle for obtaining them is to
                 identify subsystems of the determining system which
                 have a certain structure independent of $D$. This
                 method is applied to several two- and three-dimensional
                 systems. It is shown for example that the famous Lorenz
                 system in general does not allow any polynomial first
                 integrals. Furthermore some ideas are presented on how
                 these methods may be converted into algorithms such
                 that a machine may perform the necessary analysis.",
  acknowledgement = ack-nhfb,
  affiliation =  "GMD, Inst. F1, St. Augustin, Germany",
  classification = "C1120 (Analysis); C4170 (Differential equations);
                 C4180 (Integral equations)",
  keywords =     "algorithms; Applied mathematics; Autonomous systems;
                 Computer algebra package; DYNSYS; Lorenz system;
                 Ordinary differential equations; Polynomial first
                 integrals; theory; Three-dimensional systems",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Special-purpose algebraic
                 systems.",
  thesaurus =    "Differential equations; Integral equations;
                 Polynomials",
}

@InProceedings{Shoup:1991:FDA,
  author =       "Victor Shoup",
  title =        "A fast deterministic algorithm for factoring
                 polynomials over finite fields of small
                 characteristic",
  crossref =     "Watt:1991:IPI",
  pages =        "14--21",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p14-shoup/",
  abstract =     "Presents a new algorithm for factoring polynomials
                 over finite fields. The algorithm is deterministic, and
                 its running time is `almost' quadratic when the
                 characteristic is a small fixed prime. As such, the
                 algorithm is asymptotically faster than previously
                 known deterministic algorithms for factoring
                 polynomials over finite fields of small
                 characteristic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Toronto Univ., Toronto, Ont.,
                 Canada",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Deterministic algorithm; Finite fields;
                 Polynomial factorisation; Small characteristic; Small
                 fixed prime; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields.",
  thesaurus =    "Computational complexity; Polynomials",
}

@InProceedings{Sit:1991:TPL,
  author =       "William Y. Sit",
  title =        "A theory for parametric linear systems",
  crossref =     "Watt:1991:IPI",
  pages =        "112--121",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p112-sit/",
  abstract =     "Presents a theoretical foundation for studying
                 parametric systems of linear equations and proves an
                 efficient algorithm for identifying all parametric
                 values (including degenerate cases) for which the
                 system is consistent. The algorithm gives a small set
                 of regimes where for each regime, the solutions of the
                 specialized systems may be given uniformly. For
                 homogeneous systems, or for systems where the right
                 hand side is arbitrary, this small set is irredundant.
                 A complexity analysis of the Gaussian elimination
                 method is given and compared with the algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., City Coll. of New York, NY, USA",
  classification = "C4140 (Linear algebra); C4240 (Programming and
                 algorithm theory)",
  keywords =     "algorithms; Complexity analysis; Degenerate cases;
                 Gaussian elimination; Homogeneous systems; Linear
                 equations; Parametric systems; Parametric values;
                 Regimes; Right hand side; Specialized systems; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
                 systems (direct and iterative methods).",
  thesaurus =    "Computational complexity; Linear algebra",
}

@InProceedings{Stein:1991:ADR,
  author =       "Andreas Stein and Horst G{\"u}nter Zimmer",
  title =        "An algorithm for determining the regulator and the
                 fundamental unit of a hyperelliptic congruence function
                 field",
  crossref =     "Watt:1991:IPI",
  pages =        "183--184",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p183-stein/",
  abstract =     "A continued fraction algorithm (baby steps) is
                 described by B. Weis, H. G. Zimmer (Mitt. Math. Ges:
                 Hamburg, 1991) for determining the regulator and the
                 fundamental unit of the congruence function field $K/k$
                 with respect to the indeterminate $X$. The algorithm is
                 based on work of Artin (Math Z vol. 19, p. 153--246,
                 1924) and was implemented within the computer algebra
                 system SIMATH. The authors show how the algorithm can
                 be substantially improved by applying to the function
                 field case D. Shanks' (1972) idea of the infrastructure
                 of a real quadratic number field. The improved version
                 of this algorithm has been implemented within the
                 computer algebra system SIMATH, too.",
  acknowledgement = ack-nhfb,
  affiliation =  "Saarlandes Univ., Saarbrucken, Germany",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C7310 (Mathematics)",
  keywords =     "algorithms; Baby steps; Computer algebra system;
                 Congruence function field; Continued fraction
                 algorithm; Function field; Fundamental unit;
                 Hyperelliptic congruence function field; Indeterminate;
                 Real quadratic number field; Regulator; SIMATH",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Algebra; Number theory; Symbol manipulation",
}

@InProceedings{Surguladze:1991:APC,
  author =       "Levan R. Surguladze and Mark A. Samuel",
  title =        "Algebraic perturbative calculations in high energy
                 physics. {Methods}, algorithms, computer programs and
                 physical applications",
  crossref =     "Watt:1991:IPI",
  pages =        "439--447",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p439-surguladze/",
  abstract =     "The methods and algorithms for high order algebraic
                 perturbative calculations in theoretical high energy
                 physics are briefly reviewed. The SCHOONSCHIP program
                 MINCER and the REDUCE program LOOPS for analytical
                 computation of arbitrary massless, one-, two- and
                 three-loop Feynman diagrams of the propagator type are
                 described. The version of the program LOOPS for
                 personal computers and the extended version of the
                 program MINCER for four-loop renormalization group
                 calculations are presented. The new program for
                 algebraic perturbative calculations is also discussed.
                 This program is written on the new algebraic
                 programming system FORM. Some recent results of
                 application to the high energy physics are given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Nucl. Res., Acad. of Sci., Moscow, USSR",
  classification = "A0270 (Computational techniques); A1110G
                 (Renormalization); C7320 (Physics and Chemistry)",
  keywords =     "Algebraic perturbative calculations; algorithms;
                 Feynman diagrams; High energy physics; LOOPS; MINCER;
                 REDUCE; SCHOONSCHIP program",
  subject =      "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General. {\bf I.1.2} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.4} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE.",
  thesaurus =    "Feynman diagrams; Physics computing; Renormalisation;
                 Symbol manipulation",
}

@InProceedings{Trenkov:1991:ARS,
  author =       "I. Trenkov and M. Spiridonova and M. Daskalova",
  title =        "An application of the {REDUCE} system for solving a
                 mathematical geodesy problem",
  crossref =     "Watt:1991:IPI",
  pages =        "448--449",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p448-trenkov/",
  abstract =     "A REDUCE program package for solving some mathematical
                 geodesy problems now under development includes
                 capabilities for solving the problem: the geographical
                 coordinates (the geographical density $B_p$ and the
                 geographical longitude $L_p$) of a point $P$ on the
                 earthly ellipsoid are to be calculated when $n$
                 different points $C_i(i=1, 2, \ldots{}, n)$ with their
                 geographical coordinates $B_i$ and $L_i$ are given and
                 the azimuths $A_{ip}$ in all points $C_i$ to the point
                 $P$ are measured.",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Lab. for Geodesy, Bulgarian Acad. of Sci.,
                 Sofia, Bulgaria",
  classification = "A9110B (Mathematical geodesy: general theory); C7310
                 (Mathematics); C7340 (Geophysics)",
  keywords =     "algorithms; Geographical coordinates; Mathematical
                 geodesy; Program package; REDUCE system",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf J.2}
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics. {\bf J.2}
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Earth and atmospheric sciences.",
  thesaurus =    "Computational geometry; Geodesy; Geophysics computing;
                 Symbol manipulation",
}

@InProceedings{Trevisan:1991:PFU,
  author =       "Vilmar Trevisan and Paul Wang",
  title =        "Practical factorization of univariate polynomials over
                 finite fields",
  crossref =     "Watt:1991:IPI",
  pages =        "22--31",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p22-trevisan/",
  abstract =     "The research presented is part of an effort to
                 establish state-of-the-art factoring routines for
                 polynomials. The foundation of such algorithms lies in
                 the efficient factorization over a finite field
                 $\mbox{GF}(p^k)$. The Cantor--Zassenhaus algorithm
                 together with innovative ideas suggested by others is
                 compared with the Berlekamp algorithm. The studies led
                 to the design of a hybrid algorithm that combines the
                 strengths of the different approaches. The algorithms
                 are also implemented and machine timings are obtained
                 to measure the performance of these algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
                 USA",
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Berlekamp algorithm; Cantor--Zassenhaus
                 algorithm; Factoring routines; Factorization; Finite
                 fields; Hybrid algorithm; performance; Univariate
                 polynomials",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations in finite fields.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms.",
  thesaurus =    "Computational complexity; Polynomials",
}

@InProceedings{Vinette:1991:FSC,
  author =       "F. Vinette",
  title =        "Features of symbolic computation exploited in the
                 calculation of lower energy bounds of cyclic polyene
                 models",
  crossref =     "Watt:1991:IPI",
  pages =        "458--459",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p458-vinette/",
  abstract =     "Symbolic computation has been applied in many
                 scientific disciplines and has proved to be a very
                 valuable research tool. In earlier studies, features of
                 symbolic computation including algebraic manipulations
                 and high decimal precision, were shown to be very
                 useful to solve nonrelativistic quantum mechanical
                 problems. The author illustrates the valuable
                 assistance of symbolic computation in solving quantum
                 chemical problems. The symbolic computational language
                 MAPLE is used throughout this study. The computational
                 aspects of the application of Lowdin's Optimized Inner
                 Projection (OIP) to determine lower bounds to the
                 ground state energy of the Pariser--Parr--Pople (PPP)
                 model of cyclic polyenes, is briefly presented. A
                 diagrammatic approach for evaluating the required
                 matrix elements is needed: this method is often used in
                 quantum chemistry. The evaluation of Brandow diagrams,
                 which is very tedious and almost impossible to do by
                 hand, is easily obtained using MAPLE.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Stat., York Univ., North York,
                 Ont., Canada",
  classification = "A3115 (General mathematical and computational
                 developments); A3120 (Specific calculations and
                 results); C7320 (Physics and Chemistry)",
  keywords =     "algorithms; Brandow diagrams; Cyclic polyene models;
                 Ground state energy; languages; Lower energy bounds;
                 MAPLE; Optimized Inner Projection;
                 Pariser--Parr--Pople; Quantum chemical problems;
                 Symbolic computation",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Chemistry. {\bf I.1.4} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN.",
  thesaurus =    "Chemistry computing; Molecular energy level
                 calculations; Organic compounds; Quantum chemistry;
                 Symbol manipulation",
}

@InProceedings{Wang:1991:TMI,
  author =       "Dongming Wang",
  title =        "A toolkit for manipulating indefinite summations with
                 application to neural networks",
  crossref =     "Watt:1991:IPI",
  pages =        "462--463",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p462-wang/",
  abstract =     "Presents the design of some rules and the
                 implementation of an application-oriented toolkit in
                 Macsyma by amending some of its incorrect computations
                 for the manipulation of indefinite summations. The
                 application of this toolkit to the analysis and
                 derivation of neural networks is briefly discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C6115 (Programming support); C6170 (Expert
                 systems)",
  keywords =     "algorithms; Application-oriented toolkit; design;
                 Indefinite summations; Macsyma; Neural networks",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.4}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Applications. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA. {\bf I.2.6} Computing
                 Methodologies, ARTIFICIAL INTELLIGENCE, Learning,
                 Connectionism and neural nets.",
  thesaurus =    "Neural nets; Software tools; Symbol manipulation",
}

@InProceedings{Weibel:1991:AP,
  author =       "Trudy Weibel and Gaston H. Gonnet",
  title =        "An algebra of properties",
  crossref =     "Watt:1991:IPI",
  pages =        "352--359",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p352-weibel/",
  abstract =     "The purpose of the paper is to build a framework and
                 give algorithms to solve queries of the form obj in
                 Prop where the object obj is expressible in terms of
                 other given objects. The authors develop an algebra of
                 properties, PROP, in which we carry out computations.
                 They present a set of rules (axioms Ax1-Ax7) for the
                 behaviour of the basic functions on properties. In
                 addition, they represent the algorithmic components
                 such as if and while by the algebra operations meet and
                 join. They conclude by proposing an implementation of
                 the algebra PROP.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Theor. Comput. Sci., Zurich, Switzerland",
  classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
  keywords =     "Algebra; Algebra of properties; Algorithmic
                 components; algorithms; PROP",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf G.2.m}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous.",
  thesaurus =    "Symbol manipulation",
}

@InProceedings{Yakubovich:1991:EIS,
  author =       "S. B. Yakubovich and Yu. F. Luchko",
  title =        "The evaluation of integrals and series with respect to
                 indices (parameters) of hypergeometric functions",
  crossref =     "Watt:1991:IPI",
  pages =        "271--280",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p271-yakubovich/",
  abstract =     "A general method for the evaluation of some integrals
                 of hypergeometric functions, and programming package,
                 which works on the basis of this method, were described
                 in Adamchik, Luchko, Marichev (1990). But many
                 integrals which have appeared in practice don't belong
                 to the class of convolution type integrals and,
                 consequently, one can't use the previous method for the
                 evaluation of such integrals. In particular, one needs
                 original methods for the evaluation of integrals and
                 series with respect to indices of special functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Byelorussian State Univ., Minsk, Byelorussian SSR,
                 USSR",
  classification = "C4160 (Numerical integration and differentiation)",
  keywords =     "algorithms; Evaluation of integrals; Hypergeometric
                 functions; Indices; Integrals; Special functions;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations.",
  thesaurus =    "Integration; Series [mathematics]",
}

@InProceedings{Ziel:1991:RFD,
  author =       "Richard Ziel",
  title =        "Rational function decomposition",
  crossref =     "Watt:1991:IPI",
  pages =        "1--6",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p1-zippel/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}

@InProceedings{Zippel:1991:RFD,
  author =       "R. Zippel",
  title =        "Rational function decomposition",
  crossref =     "Watt:1991:IPI",
  pages =        "1--6",
  year =         "1991",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Presents a polynomial time algorithm for determining
                 whether a given univariate rational function over an
                 arbitrary field is the composition of two rational
                 functions over that field, and finds them if so.",
  acknowledgement = ack-nhfb,
  affiliation =  "Cornell Univ., Ithaca, NY, USA",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "Arbitrary field; Polynomial time algorithm; Univariate
                 rational function",
  thesaurus =    "Polynomials",
}

@InProceedings{Zolotykh:1991:PCS,
  author =       "A. A. Zolotykh",
  title =        "A package for computations in simple {Lie} algebra
                 representations",
  crossref =     "Watt:1991:IPI",
  pages =        "237--238",
  year =         "1991",
  bibdate =      "Thu Mar 12 08:38:03 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p237-zolotykh/",
  abstract =     "The author present a software package for calculations
                 of some numerical characteristics of simple Lie
                 algebras of rank not more than 12 and their irreducible
                 finite-dimensional representations over algebraically
                 closed fields of characteristic zero (for example, over
                 the field of complex numbers). Times of some
                 computations on an IBM PC/AT (processor 286) are given:
                 the times of character computations and times of tensor
                 square computations for the fundamental (basic)
                 representation of exceptional Lie algebras and of
                 12-rank Lie algebras. The table contains also the
                 dimensions of corresponding fundamental
                 representations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Mech. and Math., Moscow State Univ., USSR",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Algebraically closed fields; algorithms; IBM PC/AT;
                 Irreducible finite-dimensional representations;
                 Numerical characteristics; Simple Lie algebra
                 representations; Tensor square computations; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Special-purpose
                 algebraic systems.",
  thesaurus =    "Algebra; Mathematics computing; Microcomputer
                 applications",
  xxtitle =      "A package for computation in simple {Lie} algebra
                 representations",
}

@InProceedings{Bischof:1992:AAD,
  author =       "Christian Bischof and Alan Carle and George Corliss
                 and Andreas Griewank",
  title =        "{ADIFOR}: {Automatic} differentiation in a source
                 translator environment",
  crossref =     "Wang:1992:PII",
  pages =        "294--302",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p294-bischof/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; experimentation; languages",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.6}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Gradient methods. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems.",
}

@InProceedings{Bronstein:1992:LOD,
  author =       "Manuel Bronstein",
  title =        "Linear ordinary differential equations: breaking
                 through the order 2 barrier",
  crossref =     "Wang:1992:PII",
  pages =        "42--48",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 Theory/cathode.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p42-bronstein/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
}

@InProceedings{Burnel:1992:CCY,
  author =       "A. Burnel and H. Caprasse",
  title =        "The computation of $1$-loop contributions in {Y.M.}
                 theories with class {III} nonrelativistic gauges and
                 {REDUCE}",
  crossref =     "Wang:1992:PII",
  pages =        "103--107",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p103-burnel/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; Yang--Mills",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms.",
}

@InProceedings{Butler:1992:ECA,
  author =       "Greg Butler",
  title =        "Experimental comparison of algorithms for {Sylow}
                 subgroups",
  crossref =     "Wang:1992:PII",
  pages =        "251--262",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p251-butler/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.2.m}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous.",
}

@InProceedings{Cetinkaya:1992:SAL,
  author =       "Cetin Cetinkaya",
  title =        "On stability analysis of linear stochastic and
                 time-varying deterministic systems",
  crossref =     "Wang:1992:PII",
  pages =        "278--283",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p278-cetinkaya/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Eigenvalues and eigenvectors (direct
                 and iterative methods). {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@InProceedings{Codutti:1992:NNL,
  author =       "M. Codutti",
  title =        "{NODES}: non linear ordinary differential equations
                 solver",
  crossref =     "Wang:1992:PII",
  pages =        "69--79",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 Theory/cathode.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p69-codutti/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@InProceedings{Collins:1992:EAI,
  author =       "George E. Collins and Werner Krandick",
  title =        "An efficient algorithm for infallible polynomial
                 complex root isolation",
  crossref =     "Wang:1992:PII",
  pages =        "189--194",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p189-collins/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
}

@InProceedings{Cook:1992:CGA,
  author =       "Grant O. {Cook, Jr.}",
  title =        "Code generation in {ALPAL} using symbolic techniques",
  crossref =     "Wang:1992:PII",
  pages =        "27--35",
  year =         "1992",
  DOI =          "https://doi.org/10.1145/143242.143260",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p27-cook/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
                 Language Classifications, C. {\bf G.1.6} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization. {\bf
                 D.3.4} Software, PROGRAMMING LANGUAGES, Processors,
                 Code generation.",
}

@InProceedings{Cooperman:1992:FCB,
  author =       "Gene Cooperman and Larry Finkelstein",
  title =        "A fast cyclic base change for permutation groups",
  crossref =     "Wang:1992:PII",
  pages =        "224--232",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p224-cooperman/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.2.2}
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Trees. {\bf G.3} Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Probabilistic algorithms
                 (including Monte Carlo).",
}

@InProceedings{Crouch:1992:ECI,
  author =       "P. E. Crouch and R. L. Grossman",
  title =        "The explicit computation of integration algorithms and
                 first integrals for ordinary differential equations
                 with polynomial coefficients using trees",
  crossref =     "Wang:1992:PII",
  pages =        "89--94",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p89-crouch/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.2.2}
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Trees. {\bf G.1.7} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms.",
}

@InProceedings{Dalmas:1992:PFL,
  author =       "St{\'e}phane Dalmas",
  title =        "A polymorphic functional language applied to symbolic
                 computation",
  crossref =     "Wang:1992:PII",
  pages =        "369--375",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p369-dalmas/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; languages",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf F.3.3} Theory
                 of Computation, LOGICS AND MEANINGS OF PROGRAMS,
                 Studies of Program Constructs, Type structure. {\bf
                 F.3.3} Theory of Computation, LOGICS AND MEANINGS OF
                 PROGRAMS, Studies of Program Constructs, Functional
                 constructs. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, SCRATCHPAD.",
}

@InProceedings{Davenport:1992:PTR,
  author =       "J. H. Davenport",
  title =        "Primality testing revisited",
  crossref =     "Wang:1992:PII",
  pages =        "123--129",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p123-davenport/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations.",
}

@InProceedings{Dewar:1992:UCA,
  author =       "Michael C. Dewar",
  title =        "Using computer algebra to select numerical
                 algorithms",
  crossref =     "Wang:1992:PII",
  pages =        "1--8",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p1-dewar/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE.",
}

@InProceedings{Fateman:1992:HPG,
  author =       "Richard Fateman",
  title =        "Honest plotting, global extrema, and interval
                 arithmetic",
  crossref =     "Wang:1992:PII",
  pages =        "216--223",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p216-fateman/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.2.2} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.",
}

@InProceedings{Ganzha:1992:NSA,
  author =       "V. G. Ganzha and E. V. Vorozhtsov and J. A. {van
                 Hulzen}",
  title =        "A new symbolic-numeric approach to stability analysis
                 of difference schemes",
  crossref =     "Wang:1992:PII",
  pages =        "9--15",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p9-ganzha/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.4}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation, Finite
                 difference methods. {\bf D.3.2} Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE.",
}

@InProceedings{Gao:1992:SPA,
  author =       "Xiao-Shan Gao and Shang-Ching Chou",
  title =        "Solving parametric algebraic systems",
  crossref =     "Wang:1992:PII",
  pages =        "335--341",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p335-gao/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
}

@InProceedings{Geddes:1992:HSI,
  author =       "K. O. Geddes and G. J. Fee",
  title =        "Hybrid symbolic-numeric integration in {MAPLE}",
  crossref =     "Wang:1992:PII",
  pages =        "36--41",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p36-geddes/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@InProceedings{Gil:1992:CJC,
  author =       "Isabelle Gil",
  title =        "Computation of the {Jordan} canonical form of a square
                 matrix (using the {Axiom} programming language)",
  crossref =     "Wang:1992:PII",
  pages =        "138--145",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p138-gil/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Eigenvalues and eigenvectors (direct
                 and iterative methods). {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
}

@InProceedings{Grigoriev:1992:ESP,
  author =       "Dima Y. u. Grigoriev and Marek Karpinski and Andrew M.
                 Odlyzko",
  title =        "Existence of short proofs for nondivisibility of
                 sparse polynomials under the extended {Riemann}
                 hypothesis",
  crossref =     "Wang:1992:PII",
  pages =        "117--122",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p117-grigoriev/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms. {\bf
                 I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Representations (general and polynomial).",
}

@InProceedings{Gutierrez:1992:PIT,
  author =       "Jaime Gutierrez and Tomas Recio",
  title =        "A practical implementation of two rational function
                 decomposition algorithms",
  crossref =     "Wang:1992:PII",
  pages =        "152--157",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p152-gutierrez/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
}

@InProceedings{Hietarinta:1992:SCQ,
  author =       "Jarmo Hietarinta",
  title =        "Solving the constant quantum {Yang--Baxter} equation
                 in $2$ dimensions with massive use of factorizing
                 {Gr{\"o}bner} basis computations",
  crossref =     "Wang:1992:PII",
  pages =        "350--357",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p350-hietarinta/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices.",
}

@InProceedings{Hong:1992:SSF,
  author =       "Hoon Hong",
  title =        "Simple solution formula construction in cylindrical
                 algebraic decomposition based quantifier elimination",
  crossref =     "Wang:1992:PII",
  pages =        "177--188",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p177-hong/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.4} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications.",
}

@InProceedings{Johnson:1992:RAN,
  author =       "J. R. Johnson",
  title =        "Real algebraic number computation using interval
                 arithmetic",
  crossref =     "Wang:1992:PII",
  pages =        "195--205",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p195-johnson/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
}

@InProceedings{Kajler:1992:CPE,
  author =       "Norbert Kajler",
  title =        "{CAS\slash PI}: a portable and extensible interface
                 for computer algebra systems",
  crossref =     "Wang:1992:PII",
  pages =        "376--386",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p376-kajler/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; languages",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 H.5.2} Information Systems, INFORMATION INTERFACES AND
                 PRESENTATION, User Interfaces. {\bf D.2.2} Software,
                 SOFTWARE ENGINEERING, Design Tools and Techniques, User
                 interfaces. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}

@InProceedings{Kaltofen:1992:CDM,
  author =       "Erich Kaltofen",
  title =        "On computing determinants of matrices without
                 divisions",
  crossref =     "Wang:1992:PII",
  pages =        "342--349",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p342-kaltofen/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
}

@InProceedings{Kirrinnis:1992:FCN,
  author =       "Peter Kirrinnis",
  title =        "Fast computation of numerical partial fraction
                 decompositions and contour integrals of rational
                 functions",
  crossref =     "Wang:1992:PII",
  pages =        "16--26",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p16-kirrinnis/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@InProceedings{Kuhn:1992:CPS,
  author =       "Norbert Kuhn and Klaus Madlener and Friedrich Otto",
  title =        "Computing presentations for subgroups of context-free
                 groups",
  crossref =     "Wang:1992:PII",
  pages =        "240--250",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p240-kuhn/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Grammars and Other Rewriting Systems, Decision
                 problems. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes.",
}

@InProceedings{Lamagna:1992:DUI,
  author =       "Edmund A. Lamagna and Michael B. Hayden and Catherine
                 W. Johnson",
  title =        "The design of a user interface to a computer algebra
                 system for introductory calculus",
  crossref =     "Wang:1992:PII",
  pages =        "358--368",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p358-lamagna/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; human factors",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple. {\bf H.5.2} Information
                 Systems, INFORMATION INTERFACES AND PRESENTATION, User
                 Interfaces, Interaction styles. {\bf H.5.2} Information
                 Systems, INFORMATION INTERFACES AND PRESENTATION, User
                 Interfaces, Input devices and strategies.",
}

@InProceedings{Lempken:1992:SPS,
  author =       "W. Lempken and R. Staszewski",
  title =        "The structure of the {PIMs} of {SL(3,4)} in
                 characteristic 2",
  crossref =     "Wang:1992:PII",
  pages =        "233--239",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p233-lempken/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Representations
                 (general and polynomial).",
}

@InProceedings{Manocha:1992:MRL,
  author =       "Dinesh Manocha and John F. Canny",
  title =        "Multipolynomial resultants and linear algebra",
  crossref =     "Wang:1992:PII",
  pages =        "158--167",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p158-manocha/",
  acknowledgement = ack-nhfb,
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Sparse, structured, and very
                 large systems (direct and iterative methods). {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
}

@InProceedings{Marinuzzi:1992:LNS,
  author =       "Francesco Marinuzzi and Stefano Soliani",
  title =        "{LISA}: {A} new symbolic package for the definition,
                 analysis and resolution of {Markovian} processes:
                 symbolic and inductive techniques",
  crossref =     "Wang:1992:PII",
  pages =        "303--311",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p303-marinuzzi/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
                 Computation, Parallelism and concurrency. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, LISP. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic.",
}

@InProceedings{Moller:1992:GBC,
  author =       "H. Michael M{\"o}ller and Teo Mora and Carlo
                 Traverso",
  title =        "Gr{\"o}bner bases computation using syzygies",
  crossref =     "Wang:1992:PII",
  pages =        "320--328",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p320-moller/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Simplification of expressions. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
}

@InProceedings{Morain:1992:ENE,
  author =       "F. Morain",
  title =        "Easy numbers for the elliptic curve primality proving
                 algorithm",
  crossref =     "Wang:1992:PII",
  pages =        "263--268",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p263-morain/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf G.2.m} Mathematics of
                 Computing, DISCRETE MATHEMATICS, Miscellaneous.",
}

@InProceedings{Mutrie:1992:AFE,
  author =       "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
                 Char",
  title =        "An approach for floating-point error analysis using
                 computer algebra",
  crossref =     "Wang:1992:PII",
  pages =        "284--293",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple. {\bf G.2.2} Mathematics
                 of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
                 algorithms.",
}

@InProceedings{Noro:1992:RCA,
  author =       "Masayuki Noro and Taku Takeshima",
  title =        "{Risa\slash Asir} --- a computer algebra system",
  crossref =     "Wang:1992:PII",
  pages =        "387--396",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p387-noro/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms. {\bf D.2.5} Software,
                 SOFTWARE ENGINEERING, Testing and Debugging, Debugging
                 aids.",
}

@InProceedings{Painter:1992:MES,
  author =       "Jeffrey F. Painter",
  title =        "The matrix editor for symbolic {Jacobians} in
                 {ALPAL}",
  crossref =     "Wang:1992:PII",
  pages =        "312--319",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p312-painter/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, MACSYMA.",
}

@InProceedings{Reid:1992:ADC,
  author =       "G. J. Reid and I. G. Lisle and A. Boulton and A. D.
                 Wittkopf",
  title =        "Algorithmic determination of commutation relations for
                 {Lie} symmetry algebras of {PDEs}",
  crossref =     "Wang:1992:PII",
  pages =        "63--68",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 Theory/cathode.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p63-reid/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}

@InProceedings{Richardson:1992:ECP,
  author =       "Daniel Richardson",
  title =        "The elementary constant problem",
  crossref =     "Wang:1992:PII",
  pages =        "108--116",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p108-richardson/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
}

@InProceedings{Rioboo:1992:RAC,
  author =       "Renaud Rioboo",
  title =        "Real algebraic closure of an ordered field:
                 implementation in {Axiom}",
  crossref =     "Wang:1992:PII",
  pages =        "206--215",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p206-rioboo/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Representations (general and polynomial).",
}

@InProceedings{Russo:1992:CSA,
  author =       "Mark F. Russo",
  title =        "A combined symbolic\slash numeric approach for the
                 integration of stiff nonlinear systems of {ODE}'s",
  crossref =     "Wang:1992:PII",
  pages =        "80--88",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p80-russo/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear
                 approximation.",
}

@InProceedings{Salvy:1992:AEF,
  author =       "Bruno Salvy and John Shackell",
  title =        "Asymptotic expansions of functional inverses",
  crossref =     "Wang:1992:PII",
  pages =        "130--137",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p130-salvy/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Analysis of algorithms.",
}

@InProceedings{Schwarz:1992:RCA,
  author =       "Fritz Schwarz",
  title =        "Reduction and completion algorithms for partial
                 differential equations",
  crossref =     "Wang:1992:PII",
  pages =        "49--56",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 Theory/cathode.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p49-schwarz/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
}

@InProceedings{Singer:1992:LST,
  author =       "Michael F. Singer and Felix Ulmer",
  title =        "{Liouvillian} solutions of third order linear
                 differential equations: new bounds and necessary
                 conditions",
  crossref =     "Wang:1992:PII",
  pages =        "57--62",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 Theory/cathode.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p57-singer/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}

@InProceedings{Viklund:1992:OLS,
  author =       "Lars Viklund and Peter Fritzson",
  title =        "An object-oriented language for symbolic computation
                 --- applied to machine element analysis",
  crossref =     "Wang:1992:PII",
  pages =        "397--405",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p397-viklund/",
  acknowledgement = ack-nhfb,
  keywords =     "design; languages",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Object-oriented languages. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C++. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
}

@InProceedings{Villard:1992:PLB,
  author =       "Gilles Villard",
  title =        "Parallel lattice basis reduction",
  crossref =     "Wang:1992:PII",
  pages =        "269--277",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p269-villard/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; performance",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
                 Computation, Parallelism and concurrency. {\bf F.4.1}
                 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic. {\bf G.2.m} Mathematics
                 of Computing, DISCRETE MATHEMATICS, Miscellaneous.",
}

@InProceedings{Wang:1992:PUA,
  author =       "Paul S. Wang",
  title =        "Parallel univariate $p$-adic lifting on shared-memory
                 multiprocessors",
  crossref =     "Wang:1992:PII",
  pages =        "168--176",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p168-wang/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
}

@InProceedings{Weispfenning:1992:FGB,
  author =       "V. Weispfenning",
  title =        "Finite {Gr{\"o}bner} bases in {non-Noetherian} skew
                 polynomial rings",
  crossref =     "Wang:1992:PII",
  pages =        "329--334",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p329-weispfenning/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
}

@InProceedings{Weisss:1992:HDP,
  author =       "J{\"u}rgen Weis{\ss}",
  title =        "Homogeneous decomposition of polynomials",
  crossref =     "Wang:1992:PII",
  pages =        "146--151",
  year =         "1992",
  bibdate =      "Wed Feb 06 10:44:34 2002",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p146-weiszlig/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
}

@InProceedings{Ye:1992:SLI,
  author =       "Honglin Ye and Robert M. Corless",
  title =        "Solving linear integral equations in {Maple}",
  crossref =     "Wang:1992:PII",
  pages =        "95--102",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p95-ye/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Nonalgebraic algorithms. {\bf G.1.7} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations.",
}

@InProceedings{Abramov:1993:DS,
  author =       "S. A. Abramov",
  title =        "On {d'Alembert} substitution",
  crossref =     "Bronstein:1993:IPI",
  pages =        "20--26",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p20-abramov/",
  abstract =     "Let some homogeneous linear ordinary differential
                 equation with coefficients in a differential field $F$
                 be given. If we know a nonzero solution $\psi$, then
                 the order of the equation can be reduced by d'Alembert
                 substitution $y= \psi integral \nu dx$, where $\nu$ is
                 a new unknown function. In the situation when
                 $\psi\in{}F$, after d'Alembert substitution an equation
                 with coefficients in $F$ arises again. Let the obtained
                 equation have a nonzero solution $\psi \in F$, then it
                 is possible to reduce the order of the equation again
                 and so on, until an equation without nonzero solutions
                 in $F$ is obtained. If we can find solutions not only
                 in $F$ but in some larger set $L$ as well ($L$ can be a
                 field or a linear space), then we can build up a
                 certain subspace $M$ (d'Alembertian subspace) of the
                 space of all solutions of the original equation. Thus
                 if we have algorithms $A_F$ and $A_L$ to search for the
                 solutions in $F$ and $L$, then by incorporating
                 d'Alembert substitution we can design a more general
                 algorithm (in case $L=F$ we will obtain a more general
                 algorithm than $A_F$). We would like, certainly, to
                 know the kind of solutions that can be found by the new
                 algorithm. The construction of the subspace $M$ is
                 described.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, Russia",
  classification = "C1180 (Optimisation techniques); C4170 (Differential
                 equations); C6130 (Data handling techniques); C7310
                 (Mathematics computing)",
  keywords =     "Alembert substitution; algorithms; Computer algebra
                 algorithms; Differential field; General algorithm;
                 Homogeneous linear ordinary differential equation;
                 Linear space; Nonzero solution; Search problems;
                 Subspace; theory; verification",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Linear differential equations; Search problems; Symbol
                 manipulation",
}

@InProceedings{Abramov:1993:DSP,
  author =       "S. A. Abramov",
  title =        "On {d'Alembert} substitution",
  crossref =     "Bronstein:1993:IPI",
  pages =        "20--26",
  year =         "1993",
  bibdate =      "Thu Sep 26 05:34:21 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ACM; algebraic computation; ISSAC; SIGSAM; symbolic
                 computation",
}

@InProceedings{Abramov:1993:GCD,
  author =       "S. A. Abramov and K. Y. u. Kvashenko",
  title =        "On the greatest common divisor of polynomials which
                 depend on a parameter",
  crossref =     "Bronstein:1993:IPI",
  pages =        "152--156",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p152-abramov/",
  abstract =     "The following computer algebra problem is considered:
                 how to compute the gcd of the polynomials $u(x,a)$ and
                 $v(x,a)$ for various values of the parameter $a$?. This
                 problem appears, for example, in solving systems of
                 algebraic equations by elimination methods, in
                 computing the logarithmic part of the integral of a
                 rational function, in solving difference and
                 differential equations, in summing rational functions,
                 etc. A fast algorithm to solve this problem is
                 described, and some applications of this algorithm are
                 discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, Russia",
  classification = "B0210 (Algebra); B0290F (Interpolation and function
                 approximation); C1110 (Algebra); C4130 (Interpolation
                 and function approximation); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; Algebraic equations;
                 algorithms; Computer algebra problem; Differential
                 equations; Elimination methods; Fast algorithm, ISSAC;
                 Greatest common divisor; languages; Polynomials;
                 Rational function; Rational functions; SIGSAM; symbolic
                 computation; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Babai:1993:DCA,
  author =       "L{\'a}szl{\'o} Babai and Katalin Friedl and Markus
                 Stricker",
  title =        "Decomposition of $0*$-closed algebras in polynomial
                 time",
  crossref =     "Bronstein:1993:IPI",
  pages =        "86--94",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p86-babai/",
  abstract =     "Let A be a matrix algebra over $C$, closed under
                 Hermitian adjoints, and given by a basis. The authors
                 consider the classical problem of splitting the space
                 into the sum of A-irreducible subspaces. This includes
                 the problem of finding irreducible constituents of a
                 given unitary representation of a finite group. The
                 authors describe an algorithm which accomplishes the
                 splitting in a polynomial number of arithmetic
                 operations. Their model of computation assumes exact
                 arithmetic with complex numbers. Floating point
                 arithmetic is a reasonable approximation to this model;
                 they prove that their procedures are stable under minor
                 perturbation. The basic idea of their algorithms is
                 averaging via generalized Casimir operators. The result
                 generalizes to Frobenius algebras (algebras with a
                 non-degenerate associative bilinear form). The
                 corresponding problem in the model of exact symbolic
                 arithmetic does not seem tractable since it appears to
                 require handling field extensions of exponentially
                 large degree.",
  acknowledgement = ack-nhfb,
  affiliation =  "Chicago Univ., IL, USA",
  classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
                 (Programming and algorithm theory)",
  keywords =     "A-irreducible subspaces; ACM; algebraic computation;
                 Algorithm; algorithms; Arithmetic operations; Asterisk
                 closed algebra; Complex numbers; Computation theory;
                 Decomposition; Floating point arithmetic; Frobenius
                 algebra; Generalized Casimir operator; Hermitian
                 adjoints; Irreducible constituents; ISSAC; Matrix
                 algebra; Model; Nondegenerate associative bilinear
                 form; Polynomial number; Polynomial time; SIGSAM; Space
                 splitting; Subspace; Symbolic arithmetic; symbolic
                 computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Error analysis. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Algorithm theory; Matrix algebra; Matrix
                 decomposition; Polynomial matrices",
  xxtitle =      "Decomposition of $*$-closed algebras in polynomial
                 time",
}

@InProceedings{Babai:1993:DFM,
  author =       "L{\'a}szl{\'o} Babai and Robert Beals and Daniel
                 Rockmore",
  title =        "Deciding finiteness of matrix groups in deterministic
                 polynomial time",
  crossref =     "Bronstein:1993:IPI",
  pages =        "117--126",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p117-babai/",
  abstract =     "Let $G$ be a group of matrices with entries over an
                 algebraic number field $F$ (given symbolically). The
                 group $G$ is given by a list of generators. The authors
                 give several algorithms, both deterministic and
                 randomized, which can decide in polynomial time whether
                 or not $G$ is finite. It is easy to reduce the problem
                 to the case $F=Q$. As a next step, they present a
                 polynomial time algorithm which transforms $G$ into a
                 group of integral matrices whenever possible. Having
                 done so, the main results of the paper are several
                 polynomial time algorithms to handle the case of
                 integral matrices. They give both randomized and
                 deterministic algorithms to decide finiteness for
                 finitely generated integral matrix groups. Although
                 they are able to prove much better upper bounds for the
                 complexity of the deterministic algorithms, in
                 practice, the randomized algorithms support a much more
                 efficient implementation. Thus, both kinds of
                 algorithms are presented but only the implementation of
                 the randomized algorithm is explored.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Chicago Univ., IL, USA",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4240 (Programming and algorithm theory)",
  keywords =     "ACM; algebraic computation; Algorithm theory;
                 algorithms; Complexity; Deciding finiteness;
                 Deterministic algorithm; Deterministic polynomial time;
                 Finitely generated integral matrix groups; Group
                 theory; Integral matrices; Las Vegas algorithm, ISSAC;
                 Matrix algebra; Matrix groups; Monte Carlo algorithms;
                 Polynomial time algorithm; Randomized algorithm;
                 SIGSAM; Size; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes. {\bf G.3} Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Random number generation.",
  thesaurus =    "Decidability; Deterministic algorithms; Group theory;
                 Matrix algebra; Polynomial matrices; Randomised
                 algorithms",
}

@InProceedings{Beals:1993:EAC,
  author =       "Robert Beals",
  title =        "An elementary algorithm for computing the composition
                 factors of a permutation group",
  crossref =     "Bronstein:1993:IPI",
  pages =        "127--134",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p127-beals/",
  abstract =     "A permutation group $G$ may be concisely described by
                 a set $S$ of generators ($mod S mod$ need not be larger
                 than $\log\bmod{}G mod$ ). From such a short
                 description, however, it is not immediately clear how
                 to efficiently obtain various kinds of information
                 about the group. Furst, Hopcroft, and Luks (1980)
                 showed that an algorithm of Sims (1971) for computing
                 the order of $G$ and performing membership tests runs
                 in polynomial time. Sims's algorithm relies on
                 combinatorial methods, and there is no deep group
                 theory involved in the analysis. Polynomial time
                 algorithms for determining various aspects of the
                 structure of $G$ are also known. However, it seems that
                 algorithms which give us more information about $G$
                 require increasing amounts of group theory for their
                 analyses. An example is Luks's algorithm (1987) to find
                 composition factors (the `building blocks' of $G$),
                 which requires the classification of finite simple
                 groups (CFSG) for its proof of correctness. Kantor's
                 algorithm (1985) for finding Sylow subgroups likewise
                 requires CFSG. As the proof of CFSG is 15,000
                 manuscript pages long, it is reasonable to ask whether
                 so much group theory is necessary to study the
                 computational complexity of permutation group problems.
                 We give a deterministic polynomial time algorithm to
                 compute the composition factors of a permutation group,
                 given by a set of generators. This is the first
                 polynomial time algorithm for the composition factor
                 problem with an analysis that does not depend on CFSG.
                 In addition, we give a Monte Carlo version of our
                 algorithm which runs in nearly linear ($0(n \log^c n)$)
                 time for the class of `small-base' permutation groups
                 introduced by (Babai et al., 1991).",
  acknowledgement = ack-nhfb,
  classification = "C1110 (Algebra); C1140G (Monte Carlo methods);
                 C4240C (Computational complexity)",
  keywords =     "ACM; algebraic computation; algorithms; CFSG;
                 Combinatorial methods; Composition factors;
                 Computational complexity; Deterministic polynomial time
                 algorithm; Elementary algorithm; Finite simple groups;
                 Group theory; Membership tests; Monte Carlo version,
                 ISSAC; Permutation group; Permutation group problems;
                 Polynomial time; Polynomial time algorithms; SIGSAM;
                 symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf G.2.1} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Combinatorics, Permutations and
                 combinations. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes.",
  thesaurus =    "Computational complexity; Group theory; Monte Carlo
                 methods",
}

@InProceedings{Bini:1993:PCT,
  author =       "Dario Bini and Victor Pan",
  title =        "Parallel computations with {Toeplitz-like} and
                 {Hankel-like} matrices",
  crossref =     "Bronstein:1993:IPI",
  pages =        "193--200",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p193-bini/",
  abstract =     "The known fast algorithms for computations with
                 general Toeplitz, Hankel, Toeplitz-like, and
                 Hankel-like matrices are inherently sequential. We
                 develop some new techniques in order to devise fast
                 parallel algorithms for computations with such
                 matrices, including the evaluation of their
                 characteristic polynomials, with further extensions to
                 computing the solution to a linear system of equations
                 with such a matrix and to several polynomial
                 computations (such as computing gcd, lcm, Pad{\'e}
                 approximation and extended Euclidean scheme for two
                 polynomials), as well as to computing the minimum span
                 of a linear recurrence sequence. The algorithms can be
                 applied over any field of constants, consist of simple
                 computational blocks (mostly reduced to fast Fourier
                 transforms, FFT's), and have potential practical value.
                 We also extend them to the case of matrices
                 representable as the sums of Toeplitz-like and
                 Hankel-like matrices.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Pisa Univ., Italy",
  classification = "B0290F (Interpolation and function approximation);
                 B0290H (Linear algebra); B0290Z (Other numerical
                 methods); C4130 (Interpolation and function
                 approximation); C4140 (Linear algebra); C4190 (Other
                 numerical methods); C4240P (Parallel programming and
                 algorithm theory)",
  keywords =     "ACM; algebraic computation; algorithms; Characteristic
                 polynomials; Computational blocks; Extended Euclidean
                 scheme; Fast Fourier transforms, ISSAC; Hankel-like
                 matrices; Pad{\'e} approximation; Parallel algorithms;
                 Parallel computations; Polynomials; SIGSAM; symbolic
                 computation; theory; Toeplitz-like matrices",
  subject =      "{\bf I.0} Computing Methodologies, GENERAL. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computation of transforms.",
  thesaurus =    "Fast Fourier transforms; Hankel matrices; Parallel
                 algorithms; Polynomials; Toeplitz matrices",
}

@InProceedings{Bronstein:1993:FPF,
  author =       "Manuel Bronstein and Bruno Salvy",
  title =        "Full Partial Fraction Decomposition of Rational
                 Functions",
  crossref =     "Bronstein:1993:IPI",
  pages =        "157--160",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p157-bronstein/",
  abstract =     "We describe a rational algorithm that computes the
                 full partial fraction expansion of a rational function
                 over the algebraic closure of its field of definition.
                 The algorithm uses only gcd operations over the initial
                 field but the resulting decomposition is expressed with
                 linear denominators. We give examples from its Axiom
                 and Maple implementations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Wissenschaftliches Rechnen, Eidgenossische Tech.
                 Hochschule, Zurich, Switzerland",
  classification = "B0290D (Functional analysis); B0290H (Linear
                 algebra); B0290M (Numerical integration and
                 differentiation); C4120 (Functional analysis); C4140
                 (Linear algebra); C4160 (Numerical integration and
                 differentiation); C7310 (Mathematics computing)",
  keywords =     "ACM; Algebraic closure; algebraic computation; Axiom;
                 Decomposition; Full partial fraction decomposition; Gcd
                 operations; Maple; Polynomial; Rational functions;
                 SIGSAM; symbolic computation; Symbolic integration,
                 ISSAC; theory; verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms.",
  thesaurus =    "Function evaluation; Integration; Matrix
                 decomposition; Polynomial matrices; Symbol
                 manipulation",
}

@InProceedings{Caboara:1993:DAG,
  author =       "Massimo Caboara",
  title =        "A Dynamic Algorithm for {Gr{\"o}bner} basis
                 computation",
  crossref =     "Bronstein:1993:IPI",
  pages =        "275--283",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p275-caboara/",
  abstract =     "We recall preliminaries on Gr{\"o}bner bases,
                 Gr{\"o}bner Fans and Hilbert functions. We give an
                 outline of the dynamic algorithm. We report statistics
                 on some experiments and a few conclusions are given.
                 Experiments performed (and reported in this paper) show
                 an actual improvement of the combinatorial complexity.
                 However this doesn't reflect on timings, since the
                 `arithmetical' complexity both of the basis (number of
                 monomials appearing in it) and of the algorithm (number
                 of monomial operations) is not reduced. In the
                 important case of binomial ideals (where the
                 arithmetical complexity of the basis is constant), the
                 dynamic algorithm gives superior timings than the
                 classical one.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Genoa Univ., Italy",
  classification = "C4240C (Computational complexity); C6130 (Data
                 handling techniques); C7310 (Mathematics computing)",
  keywords =     "algorithms; theory; ISSAC; symbolic computation;
                 algebraic computation; ACM; SIGSAM; Dynamic algorithm;
                 Gr{\"o}bner basis computation; Gr{\"o}bner Fans;
                 Hilbert functions; Combinatorial complexity; Monomial
                 operations; Binomial ideals; Arithmetical complexity",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Computational complexity; Symbol manipulation",
}

@InProceedings{Cantone:1993:DPS,
  author =       "Domenico Cantone and Vincenzo Cutello",
  title =        "Decision procedures for stratified set-theoretic
                 syllogistics",
  crossref =     "Bronstein:1993:IPI",
  pages =        "105--110",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p105-cantone/",
  abstract =     "It is shown that a class of unquantified multi-sorted
                 set-theoretic formulae involving the notions of
                 powerset, general union, and singleton has a solvable
                 satisfiability problem. The authors show by means of a
                 model normalization procedure that any given
                 satisfiable formula in their theory has a finite model
                 whose size is bounded by a function of the number of
                 variables occurring in it.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Catania Univ., Italy",
  classification = "C1160 (Combinatorial mathematics); C4210 (Formal
                 logic); C4210L (Formal languages and computational
                 linguistics)",
  keywords =     "ACM; algebraic computation; Computation theory;
                 Decidability; Decision procedure; Finite model; Formal
                 logic, ISSAC; General union; languages; Model
                 normalization procedure; Multisorted language;
                 Powerset; Set theory; SIGSAM; Singleton; Solvability;
                 Solvable satisfiability problem; Stratified
                 set-theoretic syllogistics; Syllogistic; symbolic
                 computation; theory; Unquantified multi-sorted
                 set-theoretic formulae",
  subject =      "{\bf F.4.3} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Formal Languages, Decision
                 problems. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Computability theory. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  thesaurus =    "Computability; Computation theory; Decidability;
                 Decision theory; Set theory",
}

@InProceedings{Chou:1993:AGT,
  author =       "Shang-Ching Chou and Xiao-Shan Gao and Jing-Zhong
                 Zhang",
  title =        "Automated geometry theorem proving by vector
                 calculation",
  crossref =     "Bronstein:1993:IPI",
  pages =        "284--291",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p284-chou/",
  abstract =     "Based on a vector approach, we present a theorem
                 proving method for a class of constructive geometric
                 statements which covers a large portion of the equality
                 type geometry theorems about lines and circles. The
                 method is to eliminate the constructed points from the
                 conclusions of geometry statements based on a few basic
                 equalities on the inner and vector products of vectors
                 in the Euclidean plane. The method has been implemented
                 and the program has proved 410 nontrivial theorems
                 entirely automatically. The proofs produced by our
                 program are significantly shorter than the proofs
                 provided by programs based on the coordinate approach.
                 In spite of fact that the complexity of our algorithm
                 is exponential in the number of points in the geometry
                 statements, our program is practically very fast: 75
                 (95) percent of the 410 theorems can be proved within
                 one (five) second (seconds).",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Wichita State Univ., KS, USA",
  classification = "C1160 (Combinatorial mathematics); C4210 (Formal
                 logic); C4240C (Computational complexity); C4260
                 (Computational geometry)",
  keywords =     "algorithms; Automated geometry theorem proving;
                 Circles; Complexity; Equality type geometry theorems;
                 Euclidean plane; experimentation; Lines; theory; Vector
                 calculation; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Mechanical theorem proving. {\bf I.1.4}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Applications.",
  thesaurus =    "Computational complexity; Computational geometry;
                 Theorem proving",
}

@InProceedings{Collins:1993:HMH,
  author =       "George E. Collins and Werner Krandick",
  title =        "A Hybrid Method for High Precision Calculation of
                 Polynomial Real Roots",
  crossref =     "Bronstein:1993:IPI",
  pages =        "47--52",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p47-collins/",
  abstract =     "A straightforward implementation of Newton's method
                 for polynomial real root calculation using exact
                 arithmetic is inefficient. In each step the length of
                 the iterate multiplies by the degree of the polynomial
                 while its accuracy merely doubles. We present an exact
                 algorithm which keeps the length of each iterate
                 proportional to its accuracy. The resulting speed up is
                 dramatic. The average computing time can be further
                 reduced by trying floating point computations. Several
                 floating point Newton steps are executed; interval
                 arithmetic is used to check whether the result is
                 sufficiently close to the root; if this condition
                 cannot be verified the exact algorithm is invoked.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; algorithms; Average
                 computing time; Exact algorithm; Floating point
                 computations; Floating point Newton steps; High
                 precision calculation; Hybrid method; Interval
                 arithmetic, ISSAC; Newton method; Polynomial real
                 roots; SIGSAM; symbolic computation; verification",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Floating point arithmetic; Mathematics computing;
                 Newton method; Polynomials",
}

@InProceedings{Edneral:1993:CGN,
  author =       "Victor F. Edneral",
  title =        "Computer Generation of Normalizing Transformation for
                 Systems of Nonlinear {ODE}",
  crossref =     "Bronstein:1993:IPI",
  pages =        "14--19",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p14-edneral/",
  abstract =     "The article describes the Standard LISP program for
                 building a normal form and a corresponding normalizing
                 transformation of a system of ordinary differential
                 equations (ODE) in A. D. Bruno's notation (1972) up to
                 the specified order. This program also includes a
                 complete set of procedures of arithmetic for the
                 truncated power series and input/output services. This
                 gives us an opportunity to continue a treatment of
                 obtained results autonomically or in a REDUCE
                 environment. The program can work in a rational
                 arithmetic or in an approximate rational arithmetic, or
                 in a floating point arithmetic. The program usage is
                 illustrated by treating systems of weakly nonlinear
                 ODEs in the language of the truncated series. The
                 approximate solution is produced from the normal form
                 calculated up to enough high order and from the
                 corresponding normalizing transformation. This method
                 demonstrates rather good agreement with numerical
                 solutions of some well known equations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Nucl. Phys., Moscow Univ., Russia",
  classification = "C4170 (Differential equations); C6110 (Systems
                 analysis and programming); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "ACM; algebraic computation; algorithms; Approximate
                 rational arithmetic; Computer generation; Floating
                 point arithmetic; Input/output services; languages;
                 Nonlinear ODE systems; Normal form; Normalizing
                 transformation; Ordinary differential equations; REDUCE
                 environment; SIGSAM; Standard LISP program; symbolic
                 computation; Truncated power series; Truncated series,
                 ISSAC; verification; Weakly nonlinear ODEs",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, LISP. {\bf G.1.7} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra,
                 Eigenvalues and eigenvectors (direct and iterative
                 methods). {\bf I.1.2} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Difference equations; LISP; Programming; Series
                 [mathematics]; Symbol manipulation",
}

@InProceedings{Emiris:1993:PMS,
  author =       "Ioannis Emiris and John Canny",
  title =        "A Practical Method for the Sparse Resultant",
  crossref =     "Bronstein:1993:IPI",
  pages =        "183--192",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p183-emiris/",
  abstract =     "We propose an efficient method for computing the
                 resultant of a sparse polynomial system of $n+1$
                 equations in $n$ unknowns. Our approach constructs a
                 matrix whose determinant is a non-zero multiple of the
                 resultant and from which the latter is easily
                 extracted. For certain classes of systems, it attains
                 optimality by expressing the resultant as a single
                 determinant. An implementation of the algorithm is
                 described and empirical results presented and compared
                 with previous works. In addition, the important
                 subproblem of computing mixed volumes is examined and
                 an efficient algorithm is implemented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Comput. Sci., California Univ., Berkeley, CA,
                 USA",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  keywords =     "ACM; algebraic computation; algorithms;
                 experimentation; Mixed volumes, ISSAC; SIGSAM; Sparse
                 polynomial system; Sparse resultant; symbolic
                 computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.2.9} Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Robotics. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Polynomials",
}

@InProceedings{Ganzha:1993:PSM,
  author =       "V. G. Ganzha and E. V. Vorozhtsov",
  title =        "A Probabilistic Symbolic-Numerical Method for the
                 Stability Analyses of Difference Schemes for {PDEs}",
  crossref =     "Bronstein:1993:IPI",
  pages =        "9--13",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p9-ganzha/",
  abstract =     "We present a new symbolic numerical method for an
                 automatic stability analysis of difference schemes
                 approximating scalar linear of nonlinear partial
                 differential equations (PDEs) of hyperbolic or
                 parabolic type. In this method the grid values of the
                 numerical solution for any fixed moment of time are
                 considered as random correlated variables obeying the
                 normal distribution law. Therefore, one can apply the
                 notion of the C. E. Shannon's (1948) entropy to
                 characterize the stability of a difference scheme. The
                 reduction of this entropy, or uncertainty, is taken as
                 a stability criterion. It is shown at a number of
                 examples that this criterion yields the same stability
                 regions in the cases of linear difference initial value
                 problems, as the Fourier method. In the case of two
                 spatial variables the present probabilistic method is
                 computationally faster than the Fourier method by two
                 orders of magnitude.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
                 Novosibirsk, Russia",
  classification = "C1140Z (Other topics in statistics); C4170
                 (Differential equations); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "ACM; algebraic computation; algorithms; Automatic
                 stability analysis; Difference schemes; Fixed moment;
                 Fourier method; Grid values; Linear difference initial
                 value problems; Nonlinear partial differential
                 equations; Normal distribution law; Parabolic type;
                 PDEs; Probabilistic symbolic-numerical method; Random
                 correlated variables; SIGSAM; Spatial variables, ISSAC;
                 Stability analyses; Stability criterion; symbolic
                 computation; Symbolic numerical method; theory",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf G.1.4} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Finite difference methods.",
  thesaurus =    "Difference equations; Nonlinear differential
                 equations; Normal distribution; Numerical stability;
                 Partial differential equations; Symbol manipulation",
}

@InProceedings{Godlevsky:1993:PPA,
  author =       "A. B. Godlevsky and A. E. Doroshenko",
  title =        "Parallelizing Programs with {APS}",
  crossref =     "Bronstein:1993:IPI",
  pages =        "55--62",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p55-godlevsky/",
  abstract =     "An approach to parallelizing sequential programs as
                 rewriting rules application by means of the algebraic
                 programming system APS is considered. It gives the
                 advantages of rapid prototyping and evolutionary
                 development of efficient parallelizers.",
  acknowledgement = ack-nhfb,
  affiliation =  "V. M. Glushkov Inst. of Cybern., Acad. of Sci., Kiev,
                 Ukraine",
  classification = "C4210L (Formal languages and computational
                 linguistics); C5440 (Multiprocessing systems); C6110P
                 (Parallel programming); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "ACM; algebraic computation; Algebraic programming
                 system; algorithms; APS; Distributed memory parallel
                 computers; Efficient parallelizers; Evolutionary
                 development; ISSAC; languages; Massively parallel
                 computer systems; Rapid prototyping; Rewriting rules;
                 SIGSAM, Sequential program parallelization; symbolic
                 computation",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 D.1.3} Software, PROGRAMMING TECHNIQUES, Concurrent
                 Programming, Parallel programming.",
  thesaurus =    "Distributed memory systems; Parallel programming;
                 Rewriting systems; Software prototyping; Symbol
                 manipulation",
}

@InProceedings{Gruntz:1993:NAC,
  author =       "Dominik Gruntz",
  title =        "A New Algorithm for Computing Asymptotic Series",
  crossref =     "Bronstein:1993:IPI",
  pages =        "239--244",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p239-gruntz/",
  abstract =     "We describe a new algorithm for computing asymptotic
                 expansions for a large class of expressions, whereby
                 the asymptotic series are of a form more complicated
                 than mere Puiseux series. Today's computer algebra
                 systems still lack good algorithms for handling such
                 asymptotic expansions, although in theory some
                 algorithms have been presented. The algorithm we
                 present in this article is directly induced by the
                 limit computation algorithm presented in Gonnet and
                 Gruntz (1992) which is based on series computations in
                 terms of the most rapidly varying subexpression of a
                 given expression. Examples of the algorithm implemented
                 in Maple are shown.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Sci. Comput., Eidgenossische Tech.
                 Hochschule, Zurich, Switzerland",
  classification = "C1100 (Mathematical techniques); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; algorithms; Asymptotic
                 expansions; Computer algebra; ISSAC; Maple; SIGSAM,
                 Asymptotic series; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems.",
  thesaurus =    "Series [mathematics]; Symbol manipulation",
}

@InProceedings{Gutnik:1993:ACA,
  author =       "S. A. Gutnik",
  title =        "Application of Computer Algebra to Investigation of
                 the Relative Equilibria of a Satellite",
  crossref =     "Bronstein:1993:IPI",
  pages =        "63--64",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p63-gutnik/",
  abstract =     "A new approach for the symbolic analysis of the
                 satellites dynamical equations is presented. The
                 investigation is made by means of Gr{\"o}bner Basis
                 method. The presence of various perturbations is
                 supposed, such as gravitational and constant torques.
                 It is shown that a satellite moving in a circular orbit
                 with a prescribed constant torque and prescribed
                 central moments of inertia has at most 24 equilibrium
                 positions in an orbiting frame in the general case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Comput. Aided Design, Acad. of Sci., Moscow,
                 Russia",
  classification = "C7310 (Mathematics computing)",
  keywords =     "algorithms; Computer algebra; Relative equilibria;
                 Symbolic analysis; Satellites dynamical equations;
                 Gr{\"o}bner Basis; Perturbations; Gravitational
                 torques; Constant torques; Circular orbit, ISSAC;
                 symbolic computation; algebraic computation; ACM;
                 SIGSAM",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Aerospace. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms.",
  thesaurus =    "Angular velocity; Symbol manipulation",
}

@InProceedings{Halstead:1993:APS,
  author =       "R. H. Halstead and T. Chikayama and R. Gabriel and D.
                 Waltz",
  title =        "Applications for Parallel Symbolic Computation",
  crossref =     "Halstead:1993:PSC",
  pages =        "417--417",
  year =         "1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hong:1993:QEF,
  author =       "Hoon Hong",
  title =        "Quantifier elimination for formulas constrained by
                 quadratic equations",
  crossref =     "Bronstein:1993:IPI",
  pages =        "264--274",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p264-hong/",
  abstract =     "An algorithm is given for constructing a quantifier
                 free formula (a boolean expression of polynomial
                 equations and inequalities) equivalent to a given
                 formula of the form: (There exists $x$ in
                 $R$)($a_2x^2+a_1x+a_0=O V-product F$), where $F$ is a
                 quantifier free formula in $x_1,\ldots{},x_r,x,$ and
                 $a_2, a_1, a_0$ are polynomials in $x_1,\ldots{},x_r$
                 with real coefficients such that the system
                 ($a_2=0,a_1=0, a_0=0$) has no solution in $R^r$.
                 Formulas of this form frequently occur in the context
                 of constraint logic programming over the real numbers.
                 The output formulas are made of resultants and two
                 variants, which we call trace and slope resultants.
                 Both of these variant resultants can be expressed as
                 determinants of certain matrices.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1230 (Artificial intelligence); C4130
                 (Interpolation and function approximation); C4210
                 (Formal logic); C6110L (Logic programming)",
  keywords =     "algorithms; Boolean expression; Constraint logic
                 programming; Determinants; Inequalities; Polynomial
                 equations; Polynomials; Quadratic equations; Quantifier
                 elimination; Quantifier free formula; theory;
                 verification",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf F.4.1}
                 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Analysis of algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Boolean algebra; Logic programming; Polynomials",
}

@InProceedings{Ito:1993:MPA,
  author =       "T. Ito and R. Nikhil and J. Padget and N. Suzuki",
  title =        "Massively Parallel Architectures and Symbolic
                 Computation",
  crossref =     "Halstead:1993:PSC",
  pages =        "408--416",
  year =         "1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jebelean:1993:GBG,
  author =       "T. Jebelean",
  title =        "A Generalization of the Binary {GCD} Algorithm",
  crossref =     "Bronstein:1993:IPI",
  pages =        "111--116",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p111-jebelean/",
  abstract =     "A generalization of the binary algorithm for operation
                 at `word level' by using a new concept of `modular
                 conjugates' computes the GCD of multiprecision integers
                 two times faster than the Lehmer--Euclid method. Most
                 importantly, however, the new algorithm is suitable for
                 systolic parallelization, in `least-significant digits
                 first' pipelined manner and for aggregation with other
                 systolic algorithms for the arithmetic of
                 multiprecision rational numbers.",
  acknowledgement = ack-nhfb,
  affiliation =  "RISC, Linz, Austria",
  classification = "C4240P (Parallel programming and algorithm theory)",
  keywords =     "ACM; algebraic computation; algorithms; Arithmetic;
                 Binary algorithm; Binary GCD algorithm; Computation
                 speed; Computational efficiency; experimentation;
                 Least-significant digits first; Modular conjugates;
                 Multiprecision integer; Multiprecision rational
                 numbers; Parallel processing; Pipelined; SIGSAM;
                 symbolic computation; Systolic algorithm; Systolic
                 array, ISSAC; Systolic parallelization; Word level",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf F.1.2}
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Modes of Computation, Parallelism and concurrency. {\bf
                 I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
  thesaurus =    "Algorithm theory; Parallel algorithms; Symbol
                 manipulation; Systolic arrays",
}

@InProceedings{Jeffrey:1993:IOE,
  author =       "D. J. Jeffrey",
  title =        "Integration to obtain expressions valid on domains of
                 maximum extent",
  crossref =     "Bronstein:1993:IPI",
  pages =        "34--41",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p34-jeffrey/",
  abstract =     "In certain circumstances, the integration routines
                 used by computer algebra systems return expressions
                 whose domains of validity are unnecessarily restricted
                 by the presence of discontinuities. It is argued that
                 this is undesirable and that integration routines
                 should meet an additional requirement: they should
                 return expressions that are valid on domains of maximum
                 extent. The contention is supported by general
                 mathematical arguments, by an examination of existing
                 practises and by a demonstration that two standard
                 algorithms can be modified to meet the requirement.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Appl. Math., Univ. of Western Ontario,
                 London, Ont., Canada",
  classification = "C4160 (Numerical integration and differentiation);
                 C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; algorithms; Computer
                 algebra systems; Discontinuities; General mathematical
                 arguments; Integration routines; languages; Maximum
                 extent; SIGSAM; Standard algorithms, ISSAC; symbolic
                 computation; Validity domains",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Mathematica. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple.",
  thesaurus =    "Integration; Symbol manipulation",
}

@InProceedings{Jinzhao:1993:RPG,
  author =       "Wu-Jinzhao and Li-Lian",
  title =        "The regular problem and {Green} equivalences for
                 special monoids",
  crossref =     "Bronstein:1993:IPI",
  pages =        "78--85",
  year =         "1993",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "For the monoid presented by a finite special
                 Church--Rosser Thue system, whether it is a regular
                 semigroup is decidable in polynomial time. The number
                 of each kind of Green equivalence classes is either one
                 or infinite and it is computable in polynomial time.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
  classification = "C1160 (Combinatorial mathematics); C4210L (Formal
                 languages and computational linguistics)",
  keywords =     "ACM; algebraic computation; Computability; Computation
                 theory; Decidability; Decidable; Finite special
                 Church--Rosser Thue system; Green equivalences; ISSAC;
                 Polynomial time; Regular problem; Regular semigroup;
                 SIGSAM; Special monoid; String rewriting Green
                 equivalence class; symbolic computation",
  thesaurus =    "Computability; Decidability; Equivalence classes;
                 Group theory; Rewriting systems",
}

@InProceedings{Kalkbrener:1993:UBN,
  author =       "Michael Kalkbrener",
  title =        "An upper bound on the number of monomials in the
                 {Sylvester} resultant",
  crossref =     "Bronstein:1993:IPI",
  pages =        "161--163",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p161-kalkbrener/",
  abstract =     "The Sylvester resultant is not only a classical
                 concept in commutative algebra but also a useful tool
                 for actually computing solutions of systems of
                 algebraic equations. We derive an upper bound on the
                 number of monomials in the Sylvester resultant using a
                 result from the theory of partially ordered sets.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Eidgenossische Tech. Hochschule,
                 Zurich, Switzerland",
  classification = "B0210 (Algebra); B0250 (Combinatorial mathematics);
                 B0290F (Interpolation and function approximation);
                 C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4130 (Interpolation and function approximation); C7310
                 (Mathematics computing)",
  keywords =     "ACM; algebraic computation; Algebraic equations;
                 algorithms; Commutative algebra $b$; Monomials;
                 Partially ordered sets, ISSAC; SIGSAM; Sylvester
                 resultant; symbolic computation; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
  thesaurus =    "Polynomials; Set theory; Symbol manipulation",
}

@InProceedings{Keady:1993:AIS,
  author =       "G. Keady and M. G. Richardson",
  title =        "An application of {IRENA} to systems of nonlinear
                 equations arising in equilibrium flows in networks",
  crossref =     "Bronstein:1993:IPI",
  pages =        "311--320",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p311-keady/",
  abstract =     "IRENA --- an Interface from REDUCE to NAG --- runs
                 under the REDUCE Computer Algebra (CA) system and
                 provides an interactive front end to the NAG Fortran
                 Library. Here IRENA is tested on a problem closer to an
                 engineering problem than previously published
                 examples. We also illustrate the use of the codeonly
                 switch, which is relevant to larger scale problems. We
                 describe progress on an issue raised in the `Future
                 Developments' section in our SIGSAM Bulletin article by
                 K. A. Broughan et al. (1991): the progress improves the
                 practical effectiveness of IRENA.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Western Australia Univ., Nedlands, WA,
                 Australia",
  classification = "C4150 (Nonlinear and functional equations); C6130
                 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; algorithms; Codeonly
                 switch; Equilibrium flows; Interactive front end;
                 Interface from REDUCE to NAG; ISSAC; languages; NAG
                 Fortran Library; REDUCE Computer Algebra; SIGSAM,
                 IRENA; symbolic computation; Systems of nonlinear
                 equations; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, REDUCE. {\bf G.2.2} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory, Network problems.
                 {\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures. {\bf I.1.4} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Mathematics computing; Nonlinear equations; Symbol
                 manipulation",
}

@InProceedings{Klimov:1993:SEN,
  author =       "D. M. Klimov and V. M. Rudenko and V. V. Leonov",
  title =        "Symbolic Evaluation in the Nonlinear Mechanical
                 Systems",
  crossref =     "Bronstein:1993:IPI",
  pages =        "53--54",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p53-klimov/",
  abstract =     "The paper presents the features of a program package,
                 Polymech-symbol, helping to solve some laborious
                 mechanical problems. The package was written by means
                 of the REDUCE system and contains several algorithms in
                 a form of REDUCE procedures. The computer algebra
                 methods may be successfully used for solving the
                 problems of navigation and defining the trajectory of
                 satellite mass centre motion. The preliminary
                 analytical research provides the effective algorithm
                 for on-board solving the problem of prediction. To
                 assure necessary accuracy, we need to construct several
                 higher approximations. Such sophisticated problems can
                 be solved only with the help of symbolic computations
                 that deal with the processing of cumbersome analytical
                 expressions. For effective analytical investigation of
                 such kinds of problems, the choice of parameters which
                 describe the perturbed orbital motion is critical. In
                 addition to the natural requirements of the calculation
                 process efficiency and the absence of singularities in
                 equations of motion, it is useful to have a unified
                 mathematical description for the angular motion and for
                 the motion of the mass centre.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Problems of Mech., Acad. of Sci., Moscow,
                 Russia",
  classification = "C7310 (Mathematics computing); C7320 (Physics and
                 chemistry computing)",
  keywords =     "ACM; algebraic computation; algorithms; Analytical
                 expressions; Angular motion; Calculation process
                 efficiency; Computer algebra methods; Higher
                 approximations; languages; Mass centre motion, ISSAC;
                 Mechanical problems; Nonlinear mechanical systems;
                 Perturbed orbital motion; Polymech-symbol; Prediction;
                 Program package; REDUCE procedures; REDUCE system;
                 Satellite mass centre motion; SIGSAM; symbolic
                 computation; Symbolic computations; Symbolic
                 evaluation; Trajectory; Unified mathematical
                 description",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE.",
  thesaurus =    "Mechanics; Physics computing; Symbol manipulation",
}

@InProceedings{Lin:1993:SRT,
  author =       "Dongdai Lin and Zhuojun Liu",
  title =        "Some results on theorem proving in geometry over
                 finite fields",
  crossref =     "Bronstein:1993:IPI",
  pages =        "292--300",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p292-lin/",
  abstract =     "In this paper, we discuss Wu's well ordering principle
                 and theorem proving over finite fields, try to prove
                 some theorems in the geometry over finite fields.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
  classification = "C1230 (Artificial intelligence); C4210 (Formal
                 logic); C4240 (Programming and algorithm theory); C4260
                 (Computational geometry)",
  keywords =     "ACM; algebraic computation; algorithms; Finite fields;
                 ISSAC; SIGSAM; symbolic computation; Theorem proving;
                 theory; verification; Well ordering principle",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations in finite fields. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic, Mechanical theorem proving. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Computational geometry; Theorem proving",
}

@InProceedings{Madlener:1993:CGB,
  author =       "Klaus Madlener and Birgit Reinert",
  title =        "Computing {Gr{\"o}bner} Bases in Monoid and Group
                 Rings",
  crossref =     "Bronstein:1993:IPI",
  pages =        "254--263",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p254-madlener/",
  abstract =     "Following Buchberger's approach to computing a
                 Gr{\"o}bner basis of a polynomial ideal in polynomial
                 rings, a completion procedure for finitely generated
                 right ideals in $Z(H)$ is given, where $H$ is an
                 ordered monoid presented by a finite, convergent
                 semi-Thue system $(\Sigma,T)$. Taking a finite set $F$
                 contained in $Z(H)$ we get a (possibly infinite) basis
                 of the right ideal generated by $F$, such that using
                 this basis we have unique normal forms for all $p$ in
                 $Z(H)$ (especially the normal form is zero in case $p$
                 is an element of the right ideal generated by $F$). As
                 the ordering and multiplication on H need not be
                 compatible, reduction has to be defined carefully in
                 order to make it Noetherian. Further we no longer have
                 $p.x$ to $-{}_p0$ for $p$ in $Z(H)$, $x$ in $H$.
                 Similar to Buchberger's $s$-polynomials, confluence
                 criteria are developed and a completion procedure is
                 given. In case $T= \phi$ or $(\Sigma,T)$ is a
                 convergent, 2-monadic presentation of a group with
                 inverses of length 1, termination can be shown. An
                 application to the subgroup problem is discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Inf., Kaiserslautern Univ., Germany",
  classification = "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics computing)",
  keywords =     "algorithms; theory; verification; ISSAC; symbolic
                 computation; algebraic computation; ACM; SIGSAM, Group
                 rings; Gr{\"o}bner bases; Polynomial rings; Semi-Thue
                 system; Monoid rings",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
  thesaurus =    "Group theory; Polynomials; Symbol manipulation",
}

@InProceedings{Monagan:1993:GAD,
  author =       "Michael B. Monagan and Walter M. Neuenschwander",
  title =        "{GRADIENT}: algorithmic differentiation in {Maple}",
  crossref =     "Bronstein:1993:IPI",
  pages =        "68--76",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p68-monagan/",
  abstract =     "Many scientific applications require computation of
                 the derivatives of a function $f:R^n$ to $R^m$ as well
                 as the function values of $f$ itself. All computer
                 algebra systems can differentiate functions represented
                 by formulae. But not all functions can be described by
                 formulae. And formulae are not always the most
                 effective means for representing functions and
                 derivatives. In this paper we describe the algorithms
                 used by the Maple (2) routine GRADIENT that accepts as
                 input a Maple procedure for the computation of $f$ and
                 outputs a new Maple procedure that computes the
                 gradient of $f$. The design of the GRADIENT routine is
                 such that it is also trivial to generate Maple
                 procedures for the computation of Jacobians and
                 Hessians.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
                 Tech. Hochschule, Zurich, Switzerland",
  classification = "C4160 (Numerical integration and differentiation);
                 C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; Algorithmic
                 differentiation; algorithms; Computer algebra systems;
                 Function values; GRADIENT; Hessians, ISSAC; Jacobians;
                 languages; Maple; Scientific applications; SIGSAM;
                 symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf G.2.2} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf F.2.2}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Computations on discrete structures.",
  thesaurus =    "Differentiation; Mathematics computing; Symbol
                 manipulation",
}

@InProceedings{Mourrain:1993:GPP,
  author =       "B. Mourrain",
  title =        "The 40 ``generic'' positions of a parallel robot",
  crossref =     "Bronstein:1993:IPI",
  pages =        "173--182",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p173-mourrain/",
  abstract =     "We consider the direct kinematic problem of a parallel
                 robot (called the Stewart platform or left hand). We
                 want to show how the use of formal tools help us to
                 guess the solution of this problem and then to
                 establish it. We do not try to give real-time and
                 numerical solutions to the problem of inverse images
                 but focus on tools of effective algebra, which can help
                 us to know a little more about the geometric aspects of
                 the question. We describe experiments done in order to
                 obtain the number of generic positions of this robot,
                 once the length of the arms are known. We also sketch
                 the proof that the degree of the corresponding map is
                 40. We use explicit elimination techniques in order to
                 remove the solution at infinity and we use Bezout's
                 theorem on surfaces with circularity as a conclusion.",
  acknowledgement = ack-nhfb,
  affiliation =  "SAFIR, Valbonne, France",
  classification = "C1110 (Algebra); C1310 (Control system analysis and
                 synthesis methods); C3390M (Manipulators); C4260
                 (Computational geometry); C7420D (Control system design
                 and analysis)",
  keywords =     "ACM; algebraic computation; Arms; Bezout's theorem;
                 Circularity, ISSAC; Direct kinematic problem; Effective
                 algebra; experimentation; Explicit elimination
                 techniques; Formal tools; Generic positions; Geometric
                 aspects; Left hand; Parallel robot; Proof; SIGSAM;
                 Stewart platform; Surfaces; symbolic computation;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf I.2.9}
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Robotics. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures.",
  thesaurus =    "Algebra; Computational geometry; Control system
                 analysis computing; Manipulator kinematics; Theorem
                 proving",
}

@InProceedings{Petkovsek:1993:FAH,
  author =       "M. Petkovsek and B. Salvy",
  title =        "Finding All Hypergeometric Solutions of Linear
                 Differential Equations",
  crossref =     "Bronstein:1993:IPI",
  pages =        "27--33",
  year =         "1993",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Hypergeometric sequences are such that the quotient of
                 two successive terms is a fixed rational function of
                 the index. We give a generalization of M. Petkovsek's
                 algorithm (1992) to find all hypergeometric sequence
                 solutions of linear recurrences, and we describe a
                 program to find all hypergeometric functions that solve
                 a linear differential equation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Ljubljana Univ., Slovenia",
  classification = "C4170 (Differential equations); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "ACM; algebraic computation; Computer algebra, ISSAC;
                 Fixed rational function; Hypergeometric sequences;
                 Hypergeometric solutions; Linear differential
                 equations; Linear recurrences; Quotient; SIGSAM;
                 Successive terms; symbolic computation",
  thesaurus =    "Linear differential equations; Sequences; Series
                 [mathematics]; Symbol manipulation",
}

@InProceedings{Petkovsek:1993:FAHb,
  author =       "Marko Petkov{\v{s}}ek and Bruno Salvy",
  title =        "Finding all hypergeometric solutions of linear
                 differential equations",
  crossref =     "Bronstein:1993:IPI",
  pages =        "27--33",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p27-petkovscaronek/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Richardson:1993:ZST,
  author =       "Daniel Richardson",
  title =        "A Zero Structure Theorem for Exponential Polynomials",
  crossref =     "Bronstein:1993:IPI",
  pages =        "144--151",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p144-richardson/",
  abstract =     "An exponential system is a system of equations
                 $(S=O,E=O)$, where $S$ is a finite set of polynomials
                 in $Q(x_1,\ldots{},x_n,y_1,\ldots{},y_n)$, and $E$ is a
                 subset of $(y_1-e^{x1},\ldots{},y_n-e^{xn})$. Wu's
                 method (1984) is used effectively to decompose such
                 systems into finitely many subsystems which have
                 triangular algebraic part, and whose solution sets in
                 $C^{2n}$ are equidimensional and also, in a sense
                 explained, non singular. The problem of solving
                 exponential systems in bounded regions of $R^n$ is also
                 discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Bath Univ., UK",
  classification = "B0210 (Algebra); B0290F (Interpolation and function
                 approximation); B0290H (Linear algebra); C1110
                 (Algebra); C4130 (Interpolation and function
                 approximation); C4140 (Linear algebra)",
  keywords =     "ACM; algebraic computation; algorithms; Bounded
                 regions; Exponential polynomials; Exponential system;
                 ISSAC; SIGSAM, Zero structure theorem; Solution sets;
                 symbolic computation; theory; Triangular algebraic
                 part",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.1.3} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Measures and Classes. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms.",
  thesaurus =    "Matrix decomposition; Polynomial matrices",
}

@InProceedings{Roy:1993:AGA,
  author =       "Marie-Fran{\c{c}}oise Roy and T. {Van Effelterre}",
  title =        "Aspect graphs of algebraic surfaces",
  crossref =     "Bronstein:1993:IPI",
  pages =        "135--143",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p135-roy/",
  abstract =     "An aspect graph is a representation of 3D objects that
                 is used in the field of computer vision for recognition
                 in 2D images. The viewspace around the object is
                 tesselated in a finite number of cells by the semi
                 algebraic visual events locus. The topology of the
                 image contour remains stable in each cell and may only
                 change on the visual events locus. An aspect graph
                 represents a 3D object whose surface boundary is
                 algebraic or semi algebraic by the finite number of
                 different topological aspects of its image contour and
                 by the visual events that make a stable aspect switch
                 to another one. We show that the number of different
                 topological aspects of an algebraic surface of degree
                 $d$ is upper bounded by a $O(d^{12})$ for orthographic
                 projection and $O(d^{18})$ for perspective projection.
                 This result is a generalisation of the upper bound of
                 $O(d^6)$ obtained by M.-F. Roy and T. Van Effelterre
                 (1992) for surfaces of revolution under perspective
                 projection and improves the most recent upper bounds of
                 $O(d^{20})$ for orthographic projection and $O(d^{30})$
                 for perspective projection. We also show how to compute
                 the equations of the visual events locus with
                 Gr{\"o}bner bases systems and Hermite's method.",
  acknowledgement = ack-nhfb,
  affiliation =  "IRMAR, Rennes I Univ., France",
  classification = "C1160 (Combinatorial mathematics); C4260
                 (Computational geometry); C5260B (Computer vision and
                 image processing techniques)",
  keywords =     "algorithms; design; Aspect graph; Algebraic surfaces;
                 3D objects; Computer vision; 2D image recognition;
                 Viewspace; Semi algebraic visual events locus; Image
                 contour; Visual events locus; Surface boundary;
                 Orthographic projection; Perspective projection;
                 Gr{\"o}bner bases systems; Hermite method, ISSAC;
                 symbolic computation; algebraic computation; ACM;
                 SIGSAM",
  subject =      "{\bf I.0} Computing Methodologies, GENERAL. {\bf
                 I.5.4} Computing Methodologies, PATTERN RECOGNITION,
                 Applications, Computer vision. {\bf J.6} Computer
                 Applications, COMPUTER-AIDED ENGINEERING,
                 Computer-aided design (CAD).",
  thesaurus =    "Computational geometry; Computer vision; Graph theory;
                 Object recognition",
}

@InProceedings{Santas:1993:TSC,
  author =       "Phillip S. Santas",
  title =        "A type system for computer algebra (abstract)",
  crossref =     "Bronstein:1993:IPI",
  pages =        "77--77",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p77-santas/",
  abstract =     "Summary form only given. Examines type systems for
                 support of subtypes and categories in computer algebra
                 systems. By modelling representation of instances in
                 terms of existential types instead of recursive types,
                 the author obtains not only a simplified model, but
                 also builds a basis for defining subtyping among
                 algebraic domains. The introduction of metaclasses
                 facilitates the task by allowing the inference of type
                 classes. By means of type classes and existential
                 subtypes, relations are constructed without involving
                 coercions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Sci. Comput., Eidgenossische Tech.
                 Hochschule, Zurich, Switzerland",
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory)",
  keywords =     "ACM; algebraic computation; Algebraic domain;
                 Categories; Computer algebra; design; Existential
                 subtype; Existential type; ISSAC; Metaclass; Model;
                 Representation of instances; SIGSAM, Type system;
                 Subtype; Subtyping; symbolic computation",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.3.3} Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Type structure.",
  thesaurus =    "Process algebra; Symbol manipulation; Type theory",
}

@InProceedings{Sendra:1993:EAH,
  author =       "Juan R. Sendra and Juan Llovet",
  title =        "Efficient algorithms for {Hankel} matrices over
                 ${Z}(x_1,\ldots{},x_r)$",
  crossref =     "Bronstein:1993:IPI",
  pages =        "201--208",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p201-sendra/",
  abstract =     "In this paper, we investigate the problem of the rank
                 and the determinant of Hankel matrices over
                 $Z(x_1,\ldots{},x_r)$. A modular algorithm for
                 determining the rank of a Hankel matrix with entries
                 that are multivariate polynomials over the integers is
                 presented. The algorithm is based on modular
                 techniques, which consist in computing the rank of
                 Hankel matrices over finite fields by a special
                 algorithm that needs $O(n^2)$ arithmetic operations,
                 where $n$ is the order of the matrix. The general
                 solution is achieved by determining the maximum of the
                 ranks computed over the finite fields. Similarly, we
                 give a theorem that shows how to compute Hankel
                 determinants in $O(n^2)$ arithmetic operations. The
                 worst case complexity of the algorithm is
                 $O((n^{r+3}G^r+n^{r+2}G^{r+1}) \log{}n \log^2 L)$,
                 where $G$ and $L$ are some appropriate bounds for the
                 degree and the norm of the entries respectively.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Alcala Univ., Madrid, Spain",
  classification = "C4140 (Linear algebra); C4240C (Computational
                 complexity)",
  keywords =     "ACM; algebraic computation; algorithms; Determinant;
                 Hankel matrices; Modular algorithm; Multivariate
                 polynomials, ISSAC; Rank; SIGSAM; symbolic computation;
                 theory; verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations in finite fields. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Computational complexity; Determinants; Hankel
                 matrices; Polynomials",
}

@InProceedings{Shackell:1993:NEH,
  author =       "John Shackell",
  title =        "Nested Expansions and {Hardy} Fields",
  crossref =     "Bronstein:1993:IPI",
  pages =        "234--238",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p234-shackell/",
  abstract =     "Let $X$ denote the ring of germs, at $+ \infty$, of
                 $C^\infty$ real-valued functions each defined on some
                 subinterval of $R$ of the form $(a, infinity )$. Using
                 a common abuse of terminology we shall often treat
                 elements of $X$ as functions rather than the germs of
                 functions. A Hardy field is a subfield of $X$ closed
                 under differentiation. The definition is simple and
                 natural, but the connection with asymptotics is perhaps
                 not apparent at first sight. Let $F$ be any Hardy
                 field. A non-zero element, $f$, of $F$ has to have an
                 inverse in $F$ and so cannot have arbitrarily large
                 zeros. Therefore $f$ is either ultimately positive or
                 ultimately negative. If $g$ is another element of $F$
                 we can define $f > g$ to mean that $f-g$ is ultimately
                 positive. This makes $F$ into a totally ordered field
                 with the order reflecting the asymptotic behaviour of
                 elements. Since $F$ is closed under differentiation,
                 its elements must either be ultimately increasing,
                 ultimately decreasing or ultimately constant. Hardy,
                 showed that the exp-log functions form a field with
                 these properties. One of the obvious difficulties with
                 nested expansions is the fact that they are complicated
                 to manipulate. However that need not be a barrier for
                 computer algebra systems. A complexity which is doubly
                 exponential in the number of terms could be more
                 serious though. Perhaps only experience will determine
                 whether this is a real obstacle in practice.",
  acknowledgement = ack-nhfb,
  classification = "C4170 (Differential equations); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; algorithms; Asymptotics;
                 Complexity; Computer algebra systems; Hardy field;
                 ISSAC; Nested expansions; SIGSAM, Hardy fields;
                 symbolic computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Shevchenko:1993:SRP,
  author =       "Ivan I. Shevchenko and Andrej G. Sokolsky",
  title =        "Studies of Regular Precessions of a Symmetric
                 Satellite by Means of Computer Algebra",
  crossref =     "Bronstein:1993:IPI",
  pages =        "65--67",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p65-shevchenko/",
  abstract =     "The perturbed motion in the neighbourhood of regular
                 precessions of a dynamically symmetric satellite on a
                 circular orbit is studied. The `Norma' specialized
                 program package (A. G. Sokolsky, I. I. Shevenko, 1990;
                 1991), intended for normalization of autonomous
                 Hamiltonian systems by means of computer algebra, is
                 used to obtain normal forms of the Hamiltonian. A full
                 catalogue of non resonant and resonant normal forms up
                 to the 6th order of normalization is constructed for
                 the case of hyperboloidal precession. The case of
                 cylindrical precession, more complicated in analytical
                 sense, is considered as well. Analytical expressions
                 for coefficients of terms of the normal forms are
                 derived as dependences on the frequencies and the
                 initial physical parameters of the system. Though the
                 intermediary expressions occupy megabytes of computer
                 memory, the final normal forms are compact.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. Astron., Acad. of Sci., St.
                 Petersburg, Russia",
  classification = "C4140 (Linear algebra); C6130 (Data handling
                 techniques); C7310 (Mathematics computing); C7350
                 (Astronomy and astrophysics computing)",
  keywords =     "ACM; algebraic computation; algorithms; Analytical
                 expressions; Autonomous Hamiltonian systems; Circular
                 orbit; Computer algebra; Cylindrical precession;
                 design; Dynamically symmetric satellite; Hyperboloidal
                 precession; Initial physical parameters; Intermediary
                 expressions, ISSAC; Norma specialized program package;
                 Perturbed motion; Regular precessions; Resonant normal
                 forms; SIGSAM; symbolic computation; Symmetric
                 satellite",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General. {\bf J.2} Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Aerospace.",
  thesaurus =    "Astronomy computing; Matrix algebra; Series
                 [mathematics]; Symbol manipulation",
}

@InProceedings{Siegl:1993:PAS,
  author =       "K. Siegl",
  title =        "Parallelizing algorithms for symbolic computation
                 using $\parallel${Maple}$\parallel$",
  crossref =     "ACM:1993:PFA",
  pages =        "179--186",
  year =         "1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  standardno =   "1",
}

@InProceedings{Stifter:1993:GTP,
  author =       "Sabine Stifter",
  title =        "Geometry Theorem Proving in Vector Spaces by Means of
                 {Gr{\"o}bner} Bases",
  crossref =     "Bronstein:1993:IPI",
  pages =        "301--310",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p301-stifter/",
  abstract =     "Within the last few years several approaches to
                 automated geometry theorem proving have been developed
                 and proposed that are based (1) on the formulation of a
                 geometric statement as the implication of a polynomial
                 equation (the `conclusion') from a set of polynomial
                 equations (the `hypotheses'), and (2) the proof of the
                 implication by algebraic methods, namely Gr{\"o}bner
                 bases and Ritt's bases. All these approaches require
                 the introduction of coordinates for the points
                 involved. Many geometric theorems, however, can be
                 formulated as relations between points directly,
                 without needing coordinates. In this paper we develop a
                 new method, based on Gr{\"o}bner bases in vector
                 spaces, that can prove geometric theorems that are
                 formulated as relations between points directly. Our
                 approach has the advantages that theorems can be
                 formulated more naturally and fewer variables are
                 needed for their formulations. This results in shorter
                 and faster proofs.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1230 (Artificial intelligence); C4210 (Formal
                 logic); C4260 (Computational geometry)",
  keywords =     "theory; Geometry theorem proving; Vector spaces;
                 Gr{\"o}bner bases; Geometric statement; Coordinates;
                 Geometric theorems, ISSAC; symbolic computation;
                 algebraic computation; ACM; SIGSAM",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Mechanical theorem proving. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Computational geometry; Theorem proving",
}

@InProceedings{Vallier:1993:ACN,
  author =       "L. Vallier",
  title =        "An Algorithm for the Computation of Normal Forms and
                 Invariant Manifolds",
  crossref =     "Bronstein:1993:IPI",
  pages =        "225--233",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p225-vallier/",
  abstract =     "This paper deals with an algorithm to compute normal
                 forms and invariant manifolds of ordinary differential
                 equations. This algorithm based on transformation
                 theory, gives us a useful tool in the study of such
                 equations, in the neighborhood of singular points. This
                 tool involves a lot of computations on homogeneous
                 polynomials. Then in addition, a tree data structure is
                 described to represent homogeneous polynomials in an
                 efficient way, and we give the cost of the algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "LMC, IMAG, Grenoble, France",
  classification = "B0290F (Interpolation and function approximation);
                 B0290P (Differential equations); C4130 (Interpolation
                 and function approximation); C4170 (Differential
                 equations); C4240C (Computational complexity)",
  keywords =     "ACM; algebraic computation; Algorithm, ISSAC;
                 algorithms; Homogeneous polynomials; Invariant
                 manifolds; Normal forms; Ordinary differential
                 equations; SIGSAM; Singular points; symbolic
                 computation; theory; Transformation theory; Tree data
                 structure",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf E.1} Data, DATA
                 STRUCTURES, Trees. {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative
                 methods).",
  thesaurus =    "Computational complexity; Differential equations;
                 Polynomials; Tree data structures",
}

@InProceedings{vanderPut:1993:RRK,
  author =       "Marius {van der Put} and Peter A. Hendriks",
  title =        "A rationality result for {Kovacic}'s algorithm",
  crossref =     "Bronstein:1993:IPI",
  pages =        "4--8",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p4-van_der_put/",
  abstract =     "We want to prove the following rationality result (J.
                 J. Kovacic, 1986). Suppose that the Riccati equation
                 $u^1+u^2=r$ has a solution, which is algebraic over
                 $Q^{cl}(x)$. Then there exists an algebraic solution
                 $u$ of minimal degree $n$ of the Riccati equation such
                 that the coefficients of the minimum polynomial of $u$
                 over $Q^{cl}(x)$ lie in a field $K(x)$ with $(K:Q)<=2$.
                 Moreover, only in the cases: $n=1$ and $G$ is the
                 multiplicative group $G_m$ or a finite cyclic group of
                 order $>2$ or $n=4$ and $G$ the tetrahedral group, a
                 field extension $K$ of degree 2 of $Q$ can be needed.",
  acknowledgement = ack-nhfb,
  classification = "C1160 (Combinatorial mathematics); C4140 (Linear
                 algebra); C4170 (Differential equations)",
  keywords =     "ACM; algebraic computation; Algebraic solution;
                 algorithms; Field extension; Finite cyclic group;
                 ISSAC; Kovacic algorithm; Minimum polynomial;
                 Multiplicative group; Riccati equation; SIGSAM,
                 Rationality result; symbolic computation; Tetrahedral
                 group; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic.",
  thesaurus =    "Group theory; Linear differential equations; Riccati
                 equations",
}

@InProceedings{Villard:1993:CSN,
  author =       "Gilles Villard",
  title =        "Computation of the {Smith} normal form of polynomial
                 matrices",
  crossref =     "Bronstein:1993:IPI",
  pages =        "209--217",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p209-villard/",
  abstract =     "We describe a new algorithm for the computation of the
                 Smith normal form of polynomial matrices. This
                 algorithm computes the normal form and pre- and
                 post-multipliers in deterministic polynomial time.
                 Noticing that the computation reduces to a linear
                 algebra problem over the field of the coefficients, we
                 obtain a good worst-case complexity bound.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. LMC, IMAG, Grenoble, France",
  classification = "C4140 (Linear algebra); C4240C (Computational
                 complexity)",
  keywords =     "ACM; algebraic computation; algorithms; Deterministic
                 polynomial time; Linear algebra, ISSAC; Polynomial
                 matrices; SIGSAM; Smith normal form; symbolic
                 computation; theory; Worst-case complexity",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Computational complexity; Linear algebra; Polynomial
                 matrices",
}

@InProceedings{Volcheck:1993:NSS,
  author =       "E. J. Volcheck",
  title =        "{Noether}'s {S-transformation} simplifies curve
                 singularities rationally: a local analysis",
  crossref =     "Bronstein:1993:IPI",
  pages =        "164--172",
  year =         "1993",
  bibdate =      "Thu Sep 26 05:34:21 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The singularities of algebraic plane curves over $Q$
                 may be resolved into ordinary multiple points by the
                 classical method of standard quadratic transformations.
                 The author analyzes a birational plane transformation
                 described by Max Noether (1884) which improves upon the
                 classical method in two ways: first, it requires no
                 ground field extension; second, the degree of the curve
                 it produces is an exponential factor lower than that
                 produced by the standard method.",
  acknowledgement = ack-nhfb,
  classification = "B0210 (Algebra); B0230 (Integral transforms); C1110
                 (Algebra); C1130 (Integral transforms); C7310
                 (Mathematics computing)",
  keywords =     "ACM; algebraic computation; Algebraic plane curves;
                 Birational plane transformation; Curve singularities;
                 ISSAC; Local analysis; Quadratic transformations;
                 SIGSAM, Noether S-transformation; Singularities;
                 symbolic computation",
  thesaurus =    "Polynomials; Symbol manipulation; Transforms",
}

@InProceedings{Volcheck:1993:NTS,
  author =       "Emil J. Volcheck",
  title =        "{Noether}'s ${S}$-transformation simplifies curve
                 singularities rationally: a local analysis",
  crossref =     "Bronstein:1993:IPI",
  pages =        "164--172",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p164-volcheck/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple.",
}

@InProceedings{Weispfenning:1993:DT,
  author =       "Volker Weispfenning",
  title =        "Differential term-orders",
  crossref =     "Bronstein:1993:IPI",
  pages =        "245--253",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p245-weispfenning/",
  abstract =     "In the theory of Gr{\"o}bner bases for multivariate
                 polynomials the concept of a term-order plays a central
                 role. Such term-orders can be characterized by linear
                 forms, whose coefficients are univariate real
                 polynomials. For multivariate partial differential
                 polynomials a corresponding concept is of great
                 importance for potential extensions of the
                 Riquier--Janet technique. So far, only the weaker
                 concepts of rankings and comparative rank have been
                 defined by Kolchin. This note presents an axiomatic
                 definition of differential term-orders on arbitrary
                 partial differential terms and proves that all these
                 orders are well-orders. Moreover, we give a
                 characterization of differential term-orders in terms
                 of systems of linear forms whose coefficients are
                 univariate real polynomials. This characterization
                 provides an explicit construction of an abundance of
                 differential term-orders. As an application, we obtain
                 a simple characterization of differential term-orders
                 on finite sets of differential terms and an algorithm
                 for computing all differential term-orders on such
                 sets. Finally, we characterize the term-orders, for
                 which differentiation preserves the ordering between
                 the highest terms of non-zero differential
                 polynomials.",
  acknowledgement = ack-nhfb,
  affiliation =  "Passau Univ., Germany",
  classification = "C4240 (Programming and algorithm theory); C7310
                 (Mathematics computing)",
  keywords =     "algorithms; theory; verification; Gr{\"o}bner bases;
                 Multivariate polynomials; Multivariate partial
                 differential polynomials; Differential term-orders;
                 Term-order",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation. {\bf F.4.1}
                 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Weispfenning:1993:DTP,
  author =       "V. Weispfenning",
  title =        "Differential Term-Orders",
  crossref =     "Bronstein:1993:IPI",
  pages =        "245--253",
  year =         "1993",
  bibdate =      "Thu Sep 26 05:34:21 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ACM; algebraic computation; ISSAC; SIGSAM; symbolic
                 computation",
}

@InProceedings{Willis:1993:CSP,
  author =       "T. J. Willis and E. A. Bogucz",
  title =        "Coupling Symbolic Processing with Parallel Numeric
                 Computation",
  crossref =     "Sincovec:1993:PSS",
  pages =        "788--792",
  year =         "1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wu:1993:ACU,
  author =       "Hongzhong Wu",
  title =        "On the assignment complexity of uniform trees",
  crossref =     "Bronstein:1993:IPI",
  pages =        "95--104",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p95-wu/",
  abstract =     "This paper discusses the assignment complexity of the
                 uniform tree, which is made up of identical cells
                 realizing a function $f$. The assignment complexity of
                 a tree is defined as the cardinal number of the minimum
                 complete assignment set of the tree. When a complete
                 assignment set is applied to the primary input lines of
                 the tree, every internal $f$ cell in the tree can be
                 excited by all possible input combinations. The
                 assignment problem is a basic problem in the VLSI
                 system design, test and optimization. The relation
                 between the property of $f$ and the assignment
                 complexity of the uniform tree is analyzed. It is shown
                 that, the assignment complexity of a balanced uniform
                 tree with $n$ primary input lines is either $O(1)$ or
                 $Omega ((\lg{}n)^{\alpha}) (\alpha in (0,1))$. In the
                 first case, the cardinal number of the minimum complete
                 assignment set for a tree is constant and independent
                 of the size and structure of the tree. In the second
                 case, the assignment complexity depends on the number
                 of the primary input lines of the tree. If a balanced
                 uniform tree is based on a commutative function, then
                 it is either $Theta (1)$ or $Theta (\lg{}n)$
                 assignable.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Inf., Saarlandes Univ., Saarbrucken,
                 Germany",
  classification = "B0250 (Combinatorial mathematics); B1110 (Network
                 topology); B1130 (General circuit analysis and
                 synthesis methods); C1160 (Combinatorial mathematics);
                 C4240C (Computational complexity)",
  keywords =     "ACM; algebraic computation; algorithms; Assignable;
                 Assignment complexity; Cardinal number; Commutative
                 function; Computational complexity; Computer circuit
                 design; design; Identical cells; ISSAC; Minimum
                 complete assignment set; Optimization; SIGSAM; symbolic
                 computation; Test; theory; Tree; Uniform trees; VLSI
                 system design",
  subject =      "{\bf B.7.1} Hardware, INTEGRATED CIRCUITS, Types and
                 Design Styles, VLSI (very large scale integration).
                 {\bf G.2.2} Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory, Trees. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Computational complexity; Network synthesis; Network
                 topology; Trees [mathematics]; VLSI",
}

@InProceedings{Wu:1993:RPG,
  author =       "Jinzhao Wu and Lian Li",
  title =        "The regular problem and green equivalences for special
                 monoids",
  crossref =     "Bronstein:1993:IPI",
  pages =        "78--85",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p78-wu/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Grammars and Other Rewriting Systems. {\bf F.1.3}
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Measures and Classes. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms.",
}

@InProceedings{Yokoyama:1993:HCE,
  author =       "Kazuhiro Yokoyama and Taku Takeshima",
  title =        "On {Hensel} Construction of Eigenvalues and
                 Eigenvectors of Matrices with Polynomial Entries",
  crossref =     "Bronstein:1993:IPI",
  pages =        "218--224",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p218-yokoyama/",
  abstract =     "Hensel's lemma is now widely used in algebraic
                 computation as a tool of lifting procedure in modular
                 methods, and this lifting procedure based on Hensel's
                 lemma is called a Hensel construction. Significant
                 examples are found in polynomial computation problems;
                 factorization, GCD computation and division.
                 Furthermore, several Hensel constructions are applied
                 to solve systems of polynomial equations or to compute
                 inverses of matrices with polynomial entries
                 (Krishnamurthy, 1985). For a natural application, we
                 propose a method for finding eigenvalues and
                 eigenvectors of matrices simultaneously. The authors
                 study the problem and show several Hensel constructions
                 for the problem. For simplicity, they only deal with
                 matrices with univariate polynomial entries over a
                 field and they consider linear lifting.",
  acknowledgement = ack-nhfb,
  affiliation =  "IIAS-SIS, Fujitsu Labs. Ltd., Shizuoka, Japan",
  classification = "C4140 (Linear algebra); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; Algebraic computation;
                 algorithms; Eigenvalues; Eigenvectors; Hensel
                 construction; Linear lifting; Matrices; Polynomial
                 computation, ISSAC; Polynomial entries; SIGSAM;
                 symbolic computation; theory; Univariate polynomial
                 entries; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra,
                 Eigenvalues and eigenvectors (direct and iterative
                 methods). {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
  thesaurus =    "Eigenvalues and eigenfunctions; Polynomial matrices;
                 Symbol manipulation",
}

@InProceedings{Zharkov:1993:ASF,
  author =       "Alexey Y. Zharkov",
  title =        "On algebraic solutions of first order {Riccatti}
                 equation",
  crossref =     "Bronstein:1993:IPI",
  pages =        "1--3",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p1-zharkov/",
  abstract =     "In this paper we prove the following theorem. If the
                 Riccatti equation $w^1+w^2=R(x)$, $R$ in $Q(x)$, has
                 algebraic solutions then one can find a minimal
                 polynomial defining such solutions whose coefficients
                 are in a quadratic extension of the field $Q$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Saratov Univ., Russia",
  classification = "C4140 (Linear algebra); C4170 (Differential
                 equations)",
  keywords =     "ACM; algebraic computation; Algebraic solutions;
                 algorithms; Coefficients; Differential equations,
                 ISSAC; First order Riccatti equation; Minimal
                 polynomial; Quadratic extension; SIGSAM; symbolic
                 computation; Theorem proving; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic. {\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations.",
  thesaurus =    "Differential equations; Polynomials; Riccati
                 equations; Theorem proving",
}

@InProceedings{Zima:1993:NCO,
  author =       "E. V. Zima",
  title =        "Numeric Code Optimization in Computer Algebra Systems
                 and Recurrent Relations Technique",
  crossref =     "Bronstein:1993:IPI",
  pages =        "42--46",
  year =         "1993",
  bibdate =      "Thu Mar 12 08:40:26 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p42-zima/",
  abstract =     "Computer algebra provides good tools for code
                 optimization. In particular it concerns
                 source-to-source optimization. But existing tools
                 (SCOPE, Gentran, etc.) provide code transmission from
                 computer algebra system to numeric system only. That's
                 why we have started developing in MSU a
                 source-to-source optimization library using Reduce as
                 an intellectual tool. This library contains algorithms
                 and special tools that provide reliable bilateral
                 connection between Reduce and systems for numeric
                 computations on MS DOS computers (Turbo-Pascal,
                 Turbo-C, MathCad, etc.).",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Math. and Cybern., Moscow State
                 Univ., Russia",
  classification = "C6110 (Systems analysis and programming); C6130
                 (Data handling techniques); C6150C (Compilers,
                 interpreters and other processors); C7310 (Mathematics
                 computing)",
  keywords =     "ACM; algebraic computation; algorithms; Code
                 optimization; Code transmission; Computer algebra
                 systems; Gentran; Intellectual tool; languages; MS DOS
                 computers, ISSAC; Numeric code optimization;
                 performance; Recurrent relations technique; Reduce;
                 Reliable bilateral connection; SCOPE; SIGSAM;
                 Source-to-source optimization; Source-to-source
                 optimization library; symbolic computation",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Pascal.",
  thesaurus =    "Optimising compilers; Programming; Symbol
                 manipulation",
}

@InProceedings{Abramov:1994:DSL,
  author =       "Sergei A. Abramov and Marko Petkov{\v{s}}ek",
  title =        "{D'Alembertian} solutions of linear differential and
                 difference equations",
  crossref =     "ACM:1994:IPI",
  pages =        "169--174",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p169-abramov/",
  abstract =     "D'Alembertian solutions of differential (resp.
                 difference) equations are those expressible as nested
                 indefinite integrals (resp. sums) of hyperexponential
                 functions. They are a subclass of Liouvillian
                 solutions, and can be constructed by recursively
                 finding hyperexponential solutions and reducing the
                 order. Knowing d'Alembertian solutions of $Ly=0$, one
                 can write down the corresponding solutions of $Ly=f$
                 and of $L*y=0$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, Russia",
  classification = "C4170 (Differential equations)",
  keywords =     "algorithms; D'Alembertian solutions; Difference
                 equations; Hyperexponential functions; Hyperexponential
                 solutions; Linear differential equations; Liouvillian
                 solutions; Nested indefinite integrals; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Nonalgebraic algorithms. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Difference equations; Linear differential equations",
}

@InProceedings{Andreoli:1994:CKB,
  author =       "J.-M. Andreoli and U. M. Borghoff and R. Pareschi",
  title =        "Constraint-Based Knowledge Brokers",
  crossref =     "Hong:1994:FIS",
  pages =        "1--11",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Attardi:1994:SPB,
  author =       "G. Attardi and C. Traverso",
  title =        "A strategy-accurate parallel {Buchberger} algorithm",
  crossref =     "Hong:1994:FIS",
  pages =        "12--21",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bachmann:1994:CRM,
  author =       "Olaf Bachmann and Paul S. Wang and Eugene V. Zima",
  title =        "Chains of recurrences --- a method to expedite the
                 evaluation of closed-form functions",
  crossref =     "ACM:1994:IPI",
  pages =        "242--249",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p242-bachmann/",
  abstract =     "Chains of Recurrences (CRs) are introduced as an
                 effective method to evaluate functions at regular
                 intervals. Algebraic properties of CRs are examined and
                 an algorithm that constructs a CR for a given function
                 is explained. Finally, an implementation of the method
                 in MAXIMA/Common Lisp is discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
                 USA",
  classification = "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  keywords =     "Algebraic properties; algorithms; Chains of
                 recurrences; Closed-form functions; languages;
                 MAXIMA/Common Lisp; performance; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf D.3.2} Software, PROGRAMMING
                 LANGUAGES, Language Classifications, Common Lisp. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Function evaluation; Symbol manipulation",
}

@InProceedings{Baddoura:1994:CIF,
  author =       "Jamil Baddoura",
  title =        "A conjecture on integration in finite terms with
                 elementary functions and polylogarithms",
  crossref =     "ACM:1994:IPI",
  pages =        "158--162",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p158-baddoura/",
  abstract =     "In this abstract, we report on a conjecture that gives
                 the form of an integral if it can be expressed using
                 elementary functions and polylogarithms. The conjecture
                 is proved by the author in the cases of the dilogarithm
                 and the trilogarithm (1993) and consists of a
                 generalization of Liouville's theorem on integration in
                 finite terms with elementary functions. Those last
                 structure theorems, for the dilogarithm and the
                 trilogarithm, are the first case of structure theorems
                 where logarithms can appear with non-constant
                 coefficients. In order to prove the conjecture for
                 higher polylogarithms we need to find the functional
                 identities, for the polylogarithms that we are using,
                 that characterize all the possible algebraic relations
                 among the considered polylogarithms of functions that
                 are built up from the rational functions by taking the
                 considered polylogarithms, exponentials, logarithms and
                 algebraics. The task of finding those functional
                 identities seems to be a difficult one and is an
                 unsolved problem for the most part to this date.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., MIT, Cambridge, MA, USA",
  classification = "C4160 (Numerical integration and differentiation);
                 C7310 (Mathematics computing)",
  keywords =     "algorithms; Elementary functions; Integration;
                 Polylogarithms; Structure theorems; theory;
                 Trilogarithm; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms. {\bf G.1.4} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation.",
  thesaurus =    "Integration; Symbol manipulation",
}

@InProceedings{Becker:1994:SSL,
  author =       "Eberhard Becker and Teo Mora and Maria Grazia Marinari
                 and Carlo Traverso",
  title =        "The shape of the {Shape Lemma}",
  crossref =     "ACM:1994:IPI",
  pages =        "129--133",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p129-becker/",
  abstract =     "The Shape Lemma was originally introduced in 1989 and
                 so christened by Lakshman (1990). It is an easy
                 generalization of the Primitive Element Theorem and it
                 states that a $O$-dimensional radical ideal in a
                 polynomial ring$ k(X_1,\ldots{},X_n)$, after most
                 changes of coordinates, has a basis
                 $(g_1(X_1),X_2-g_2(X_2),\ldots{},X_n-g_n(X_1))$.
                 Notwithstanding its triviality, it has proved
                 ubiquitous in recent papers on polynomial system
                 solving. The obvious example $(X^2, XY, Y^2)$ is
                 sufficient to show that some assumption is needed on a
                 $O$-dimensional ideal in order that it holds; the
                 obvious example $(X^2, Y)$ is sufficient to show that
                 radicality is too strong an assumption. Since most of
                 the results making use of the Shape Lemma are valid
                 whenever the Shape Lemma holds and are of interest also
                 for non radical ideals, it is worthwhile to exactly
                 characterize those $O$-dimensional ideals to which the
                 Shape Lemma applies. It turns out that this exact
                 characterization is as trivial as the original Shape
                 Lemma itself. In fact both this characterization and
                 the generalization of it we give are easy
                 specializations of a classical result in algebraic
                 geometry on the minimum dimension of a generic
                 biregular projection of a variety as a function of its
                 dimension and of the dimension of its tangent bundle.
                 We give a direct, elementary, self-contained proof of
                 this specialization.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Math., Dortmund Univ., Germany",
  classification = "C1160 (Combinatorial mathematics); C4260
                 (Computational geometry); C7310 (Mathematics
                 computing)",
  keywords =     "Algebraic geometry; algorithms; Polynomial ring;
                 Primitive Element Theorem; Shape lemma; theory;
                 verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations.",
  thesaurus =    "Computational geometry; Polynomials; Symbol
                 manipulation",
}

@InProceedings{Berman:1994:OCR,
  author =       "Benjamin P. Berman and Richard J. Fateman",
  title =        "Optical character recognition for typeset
                 mathematics",
  crossref =     "ACM:1994:IPI",
  pages =        "348--353",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p348-berman/",
  abstract =     "There is a wealth of mathematical knowledge that could
                 be potentially very useful in many computational
                 applications, but is not available in electronic form.
                 This knowledge comes in the form of mechanically
                 typeset books and journals going back more than a
                 hundred years. Besides these older sources, there are a
                 great many current publications, filled with useful
                 mathematical information, which are difficult if not
                 impossible to obtain in electronic form. What we would
                 like to do is extract character information from these
                 documents, which could then be passed to higher-level
                 parsing routines for further extraction of mathematical
                 content (or any other useful $2$-dimensional semantic
                 content). Unfortunately, current commercial OCR
                 (optical character recognition) software packages are
                 quite unable to handle mathematical formulas, since
                 their algorithms at all levels use heuristics developed
                 for other document styles. We are concerned with the
                 development of OCR methods that are able to handle this
                 specialized task of mathematical expression
                 recognition.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Comput. Sci., California Univ., Berkeley, CA,
                 USA",
  classification = "C1250B (Character recognition); C5260B (Computer
                 vision and image processing techniques); C7310
                 (Mathematics computing)",
  keywords =     "algorithms; Character information; Higher-level
                 parsing routines; Journals; Mechanically typeset books;
                 Optical character recognition; Software packages;
                 Typeset mathematics",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf B.4.2}
                 Hardware, INPUT/OUTPUT AND DATA COMMUNICATIONS,
                 Input/Output Devices. {\bf I.5.4} Computing
                 Methodologies, PATTERN RECOGNITION, Applications, Text
                 processing.",
  thesaurus =    "Grammars; Optical character recognition; Symbol
                 manipulation",
}

@InProceedings{Bertrand:1994:INA,
  author =       "Laurent Bertrand",
  title =        "On the implementation of a new algorithm for the
                 computation of hyperelliptic integrals",
  crossref =     "ACM:1994:IPI",
  pages =        "211--215",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p211-bertrand/",
  abstract =     "We present an implementation in Maple of a new
                 algorithm for the algebraic function integration
                 problem in the particular case of hyperelliptic
                 integrals. This algorithm is based on the general
                 algorithm of Trager (1984) and on the arithmetic in the
                 Jacobian of hyperelliptic curves of Cantor (1987).",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. d'Arithmetique, Calcul Formel et Optimisation,
                 Limoges Univ., France",
  classification = "B0290M (Numerical integration and differentiation);
                 B0290R (Integral equations); C4160 (Numerical
                 integration and differentiation); C4180 (Integral
                 equations); C7310 (Mathematics computing)",
  keywords =     "Algebraic function integration problem; algorithms;
                 Hyperelliptic curves; Hyperelliptic integrals; Maple;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
  thesaurus =    "Elliptic equations; Integral equations; Integration;
                 Symbol manipulation",
}

@InProceedings{Bonacina:1994:RPD,
  author =       "M. P. Bonacina",
  title =        "On the reconstruction of proofs in distributed theorem
                 proving with contraction: a modified {Clause-Diffusion}
                 method",
  crossref =     "Hong:1994:FIS",
  pages =        "22--33",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Borst:1994:GRP,
  author =       "W. N. Borst and V. V. Goldman and J. A. {Van Hulzen}",
  title =        "{GENTRAN} 90: a {REDUCE} package for the generation of
                 {Fortran} 90 code",
  crossref =     "ACM:1994:IPI",
  pages =        "45--51",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p45-borst/",
  abstract =     "GENTRAN is a code generator and translator running
                 under REDUCE and MACSYMA. It is a tool for generating
                 Fortran 77, RATFOR or C programs from program
                 specifications and symbolic expressions. Its facilities
                 include template processing, automatic segmentation of
                 large expressions and a file handling mechanism.
                 GENTRAN can be used in combination with SCOPE 1.5, a
                 source code optimization package for REDUCE. We present
                 an extension of the REDUCE version of GENTRAN, called
                 GENTRAN 90. It makes generation of Fortran 90 code
                 possible.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Twente Univ., Enschede,
                 Netherlands",
  classification = "C6115 (Programming support); C6140D (High level
                 languages); C6150C (Compilers, interpreters and other
                 processors); C7310 (Mathematics computing)",
  keywords =     "algorithms; C; Code generation; Code generator; Code
                 translator; design; File handling; Fortran 77; Fortran
                 90 code; GENTRAN 90; languages; MACSYMA; Program
                 specifications; RATFOR; REDUCE; REDUCE package; SCOPE
                 1.5; Source code optimization package; Symbolic
                 expression; Template processing",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Code generation. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Fortran 90. {\bf D.3.4} Software, PROGRAMMING
                 LANGUAGES, Processors, Translator writing systems and
                 compiler generators.",
  thesaurus =    "FORTRAN; Optimisation; Program interpreters; Software
                 packages; Software tools; Symbol manipulation",
}

@InProceedings{Bosma:1994:PAS,
  author =       "Wieb Bosma and John Cannon and Graham Matthews",
  title =        "Programming with algebraic structures: design of the
                 {Magma} language",
  crossref =     "ACM:1994:IPI",
  pages =        "52--57",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p52-bosma/",
  abstract =     "MAGMA is a new software system for computational
                 algebra, number theory and geometry whose design is
                 centred on the concept of algebraic structure (magma).
                 The use of algebraic structure as a design paradigm
                 provides a natural strong typing mechanism. Further,
                 structures and their morphisms appear in the language
                 as first class objects. Standard mathematical notions
                 are used for the basic data types. The result is a
                 powerful, clean language which deals with objects in a
                 mathematically rigorous manner. The conceptual and
                 implementation ideas behind MAGMA will be examined in
                 this paper. This conceptual base differs significantly
                 from those underlying other computer algebra systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math., Sydney Univ., NSW, Australia",
  classification = "C1160 (Combinatorial mathematics); C6110 (Systems
                 analysis and programming); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "Algebraic structures; algorithms; Computational
                 algebra; Computer algebra systems; Data types; design;
                 Magma language; Mathematical notions; Number theory;
                 Software system; Strong typing mechanism",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf D.3.3}
                 Software, PROGRAMMING LANGUAGES, Language Constructs
                 and Features, Data types and structures. {\bf F.3.3}
                 Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
                 Studies of Program Constructs, Type structure. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C.",
  thesaurus =    "Number theory; Programming; Symbol manipulation",
}

@InProceedings{Bratvold:1994:PFP,
  author =       "T. A. Bratvold",
  title =        "Parallelising a Functional Program Using a
                 List-Homomorphism Skeleton",
  crossref =     "Hong:1994:FIS",
  pages =        "44--53",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Briek:1994:SCT,
  author =       "S. Briek and A. Rauzy",
  title =        "Synchronization of Constrained Transition Systems",
  crossref =     "Hong:1994:FIS",
  pages =        "54--62",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bronstein:1994:IAF,
  author =       "Manuel Bronstein",
  title =        "An improved algorithm for factoring linear ordinary
                 differential operators",
  crossref =     "ACM:1994:IPI",
  pages =        "336--340",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p336-bronstein/",
  abstract =     "We describe an efficient algorithm for computing the
                 associated equations appearing in the Beke--Schlesinger
                 factorisation method for linear ordinary differential
                 operators. This algorithm, which is based on elementary
                 operations with sets of integers, can be easily
                 implemented for operators of any order, produces
                 several possible associated equations, of which only
                 the simplest can be selected for solving, and often
                 avoids the degenerate case, where the order of the
                 associated equation is less than in the generic case.
                 We conclude with some fast heuristics that can produce
                 some factorisations while using only linear
                 computations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
                 Tech. Hochschule, Zurich, Switzerland",
  classification = "B0290P (Differential equations); C4170 (Differential
                 equations); C4240 (Programming and algorithm theory)",
  keywords =     "algorithms; Beke--Schlesinger factorisation method;
                 Efficient algorithm; Elementary operations; Fast
                 heuristics; Improved algorithm; Integer sets; Linear
                 ordinary differential operator factoring; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems.",
  thesaurus =    "Algorithm theory; Difference equations; Mathematical
                 operators",
}

@InProceedings{Buendgen:1994:MAT,
  author =       "R. Buendgen and M. Goebel and W. Kuechlin",
  title =        "Multi-Threaded {AC} Term Rewriting",
  crossref =     "Hong:1994:FIS",
  pages =        "84--93",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bueno:1994:CSM,
  author =       "F. Bueno and M. {Garcia de la Banda} and M.
                 Hermenegildo",
  title =        "A Comparative Study of Methods for Automatic
                 Compile-time Parallelization of Logic Programs",
  crossref =     "Hong:1994:FIS",
  pages =        "63--73",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bundgen:1994:FPC,
  author =       "Reinhard B{\"u}ndgen and Manfred G{\"o}bel and
                 Wolfgang K{\"u}chlin",
  title =        "A fine-grained parallel completion procedure",
  crossref =     "ACM:1994:IPI",
  pages =        "269--277",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p269-bundgen/",
  abstract =     "We present a parallel Knuth--Bendix completion
                 algorithm where the inner loop, deriving the
                 consequences of adding a new rule to the system, is
                 multithreaded. The selection of the best new rule in
                 the outer loop, and hence the completion strategy, is
                 exactly the same as for the sequential algorithm. Our
                 implementation, which is within the PARSAC-2 parallel
                 symbolic computation system, exhibits good parallel
                 speedups on a standard multiprocessor workstation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Wilhelm-Schickard-Inst. fur Inf., Tubingen Univ.,
                 Germany",
  classification = "C4210L (Formal languages and computational
                 linguistics); C4240P (Parallel programming and
                 algorithm theory); C6130 (Data handling techniques);
                 C6150N (Distributed systems software); C7310
                 (Mathematics computing)",
  keywords =     "algorithms; Fine grained parallel completion
                 procedure; Fine-grained parallel completion procedure;
                 Multithreaded inner loop; Parallel Knuth--Bendix
                 completion algorithm; Parallel speedups; PARSAC-2
                 parallel symbolic computation system; Standard
                 multiprocessor workstation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf F.4.2} Theory
                 of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Grammars and Other Rewriting Systems,
                 Parallel rewriting systems. {\bf F.1.2} Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
                 Computation, Parallelism and concurrency.",
  thesaurus =    "Parallel algorithms; Parallel machines; Rewriting
                 systems; Symbol manipulation",
}

@InProceedings{Burke-Perline:1994:PCU,
  author =       "T. Burke-Perline",
  title =        "The Parallel Computation of $f(x)0(00-010)0/02 \bmod
                 h(x)$ using {Sugarbush 1.1}",
  crossref =     "Hong:1994:FIS",
  pages =        "74--83",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Char:1994:AIT,
  author =       "Bruce W. Char and Mark F. Russo",
  title =        "Automatic identification of time scales in enzyme
                 kinetics models",
  crossref =     "ACM:1994:IPI",
  pages =        "74--83",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p74-char/",
  abstract =     "Many chemical reaction systems studied in the
                 pharmaceutical industry have phenomena that occur on
                 two or more vastly different time scales. When modeling
                 the chemical reaction system as ordinary differential
                 equations, if a small parameter $E$ can be identified
                 then one can isolate the behavior of the system on long
                 and short time scales using singular perturbation
                 theory. In practice, the small parameter is discovered
                 using knowledge about the chemical reaction system that
                 is not necessarily contained in the mathematics of the
                 model. If a small parameter cannot be easily
                 identified, then the approach is typically abandoned.
                 The authors present a procedure that derives algebraic
                 expressions for dual time scales in mathematical models
                 of chemical reaction systems. Unlike conventional
                 practice, this derivation proceeds using only
                 information contained in the model, without knowledge
                 of a small parameter derived through external
                 considerations. The authors' procedure, Scales, is
                 based on rules that arise from the `art and practice'
                 of applying the quasi-steady-state assumption to derive
                 the Michaelis--Menton equations. The authors depart
                 from standard practice of singular perturbation theory,
                 using instead the viewpoint of Segel and Slemrod
                 (1989). They have implemented Scales in Maple. Scales
                 is closer to an `expert system' than a `scale oracle'
                 or decision procedure. Its shortcomings necessitate
                 subsequent verification of its results, typically
                 through numerical or laboratory experimentation. If
                 validated, additional computer algebra techniques can
                 be used to simplify the mathematical model and isolate
                 the long time scale behavior.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  classification = "A8220W (Computational modelling of chemical
                 kinetics); A8230V (Homogeneous catalysis); A8240
                 (Chemical kinetics and reactions: special regimes);
                 A8715D (Physical chemistry of biomolecular solutions;
                 C1220 (Simulation, modelling and identification); C4170
                 (Differential equations); C6170 (Expert systems); C7320
                 (Physics and chemistry computing); C7450 (Chemical
                 engineering computing); condensed states)",
  keywords =     "Algebraic expression; algorithms; Automatic
                 identification; Biochemistry; Biology computing;
                 Catalysis; Chemical kinetics model; Chemical reaction;
                 Dual time scale; Enzyme; Maple; Mathematical model;
                 Metabolism; Michaelis--Menton equations; Ordinary
                 differential equations; Pharmaceutical; Reaction
                 kinetics; Scales; Singular perturbation theory; Time
                 scale; verification",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Chemistry. {\bf G.1.7} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems. {\bf G.1.4} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation.",
  thesaurus =    "Chemical engineering computing; Differential
                 equations; Identification; Knowledge based systems;
                 Pharmaceutical industry; Proteins; Reaction kinetics
                 theory; Scaling phenomena; Symbol manipulation",
}

@InProceedings{Char:1994:SEP,
  author =       "B. Char and J. Johnson and D. Saunders and A. P.
                 Wack",
  title =        "Some Experiments with Parallel Bignum Arithmetic",
  crossref =     "Hong:1994:FIS",
  pages =        "94--103",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cooperman:1994:CPR,
  author =       "Gene Cooperman and Larry Finkelstein and Bryant York
                 and Michael Tselman",
  title =        "Constructing permutation representations for large
                 matrix groups",
  crossref =     "ACM:1994:IPI",
  pages =        "134--138",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p134-cooperman/",
  abstract =     "New techniques, both theoretical and practical, are
                 presented for constructing a permutation representation
                 for a matrix group. We assume that the resulting
                 permutation degree, $n,$ can be 10,000,000 and larger.
                 The key idea is to build the new permutation
                 representation using the conjugation action on a
                 conjugacy class of subgroups of prime order. A unique
                 signature for each group element corresponding to the
                 conjugacy class is used in order to avoid matrix
                 multiplication. The requirement of at least $n$ matrix
                 multiplications would otherwise have made the
                 computation hopelessly impractical. Additional software
                 optimizations are described, which reduce the CPU time
                 by at least an additional factor of 10. Further, a
                 special data structure is designed that serves both as
                 a search tree and as a hash array, while requiring
                 space of only $1.6 n log_2 n$ bits. The technique has
                 been implemented and tested on the sporadic simple
                 group Ly, discovered by Lyons (1972), in both a
                 sequential (SPARCserver 670 MP) and parallel SIMD
                 (MasPar MP-1) version. Starting with a generating set
                 for $Ly$ as a subgroup of $GL(111, 5)$, a set of
                 generating permutations for $Ly$ acting on 9, 606, 125
                 points is constructed as well as a base for this
                 permutation representation. The sequential version
                 required four days of CPU time to construct a data
                 structure which can be used to compute the permutation
                 image of an arbitrary matrix. The parallel version did
                 so in 12 hours. Work is in progress on a faster
                 parallel implementation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
                 USA",
  classification = "C4140 (Linear algebra); C4240C (Computational
                 complexity); C7310 (Mathematics computing)",
  keywords =     "algorithms; Conjugacy class; Conjugation action; Data
                 structure; design; Hash array; Large matrix groups;
                 Parallel version; performance; Permutation
                 representation; Permutation representations; Search
                 tree",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.2.1}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Permutations and combinations. {\bf E.1}
                 Data, DATA STRUCTURES, Arrays. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
  thesaurus =    "Computational complexity; Matrix multiplication;
                 Symbol manipulation",
}

@InProceedings{Corless:1994:SAC,
  author =       "Robert M. Corless",
  title =        "Sufficiency analysis for the calculus of variations",
  crossref =     "ACM:1994:IPI",
  pages =        "197--204",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p197-corless/",
  abstract =     "Many of the computations in the calculus of variations
                 are algebraic in nature: computing the Euler--Lagrange
                 equations and solving them, for example. However,
                 deciding whether or not the computed extremals provide
                 minima or maxima is an analytic problem, and one that
                 has not been previously attempted in a computer algebra
                 package. I describe here a Maple implementation of some
                 techniques for making these decisions, and detail some
                 successes and failures. Some of the failures point to
                 areas where computer algebra systems could be
                 improved.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Appl. Math., Univ. of Western Ontario,
                 London, Ont., Canada",
  classification = "C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algorithms; Calculus of variations; Computer algebra
                 package; Computer algebra systems; Euler--Lagrange
                 equations; Maple implementation; Sufficiency analysis;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Special-purpose algebraic systems.",
  thesaurus =    "Mathematics computing; Symbol manipulation",
}

@InProceedings{Cremanns:1994:CCP,
  author =       "Robert Cremanns and Friedrich Otto",
  title =        "Constructing canonical presentations for subgroups of
                 context-free groups in polynomial time-extended
                 abstract",
  crossref =     "ACM:1994:IPI",
  pages =        "147--153",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p147-cremanns/",
  abstract =     "Canonical presentations of groups are of interest,
                 since they provide structurally simple algorithms for
                 computing normal forms. A class of groups that has
                 received much attention is the class of context-free
                 groups. This class of groups can be characterized
                 algebraically as well as through some language
                 theoretical properties as well as through certain
                 combinatorial properties of presentations. Here we use
                 the fact that a finitely generated group is
                 context-free if and only if it admits a finite
                 canonical presentation of a certain form that we call a
                 virtually free presentation. Since finitely generated
                 subgroups of context-free groups are again
                 context-free, they admit presentations of the same
                 form. We present a polynomial-time algorithm that,
                 given a finite virtually free presentation of a
                 context-free group $G$ and a finite subset $U$ of $G$
                 as input, computes a virtually free presentation for
                 the subgroup $<U>$ of $G$ that is generated by $U$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Math./Inf., Kassel Univ., Germany",
  classification = "C1110 (Algebra); C4210L (Formal languages and
                 computational linguistics); C4240C (Computational
                 complexity)",
  keywords =     "algorithms; Canonical presentations; Context-free
                 groups; Language theoretical properties; languages;
                 Polynomial time; Subgroups; theory; verification;
                 Virtually free presentation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf F.4.2} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
                 Other Rewriting Systems, Grammar types. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Computational complexity; Context-free languages;
                 Group theory",
}

@InProceedings{Dalmas:1994:DCA,
  author =       "S. Dalmas and M. Gaetano and A. Sausse",
  title =        "Distributed Computer Algebra: the Central Control
                 Approach",
  crossref =     "Hong:1994:FIS",
  pages =        "104--113",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{DeBosschere:1994:LCB,
  author =       "K. {De Bosschere} and J.-M. Jacquet",
  title =        "Local and Conditional Blackboard Operations in Log:
                 Semantics, Applicability, and Implementation",
  crossref =     "Hong:1994:FIS",
  pages =        "34--43",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{DelPozo-Prieto:1994:ISP,
  author =       "A. {Del Pozo-Prieto} and J. J. Moreno-Navarro",
  title =        "Independent Subexpressions Parallelism with Delayed
                 Synchronization for Functional Logic Languages",
  crossref =     "Hong:1994:FIS",
  pages =        "316--325",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Denzinger:1994:RAP,
  author =       "J. Denzinger and S. Schulz",
  title =        "Recording, Analyzing and Presenting Distributed
                 Deduction Processes",
  crossref =     "Hong:1994:FIS",
  pages =        "114--123",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dingle:1994:BCC,
  author =       "Adam Dingle and Richard J. Fateman",
  title =        "Branch cuts in computer algebra",
  crossref =     "ACM:1994:IPI",
  pages =        "250--257",
  year =         "1994",
  DOI =          "https://doi.org/10.1145/190347.190424",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p250-dingle/",
  abstract =     "Most computer algebra systems provide little
                 assistance in working with expressions involving
                 functions with complex branch cuts. Worse, by their
                 ignorance of the existence of branch cuts, algebra
                 systems sometimes simplify complex expressions
                 incorrectly. We propose a computer representation for
                 branch cuts; we show how a complex expression's branch
                 cuts may be mechanically computed, and how an
                 expression with branch cuts may sometimes be
                 algebraically simplified within each of its branches.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Comput. Sci., California Univ., Berkeley, CA,
                 USA",
  classification = "C1100 (Mathematical techniques); C6130 (Data
                 handling techniques); C7310 (Mathematics computing)",
  keywords =     "Algebraic simplification; algorithms; Complex branch
                 cuts; Complex expressions; Computer algebra systems;
                 Computer representation; languages",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems. {\bf I.1.1} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Simplification of expressions. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Mathematica.",
  thesaurus =    "Functions; Symbol manipulation",
}

@InProceedings{Du:1994:ISA,
  author =       "Hong Du",
  title =        "On the isomorphisms of smooth algebraic curves",
  crossref =     "ACM:1994:IPI",
  pages =        "15--19",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p15-du/",
  abstract =     "I consider some problems of algebraic curves in a
                 constructive way, especially, I provide an algorithm
                 for determining whether two given smooth plane curves
                 are isomorphic and find all isomorphic maps. I present
                 a survey of some miscellaneous results related to the
                 classification of curves. In the appendix, I give some
                 other results which implies a more efficient algorithm
                 for deciding whether two plane curves are isomorphic
                 and find all isomorphic maps. The method can be
                 generalized to smooth projective complete intersection
                 varieties.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
  classification = "C4130 (Interpolation and function approximation);
                 C4260 (Computational geometry)",
  keywords =     "algorithms; Curve classification; Isomorphic maps;
                 Isomorphisms; Plane curves; Smooth algebraic curves;
                 Smooth plane curves; Smooth projective complete
                 intersection; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations.",
  thesaurus =    "Computational geometry; Curve fitting",
  xxabstract =   "In this paper, I have considered some problems of
                 algebraic curves in some constructive way, especially,
                 I give an algorithm for determining whether two given
                 smooth plane curves are isomorphic and finding all
                 isomorphic maps. I also have given a survey of some
                 miscellaneous results related to the classification of
                 curves. In the appendix, I give some other results
                 which implies a more efficient algorithm for deciding
                 whether two plane curves are isomorphic and finding all
                 isomorphic maps. It is clear our method in this paper
                 can be generalized to smooth projective complete
                 intersection varieties.",
}

@InProceedings{Dyer:1994:ASC,
  author =       "Charles C. Dyer",
  title =        "An application of symbolic computation in the physical
                 sciences",
  crossref =     "ACM:1994:IPI",
  pages =        "181--186",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p181-dyer/",
  abstract =     "An example of a problem in the physical sciences is
                 discussed where application of various symbolic
                 computation facilities available in many algebraic
                 computing systems leads to a significant expansion of
                 the range of problems that can be solved. Since most
                 interesting problems in the physical sciences
                 eventually require the numerical solution of systems of
                 equations, of various types, we introduce an example
                 and describe an approach to a solution, beginning at
                 the development of relevant differential equations,
                 using, for example REDUCE, and leading eventually to
                 the generation of highly efficient and stable numerical
                 code for the solution, using, in our case, the C
                 language. The use of SCOPE and GENTRAN, as well as
                 series packages in REDUCE are discussed. In many areas
                 of interest, a considerable amount of work has to be
                 performed to arrive at the symbolic equations to solve,
                 and this is particularly true in General Relativity and
                 related gravitation theories. Some packages, such as
                 REDTEN, for calculation in this field are discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Astron., Toronto Univ., Ont., Canada",
  classification = "C4170 (Differential equations); C7310 (Mathematics
                 computing); C7320 (Physics and chemistry computing)",
  keywords =     "Algebraic computing systems; algorithms; C language;
                 Calculation; Differential equations; General
                 Relativity; GENTRAN; Gravitation theories; languages;
                 Numerical code; Numerical solution; Physical sciences;
                 REDTEN; REDUCE; reliability; SCOPE; Series packages;
                 Symbolic computation; Symbolic equations;
                 verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, REDUCE. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf J.2} Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics. {\bf D.2.5} Software, SOFTWARE ENGINEERING,
                 Testing and Debugging, Debugging aids.",
  thesaurus =    "Differential equations; Gravitation; Mathematics
                 computing; Physics computing; Symbol manipulation",
}

@InProceedings{Emiris:1994:MBP,
  author =       "Ioannis Z. Emiris and Ashutosh Rege",
  title =        "Monomial bases and polynomial system solving (extended
                 abstract)",
  crossref =     "ACM:1994:IPI",
  pages =        "114--122",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p114-emiris/",
  abstract =     "This paper addresses the problem of efficient
                 construction of monomial bases for the coordinate rings
                 of zero-dimensional varieties. Existing approaches rely
                 on Gr{\"o}bner bases methods-in contrast, we make use
                 of recent developments in sparse elimination techniques
                 which allow us to strongly exploit the structural
                 sparseness of the problem at hand. This is done by
                 establishing certain properties of a matrix formula for
                 the sparse resultant of the given polynomial system. We
                 use this matrix construction to give a simpler proof of
                 the result of Pedersen and Sturmfels (1994) for
                 constructing monomial bases. The monomial bases so
                 obtained enable the efficient generation of
                 multiplication maps in coordinate rings and provide a
                 method for computing the common roots of a generic
                 system of polynomial equations with complexity singly
                 exponential in the number of variables and polynomial
                 in the number of roots. i.e. describe the
                 implementations based on our algorithms and provide
                 empirical results on the well-known problem of cyclic
                 $n$-roots; our implementation gives the first known
                 upper bounds in the case of $n=10$ and $n=11$. We also
                 present some preliminary results on root finding for
                 the Stewart platform and motion from point matches
                 problems in robotics and vision respectively.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Sci. Div., California Univ., Berkeley, CA,
                 USA",
  classification = "C7310 (Mathematics computing)",
  keywords =     "algorithms; theory; verification; Polynomial system
                 solving; Monomial bases; Coordinate rings;
                 Zero-dimensional varieties; Gr{\"o}bner bases; Sparse
                 elimination techniques; Matrix formula; Multiplication
                 maps; Root finding",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Encarnacion:1994:MAC,
  author =       "Mark J. Encarnaci{\'o}n",
  title =        "On a modular algorithm for computing {GCDs} of
                 polynomials over algebraic number fields",
  crossref =     "ACM:1994:IPI",
  pages =        "58--65",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p58-encarnacion/",
  abstract =     "Modular methods for computing the gcd of two
                 univariate polynomials over an algebraic number field
                 require {\em a priori\/} knowledge about the
                 denominators of the rational numbers in the
                 representation of the gcd. We derive a multiplicative
                 bound for these denominators without assuming that the
                 number generating the field is an algebraic integer.
                 Consequently, the gcd algorithm of Langemyr and
                 McCallum [{\em J. Symbolic Computation\/}, 8:429-448,
                 1989] can now be applied directly to polynomials that
                 are not necessarily represented in terms of an
                 algebraic integer. Worst-case analyses and experiments
                 with an implementation show that by avoiding a
                 conversion of representation the reduction in the
                 computing time can be significant. We also suggest the
                 use of an algorithm for recovering a rational number
                 from its modular residue so that the denominator bound
                 need not be computed explicitly. Experiments and
                 analyses indicate that this is a good practical
                 alternative.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C6130
                 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "A priori knowledge; Algebraic number fields;
                 algorithms; Computing GCDs; Denominators;
                 experimentation; Modular algorithm; Multiplicative
                 bound; Polynomials; theory; verification; Worst-case
                 analysis",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Faugere:1994:PGB,
  author =       "J. C. Faugere",
  title =        "Parallelization of {Gr{\"o}bner} Basis",
  crossref =     "Hong:1994:FIS",
  pages =        "124--132",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ganzha:1994:SSI,
  author =       "V. G. Ganzha and E. V. Vorozhtsov and J. Boers and J.
                 A. {van Hulzen}",
  title =        "Symbolic-numeric stability investigations of
                 {Jameson}'s schemes for the thin-layer {Navier--Stokes}
                 equations",
  crossref =     "ACM:1994:IPI",
  pages =        "234--241",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p234-ganzha/",
  abstract =     "The Navier--Stokes equations governing the
                 three-dimensional flows of a viscous, compressible,
                 heat-conducting gas and augmented by turbulence
                 modeling present the most realistic model for gas flows
                 around the elements of aircraft configurations. We
                 study the stability of one of the Jameson's schemes of
                 1981, which approximates the set of five Navier--Stokes
                 equations completed by the turbulence model of Baldwin
                 and Lomax (1978). The analysis procedure implements the
                 check-up of the necessary von Neumann stability
                 criterion. It is shown with the aid of the proposed
                 symbolic-numeric strategy that the physical viscosity
                 terms in the Navier--Stokes equations have a dominant
                 effect on the sizes of the stability region in
                 comparison with the heat conduction terms. It turns out
                 that the consideration of turbulence with the aid of
                 eddy viscosity model of Baldwin and Lomax has an
                 insignificant effect on the size of the necessary
                 stability region.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
                 Novosibirsk, Russia",
  classification = "A0260 (Numerical approximation and analysis); A4710
                 (General fluid dynamics theory, simulation and other
                 computational methods); A4725 (Turbulent flows,
                 convection, and heat transfer); C4170 (Differential
                 equations); C7320 (Physics and chemistry computing)",
  keywords =     "3D flows; Aircraft configurations; algorithms;
                 Compressible gas; Eddy viscosity model; Heat-conducting
                 gas; Jameson schemes; languages; Stability region;
                 Symbolic-numeric stability; Thin-layer Navier--Stokes
                 equations; Turbulence modeling; Viscosity terms;
                 Viscous gas; Von Neumann stability",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Aerospace. {\bf J.2} Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Physics. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.4} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation.",
  thesaurus =    "Navier--Stokes equations; Numerical stability; Physics
                 computing; Symbol manipulation; Turbulence; Viscosity",
}

@InProceedings{Gautier:1994:PSP,
  author =       "T. Gautier and J.-L. Roch",
  title =        "{PAC++} System and Parallel Algebraic Numbers
                 Computation",
  crossref =     "Hong:1994:FIS",
  pages =        "145--153",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:1994:FAR,
  author =       "Mark Giesbrecht",
  title =        "Fast algorithms for rational forms of integer
                 matrices",
  crossref =     "ACM:1994:IPI",
  pages =        "305--311",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p305-giesbrecht/",
  abstract =     "A Monte Carlo type probabilistic algorithm is
                 presented for finding the Frobenius rational form $F$
                 in $Z^{n*n}$ of any $A$ in $Z^{n*n}$ which requires an
                 expected number of $O(n^4(\log{}n+//A//)^2)$ bit
                 operations using standard integer and matrix arithmetic
                 (where $//A//$ is the largest absolute value of any
                 entry of $A$). This improves dramatically on the
                 fastest previously known algorithm, which requires
                 $O(n^6\log{}//A//)$ bit operations using fast integer
                 arithmetic. We also give a Las Vegas type probabilistic
                 algorithm which finds the Frobenius form $F$ and a
                 transition matrix $U$ in $Q^{n*n}$ such that
                 $U^{-1}/AU=F$ and requires an expected number of
                 $O(n^5(\log{}n+log //A//)^{52})$ bit operations.
                 Finally, a Las Vegas algorithm for computing the
                 rational Jordan form of an integer matrix is shown,
                 which requires about the same number of bit operations
                 as our algorithm to find the Frobenius form, plus the
                 time required to factor the characteristic polynomial
                 of that matrix.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  classification = "C1140G (Monte Carlo methods); C4140 (Linear
                 algebra); C4240C (Computational complexity); C7310
                 (Mathematics computing)",
  keywords =     "algorithms; Bit operations; Characteristic polynomial;
                 Expected number; Fast algorithms; Fast integer
                 arithmetic; Frobenius rational form; Integer matrices;
                 Largest absolute value; Las Vegas type probabilistic
                 algorithm; Matrix arithmetic; Monte Carlo type
                 probabilistic algorithm; Rational Jordan form; Standard
                 integer arithmetic; Transition matrix; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo). {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
  thesaurus =    "Computational complexity; Matrix algebra; Monte Carlo
                 methods; Symbol manipulation",
}

@InProceedings{Gladitz:1994:PIG,
  author =       "K. Gladitz and H. Kuchen",
  title =        "Parallel Implementation of the Gamma-Operation on
                 Bags",
  crossref =     "Hong:1994:FIS",
  pages =        "154--163",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gonzalez:1994:MPE,
  author =       "A. Gonzalez and J. Tubella",
  title =        "The Multipath Parallel Execution Model for {Prolog}",
  crossref =     "Hong:1994:FIS",
  pages =        "164--173",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Goriely:1994:HCM,
  author =       "Alain Goriely and Michael Tabor",
  title =        "How to compute the {Melnikov} vector?",
  crossref =     "ACM:1994:IPI",
  pages =        "205--210",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p205-goriely/",
  abstract =     "It is shown that transverse homoclinic intersections
                 such as the ones described by the Melnikov theory can
                 be computed by a local analysis of the complex-time
                 singularities of the solutions. This provides a new
                 algorithmic procedure to compute homoclinic
                 intersections in $n$-dimensions once the homoclinic
                 manifold is known. It also gives new insights on the
                 singularity structure of integrable and nonintegrable
                 systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Libre de Bruxelles, Belgium",
  classification = "C1110 (Algebra); C4170 (Differential equations);
                 C4240 (Programming and algorithm theory)",
  keywords =     "Algorithm; algorithms; Complex-time singularities;
                 Differential equations; Homoclinic intersection;
                 Homoclinic manifold; Local analysis; Melnikov theory;
                 Melnikov vector; N-dimensions; Singularity structure;
                 Symbolic computation; theory; Transverse homoclinic
                 intersections",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures.",
  thesaurus =    "Algorithm theory; Differential equations; Symbol
                 manipulation; Vectors",
}

@InProceedings{Graebe:1994:PGF,
  author =       "H.-G. Graebe and W. Lassner",
  title =        "A Parallel {Gr{\"o}bner} Factorizer",
  crossref =     "Hong:1994:FIS",
  pages =        "174--180",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gray:1994:MPE,
  author =       "Simon Gray and Norbert Kajler and Paul Wang",
  title =        "{MP}: a protocol for efficient exchange of
                 mathematical expressions",
  crossref =     "ACM:1994:IPI",
  pages =        "330--335",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p330-gray/",
  abstract =     "The Multi Protocol (MP) is designed for integrating
                 symbolic, numeric, graphics, document processing, and
                 other tools for scientific computation, into a single
                 distributed problem-solving environment. MP is layered,
                 reflecting the logically distinct aspects of tool
                 integration. Data representation issues are addressed
                 by specifying a set of basic data types and a mechanism
                 for constructing non-basic types. MP passes all data in
                 the form of annotated parse trees. The parse tree
                 provides a simple, flexible and tool-independent way to
                 represent and exchange data, and annotations provide a
                 powerful and generic expressive facility for
                 transmitting additional information. MP also provides
                 efficient encodings for numeric data and includes
                 different types of optimizations to reduce the cost of
                 exchanging data. The optimizations are important when
                 transmitting large expressions typically encountered in
                 symbolic and numeric computation. MP is extensible.
                 Users can define additional sets of operators and
                 annotations as well as tailor the generic optimization
                 mechanisms to efficiently encode their own data
                 structures. A clear distinction between MP-defined and
                 user-defined definitions is enforced.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
                 USA",
  classification = "C1180 (Optimisation techniques); C4210L (Formal
                 languages and computational linguistics); C5640
                 (Protocols); C6115 (Programming support); C6120 (File
                 organisation); C6130B (Graphics techniques); C6130D
                 (Document processing techniques); C6150N (Distributed
                 systems software); C6170K (Knowledge engineering
                 techniques); C7310 (Mathematics computing)",
  keywords =     "algorithms; Annotated parse trees; Annotations; Basic
                 data types; Data exchange cost reduction; Data
                 representation issues; design; Distributed
                 problem-solving environment; Document processing;
                 Efficient encodings; Efficient mathematical expression
                 exchange; Generic optimization mechanisms; Graphics;
                 languages; Large expression transmission; Layered; MP
                 protocol; Multi Protocol; Nonbasic types; Numeric
                 processing; Operators; performance; Scientific
                 computation; Symbolic processing; Tool integration",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C. {\bf D.2.2} Software, SOFTWARE
                 ENGINEERING, Design Tools and Techniques.",
  thesaurus =    "Computer graphics; Distributed processing; Document
                 handling; Grammars; Mathematics computing; Natural
                 sciences computing; Optimisation; Problem solving;
                 Protocols; Software tools; Symbol manipulation; Tree
                 data structures",
}

@InProceedings{Guergueb:1994:EAT,
  author =       "Ahmed Guergueb and Jean Mainguen{\'e} and
                 Marie-Fran{\c{c}}oise Roy",
  title =        "Examples of automatic theorem proving in real
                 geometry",
  crossref =     "ACM:1994:IPI",
  pages =        "20--24",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p20-guergueb/",
  abstract =     "We show that computer algebra methods in mechanical
                 geometry theorem proving can also be applied to obtain
                 new theorems involving inequalities. An interesting
                 feature is that in real geometry, several cases can
                 occur, none of them being more generic than the other.
                 The examples we give come from the geometry of the
                 triangle, more precisely comparing radii of circles
                 defined in the triangle.",
  acknowledgement = ack-nhfb,
  affiliation =  "Rennes I Univ., France",
  classification = "C4260 (Computational geometry); C7310 (Mathematics
                 computing)",
  keywords =     "algorithms; Automatic theorem proving; Computer
                 algebra methods; Inequalities; Mechanical geometry
                 theorem proving; Radii of circles; theory; Triangle;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic, Mechanical theorem proving.",
  thesaurus =    "Computational geometry; Symbol manipulation; Theorem
                 proving",
  xxtitle =      "Examples of automatic theorem proving a real
                 geometry",
}

@InProceedings{Hammond:1994:PFP,
  author =       "K. Hammond",
  title =        "Parallel Functional Programming: An Introduction
                 (Invited Tutorial)",
  crossref =     "Hong:1994:FIS",
  pages =        "181--193",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Harris:1994:IRR,
  author =       "Jason F. Harris",
  title =        "Inheritance of rewrite rule structures applied to
                 symbolic computation",
  crossref =     "ACM:1994:IPI",
  pages =        "318--323",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p318-harris/",
  abstract =     "This paper defines and presents a method of
                 inheritance for structures that are defined by rewrite
                 rules. This method is natural in the sense that it can
                 be easily and cleanly implemented in rewrite rules
                 themselves. This framework of inheritance is not that
                 of classical Object-Oriented Programming. It is shown
                 that this inheritance has particular application to
                 structures implemented in rewrite rules and, more
                 generally, to symbolic computation. The treatment is
                 practical, and examples are presented in {\em
                 Mathematica\/} for concreteness.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Phys. and Astron., Canterbury Univ.,
                 Christchurch, New Zealand",
  classification = "C4210L (Formal languages and computational
                 linguistics); C6110F (Formal methods); C6120 (File
                 organisation)",
  keywords =     "Abstract data type; Algebraic specification;
                 algorithms; Inheritance; Natural method; Rewrite rule
                 structures; Rewriting; Structure; Symbolic computation;
                 Symbolic specification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Grammars and Other Rewriting Systems. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Mathematica. {\bf D.1.5} Software, PROGRAMMING
                 TECHNIQUES, Object-oriented Programming.",
  thesaurus =    "Algebraic specification; Inheritance; Rewriting
                 systems; Symbol manipulation",
}

@InProceedings{Hasegawa:1994:PMM,
  author =       "R. Hasegawa and M. Koshimura",
  title =        "An {AND} Parallelization Method for {MGTP} and Its
                 Evaluation",
  crossref =     "Hong:1994:FIS",
  pages =        "194--203",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hill:1994:VM,
  author =       "J. M. D. Hill and K. M. Clarke and R. Bornat",
  title =        "The Vectorisation Monad",
  crossref =     "Hong:1994:FIS",
  pages =        "204--213",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jacobs:1994:ANA,
  author =       "David P. Jacobs",
  title =        "The {Albert} nonassociative algebra system: a progress
                 report",
  crossref =     "ACM:1994:IPI",
  pages =        "41--44",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p41-jacobs/",
  abstract =     "After four years of experience with the nonassociative
                 algebra program Albert, we highlight its successes and
                 drawbacks. Among its successes are the discovery of
                 several new results in nonassociative algebra. Each of
                 these results has been independently verified-either
                 with a traditional mathematical proof or with an
                 independent computation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Clemson Univ., SC, USA",
  classification = "C7310 (Mathematics computing)",
  keywords =     "Albert; algorithms; Computation; Mathematical proof;
                 Nonassociative algebra system; theory",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Algebra; Mathematics computing; Symbol manipulation;
                 Theorem proving",
}

@InProceedings{Jenks:1994:HMA,
  author =       "Richard D. Jenks and Barry M. Trager",
  title =        "How to make {AXIOM} into a {Scratchpad}",
  crossref =     "ACM:1994:IPI",
  pages =        "32--40",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p32-jenks/",
  abstract =     "Scratchpad (Griesmer and Jenks, 1971) was a computer
                 algebra system that had one principal representation
                 for mathematical formulae based on expression trees.
                 Its user interface design was based on a
                 pattern-matching paradigm with infinite rewrite rule
                 semantics, providing what we believe to be the most
                 natural paradigm for interactive symbolic problem
                 solving. Like M and M, however, user programs were
                 interpreted, often resulting in poor performance
                 relative to similar facilities coded in standard
                 programming languages such as FORTRAN and C. Scratchpad
                 development stopped in 1976 giving way to a new system
                 design that evolved into AXIOM. AXIOM has a
                 strongly-typed programming language for building a
                 library of parameterized types and algorithms, and a
                 type-inferencing interpreter that accesses the library
                 and can build any of an infinite number of types for
                 interactive use. We suggest that the addition of an
                 expression tree type to AXIOM can allow users to
                 operate with the same freedom and convenience of
                 untyped systems without giving up the expressive power
                 and run-time efficiency provided by the type system. We
                 also present a design that supports a multiplicity of
                 programming styles, from the Scratchpad
                 pattern-matching paradigm to functional programming to
                 more conventional procedural programming.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C6180 (User interfaces); C7310 (Mathematics
                 computing)",
  keywords =     "algorithms; AXIOM; C; Computer algebra system; design;
                 Expression trees; FORTRAN; Functional programming;
                 Infinite rewrite rule semantics; languages; Library;
                 Mathematical formulae; Pattern-matching; performance;
                 Procedural programming; Run-time efficiency;
                 Scratchpad; Strongly-typed programming language;
                 Symbolic problem solving; Type-inferencing interpreter;
                 Untyped systems; User interface design; User programs",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf D.3.3}
                 Software, PROGRAMMING LANGUAGES, Language Constructs
                 and Features, Data types and structures. {\bf F.2.2}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Pattern matching. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions.",
  thesaurus =    "Mathematics computing; Pattern matching; Program
                 interpreters; Programming; Symbol manipulation; User
                 interfaces",
}

@InProceedings{Kaib:1994:FVG,
  author =       "M. Kaib",
  title =        "A fast variant of the {Gaussian} reduction algorithm",
  crossref =     "Adleman:1994:ANT",
  pages =        "159",
  year =         "1994",
  bibdate =      "Thu Sep 26 05:50:11 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Summary form only given. We propose a fast variant of
                 the Gaussian algorithm for the reduction of
                 two-dimensional lattices for the $\ell_1$-, $\ell_2$-
                 and $\ell_\infty-norm$. The algorithm uses at most
                 $O(M(B)(n+log B))$ bit operations for the
                 $\ell_2$-norm, $O(nM(B)\log{}B)$ bit operations for the
                 $\ell_\infty$-norm and in $O(n \log{}n M (B) \log{}B)$
                 bit operations for the $\ell_1$-norm on input vectors
                 $a$, $b$ in $Z^n$ with norm at most $2^B$ where $M(B)$
                 is a time bound for $B$-bit integer multiplication.
                 This generalizes Schonhages fast algorithm for monotone
                 reduction of binary quadratic forms (Proc. ISSAC 1991,
                 ACM 1991, p. 128--133) to the centered case and to
                 various norms. The basic idea is to perform most of the
                 arithmetic on the leading bits of the integers,
                 following the techniques of the fast gcd-algorithms due
                 to Lehmer and Schonhage. We extend the techniques to
                 the classical `centered' case. The Gaussian algorithm
                 performs reduction steps $(a, b)$ to
                 $H(\pm(b-\mu{}a),a)$ where the integer $\mu$ is chosen
                 to minimize $//b-\mu{}a//$. Our new consideration is,
                 that the core of the Gaussian algorithm operates stable
                 until the approximation error exceeds $^1/_12 //a//$,
                 what is valid for arbitrary norms. We use the
                 characterization of the transformation matrices which
                 Kaib and Schnorr gave in their sharp worst case
                 analysis for the number of reduction steps for
                 arbitrary norms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Math., Frankfurt Univ., Germany",
  classification = "C1160 (Combinatorial mathematics)",
  keywords =     "Approximation error; Arbitrary norms; B-bit integer
                 multiplication; Binary quadratic forms; Fast
                 gcd-algorithms; Fast variant; Gaussian algorithm;
                 Gaussian reduction algorithm; Input vectors; Integers;
                 Monotone reduction; Transformation matrices;
                 Two-dimensional lattices",
  thesaurus =    "Arithmetic; Data reduction; Matrix algebra; Number
                 theory",
}

@InProceedings{Kakas:1994:PAL,
  author =       "A. C. Kakas and G. A. Papadopoulos",
  title =        "Parallel Abduction in Logic Programming",
  crossref =     "Hong:1994:FIS",
  pages =        "214--224",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:1994:AFS,
  author =       "Erich Kaltofen",
  title =        "Asymptotically fast solution of {Toeplitz-like}
                 singular linear systems",
  crossref =     "ACM:1994:IPI",
  pages =        "297--304",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p297-kaltofen/",
  abstract =     "The Toeplitz likeness of a matrix (T. Kailath et al.,
                 1979) is the generalization of the notion that a matrix
                 is Toeplitz. Block matrices with Toeplitz blocks, such
                 as the Sylvester matrix corresponding to the resultant
                 of two univariate polynomials, are Toeplitz-like, as
                 are products and inverses of Toeplitz-like matrices.
                 The displacement rank of a matrix is a measure for the
                 degree of being Toeplitz-like. For example, an $r*s$
                 block matrix with Toeplitz blocks has displacement rank
                 $r+s$ whereas a generic $N*N$ matrix has displacement
                 rank $N$. A matrix of displacement rank $\alpha$ can be
                 implicitly represented by a sum of $\alpha$ matrices,
                 each of which is the product of a lower triangular and
                 an upper triangular Toeplitz matrix. Such a $\Sigma LU$
                 representation can usually be obtained efficiently. We
                 consider the problem of computing a solution to a
                 possibly singular linear system $Ax=b$ with
                 coefficients in an arbitrary field, where $A$ is an
                 $N\times{}N$ matrix of displacement rank $\alpha$ given
                 in $\Sigma LU$ representation. By use of randomization
                 we show that if the system is solvable we can find a
                 vector that is uniformly sampled from the solution
                 manifold in $O(\alpha ^2N(logN)^2 loglogN)$ expected
                 arithmetic operations in the field of entries. In case
                 no solution exists, this fact is discovered by our
                 algorithm. In asymptotically the same time we can also
                 compute the rank of $A$ and the determinant of a
                 nonsingular $A$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C4140 (Linear algebra); C4240C (Computational
                 complexity); C6130 (Data handling techniques); C7310
                 (Mathematics computing)",
  keywords =     "$\Sigma$ LU representation; Arithmetic operations;
                 Asymptotically fast solution; Block matrices;
                 Determinant; Displacement rank; Randomization; Singular
                 linear system; Solution manifold; Sylvester matrix;
                 theory; Toeplitz blocks; Toeplitz like singular linear
                 systems; Toeplitz likeness; Univariate polynomials;
                 Vector; verification",
  subject =      "{\bf G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo). {\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Computational complexity; Linear systems; Symbol
                 manipulation; Toeplitz matrices",
}

@InProceedings{Kaltofen:1994:FHP,
  author =       "Erich Kaltofen and Austin Lobo",
  title =        "Factoring high-degree polynomials by the black box
                 {Berlekamp} algorithm",
  crossref =     "ACM:1994:IPI",
  pages =        "90--98",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p90-kaltofen/",
  abstract =     "Modern techniques for solving structured linear
                 systems over finite fields, which use the coefficient
                 matrix as a black box and require an efficient
                 algorithm for multiplying this matrix by a vector, are
                 applicable to the classical algorithm for factoring a
                 univariate polynomial over a finite field by Berlekamp
                 (1967 and 1970). The present authors report on a
                 computer implementation of this idea that is based on
                 the parallel block Wiedemann linear system solver,
                 Coppersmith (1994) and Kaltofen (1993 and 1995). The
                 program uses randomization and they also study the
                 expected run time behavior of their method. The
                 asymptotically fastest known algorithm for factoring a
                 polynomial over a finite field is by von zur Gathen and
                 Shoup (1992). Shoup (1993) has subsequently implemented
                 the equal degree part of that algorithm making use of
                 FFT-based polynomial arithmetic. The present authors
                 show that a sequential version of the black box
                 Berlekamp algorithm is strongly related to their method
                 and allows for the same asymptotic speed-ups, at least
                 within a logarithmic factor. It is also possible to
                 realize the Niederreiter approach, Niederreiter and
                 Gijttfert (1994) by black box linear algebra.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4140 (Linear algebra); C4240
                 (Programming and algorithm theory)",
  keywords =     "algorithms; Black box Berlekamp algorithm; Coefficient
                 matrix; Factoring; Finite field; High-degree
                 polynomials; languages; Matrix multiplication;
                 Polynomial factorization; Structured linear system;
                 theory; Univariate polynomial",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Linear systems (direct and
                 iterative methods).",
  thesaurus =    "Algorithm theory; Matrix multiplication; Polynomial
                 matrices; Polynomials; Symbol manipulation",
}

@InProceedings{Kaltofen:1994:PST,
  author =       "E. Kaltofen and V. Pan",
  title =        "Parallel Solution of {Toeplitz} and {Toeplitz}-Like
                 Linear Systems Over Fields of Small Positive
                 Characteristic",
  crossref =     "Hong:1994:FIS",
  pages =        "225--233",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kapur:1994:AGR,
  author =       "Deepak Kapur and Tushar Saxena and Lu Yang",
  title =        "Algebraic and geometric reasoning using {Dixon}
                 resultants",
  crossref =     "ACM:1994:IPI",
  pages =        "99--107",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p99-kapur/",
  abstract =     "Dixon's method for computing multivariate resultants
                 by simultaneously eliminating many variables is
                 reviewed. The method is found to be quite restrictive
                 because often the Dixon matrix is singular, and the
                 Dixon resultant vanishes identically yielding no
                 information about solutions for many algebraic and
                 geometry problems. We extend Dixon's method for the
                 case when the Dixon matrix is singular, but satisfies a
                 condition. An efficient algorithm is developed based on
                 the proposed extension for extracting conditions for
                 the existence of affine solutions of a finite set of
                 polynomials. Using this algorithm, numerous geometric
                 and algebraic identities are derived for examples which
                 appear intractable with other techniques of
                 triangulation such as the successive resultant method,
                 the Gr{\"o}bner basis method, Macaulay resultants and
                 Characteristic set method. Experimental results suggest
                 that the resultant of a set of polynomials which are
                 symmetric in the variables is relatively easier to
                 compute using the extended Dixon's method.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., State Univ. of New York,
                 Albany, NY, USA",
  classification = "C1110 (Algebra); C1230 (Artificial intelligence);
                 C4260 (Computational geometry); C7310 (Mathematics
                 computing)",
  keywords =     "algorithms; experimentation; Geometric reasoning;
                 Dixon resultants; Multivariate resultants; Gr{\"o}bner
                 basis method; Macaulay resultants; Characteristic set
                 method; Polynomials",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Polynomials; Spatial reasoning; Symbol manipulation",
}

@InProceedings{Kaser:1994:HPR,
  author =       "O. Kaser and C. R. Ramakrishnan and R. C. Sekar",
  title =        "A High Performance Runtime System for Parallel
                 Evaluation of Lazy Languages",
  crossref =     "Hong:1994:FIS",
  pages =        "234--243",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kesseler:1994:RGC,
  author =       "M. Kesseler",
  title =        "Reducing Graph Copying Costs --- Time to Wrap it up",
  crossref =     "Hong:1994:FIS",
  pages =        "244--253",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Konno:1994:PMC,
  author =       "K. Konno and M. Nagatsuka and N. Kobayashi and S.
                 Matsuoka",
  title =        "{PARCS}: An {MPP}-Oriented {CLP} Language",
  crossref =     "Hong:1994:FIS",
  pages =        "254--263",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krandick:1994:BEI,
  author =       "W. Krandick and T. Jebelean",
  title =        "Bidirectional Exact Integer Division",
  crossref =     "Hong:1994:FIS",
  pages =        "264--272",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{LakshmanYN:1994:CSS,
  author =       "{Lakshman Y. N.} and B. David Saunders",
  title =        "On computing sparse shifts for univariate
                 polynomials",
  crossref =     "ACM:1994:IPI",
  pages =        "108--113",
  year =         "1994",
  bibdate =      "Sat Apr 25 12:53:49 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p108-lakshman/",
  abstract =     "In this paper, we consider the problem of computing
                 $t$-sparse shifts for univariate polynomials. Given a
                 polynomial $f(x)$ in $F(x)$ of degree $d$ (where $F$ is
                 a field of characteristic $O$), consider the
                 representation of $f(x)$ in the basis
                 $1,x-\alpha,(x-\alpha)^2,\ldots{}$ for some $\alpha$ in
                 $K$, an extension of $F$, i.e.,
                 $f(x)=\sum_{i=0}^d{}F_i(x-\alpha)^i$. Let $t$ be a
                 positive integer $<=I d$. We say that $\alpha$ is a
                 $t$-sparse shift for $f(x)$ (or, $f(x)$ is $t$-sparse
                 in the shifted basis
                 $1,x-\alpha,(x-\alpha)^2,\ldots{}$) if at most $t$ of
                 the coefficients $F_i$ are non-zero. The main problem
                 that we address is: given an $f(x)$ and $t$ as above,
                 can we efficiently compute a $t$-sparse shift for
                 $f(x)$ if one exists? We construct an efficient
                 algorithm for solving this problem and answer several
                 related questions of interest.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C7310
                 (Mathematics computing)",
  keywords =     "algorithms; Polynomial; Sparse shifts; theory;
                 Univariate polynomials",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{LaScala:1994:AC,
  author =       "R. La Scala",
  title =        "An algorithm for complexes",
  crossref =     "ACM:1994:IPI",
  pages =        "264--268",
  year =         "1994",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "For computing free resolutions over a polynomial ring,
                 the usual approach consists in iterating B.
                 Buchberger's (1985) algorithm for each module in the
                 resolution. We propose one single algorithm which can
                 be viewed as a generalization of Buchberger's to chain
                 complexes. The algorithm is based on the use of
                 syzygies, due to H. M. Moller, T. Mora and C. Traverso
                 (1992), as criteria for avoiding useless computation of
                 S-polynomials. Some strategies for the pairs selection
                 in complexes are studied and tested in some
                 experiments.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Pisa Univ., Italy",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics computing)",
  keywords =     "Free resolutions; Polynomial ring; Chain complexes;
                 Syzygies; S-polynomials; Pairs selection; Gr{\"o}bner
                 bases",
  thesaurus =    "Large-scale systems; Polynomials; Programming theory;
                 Symbol manipulation",
}

@InProceedings{Leung:1994:CSD,
  author =       "H.-F. Leung and K. L. Clark",
  title =        "Constraint Solving in Distributed Concurrent Logic
                 Programming",
  crossref =     "Hong:1994:FIS",
  pages =        "273--283",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Licciardi:1994:IHC,
  author =       "Sandra Licciardi and Teo Mora",
  title =        "Implicitization of hypersurfaces and curves by the
                 {Primbasissatz} and basis conversion",
  crossref =     "ACM:1994:IPI",
  pages =        "191--196",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p191-licciardi/",
  abstract =     "An algorithm for implicitizing curves and
                 hypersurfaces is proposed which reduces the problem to
                 a 0-dimensional one by the Primbasissatz and solves it
                 by FGLM. Also, a high-dimensional FGLM algorithm is
                 discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Inf. e Sci. dell'Inf., Genoa Univ.,
                 Italy",
  classification = "C4130 (Interpolation and function approximation);
                 C4260 (Computational geometry)",
  keywords =     "0-Dimensional problem; algorithms; Basis conversion;
                 Curves; FGLM; High-dimensional FGLM algorithm;
                 Hypersurfaces; Primbasissatz; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations.",
  thesaurus =    "Computational geometry; Curve fitting; Polynomials;
                 Surface fitting",
}

@InProceedings{LopezGarcia:1994:TGB,
  author =       "P. {Lopez Garcia} and M. Hermenegildo and S. K.
                 Debray",
  title =        "Towards Granularity Based Control of Parallelism in
                 Logic Programs",
  crossref =     "Hong:1994:FIS",
  pages =        "133--144",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Luks:1994:CNP,
  author =       "Eugene M. Luks and Ferenc R{\'a}k{\'o}czi and Charles
                 R. B. Wright",
  title =        "Computing normalizers in permutation $p$-groups",
  crossref =     "ACM:1994:IPI",
  pages =        "139--146",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p139-luks/",
  abstract =     "Let $G$ and $H$ be subgroups of a finite $p$-group of
                 permutations. We describe the theory and implementation
                 of a polynomial-time algorithm for computing the
                 normalizer of $H$ in $G$. The method employs the
                 imprimitivity structure and an associated canonical
                 chief series to reduce to linear problems with fast
                 solutions. An implementation in GAP exhibits marked
                 speedups over general-purpose methods applied to the
                 same groups. There are analogous procedures and timings
                 for the problem of testing conjugacy of subgroups of
                 $p$-groups, and implementations are planned. It is an
                 easy matter, also, to extend the application to general
                 nilpotent groups.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. and Inf. Sci., Oregon Univ., Eugene,
                 OR, USA",
  classification = "C4240C (Computational complexity); C7310
                 (Mathematics computing)",
  keywords =     "algorithms; Canonical chief series; Conjugacy of
                 subgroups; Nilpotent groups; Permutation $p$-groups;
                 Polynomial-time algorithm; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.2.1}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Permutations and combinations. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
  thesaurus =    "Computational complexity; Group theory;
                 Renormalisation; Series [mathematics]; Symbol
                 manipulation",
}

@InProceedings{Man:1994:FPD,
  author =       "Yiu-Kwong Man and Francis J. Wright",
  title =        "Fast polynomial dispersion computation and its
                 application to indefinite summation",
  crossref =     "ACM:1994:IPI",
  pages =        "175--180",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p175-man/",
  abstract =     "An algorithm for computing the dispersion of one or
                 two polynomials is described, based on irreducible
                 factorization. It is demonstrated that in practice it
                 is faster than the `conventional' resultant-based
                 algorithm, at least for small problems. It can be
                 applied to algorithms for indefinite summation and
                 closed-form solution of linear difference equations. A
                 brief survey of existing mostly resultant-based
                 dispersion algorithms is given and the complexity of
                 the resultant involved is analysed. The effectiveness
                 of the proposed algorithm applied to indefinite
                 summation is demonstrated by some examples that are not
                 easily summed by the standard facilities in several
                 computer algebra systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Queen Mary and Westfield Coll.,
                 London, UK",
  classification = "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  keywords =     "algorithms; Closed-form solution; Complexity; Computer
                 algebra systems; Fast polynomial dispersion
                 computation; Indefinite summation; Irreducible
                 factorization; languages; Linear difference equations;
                 performance; Resultant-based algorithm; Resultant-based
                 dispersion algorithms; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 REDUCE.",
  thesaurus =    "Computational complexity; Difference equations;
                 Polynomials; Symbol manipulation",
}

@InProceedings{Mandache:1994:GBA,
  author =       "Ana Maria Mandache",
  title =        "The {Gr{\"o}bner} basis algorithm and subresultant
                 theory",
  crossref =     "ACM:1994:IPI",
  pages =        "123--128",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p123-mandache/",
  abstract =     "We investigate the possibility of constructing for
                 Gr{\"o}bner bases a concept similar to the one provided
                 by subresultants for polynomial remainder sequences.
                 Namely, we try to express the Gr{\"o}bner basis
                 polynomials obtained during the algorithm in terms of
                 matrices having on each row the coefficients of a
                 polynomial from the input basis, shifted by
                 multiplication with a power product. We prove that for
                 the general form of Buchberger's algorithm, the
                 Gr{\"o}bner basis polynomials not only cannot be
                 expressed as determinant polynomials but, in general,
                 they cannot even be obtained by a Gaussian
                 elimination-like process from such matrices. For the
                 Gr{\"o}bner basis polynomials that can be expressed as
                 determinant polynomials we show that we can detect
                 common factors of the coefficients without computing
                 gcd's. For achieving this we generalize Bareiss' matrix
                 triangularization method.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1110 (Algebra); C7310 (Mathematics computing)",
  keywords =     "algorithms; theory; verification; Gr{\"o}bner basis;
                 Subresultant theory; Gr{\"o}bner basis polynomials;
                 Matrix triangularization; Buchberger's algorithm;
                 Determinant polynomials",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Manocha:1994:CSS,
  author =       "Dinesh Manocha",
  title =        "Computing selected solutions of polynomial equations",
  crossref =     "ACM:1994:IPI",
  pages =        "1--8",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p1-manocha/",
  abstract =     "We present efficient and accurate algorithms to
                 compute solutions of zero-dimensional multivariate
                 polynomial equations in a given domain. Earlier methods
                 for solving polynomial equations are based on iterative
                 methods, homotopy methods or symbolic elimination. The
                 total number of solutions correspond to the Bezout
                 bound for dense polynomial systems or the BKK bound for
                 sparse systems. In most applications the actual number
                 of solutions in the domain of interest is much lower
                 than the Bezout or BKK bound. Our approach is based on
                 global formulation of the problem using resultants and
                 matrix computations and localizing it to find selected
                 solutions only. The problem of finding roots is reduced
                 to computing eigenvalues of a generalized companion
                 matrix and we use the structure of the matrix to
                 compute the solutions in the domain of interest only.
                 The resulting algorithm is iterative in nature and we
                 discuss its performance on a number of applications.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., North Carolina Univ., Chapel
                 Hill, NC, USA",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; Bezout bound; BKK bound; Eigenvalues;
                 Generalized companion matrix; Global formulation;
                 Iterative; Matrix computations; Multivariate polynomial
                 equations; performance; Polynomial equations;
                 Resultants; Roots; Zero-dimensional",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues and
                 eigenvectors (direct and iterative methods).",
  thesaurus =    "Eigenvalues and eigenfunctions; Iterative methods;
                 Polynomials",
}

@InProceedings{Marti:1994:CSS,
  author =       "P. Marti and M. Rucher",
  title =        "A Cooperative Scheme for Solving Constraints over the
                 Reals",
  crossref =     "Hong:1994:FIS",
  pages =        "284--293",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Massey:1994:OCM,
  author =       "B. Massey and E. Tick",
  title =        "Optimizing Clause Matching Automata in
                 Committed-Choice Languages",
  crossref =     "Hong:1994:FIS",
  pages =        "294--303",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:1994:SFA,
  author =       "Michael B. Monagan and Gaston H. Gonnet",
  title =        "Signature functions for algebraic numbers",
  crossref =     "ACM:1994:IPI",
  pages =        "291--296",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p291-monagan/",
  abstract =     "J. T. Schwartz (1980) gave a fast probabilistic method
                 which tests if a matrix of polynomials over $Z$ is
                 singular or not. The method is based on the idea of
                 signature functions which are mappings of mathematical
                 expressions into finite rings. In Schwartz's paper,
                 they were polynomials over $Z$ into $\mbox{GF}(p)$.
                 Because computation in $\mbox{GF}(p)$ is very fast
                 compared with computing with polynomials, Schwartz's
                 method yields an enormous speedup both in theory and in
                 practice. Therefore it is desirable to extend the class
                 of expressions for which we can find effective
                 signature functions. G. H. Gonnet (1984; 1986) extended
                 the class of expressions for which signature functions
                 could be found, to include a restricted class of
                 elementary functions and integer roots. We present and
                 compare methods for constructing signature functions
                 for expressions containing algebraic numbers. Some
                 experimental results are given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
                 Tech. Hochschule, Zurich, Switzerland",
  classification = "C1140Z (Other topics in statistics); C4130
                 (Interpolation and function approximation); C6130 (Data
                 handling techniques); C7310 (Mathematics computing)",
  keywords =     "Algebraic numbers; algorithms; Elementary functions;
                 experimentation; Fast probabilistic method; Finite
                 rings; Integer roots; Mathematical expressions; Matrix;
                 Polynomials; Restricted class; Signature functions;
                 theory",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices. {\bf I.1.2} Computing Methodologies, SYMBOLIC
                 AND ALGEBRAIC MANIPULATION, Algorithms.",
  thesaurus =    "Functions; Polynomials; Probability; Symbol
                 manipulation",
}

@InProceedings{Murao:1994:MAS,
  author =       "H. Murao and T. Fujise",
  title =        "Modular Algorithm for Sparse Multivariate Polynomial
                 Interpolation and its Parallel Implementation",
  crossref =     "Hong:1994:FIS",
  pages =        "304--315",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Oaku:1994:AFS,
  author =       "Toshinori Oaku",
  title =        "Algorithms for finding the structure of solutions of a
                 system of linear partial differential equations",
  crossref =     "ACM:1994:IPI",
  pages =        "216--223",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p216-oaku/",
  abstract =     "We consider a system of linear partial differential
                 equations $M: P_1u=P_2u=\ldots{} P_su=0$ for an unknown
                 function $u$, where $P_1,\ldots{},P_s$, are linear
                 partial differential operators with polynomial
                 coefficients. Systems of differential equations for
                 various hypergeometric functions of several variables
                 are typical examples. The aim of this paper is to
                 present algorithms for finding the structure of the
                 space of solutions of such a system of differential
                 equations. Our method consists of the following three
                 steps: 1. Find the dimension of the space of the
                 solutions (i.e. the rank) of the system M. 2. Find the
                 singular locus of $M$ (i.e. the set of points where a
                 solution of $M$ can be singular). 3. Characterize the
                 asymptotic behavior of the solutions of $M$ near its
                 singular locus. We discuss mainly the second and the
                 third steps. We give an algorithm to solve the first
                 and the second steps at the same time, and algorithms
                 to solve the third step partially, i.e., under the
                 condition that $M$ is Fuchsian (or with regular
                 singularities) along its singular locus. Our methods
                 are based on the notion of Gr{\"o}bner base and the
                 Buchberger algorithm applied to rings of differential
                 operators. We use a standard term ordering for the
                 first and the second steps, but we introduce term
                 orderings of a new kind for the third step, which are
                 associated with a filtration. The algorithms presented
                 have been implemented on a computer algebra system
                 risa/asir.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Yokohama City Univ., Japan",
  classification = "B0290P (Differential equations); C4170 (Differential
                 equations); C7310 (Mathematics computing)",
  keywords =     "algorithms; theory; Linear partial differential
                 equations; Unknown function; Polynomial coefficients;
                 Hypergeometric functions; Gr{\"o}bner base; Buchberger
                 algorithm; Computer algebra system; Risa/asir",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.8} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems.",
  thesaurus =    "Partial differential equations; Symbol manipulation",
}

@InProceedings{Petitjean:1994:ACS,
  author =       "Sylvain Petitjean",
  title =        "Automating the construction of stationary
                 multiple-point classes",
  crossref =     "ACM:1994:IPI",
  pages =        "9--14",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p9-petitjean/",
  abstract =     "In this paper, we describe an algorithm to compute
                 arbitrary stationary multiple-point formulas. We report
                 its full implementation in Maple and show some examples
                 matching formulas found by hand computation. We also
                 present an application to the enumeration of lines
                 having specified contact with a projective surface.",
  acknowledgement = ack-nhfb,
  affiliation =  "CRIN, CNRS, Vandoeuvre-les-Nancy, France",
  classification = "C4260 (Computational geometry); C7310 (Mathematics
                 computing)",
  keywords =     "algorithms; Enumeration of lines; languages; Maple;
                 Multiple-point classes; Multiple-point formulas;
                 Projective surface; Stationary multiple-point formulas;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple.",
  thesaurus =    "Computational geometry; Symbol manipulation",
}

@InProceedings{Rayes:1994:PGS,
  author =       "Mohamed Omar Rayes and P. S. Wang",
  title =        "Parallel {GCD} for Sparse Multivariate Polynomials on
                 Shared Memory Multiprocessors",
  crossref =     "Hong:1994:FIS",
  pages =        "326--335",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rayes:1994:PSM,
  author =       "Mohamed Omar Rayes and Paul S. Wang and Kenneth
                 Weber",
  title =        "Parallelization of the sparse modular {GCD} algorithm
                 for multivariate polynomials on shared memory
                 multiprocessors",
  crossref =     "ACM:1994:IPI",
  pages =        "66--73",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p66-rayes/",
  abstract =     "Reported are experiences and practical results from
                 parallelizing the modular GCD algorithm for sparse
                 multivariate polynomials. The strategy is to identify
                 key computation steps in the sequential algorithm and
                 implement them in parallel. The two major steps of the
                 sequential algorithm---computing the GCD modulo several
                 primes and applying the Chinese Remainder Algorithm on
                 the integer coefficients---are easily partitioned into
                 independent subtasks. The subtask of computing the GCD
                 modulo one prime can be subdivided further. Several
                 parallel strategies for the multivariate GCD modulo a
                 prime are presented. Actual timings on a Sequent
                 Balance with 26 processors are presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
                 USA",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C5440
                 (Multiprocessing systems); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "algorithms; Chinese remainder algorithm; Computation
                 steps; GCD module; Integer coefficients; Multivariate
                 polynomials; Parallelization; Sequent Balance;
                 Sequential algorithm; Shared memory multiprocessors;
                 Sparse modular GCD algorithm",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Number-theoretic computations. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms.",
  thesaurus =    "Mathematics computing; Polynomials; Shared memory
                 systems; Symbol manipulation",
}

@InProceedings{Recio:1994:SIG,
  author =       "T. Recio and M. J. Gonz{\'a}lez-L{\'o}pez",
  title =        "On the symbolic insimplification of the general
                 $6{R}$-manipulator kinematic equations",
  crossref =     "ACM:1994:IPI",
  pages =        "354--358",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p354-recio/",
  abstract =     "When symbolically solving inverse kinematic problems
                 for robot classes, we deal with computations on ideals
                 representing these robot's geometry. Therefore, such
                 ideals must be considered over a base field {\em K\/},
                 where the parameters of the class (and also the
                 possible relations among them) are represented. In this
                 framework we shall prove that the ideal corresponding
                 to the general 6R manipulator is real and prime over
                 {\em K\/}. The practical interest of our result is that
                 it confirms that the usual inverse kinematic equations
                 of this robot class do not add redundant solutions and
                 that this ideal cannot be ``factorized'', establishing
                 therefore, Kov{\'a}cs [7] conjecture. We prove also
                 that this root class has six degrees of freedom (i.e.
                 the corresponding ideal is six-dimensional), even over
                 the extended field {\em K\/}, which is the algebraic
                 counterpart to the fact that the 6R manipulator is
                 completely general. Our proof uses, as intermediate
                 step, some dimensionality analysis of the Elbow
                 manipulator, which is a specialization of the {\em
                 6R\/}.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. de Matematicas, Estadistica y Comput., Cantabria
                 Univ., Santander, Spain",
  classification = "C3390M (Manipulators)",
  keywords =     "algorithms; Elbow manipulator; General 6R manipulator
                 kinematic equations; Ideal; Inverse kinematic problems;
                 Kinematics; Kovacs conjecture; Robot class; Robot
                 theory; Robotics; Six degrees of freedom; Symbolic
                 computation; Symbolic insimplification; Symbolically
                 solving; theory; verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations. {\bf I.2.9}
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Robotics, Manipulators. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Manipulator kinematics; Symbol manipulation",
}

@InProceedings{Richardson:1994:IPE,
  author =       "Dan Richardson and John Fitch",
  title =        "The identity problem for elementary functions and
                 constants",
  crossref =     "ACM:1994:IPI",
  pages =        "285--290",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p285-richardson/",
  abstract =     "A solution for a version of the identity problem is
                 proposed for a class of functions including the
                 elementary functions. Given $f(x)$, $g(x)$, defined at
                 some point $\beta$ we decide whether or not $f(x)$
                 identical to $g(x)$ in some neighbourhood of $\beta$.
                 This problem is first reduced to a problem about zero
                 equivalence of elementary constants. Then a semi
                 algorithm is given to solve the elementary constant
                 problem. This semi algorithm is guaranteed to give the
                 correct answer whenever it terminates, and it
                 terminates unless the problem being considered contains
                 a counter example to Schanuel's conjecture (J. Ax,
                 1971).",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Bath Univ., UK",
  classification = "C1100 (Mathematical techniques); C4240 (Programming
                 and algorithm theory); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "Algorithm termination; algorithms; Computer algebra;
                 Elementary constants; Elementary functions; Identity
                 problem; Schanuel conjecture; Semi algorithm; theory;
                 verification; Zero equivalence",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Constants; Functions; Programming theory; Symbol
                 manipulation",
}

@InProceedings{Roach:1994:SNE,
  author =       "Kelly Roach",
  title =        "Symbolic-numeric nonlinear equation solving",
  crossref =     "ACM:1994:IPI",
  pages =        "278--284",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p278-roach/",
  abstract =     "A numerical equation solving algorithm employing
                 differentiation and interval arithmetic is presented
                 which finds all solutions of $f(z)=0$ on an interval
                 $I$ when $f$ is holomorphic and has simple zeros. A two
                 dimensional generalization of this algorithm is
                 discussed. Finally, aspects of a broader symbolic
                 numeric algorithm which uses the first algorithm as a
                 foundation are considered.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
  classification = "C4150 (Nonlinear and functional equations); C4160
                 (Numerical integration and differentiation); C6130
                 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algorithms; Broader symbolic numeric algorithm;
                 Differentiation; Holomorphic; Interval arithmetic;
                 languages; Numerical equation solving algorithm; Simple
                 zeros; Symbolic numeric nonlinear equation solving;
                 Symbolic-numeric nonlinear equation solving; Two
                 dimensional generalization",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple.",
  thesaurus =    "Differentiation; Nonlinear equations; Symbol
                 manipulation",
}

@InProceedings{RuizS:1994:AGG,
  author =       "O. E. {Ruiz S.} and P. M. Ferreira",
  title =        "Algebraic geometry and group theory in geometric
                 constraint satisfaction",
  crossref =     "ACM:1994:IPI",
  pages =        "224--233",
  year =         "1994",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The determination of a set of geometric entities that
                 satisfy a series of geometric relations (constraints)
                 constitutes the Geometric Constraint Satisfaction or
                 Scene Feasibility (GCS/SF) problem. This problem
                 appears in different forms in Assembly Planning,
                 Constraint Driven Design, Computer Vision, etc. Its
                 solution is related to the existence of roots to
                 systems of polynomial equations. Previous attempts
                 using exclusively numerical (geometry) or symbolic
                 (topology) solutions for this problem present
                 shortcomings regarding characterization of solution
                 space, incapability to deal with geometric and
                 topological inconsistencies, and very high
                 computational expenses. In this investigation
                 Gr{\"o}bner Bases are used for the characterization of
                 the algebraic variety of the ideal generated by the set
                 of polynomials. Properties of Gr{\"o}bner Bases provide
                 a theoretical framework responding to questions about
                 consistency, ambiguity, and dimension of the solution
                 space. It also allows for the integration of geometric
                 and topological reasoning. The high computational cost
                 of Buchberger's algorithm for the Gr{\"o}bner Basis is
                 compensated by the choice of a non redundant set of
                 variables, determined by the characterization of
                 constraints based on the subgroups of the group of
                 Euclidean displacements SE(3). Examples have shown the
                 advantage of using group based variables. One of those
                 examples is discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Mech. and Ind. Eng., Illinois Univ., Urbana,
                 IL, USA",
  classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
                 intelligence); C4260 (Computational geometry)",
  keywords =     "Group theory; Geometric constraint satisfaction;
                 Algebraic geometry; Geometric entities; Polynomial
                 equations; Gr{\"o}bner Bases; Buchberger algorithm;
                 Euclidean displacements; Spatial reasoning",
  thesaurus =    "Computational geometry; Constraint theory; Group
                 theory; Spatial reasoning",
}

@InProceedings{S:1994:AGG,
  author =       "Oscar E. Ruiz S. and Placid M. Ferreira",
  title =        "Algebraic geometry and group theory in geometric
                 constraint satisfaction",
  crossref =     "ACM:1994:IPI",
  pages =        "224--233",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p224-ruiz_s./",
  abstract =     "The determination of a set of geometric entities that
                 satisfy a series of geometric relations (constraints)
                 constitutes the Geometric Constraint Satisfaction or
                 Scene Feasibility (GCS/SF) problem. This problem
                 appears in different forms in Assembly Planning,
                 Constraint Driven Design, Computer Vision, etc. Its
                 solution is related to the existence of roots to
                 systems of polynomial equations. Previous attempts
                 using exclusively numerical (geometry) or symbolic
                 (topology) solutions for this problem present
                 shortcomings regarding characterization of solution
                 space, incapability to deal with geometric and
                 topological inconsistencies, and very high
                 computational expenses. In this investigation
                 Gr{\"o}bner Bases are used for the characterization of
                 the algebraic variety of the ideal generated by the set
                 of polynomials. Properties of Gr{\"o}bner Bases provide
                 a theoretical framework responding to questions about
                 consistency, ambiguity, and dimension of the solution
                 space. It also allows for the integration of geometric
                 and topological reasoning. The high computational cost
                 of Buchberger's algorithm for the Gr{\"o}bner Basis is
                 compensated by the choice of a non redundant set of
                 variables, determined by the characterization of
                 constraints based on the subgroups of the group of
                 Euclidean displacements {\em SE(3)\/}. Examples have
                 shown the advantage of using group based variables. One
                 of those examples is discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf J.6}
                 Computer Applications, COMPUTER-AIDED ENGINEERING,
                 Computer-aided design (CAD).",
}

@InProceedings{Saenz:1994:SMP,
  author =       "F. Saenz and J. J. Ruz and W. Hans and S. Winkler",
  title =        "A Stack-based Machine for Parallel Execution of
                 {Babel} Programs",
  crossref =     "Hong:1994:FIS",
  pages =        "336--345",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Scala:1994:AC,
  author =       "Roberto La Scala",
  title =        "An algorithm for complexes",
  crossref =     "ACM:1994:IPI",
  pages =        "264--268",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p264-la_scala/",
  abstract =     "For computing free resolutions over a polynomial ring
                 the usual approach consists in iterating the
                 Buchburger's algorithm for each module in the
                 resolution. In this paper, we propose one single
                 algorithm which can be viewed as a generalization of
                 Buchberger's to chain complexes. The algorithm is based
                 on the use of syzygies, due to M{\"o}ller, Mora and
                 Traverso, as criteria for avoiding useless computation
                 of S-polynomials. Some strategies for the pairs
                 selection in complexes are studied and tested in some
                 experiments.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; theory; verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Schonert:1994:FBI,
  author =       "Martin Sch{\"o}nert and {\'A}kos Seress",
  title =        "Finding blocks of imprimitivity in small-base groups
                 in nearly linear time",
  crossref =     "ACM:1994:IPI",
  pages =        "154--157",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p154-schonert/",
  abstract =     "The purpose of this note is to describe a new
                 algorithm for finding blocks of imprimitivity for a
                 permutation group $G$, operating on a domain $\Omega$.
                 It runs in
                 $O(n\log^3\bmod{}G\bmod{}+ns\log\bmod{}G\bmod{})$ time,
                 where a is the size of $R$ and $s$ is the number of
                 generators for G. In many situations it is therefore
                 faster than Atkinson's method, which runs in $O(n^2s)$
                 time. A base of $G$ is a subset $B$ contained in
                 $\Omega$ such that only the identity of $G$ fixes $B$
                 pointwise. We call a family of groups small-base groups
                 if they admit bases of size $O(\log^c n)$ for some
                 fixed constant $c$. If $G$ belongs to a family of
                 small-base groups, our algorithm runs in nearly linear
                 time, namely in $O(ns\log^{c'}a)$. Beals recently gave
                 an algorithm with the same worst case estimate. Our
                 algorithm is simpler to implement and we expect faster
                 practical performance.",
  acknowledgement = ack-nhfb,
  affiliation =  "Tech. Hochschule Aachen, Germany",
  classification = "C1110 (Algebra); C4240C (Computational complexity)",
  keywords =     "algorithms; Imprimitivity; Nearly linear time;
                 Permutation group; Small-base groups; theory;
                 verification; Worst case estimate",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Analysis of
                 algorithms. {\bf G.2.1} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Combinatorics, Permutations and
                 combinations. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes. {\bf E.1} Data, DATA STRUCTURES, Arrays.",
  thesaurus =    "Computational complexity; Group theory",
  xxnote =       "Check title??",
}

@InProceedings{Schreiner:1994:PPI,
  author =       "W. Schreiner",
  title =        "A Para-Functional Programming Interface for a Parallel
                 Computer Algebra Package",
  crossref =     "Hong:1994:FIS",
  pages =        "346--355",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Siegl:1994:PFT,
  author =       "K. Siegl",
  title =        "A Parallel Factorization Tree {Gr{\"o}bner} Basis
                 Algorithm",
  crossref =     "Hong:1994:FIS",
  pages =        "356--362",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sodan:1994:SAP,
  author =       "A. Sodan and H. Bi",
  title =        "A Semi-Automatic Approach for Parallelizing Symbolic
                 Processing Programs",
  crossref =     "Hong:1994:FIS",
  pages =        "363--372",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sommeling:1994:CCI,
  author =       "Ron Sommeling",
  title =        "Characteristic classes for irregular singularities",
  crossref =     "ACM:1994:IPI",
  pages =        "163--168",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p163-sommeling/",
  abstract =     "For an endomorphism in a finite dimensional vector
                 space, one can define its characteristic polynomial and
                 rational Jordan normal form. In this article something
                 analogous is done for differential operators in a
                 finite dimensional vector space. An overview of
                 (partial) algorithms to compute these invariants is
                 also given. Proofs and more results and details can be
                 found in (Sommeling, 1993) on which this article is
                 based.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Nijmegen Univ., Netherlands",
  classification = "C4140 (Linear algebra); C4170 (Differential
                 equations)",
  keywords =     "algorithms; Characteristic classes; Characteristic
                 polynomial; Differential operators; Endomorphism;
                 Finite dimensional vector space; Irregular
                 singularities; Rational Jordan normal form; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Differential equations; Polynomial matrices",
}

@InProceedings{Takesue:1994:PSP,
  author =       "M. Takesue",
  title =        "Parallel Symbolic Processing with the Distributed
                 Lists",
  crossref =     "Hong:1994:FIS",
  pages =        "373--381",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Todd:1994:SSA,
  author =       "Philip H. Todd and Robin J. Y. McLeod and Marcia
                 Harris",
  title =        "A system for the symbolic analysis of problems in
                 engineering mechanics",
  crossref =     "ACM:1994:IPI",
  pages =        "84--89",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p84-todd/",
  abstract =     "In this paper, we present a system for the symbolic
                 solution of problems in engineering mechanics. Of
                 critical importance is a sub-system for maintaining and
                 manipulating quantities containing unevaluated
                 intermediate variables. Without this subsystem,
                 intermediate expression expansion makes symbolic
                 mechanics impractical for all but trivial problems.
                 With the subsystem, readable symbolic solutions may be
                 derived for mechanics problems of textbook complexity
                 and above. More complex symbolic solutions in a form
                 amenable to code generation may be derived for
                 mechanics problems of the complexity found in a
                 practical engineering context.",
  acknowledgement = ack-nhfb,
  affiliation =  "Saltire Software, Beaverton, OR, USA",
  classification = "C4240C (Computational complexity); C6130 (Data
                 handling techniques); C7310 (Mathematics computing);
                 C7400 (Engineering computing)",
  keywords =     "algorithms; Code generation; Complexity; Engineering
                 mechanics; Intermediate expression expansion;
                 Intermediate variables; Symbolic analysis; Symbolic
                 mechanics; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations. {\bf J.2}
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Computational complexity; Engineering computing;
                 Mathematics computing; Symbol manipulation",
}

@InProceedings{Tong:1994:IDC,
  author =       "B.-M. Tong and H.-F. Leung",
  title =        "Implementation of a Data-Parallel Concurrent
                 Constraint Programming System",
  crossref =     "Hong:1994:FIS",
  pages =        "382--393",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:1994:CPR,
  author =       "Mark {van Hoeij}",
  title =        "Computing parameterizations of rational algebraic
                 curves",
  crossref =     "ACM:1994:IPI",
  pages =        "187--190",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p187-van_hoeij/",
  abstract =     "In this paper I want to present a new method for
                 computing parametrizations of algebraic curves.
                 Basically this method is a direct application of
                 integral basis computation. Examples show that this
                 method is faster than older methods.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Nijmegen Univ., Netherlands",
  classification = "C4130 (Interpolation and function approximation)",
  keywords =     "algorithms; Integral basis computation; languages;
                 Parametrizations; Rational algebraic curves; Rational
                 functions; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.",
  thesaurus =    "Curve fitting; Functions; Integral equations",
  xxtitle =      "Computing parametrizations of rational algebraic
                 curves",
}

@InProceedings{Villard:1994:FPC,
  author =       "Gilles Villard",
  title =        "Fast parallel computation of the {Smith} normal form
                 of polynomial matrices",
  crossref =     "ACM:1994:IPI",
  pages =        "312--317",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p312-villard/",
  abstract =     "The author establishes that the Smith normal form of a
                 polynomial matrix in $F(x)^{n*n}$, where $F$ is an
                 arbitrary commutative field, can be computed in
                 $\mbox{NC}_F$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. LMC, IMAG, Grenoble, France",
  classification = "C1110 (Algebra); C4140 (Linear algebra); C4240P
                 (Parallel programming and algorithm theory)",
  keywords =     "Algorithm theory; algorithms; Arbitrary commutative
                 field; Computability; Fast parallel computation;
                 Parallel algorithm; Polynomial matrices; Polynomial
                 matrix; Smith normal form; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms.",
  thesaurus =    "Algorithm theory; Computability; Parallel algorithms;
                 Polynomial matrices",
}

@InProceedings{Wang:1994:PPO,
  author =       "P. S. Wang",
  title =        "Parallel Polynomial Operations: {A} Progress Report
                 (Invited Tutorial)",
  crossref =     "Hong:1994:FIS",
  pages =        "394--404",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Watt:1994:FRA,
  author =       "Stephen M. Watt and Peter A. Broadbery and Samuel S.
                 Dooley and Pietro Iglio and Scott C. Morrison and
                 Jonathan M. Steinbach and Robert S. Sutor",
  title =        "A first report on the ${A}^{\mbox{Hash}}$ compiler",
  crossref =     "ACM:1994:IPI",
  pages =        "25--31",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p25-watt/",
  abstract =     "The $A^{\mbox{Hash}}$ compiler allows users of
                 computer algebra to develop programs in a context where
                 multiple programming languages are employed. The
                 compiler translates programs written in the
                 $A^{\mbox{Hash}}$ programming language to a low level
                 intermediate language, Foam (Watt et al., 1994) from
                 which it can generate stand-alone programs, native
                 object libraries to be linked with other applications,
                 or code to be read into closed environments. In
                 addition, Foam code may be directly executed using an
                 interpreter provided with the $A^{\mbox{Hash}}$
                 compiler.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C6150C (Compilers, interpreters and other
                 processors); C7310 (Mathematics computing)",
  keywords =     "$A^{\mbox{Hash}}$ compiler; algorithms; Computer
                 algebra; design; Foam; Interpreter; languages; Multiple
                 programming languages; Object libraries; performance;
                 Program generation; Program translation; Stand-alone
                 programs",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Compilers. {\bf
                 F.3.3} Theory of Computation, LOGICS AND MEANINGS OF
                 PROGRAMS, Studies of Program Constructs, Type
                 structure. {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Optimization. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 LISP.",
  thesaurus =    "Program compilers; Program interpreters; Software
                 libraries; Symbol manipulation",
}

@InProceedings{Weber:1994:ATI,
  author =       "Andreas Weber",
  title =        "Algorithms for type inference with coercions",
  crossref =     "ACM:1994:IPI",
  pages =        "324--329",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p324-weber/",
  abstract =     "The paper presents algorithms that perform a type
                 inference for a type system occurring in the context of
                 computer algebra. The type system permits various
                 classes of coercions between types and the algorithms
                 are complete for the precisely defined system, which
                 can be seen as a formal description of an important
                 subset of the type system supported by the computer
                 algebra program AXIOM. Previously only algorithms for
                 much more restricted cases of coercions have been
                 described or the frameworks used have been so general
                 that the corresponding type inference problems were
                 known to be undecidable.",
  acknowledgement = ack-nhfb,
  affiliation =  "Wilhelm-Schickard-Inst. fur Inf., Tubingen Univ.,
                 Germany",
  classification = "C4240 (Programming and algorithm theory); C6130
                 (Data handling techniques)",
  keywords =     "algorithms; Algorithms; AXIOM computer algebra
                 program; Coercions; Computer algebra; Formal
                 description; languages; Precisely defined system;
                 theory; Type inference; Type system; verification",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf F.3.3} Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Type structure. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
  thesaurus =    "Algorithm theory; Symbol manipulation; Type theory",
}

@InProceedings{Weber:1994:PIA,
  author =       "K. Weber",
  title =        "Parallel Implementation of the Accelerated Integer
                 {GCD} Algorithm",
  crossref =     "Hong:1994:FIS",
  pages =        "405--411",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Weil:1994:USS,
  author =       "Jacques-Arthur Weil",
  title =        "The use of the special semi-groups for solving
                 differential equations",
  crossref =     "ACM:1994:IPI",
  pages =        "341--347",
  year =         "1994",
  bibdate =      "Sat Apr 25 12:54:38 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p341-weil/",
  abstract =     "In general, there is no method for finding closed form
                 first integrals or solutions of ordinary differential
                 equations with non constant coefficients. Thus, one
                 usually performs heuristics, but this involves
                 fastidious computations. The aim of the paper is to
                 propose strategies that computerize such heuristics to
                 help the analysis. We formulate our questions in terms
                 of differential algebra. Then, we are able to derive
                 algebraic constructive criteria for the search for
                 closed form solutions of differential equations of the
                 type
                 $s(x,y,\ldots{},y^{(n-1)})y^{(n)}+t(x,y,\ldots{},y^{(n-1)})=0$
                 (sections 2 and 3). In particular, we focus on the
                 so-called special polynomials (or Darboux curves). We
                 show how our tools link the expression of the solutions
                 to that of the first integrals, and how it gives a
                 strategy to compute them. Then, we show how these
                 techniques permit one to derive algorithmic methods to
                 find solutions of order $n-1$ for linear differential
                 equations of order $n$; we specifically detail the
                 second order case.",
  acknowledgement = ack-nhfb,
  affiliation =  "GAGE/Centre de Math., Ecole Polytech., Palaiseau,
                 France",
  classification = "C1160 (Combinatorial mathematics); C4160 (Numerical
                 integration and differentiation); C4170 (Differential
                 equations); C7310 (Mathematics computing)",
  keywords =     "Algebraic constructive criteria; Algorithmic methods;
                 algorithms; Closed form first integrals; Closed form
                 solutions; Darboux curves; Differential algebra;
                 Differential equations; Linear differential equations;
                 Non constant coefficients; Ordinary differential
                 equations; Second order case; Special polynomials;
                 Special semi group; Special semi-groups; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations.",
  thesaurus =    "Differentiation; Group theory; Linear differential
                 equations; Symbol manipulation",
}

@InProceedings{Weispfenning:1994:QER,
  author =       "Volker Weispfenning",
  title =        "Quantifier elimination for real algebra-the cubic
                 case",
  crossref =     "ACM:1994:IPI",
  pages =        "258--263",
  year =         "1994",
  bibdate =      "Thu Mar 12 08:41:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p258-weispfenning/",
  abstract =     "We present a special purpose quantifier elimination
                 method that eliminates a quantifier $\exists x$ in
                 formulas $\exists x(\phi)$ where $\phi$ is a Boolean
                 combination of polynomial inequalities of degree $<=3$
                 with respect to $x$. The method extends the virtual
                 substitution of parametrized test points developed by
                 V. Weispfenning (1988) and R. Loos and V. Weispfenning
                 (1993) for the linear case and by V. Weispfenning
                 (1993) for the quadratic case. It has similar upper
                 complexity bounds and offers similar advantages
                 (relatively large preprocessing part, explicit
                 parametric solutions). Small examples suggest that the
                 method will be of practical significance.",
  acknowledgement = ack-nhfb,
  affiliation =  "Passau Univ., Germany",
  classification = "C4130 (Interpolation and function approximation);
                 C4210 (Formal logic); C4240C (Computational
                 complexity); C6130 (Data handling techniques); C7310
                 (Mathematics computing)",
  keywords =     "Boolean combination; Cubic case; Explicit parametric
                 solutions; Large preprocessing part; Parametrized test
                 points; Polynomial inequalities; Quadratic case; Real
                 algebra; Special purpose quantifier elimination method;
                 theory; Upper complexity bounds; verification; Virtual
                 substitution",
  subject =      "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Applications. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic, Mechanical theorem proving.",
  thesaurus =    "Boolean algebra; Computational complexity;
                 Polynomials; Symbol manipulation",
}

@InProceedings{Wikstroem:1994:DPE,
  author =       "C. Wikstroem",
  title =        "Distributed Programming in {Erlang}",
  crossref =     "Hong:1994:FIS",
  pages =        "412--421",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhang:1994:CSD,
  author =       "H. Zhang and M. P. Bonacina",
  title =        "Cumulating Search in a Distributed Computing
                 Environment: {A} Case Study in Parallel
                 Satisfiability",
  crossref =     "Hong:1994:FIS",
  pages =        "422--431",
  year =         "1994",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:1995:ISR,
  author =       "S. A. Abramov",
  title =        "Indefinite sums of rational functions",
  crossref =     "Levelt:1995:IPI",
  pages =        "303--308",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p303-abramov/",
  abstract =     "We propose a new algorithm for indefinite rational
                 summation which, given a rational function $F(x)$,
                 extracts a rational part $R(s)$ from the indefinite sum
                 of $F(x): \sum F(x)=R(x)+ \sum H(x)$. If $H(x)$ is not
                 equal to $0$ then the denominator of this rational
                 function has the lowest possible degree. We then solve
                 the same problem in the $q$-difference case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, Russia",
  classification = "C1100 (Mathematical techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; Denominator;
                 Indefinite rational summation; Indefinite sums;
                 Q-difference, ISSAC; Rational functions; symbolic
                 computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Rational approximation. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
  thesaurus =    "Functions; Mathematics computing",
}

@InProceedings{Abramov:1995:PSL,
  author =       "Sergei A. Abramov and Manuel Bronstein and Marko
                 Petkov{\v{s}}ek",
  title =        "On polynomial solutions of linear operator equations",
  crossref =     "Levelt:1995:IPI",
  pages =        "290--296",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p290-abramov/",
  abstract =     "Let $K$ be a field of characteristic $0$ and $L: K(x)$
                 to $K(x)$ an endomorphism of the $K$ linear space of
                 univariate polynomials over $K$. We consider the
                 following computational tasks concerning $L$: (i)
                 homogeneous equation $Ly=0$: compute a basis of
                 $\mbox{Ker} L$ in $K(x)$; (ii) inhomogeneous equation
                 $Ly=f$: given $f$ in $K(x)$, compute a basis of the
                 affine space $L^{-l}(f)$ in $K(x)$; (iii) parametric
                 inhomogeneous equation $Ly=\sum^m_{i=1}\lambda{}_if_i$:
                 given $f_1, f_2, \ldots{}, f_m$ in $K(x)$, compute a
                 basis of $\mbox{Ker} L'$ where $L':(K(x)(+)K^m)$ to
                 $K(x)$ and $L':(y, \lambda)$ to
                 $Ly-\sum^m_{i=1}\lambda{}_if_i$, for $y$ in $K(x)$,
                 $\lambda$ in $K^m$. Many problems and algorithms in
                 differential and difference algebra contain these tasks
                 as subproblems which, however conceptually simple,
                 often account for a fair share of the overall computing
                 time.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, Russia",
  classification = "C1110 (Algebra); C1120 (Mathematical analysis);
                 C4130 (Interpolation and function approximation); C4170
                 (Differential equations); C7310 (Mathematics
                 computing)",
  keywords =     "$K$ linear space; Affine space; algebraic computation;
                 algorithms; Computational tasks; Difference algebra;
                 Endomorphism; Homogeneous equation; Inhomogeneous
                 equation; Linear operator equations; Parametric
                 inhomogeneous equation; Polynomial solutions;
                 Subproblems, ISSAC; symbolic computation; theory;
                 Univariate polynomials; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
                 systems (direct and iterative methods). {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Difference equations; Mathematics computing;
                 Polynomials",
}

@InProceedings{Abramov:1995:RSL,
  author =       "S. A. Abramov",
  title =        "Rational solutions of linear difference and
                 $q$-difference equations with polynomial coefficients",
  crossref =     "Levelt:1995:IPI",
  pages =        "285--289",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p285-abramov/",
  abstract =     "We propose a simple algorithm to construct a
                 polynomial divisible by the denominator of any rational
                 solution of a linear difference equation
                 $a_n(x)y(x+n)+\ldots{} +a_0(x)y(x)=b(x)$ with
                 polynomial coefficients and a polynomial right-hand
                 side. Then we solve the same problem for $q$-difference
                 equations. Nonhomogeneous equations with hypergeometric
                 righthand sides are considered as well.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Center, Acad. of Sci., Moscow, Russia",
  classification = "B0290F (Interpolation and function approximation);
                 B0290P (Differential equations); C4130 (Interpolation
                 and function approximation); C4170 (Differential
                 equations)",
  keywords =     "algebraic computation, Rational solutions; algorithms;
                 Denominator; ISSAC; Linear difference; Linear
                 difference equation; Nonhomogeneous equations;
                 Polynomial coefficients; Q-difference equations;
                 Rational solution; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Difference equations; Polynomials",
}

@Article{Anonymous:1995:IA,
  author =       "Anonymous",
  title =        "{ISSAC} '95: Announcement",
  journal =      j-SIGNUM,
  volume =       "30",
  number =       "2",
  pages =        "12--??",
  year =         "1995",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  bibdate =      "Fri Jan 5 07:58:42 MST 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1995:IIS,
  author =       "Anonymous",
  title =        "{ISSAC '96: International Symposium on Symbolic and
                 Algebraic Computation}",
  journal =      j-SIGSAM,
  volume =       "29",
  number =       "3\&4",
  pages =        "19--19",
  month =        dec,
  year =         "1995",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  bibdate =      "Fri Sep 06 07:11:07 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Avitzur:1995:HIP,
  author =       "Ron Avitzur and Olaf Bachmann and Norbert Kajler",
  title =        "From honest to intelligent plotting",
  crossref =     "Levelt:1995:IPI",
  pages =        "32--41",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p32-avitzur/",
  abstract =     "Adaptive and honest plotting are two techniques to
                 improve the quality of curve and surface visualization
                 packages. Beyond honest plotting, we investigate a
                 number of alternative techniques in order to improve
                 correctness and completeness of 2D and 3D plotting, to
                 increase efficiency, and to achieve better usability.
                 We refer to these techniques as intelligent plotting as
                 most of them transparently take advantage of the
                 numerical and/or symbolic capabilities available from
                 some mathematical engine in order to provide better and
                 faster graphical displays. We implemented these
                 techniques inside two very different packages: the
                 Graphing Calculator and IZIC which we used as testbeds
                 for our experiments.",
  acknowledgement = ack-nhfb,
  affiliation =  "RIACA, Amsterdam, Netherlands",
  classification = "C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; Completeness;
                 Correctness; Curve visualization packages;
                 experimentation; Graphing Calculator; Honest plotting;
                 Intelligent plotting; IZIC, ISSAC; languages;
                 reliability; Surface visualization packages; Symbolic
                 capabilities; symbolic computation",
  subject =      "{\bf I.3.4} Computing Methodologies, COMPUTER
                 GRAPHICS, Graphics Utilities, Graphics packages. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Mathematica. {\bf I.3.5} Computing Methodologies,
                 COMPUTER GRAPHICS, Computational Geometry and Object
                 Modeling, Curve, surface, solid, and object
                 representations.",
  thesaurus =    "Symbol manipulation",
}

@InProceedings{Ballarin:1995:TAI,
  author =       "Clemens Ballarin and Karsten Homann and Jacques
                 Calmet",
  title =        "Theorems and Algorithms: An Interface between
                 {Isabelle} and {Maple}",
  crossref =     "Levelt:1995:IPI",
  pages =        "150--157",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "Compendex database; http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p150-ballarin/",
  abstract =     "Solving sophisticated mathematical problems often
                 requires algebraic algorithms and theorems. However,
                 there are no environments integrating theorem provers
                 and computer algebra systems which consistently provide
                 the inference capabilities of the former and the
                 powerful arithmetic of the latter systems. As an
                 example of such a mechanized mathematics environment,
                 we describe a prototype implementation of an interface
                 between Isabelle and Maple. It is achieved by extending
                 the simplifier of Isabelle through the introduction of
                 a new class of simplification rules called `evaluation
                 rules', in order to make selected operations of Maple
                 available, and without any modification to the computer
                 algebra system. Additionally, we specify syntax
                 translations for the concrete syntax of Maple which
                 enables the communication between both systems. This is
                 illustrated by some examples that can be solved by
                 theorems and algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
                 Univ., Germany",
  classification = "721.1; 722.2; 723.1.1; 921; 921.1; 921.2; C4210
                 (Formal logic); C6150E (General utility programs);
                 C6170K (Knowledge engineering techniques); C7310
                 (Mathematics computing)",
  conference =   "Proceedings of the 1995 International Symposium on
                 Symbolic and Algebraic Computation",
  keywords =     "Algebra; Algebraic algorithms; algebraic computation;
                 Algorithms; algorithms; Arithmetic; Artificial
                 intelligence; Calculations; Computer algebra system;
                 Computer programming languages; Digital arithmetic;
                 Evaluation rules; Inference capabilities; Integration;
                 Interface; Interfaces (computer); Isabelle; languages;
                 Logical languages; Maple; Mathematical techniques;
                 Mechanized mathematics environment; Problem solving;
                 Procedural algebraic knowledge; Prototype
                 implementation; Simplification rules; Simplifier;
                 Symbolic calculations; symbolic computation; Syntax
                 translations; Syntax translations, ISSAC; Theorem
                 prover; Theorem proving; theory; verification",
  meetingaddress = "Montreal, Can",
  meetingdate =  "Jul 10--12 1995",
  meetingdate2 = "07/10--12/95",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm design and analysis. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic. {\bf I.1.4} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Applications.",
  thesaurus =    "Application program interfaces; Arithmetic; Inference
                 mechanisms; Mathematics computing; Symbol manipulation;
                 Theorem proving",
}

@InProceedings{Barkatou:1995:RVM,
  author =       "A. Barkatou",
  title =        "A rational version of {Moser}'s algorithm",
  crossref =     "Levelt:1995:IPI",
  pages =        "297--302",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p297-barkatou/",
  abstract =     "It is important to know whether a linear system of
                 differential equations has a regular or an irregular
                 singularity at a given point $x_0$ of the complex
                 domain C. Moser (1960) has given an algorithm to solve
                 this problem. His algorithm needs to compute with the
                 individual singularities of the system and requires
                 computations in algebraic extensions of the constant
                 field for the coefficients of the system. This may
                 represent an important drawback from a practical point
                 of view. This paper describes a rational version of
                 Moser's algorithm which has been implemented in the
                 Maple computer algebra system for systems of
                 differential equations with coefficients in $Q(x)$. It
                 never needs to compute with the individual
                 singularities of the system and avoids any algebraic
                 extensions. In addition, our algorithm reduces a linear
                 system of differential equations with coefficients in
                 $Q(x)$ to an `irreducible' form which is particularly
                 convenient if one wishes to compute invariants at
                 singularities.",
  acknowledgement = ack-nhfb,
  affiliation =  "LMC-IMAG, Grenoble, France",
  classification = "C4170 (Differential equations); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; Algebraic extensions;
                 algorithms; Computer algebra system, ISSAC; Irregular
                 singularity; Linear differential equations; Maple;
                 Regular singularity; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
  thesaurus =    "Linear differential equations; Mathematics computing;
                 Symbol manipulation",
}

@InProceedings{Boulier:1995:RRF,
  author =       "F. Boulier and F. Ollivier and D. Lazard and M.
                 Petitot",
  title =        "Representation for the radical of a finitely generated
                 differential ideal",
  crossref =     "Levelt:1995:IPI",
  pages =        "158--166",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p158-boulier/",
  abstract =     "We give an algorithm which represents the radical $J$
                 of a finitely generated differential ideal as an
                 intersection of radical differential ideals. The
                 computed representation provides an algorithm for
                 testing membership in $J$. This algorithm works over
                 either an ordinary or a partial differential polynomial
                 ring of characteristic zero. It has been programmed. We
                 also give a method to obtain a characteristic set of
                 $J$, if the ideal is prime.",
  acknowledgement = ack-nhfb,
  affiliation =  "LIFL, Lille I Univ., Villeneuve d'Ascq, France",
  classification = "C1110 (Algebra); C1120 (Mathematical analysis);
                 C1160 (Combinatorial mathematics)",
  keywords =     "algebraic computation; algorithms; Characteristic set;
                 Differential algebra, ISSAC; Finitely generated
                 differential ideal; Membership testing algorithm;
                 Partial differential polynomial ring; Prime ideal;
                 Programming; Radical differential ideals intersection;
                 Radical representation; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.1}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Representations (general and polynomial). {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Algebra; Differential geometry; Polynomials; Set
                 theory",
  xxauthor =     "F. Boulier and D. Lazard and F. Ollivier and M.
                 Petitot",
  xxnote =       "Check author order: Ollivier and Lazard, or Lazard and
                 Ollivier??",
}

@InProceedings{Broadbery:1995:IDE,
  author =       "P. A. Broadbery and T. G{\'o}mez-D{\'\i}az and S. M.
                 Watt",
  title =        "On the Implementation of Dynamic Evaluation",
  crossref =     "Levelt:1995:IPI",
  pages =        "77--84",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p77-broadbery/",
  abstract =     "Dynamic evaluation is a technique for producing
                 multiple results according to a decision tree which
                 evolves with program execution. Sometimes we need to
                 produce results for all possible branches in the
                 decision tree, while on other occasions it may be
                 sufficient to compute a single result which satisfies
                 certain properties. This technique finds use in
                 computer algebra where computing the correct result
                 depends on recognising and properly handling special
                 cases of parameters. In previous work, programs using
                 dynamic evaluation have explored all branches of
                 decision trees by repeating the computations prior to
                 decision points. The paper presents two new
                 implementations of dynamic evaluation which avoid
                 recomputing intermediate results. The first approach
                 uses Scheme `continuations' to record the state for
                 resuming program execution. The second implementation
                 uses the Unix `fork' operation to form new processes to
                 explore alternative branches in parallel. These
                 implementations are based on modifications to Lisp- and
                 C-based run-time systems for the Axiom Version 2
                 extension language (previously known as
                 $A^{\mbox{Hash}}$). This allows the same high-level
                 source code to be compared using the `re-evaluation',
                 the `continuation', and the `fork' implementations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Numerical Algorithms Group Ltd., Oxford, UK",
  classification = "C1140E (Game theory); C1160 (Combinatorial
                 mathematics); C6130 (Data handling techniques); C6150G
                 (Diagnostic, testing, debugging and evaluating
                 systems); C6150J (Operating systems)",
  keywords =     "algebraic computation, Dynamic evaluation; algorithms;
                 Axiom Version 2 extension language; C-based run-time
                 systems; Computer algebra; Decision points; Decision
                 tree; High-level source code; ISSAC; languages;
                 Lisp-based run-time systems; Multiple results; Program
                 execution; Re-evaluation; Scheme continuations; State
                 recording; symbolic computation; Unix fork operation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf D.3.2} Software, PROGRAMMING
                 LANGUAGES, Language Classifications, SCHEME. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C.",
  thesaurus =    "Decision theory; Symbol manipulation; System
                 monitoring; Trees [mathematics]; Unix",
}

@InProceedings{Bubeck:1995:DSC,
  author =       "T. Bubeck and M. Hiller and W. Kuechlin and W.
                 Rosenstiel",
  title =        "Distributed Symbolic Computation with {DTS}",
  crossref =     "Ferreira:1995:PAI",
  pages =        "231--248",
  year =         "1995",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chaffy:1995:ACP,
  author =       "Claudine Chaffy",
  title =        "The analytic continuation process: From computer
                 algebra to numerical analysis",
  crossref =     "Levelt:1995:IPI",
  pages =        "216--222",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p216-chaffy/",
  abstract =     "Presents an implementation of the Weierstrass process
                 of analytic continuation to compute the solution to the
                 holomorphic Cauchy problem: $f'(z)=H(z,f(z)),f(0)=a_0$,
                 along a path in the complex plane. This theoretical
                 process uses power series expansions of the solution at
                 successive points $z_k$ of this path: in practice,
                 these expansions have to be truncated; moreover, in the
                 general case, their coefficients are not exactly known.
                 But in fact, they can be computed from the holomorphic
                 function $H$. To do this, we use a computer algebra
                 system: it provides expressions that are evaluated at a
                 finite number of points $(z_k,t_k)$, where $t_k$ is an
                 approached value of the solution at the point $z_k$.
                 $t_k$ depends on
                 $z_0,z_1,\ldots{},z_{k-1},z_k,a_0,t_0,t_1,t_{k-1}$.
                 These expressions may also be transformed by using
                 convergence acceleration techniques in order to produce
                 better approximations. The method looks like the method
                 of Euler, with polynomials of degree greater than 1 or
                 even rational functions at each step, but in fact, the
                 two points of view essentially differ: to improve the
                 numerical results, instead of increasing the number of
                 steps, we let it be fixed and prefer to increase the
                 order of approximation at each step. Experiments have
                 been done with circular paths, especially to detect
                 many-valued functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "LMC, Grenoble, France",
  classification = "C1110 (Algebra); C4100 (Numerical analysis); C7310
                 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Analytic
                 continuation; Approximation order; Circular paths;
                 Complex plane; Computer algebra; Convergence
                 acceleration techniques; Euler method; Holomorphic
                 Cauchy problem; Holomorphic function; Inexactly known
                 coefficients; Many-valued functions, ISSAC; Numerical
                 analysis; Polynomials; Power series expansions;
                 Rational functions; symbolic computation; theory;
                 Truncated expansions; Weierstrass process",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Functions; Numerical analysis; Series [mathematics];
                 Symbol manipulation",
}

@InProceedings{Cooperman:1995:CMG,
  author =       "Gene Cooperman and Larry Finkelstein and Michael
                 Tselman",
  title =        "Computing with Matrix Groups using Permutation
                 Representations",
  crossref =     "Levelt:1995:IPI",
  pages =        "259--264",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p259-cooperman/",
  abstract =     "Permutation representations constructed from matrix
                 groups defined over finite fields often have very high
                 degree. New techniques are presented for performing
                 effective computations with the resulting permutation
                 group. These techniques are designed to work in an
                 environment in which the degree of the permutation
                 group is considered too large to permit the use of
                 standard permutation algorithms for solving problems
                 such as computing the order of the group and testing
                 simplicity. The theory has been successfully tested on
                 a representation of the sporadic simple group Ly. A
                 permutation representation was constructed for Ly of
                 degree 9, 606, 125 on a conjugacy class of subgroups of
                 order 3. Using this permutation representation and no
                 specific knowledge of the group, we are able to apply
                 our methods to construct a base of at most four points
                 for the resulting permutation group, compute its order
                 and verify simplicity. Monte Carlo algorithms for group
                 membership presented previously are used to improve the
                 performance of these algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
                 USA",
  classification = "B0240G (Monte Carlo methods); C1140G (Monte Carlo
                 methods); C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Finite fields;
                 Group membership, ISSAC; Matrix groups; Monte Carlo
                 algorithms; performance; Permutation algorithms;
                 Permutation representations; Sporadic simple group;
                 symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Representations (general and
                 polynomial). {\bf G.2.1} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Combinatorics, Permutations and
                 combinations. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices.",
  thesaurus =    "Monte Carlo methods; Symbol manipulation",
}

@InProceedings{Cooperman:1995:SBP,
  author =       "Gene Cooperman",
  title =        "{STAR\slash MPI}: binding a parallel library to
                 interactive symbolic algebra systems",
  crossref =     "Levelt:1995:IPI",
  pages =        "126--132",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p126-cooperman/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Special-purpose algebraic systems. {\bf D.1.3}
                 Software, PROGRAMMING TECHNIQUES, Concurrent
                 Programming, Parallel programming. {\bf D.2.2}
                 Software, SOFTWARE ENGINEERING, Design Tools and
                 Techniques, Software libraries.",
}

@InProceedings{Cooperman:1995:SMB,
  author =       "G. Cooperman",
  title =        "{STAR\slash MPI}: Binding a Parallel Library to
                 Interactive Symbolic Algebra Systems",
  crossref =     "Levelt:1995:IPI",
  pages =        "126--132",
  year =         "1995",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This work is aimed at making parallel programming more
                 accessible to users of symbolic algebra systems and to
                 users of interactive languages in general. This is done
                 by integrating MPI (Message Passing Interface), a
                 portable, parallel message-passing library, with two
                 interactive languages: GCL (GNU Common LISP), and GAP.
                 The GAP system includes a general purpose language for
                 mathematical group theory, and LISP is the basis for
                 several general-purpose symbolic algebra systems. In
                 addition, a simple master-slave abstraction is written,
                 so that end-users need not learn any of the details of
                 the MPI function calls. This work is distinct from past
                 studies in that it provides the ability to
                 interactively create, test and modify a distributed
                 environment using the original interactive language and
                 a portable parallel library.",
  abstract2 =    "Many users of symbolic algebra systems have felt the
                 need for greater CPU power. Yet few of them have
                 ventured into parallel programming due to the steep
                 learning curve and the unfamiliar programming
                 environment entailed by such an effort. In an attempt
                 to remedy that situation, the parallel library MPI has
                 been integrated into both GCL (GNU Common LISP) and GAP
                 (a general purpose language for mathematical group
                 theory). These implementations are examples that extend
                 bindings of MPI to interactive languages. (MPI already
                 has bindings to the compiled languages C and FORTRAN.)
                 Further, this binding to an interactive language
                 retains the interactive environment during execution.
                 Further, STAR/MPI represents a blueprint for binding
                 MPI to other interactive languages besides GCL and GAP,
                 from which comes the name STAR/MPI, or */MPI. STAR/MPI
                 includes a simple SPMD architecture on top of this MPI
                 binding. An important class of sequential algorithms is
                 described that can be parallelized with little effort
                 using STAR/MPI architecture. Since GAP is
                 representative of systems for discrete mathematics and
                 LISP is the basis for several symbolic algebra systems
                 with strengths in nondiscrete mathematics, it is hoped
                 to gain broad feedback on the issues involved. Although
                 vendor-specific, interactive, parallel languages exist,
                 this appears to be the first attempt at defining a
                 binding of a vendor-independent, portable, parallel
                 library to arbitrary interactive languages.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Comput. Sci., Northeastern Univ.",
  affiliationaddress = "Boston, MA, USA",
  classification = "721.1; 722.2; 722.4; 723.1; 723.5; 921.1; C6110B
                 (Software engineering techniques); C6110P (Parallel
                 programming); C6115 (Programming support); C7310
                 (Mathematics computing)",
  conference =   "Proceedings of the 1995 International Symposium on
                 Symbolic and Algebraic Computation",
  journalabr =   "Int Symp Symbol Algebraic Comput ISSAC Proc",
  keywords =     "Algebra; algebraic computation; Computational methods;
                 Computer programming; Computer programming languages;
                 Computer simulation; Computer software; GCL; GNU Common
                 LISP; Interactive computer systems; Interactive
                 languages; Interactive symbolic algebra systems;
                 Interfaces (computer); ISSAC; Mathematical group
                 theory; Mathematical techniques; Message passing
                 interface; Parallel library; Parallel processing
                 systems; STAR/MPI; Symbolic algebra; symbolic
                 computation; User interfaces",
  meetingaddress = "Montreal, Can",
  meetingdate =  "Jul 10--12 1995",
  meetingdate2 = "07/10--12/95",
  thesaurus =    "Parallel programming; Software libraries; Symbol
                 manipulation",
}

@InProceedings{Corless:1995:SVD,
  author =       "Robert M. Corless and Patrizia M. Gianni and Barry M.
                 Trager and Stephen M. Watt",
  title =        "The Singular Value Decomposition for Polynomial
                 Systems",
  crossref =     "Levelt:1995:IPI",
  pages =        "195--207",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p195-corless/",
  abstract =     "Introduces singular value decomposition (SVD)
                 algorithms for some standard polynomial computations,
                 in the case where the coefficients are inexact or
                 imperfectly known. We first give an algorithm for
                 computing univariate greatest common divisors (GCDs)
                 which gives exact results for interesting nearby
                 problems, and give efficient algorithms for computing
                 precisely how nearby. We generalize this to
                 multivariate GCD computation. Next, we adapt Lazard's
                 (1981) 21-resultant algorithm for the solution of
                 overdetermined systems of polynomial equations to the
                 inexact-coefficient case. We also briefly discuss an
                 application of the modified Lazard's method to the
                 location of singular points on approximately known
                 projections of algebraic curves.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "C1110 (Algebra)",
  keywords =     "21-Resultant algorithm; algebraic computation;
                 Algebraic curves, ISSAC; algorithms; Approximately
                 known projections; Imperfectly known coefficients;
                 Inexact coefficients; Multivariate greatest common
                 divisors; Nearby problems; Overdetermined systems;
                 Polynomial equation systems; Singular point location;
                 Singular value decomposition; symbolic computation;
                 theory; Univariate greatest common divisors;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues and
                 eigenvectors (direct and iterative methods). {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
  thesaurus =    "Equations; Polynomials; Singular value decomposition",
}

@InProceedings{Covic:1995:SFC,
  author =       "V. Covic and S. Markovic",
  title =        "Symbolic Form Computation of the Complete Dynamics of
                 Robotic Systems with the Closed Chains Structure",
  crossref =     "Aityan:1995:PNP",
  pages =        "125--128",
  year =         "1995",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Daberkow:1995:CRE,
  author =       "M. Daberkow and M. Pohst",
  title =        "Computations with relative extensions of number fields
                 with an application to the construction of {Hilbert}
                 class fields",
  crossref =     "Levelt:1995:IPI",
  pages =        "68--76",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p68-daberkow/",
  abstract =     "We present new and improved algorithms for
                 computations with relative extensions of algebraic
                 number fields. Especially, the tasks of relative normal
                 forms, relative bases, detection of subfields, and
                 embedding of these subfields are discussed. The new
                 methods are then used to compute Hilbert class fields
                 of totally real cubic and quartic fields for the first
                 time.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fachbereich Math., Tech. Univ. Berlin, Germany",
  classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
                 C4130 (Interpolation and function approximation); C4240
                 (Programming and algorithm theory); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; Algorithms; algorithms;
                 Computations; Embedded subfields; Hilbert class field
                 construction; languages; Relative algebraic number
                 field extensions; Relative bases; Relative normal
                 forms; Subfield detection; symbolic computation;
                 Totally real cubic fields; Totally real quartic fields,
                 ISSAC",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C.",
  thesaurus =    "Algorithm theory; Hilbert spaces; Number theory;
                 Polynomials; Symbol manipulation",
}

@InProceedings{Diaz:1995:CGC,
  author =       "Angel D{\'\i}az and Erich Kaltofen",
  title =        "On Computing Greatest Common Divisors with Polynomials
                 Given By Black Boxes for Their Evaluations",
  crossref =     "Levelt:1995:IPI",
  pages =        "232--239",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p232-diaz/",
  abstract =     "The black box representation of a multivariate
                 polynomial is a function that takes as input a value
                 for each variable and then produces the value of the
                 polynomial. We revisit the problem of computing the
                 greatest common divisor (GCD) in black box format of
                 several multivariate polynomials that themselves are
                 given by black boxes. To this end an improved version
                 of the algorithm sketched by E. Kaltofen and B. Trager
                 (1990) is described. Also the full analysis of the
                 improved algorithm is given. Our algorithm constructs
                 in random polynomial-time a procedure that will
                 evaluate a fixed associate of the GCD at an arbitrary
                 point (supplied as its input) in polynomial time. The
                 randomization of the black box construction is of the
                 Monte-Carlo kind, that is with controllably high
                 probability the procedures evaluating the GCD are
                 correct at all input points. Finally, a Maple prototype
                 implementation as well as our plans for developing a
                 subsystem for manipulating multivariate polynomials and
                 rational functions in black box representation are
                 presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
                 Troy, NY, USA",
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C7310
                 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Black box format;
                 Black boxes; Greatest common divisor; Greatest common
                 divisors; languages; Maple prototype implementation;
                 Monte-Carlo method; Multivariate polynomials;
                 Polynomials; Random polynomial-time; Randomization;
                 Rational functions, ISSAC; symbolic computation;
                 theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Representations (general and
                 polynomial). {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple.",
  thesaurus =    "Polynomials; Symbol manipulation",
}

@InProceedings{Doffou:1995:SCD,
  author =       "M. J. Doffou and R. L. Grossman",
  title =        "The Symbolic Computation of Differential Invariants of
                 Polynomial Vector Field Systems Using Trees",
  crossref =     "Levelt:1995:IPI",
  pages =        "26--31",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p26-doffou/",
  abstract =     "Let $K$ denote a field of characteristic 0, and let
                 $V=K^N$ denote the vector space over $K$ of dimension
                 $N$. Let $R$ denote the $K$-algebra of polynomials over
                 $V:r=\sum_{j1=1}^Na_{j1}x^{j1}+\sum_{j1,j2=1}^N{}a_{j1,j2}x^{j1}x^{j2}+\ldots{},a_{j1},a_{j1,j2},\ldots{}$
                 in $K$. Consider the algebra $D$ of derivations of $R$.
                 Given a derivation $E$ in $D$, we are interested in
                 symbolic algorithms for computing its invariants. To be
                 more precise, the action of $GL(V)$ on $V$ induces an
                 action on the space of coefficients $C$ of the
                 derivations. A polynomial over $C$ is called invariant
                 in case it is invariant under this action. Our approach
                 to computing differential invariants is to define an
                 algebraic structure on the space of rooted, labeled
                 trees $T$ and introduce an algebra homomorphism from
                 $C$ to $T$. Differential invariants are naturally
                 expressed and easily computed in terms of a few basic
                 operations on the space of trees. Our main result
                 provides a simple and direct combinatorial means of
                 computing differential invariants. The algorithm has
                 been implemented in C++. We illustrate these ideas by
                 computing all the differential invariants of vector
                 field systems in the plane $V=K^2$.",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. for Adv. Comput., Illinois Univ., Chicago, IL,
                 USA",
  classification = "C1160 (Combinatorial mathematics); C7310
                 (Mathematics computing)",
  keywords =     "Algebra; algebraic computation; Algebraic structure;
                 algorithms; C++; Differential invariants;
                 experimentation; languages; Polynomial vector field
                 systems; Rooted labeled trees; Symbolic algorithms;
                 Symbolic computation; symbolic computation; theory;
                 Trees; Vector field systems, ISSAC; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.2.2} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures.",
  thesaurus =    "Polynomials; Symbol manipulation; Trees
                 [mathematics]",
}

@InProceedings{Einwohner:1995:STI,
  author =       "T. H. Einwohner and Richard J. Fateman",
  title =        "Searching techniques for integral tables",
  crossref =     "Levelt:1995:IPI",
  pages =        "133--139",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p133-einwohner/",
  abstract =     "We describe the design of data structures and a
                 computer program for storing a table of symbolic
                 indefinite or definite integrals and retrieving
                 user-requested integrals on demand. Typical times are
                 so short that a preliminary look-up attempt prior to
                 any algorithmic integration approach seems justified.
                 In one such test for a table with around 700 entries,
                 matches were found requiring an average of 2.8
                 milliseconds per request, on a Hewlett Packard 9000/712
                 workstation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electr. Eng. and Comput. Sci., California
                 Univ., Berkeley, CA, USA",
  classification = "C4160 (Numerical integration and differentiation);
                 C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; Algorithmic integration, ISSAC;
                 algorithms; Data structures; design; Integral tables;
                 performance; symbolic computation; Symbolic indefinite
                 integrals",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems. {\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Pattern matching. {\bf F.2.2}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Sorting and searching.",
  thesaurus =    "Data structures; Integration; Symbol manipulation;
                 Table lookup",
}

@InProceedings{Estevez:1995:CAE,
  author =       "L. W. Estevez and N. D. Kehtarnavaz",
  title =        "Computer assisted enhancement of mammograms for
                 detection of microcalcifications",
  crossref =     "IEEE:1995:PEI",
  pages =        "16--23",
  year =         "1995",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The presence of microcalcifications in mammograms
                 provides an early indication of possible breast cancer.
                 Because of the difficulty associated with visual
                 identification of microcalcifications and the large
                 volume of mammograms read per day, the radiologist
                 stands a good chance of missing some small
                 microcalcification clusters. Although several
                 computer-assisted programs have been developed for the
                 automatic detection of microcalcifications in
                 mammograms, they often generate too many false
                 positives. This paper presents a computer-assisted
                 enhancement technique which is capable of coping with
                 false positive samples. More specifically, a
                 general-purpose clustering algorithm, called Issac
                 (Interactive Selective and Adaptive Clustering), has
                 been developed which achieves a compromise between
                 sensitivity and generalization attributes of existing
                 clustering algorithms. Issac comprises two parts: (i)
                 selective clustering and (ii) interactive adaptation.
                 The first part reduces the number of false positives by
                 identifying sensitive sample domains in the feature
                 space. The second part allows the radiologist to
                 improve results by interactively identifying additional
                 false positive or true negative samples. The clinical
                 evaluation of the results has indicated that the
                 developed enhancement technique has the potential of
                 being an effective mechanism to bring
                 microcalcification areas to the attention of the
                 radiologist during a routine reading session of
                 mammograms. Further clinical evaluation is being
                 carried out for the purpose of full-scale clinical
                 deployment.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electr. Eng., Texas A and M Univ., College
                 Station, TX, USA",
  classification = "B6140C (Optical information, image and video signal
                 processing); B7510B (Radiation and radioactivity
                 applications in biomedicine); C5260B (Computer vision
                 and image processing techniques); C7330 (Biology and
                 medical computing)",
  keywords =     "Breast cancer; Clinical evaluation; Computer-assisted
                 mammogram enhancement; False positive samples;
                 General-purpose clustering algorithm; Generalization;
                 Interactive adaptation; Interactive Selective and
                 Adaptive Clustering; Issac; Microcalcification
                 detection; Radiology; Routine reading session;
                 Selective clustering; Sensitive sample domains;
                 Sensitivity; Visual identification",
  thesaurus =    "Generalisation [artificial intelligence]; Interactive
                 systems; Medical image processing; Object detection;
                 Radiology",
}

@InProceedings{Giesbrecht:1995:FCS,
  author =       "Mark Giesbrecht",
  title =        "Fast Computation of the {Smith Normal Form} of an
                 Integer Matrix",
  crossref =     "Levelt:1995:IPI",
  pages =        "110--118",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p110-giesbrecht/",
  abstract =     "We present two new probabilistic algorithms for
                 computing the Smith normal form of an $A$ in $(Z^m*n)$.
                 The first requires an expected number of
                 $O(m^2n.M(m\log{}//A//))$ bit operations (ignoring
                 logarithmic factors) and is of the Las Vegas
                 type/vol/ahml/issac95/eind/Giesbrecht; that is, it
                 never produces an incorrect answer. Here
                 $//A//=max_{ij}/\bmod{}A_{ij} mod$ and $h/l(l)$ bit
                 operations are sufficient to multiply two I-bit
                 integers ($M(1) 12$ using standard arithmetic). This
                 improves on the previously best known (deterministic)
                 algorithm of Hafner and McCurley, which requires about
                 $O(m^3n \log{}//A//. M(m \log{}//A//))$ bit operations.
                 We also present an even faster, more space efficient
                 algorithm which requires an expected number of
                 $O((m^3n\log{}//A//+m^3\log^2//A//).\log(1/\epsilon))$
                 bit operations using standard integer arithmetic. This
                 algorithm is of the Monte Carlo type: it returns the
                 correct result with probability at least $1- \epsilon$
                 for a user specified tolerance $\epsilon >0$. This
                 algorithm also requires only $O(nm \log{}//A//)$ bits
                 of storage, versus $O(nm^2 \log{}//A//)$ bits required
                 by other known algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  classification = "B0290H (Linear algebra); C4140 (Linear algebra);
                 C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Integer matrix;
                 Monte Carlo type, ISSAC; Smith normal form; symbolic
                 computation; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.3}
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Probabilistic algorithms (including Monte Carlo).",
  thesaurus =    "Matrix algebra; Symbol manipulation",
}

@InProceedings{Gonzalez-Vega:1995:IPC,
  author =       "L. Gonz{\'a}lez-Vega and G. Trujillo",
  title =        "Implicitization of parametric curves and surfaces by
                 using symmetric functions",
  crossref =     "Levelt:1995:IPI",
  pages =        "180--186",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p180-gonzalez-vega/",
  abstract =     "This paper presents a new algorithm to compute the
                 implicit equation of a parametric plane curve and
                 several classes of parametric surfaces in the
                 three-dimensional Euclidean space. This algorithm does
                 not require the computation of any symbolic determinant
                 or Gr{\"o}bner basis, these tools being replaced by the
                 computation of some symmetric functions, in particular
                 the Newton sums on the solution set of a very precise
                 zero-dimensional ideal.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. de Math., Cantabria Univ., Santander, Spain",
  classification = "C1110 (Algebra); C7310 (Mathematics computing)",
  keywords =     "3D Euclidean space; algebraic computation; algorithms;
                 Implicit equation computation; Implicitization; ISSAC;
                 Newton sums; Parametric plane curve; Parametric
                 surfaces; Precise zero-dimensional ideal; Solution set;
                 symbolic computation; Symmetric functions; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
  thesaurus =    "Equations; Functions; Symbol manipulation",
}

@InProceedings{Grigoriev:1995:ACS,
  author =       "Dima Yu. Grigoriev and {Lakshman Y. N.}",
  title =        "Algorithms for Computing Sparse Shifts for
                 Multivariate Polynomials",
  crossref =     "Levelt:1995:IPI",
  pages =        "96--103",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p96-grigoriev/",
  abstract =     "We build on the results of two earlier papers,
                 (Grigoriev-Karpinski, 1993; Lakshman-Saunders, 1994),
                 and we make use of techniques used to deal with
                 zero-dimensional Gr{\"o}bner bases. The main
                 contributions are: deriving sufficient conditions for
                 uniqueness of sparse shifts for multivariate
                 polynomials; computing tight bounds on the degree of
                 the polynomial being interpolated in terms of the
                 sparsity bound and a bound on the size of the
                 coefficients of the polynomial in the standard
                 representation; two new efficient algorithms for
                 computing sparse shifts for a multivariate
                 polynomial.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Pennsylvania State Univ.,
                 University Park, PA, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4140 (Linear algebra); C4240C
                 (Computational complexity)",
  keywords =     "Sparse shift computation; Multivariate polynomials;
                 Algorithms; Zero-dimensional Gr{\"o}bner bases;
                 Interpolation; Sparsity bound; Polynomial coefficient
                 size bounds, ISSAC; symbolic computation; algebraic
                 computation; algorithms; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse,
                 structured, and very large systems (direct and
                 iterative methods). {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
  thesaurus =    "Computational complexity; Polynomial matrices; Sparse
                 matrices",
}

@InProceedings{Kapur:1995:CVM,
  author =       "Deepak Kapur and Tushar Saxena",
  title =        "Comparison of Various Multivariate Resultant
                 Formulations",
  crossref =     "Levelt:1995:IPI",
  pages =        "187--194",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p187-kapur/",
  abstract =     "Three of the most important resultant formulations are
                 the Macaulay, Dixon and sparse resultant formulations.
                 For most polynomial systems, however, the matrices
                 constructed in these formulations become singular and
                 the projection operator vanishes identically. In such
                 cases, perturbation techniques for the Macaulay
                 formulation, such as generalized characteristic
                 polynomial (GCP) and a method based on rank submatrix
                 computation (RSC), applicable to all three
                 formulations, can be used, giving four methods
                 (Macaulay/GCP, Macaulay/RSC, Dixon/RSC and Sparse/RSC)
                 for computing nontrivial projection operators. In this
                 paper, these four methods are compared. It is shown
                 that the Dixon matrix is (by a factor up to $O(e^n)$
                 for a certain class) smaller than the sparse resultant
                 matrix, which is (by a factor up to $O(e^n)$ for a
                 certain class) smaller than the Macaulay matrix.
                 Empirical results confirm that Dixon/RSC is the most
                 efficient, followed by Sparse/RSC, then Macaulay/RSC,
                 and finally Macaulay/GCP, which is found to be almost
                 impractical. All four methods are found to generate
                 extraneous factors in the projection operator.
                 Efficient heuristics for interpolation, used to expand
                 the resultant matrices, are also discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., State Univ. of New York,
                 Albany, NY, USA",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C4140 (Linear algebra); C4240C
                 (Computational complexity)",
  keywords =     "algebraic computation; algorithms; Dixon formulation;
                 Efficiency; Extraneous factors; Generalized
                 characteristic polynomial; Interpolation heuristics,
                 ISSAC; Macaulay formulation; Multivariate resultant
                 formulations; Perturbation techniques; Polynomial
                 systems; Projection operators; Rank submatrix
                 computation; Singular matrices; Sparse formulation;
                 symbolic computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
  thesaurus =    "Computational complexity; Interpolation; Matrix
                 algebra; Perturbation techniques; Polynomials; Sparse
                 matrices",
}

@InProceedings{Krishnan:1995:NAE,
  author =       "Shankar Krishnan and Dinesh Manocha",
  title =        "Numeric-symbolic algorithms for evaluating
                 one-dimensional algebraic sets",
  crossref =     "Levelt:1995:IPI",
  pages =        "59--67",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p59-krishnan/",
  abstract =     "We present efficient algorithms based on a combination
                 of numeric and symbolic techniques for evaluating
                 one-dimensional algebraic sets in a subset of the real
                 domain. Given a description of a one-dimensional
                 algebraic set, we compute its projection using
                 resultants. We represent the resulting plane curve as a
                 singular set of a matrix polynomial as opposed to roots
                 of a bivariate polynomial. Given the matrix
                 formulation, we make use of algorithms from numerical
                 linear algebra to compute start points on all the
                 components, partition the domain such that each
                 resulting region contains only one component and
                 evaluate it accurately using marching methods. We also
                 present techniques to handle singularities for
                 well-conditioned inputs. The resulting algorithm is
                 iterative and its complexity is output sensitive. It
                 has been implemented in floating-point arithmetic and
                 we highlight its performance in the context of
                 computing intersection of high-degree algebraic
                 surfaces.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., North Carolina Univ., Chapel
                 Hill, NC, USA",
  classification = "B0290H (Linear algebra); C4140 (Linear algebra);
                 C4240C (Computational complexity); C6130 (Data handling
                 techniques); C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Bivariate
                 polynomial; Complexity; Floating-point arithmetic;
                 High-degree algebraic surfaces, ISSAC; Marching
                 methods; Matrix polynomial; Numeric-symbolic
                 algorithms; Numerical linear algebra; One-dimensional
                 algebraic sets; Plane curve; Real domain; symbolic
                 computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Eigenvalues and eigenvectors (direct
                 and iterative methods).",
  thesaurus =    "Computational complexity; Linear algebra; Symbol
                 manipulation",
}

@InProceedings{Liao:1995:EHP,
  author =       "Hsin-Chao Liao and Richard J. Fateman",
  title =        "Evaluation of the heuristic polynomial {GCD}",
  crossref =     "Levelt:1995:IPI",
  pages =        "240--247",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p240-liao/",
  abstract =     "The heuristic polynomial GCD procedure (GCDHEU) is
                 used by the Maple computer algebra system, but no
                 other. Because Maple has an especially efficient kernel
                 that provides fast integer arithmetic, but a relatively
                 slower interpreter for non-kernel code, the GCDHEU
                 routine is especially effective in that it moves much
                 of the computation into `bignum' arithmetic and hence
                 executes primarily in the kernel. We speculated that in
                 other computer algebra systems an implementation of
                 GCDHEU would not be advantageous. In particular, if all
                 the system code is compiled to run at `full speed' in a
                 (presumably more bulky) kernel that is entirely written
                 in C or compiled Lisp, then there would seem to be no
                 point in recasting the polynomial GCD problem into a
                 bignum GCD problem. Manipulating polynomials that are
                 vectors of coefficients would seem to be equivalent
                 computationally to manipulating vectors of big digits.
                 Yet our evidence suggests that one can take advantage
                 of the GCDHEU in a Lisp system as well. Given a good
                 implementation of bignums, for most small problems and
                 many large ones, a substantial speedup can be obtained
                 by the appropriate choice of GCD algorithm, including
                 often enough, the GCDHEU approach. Another major winner
                 seem to be the subresultant polynomial remainder
                 sequence algorithm. Because more sophisticated sparse
                 algorithms are relatively slow on small problems and
                 only occasionally emerge as superior (on larger
                 problems) it seems the choice of a fast GCD algorithm
                 is tricky.",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Sci. Div., California Univ., Berkeley, CA,
                 USA",
  classification = "C4130 (Interpolation and function approximation);
                 C6130 (Data handling techniques); C6140D (High level
                 languages); C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; C language;
                 Compiled Lisp; Computer algebra systems; Heuristic
                 polynomial GCD; Integer arithmetic; ISSAC; languages;
                 Maple computer algebra system; Sparse algorithms;
                 symbolic computation; System code",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Number-theoretic computations.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, Maple.",
  thesaurus =    "C language; LISP; Polynomials; Symbol manipulation",
}

@InProceedings{Lisle:1995:ADS,
  author =       "I. G. Lisle and G. J. Reid and A. Boulton",
  title =        "Algorithmic determination of structure of infinite
                 {Lie} pseudogroups of symmetries of {PDEs}",
  crossref =     "Levelt:1995:IPI",
  pages =        "1--6",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p1-lisle/",
  abstract =     "We describe a method which uses a finite number of
                 differentiations and linear operations to determine the
                 Cartan structure coefficients of a structurally
                 transitive Lie pseudogroup from its infinitesimal
                 defining equations. If the defining system is of first
                 order and the pseudogroup has no scalar invariants, the
                 structure coefficients can be simply extracted from the
                 coefficients of the infinitesimal system. We give an
                 algorithm which reduces the higher order case to the
                 first order case. The reduction process uses only
                 differentiation and linear eliminations, for which
                 several well-known algorithms are available. Our method
                 makes feasible the calculation of the Cartan structure
                 of infinite Lie pseudogroups of symmetries of
                 differential equations. Examples including the KP
                 equation and Liouville's equation are given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., British Columbia Univ., Vancouver, BC,
                 Canada",
  classification = "C4160 (Numerical integration and differentiation);
                 C4170 (Differential equations); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; Cartan structure
                 coefficients; Differentiation; KP equation; languages;
                 Lie pseudogroups; Linear eliminations; Liouville's
                 equation, ISSAC; PDEs; Reduction; Structurally
                 transitive Lie pseudogroup; symbolic computation;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Differentiation; Lie groups; Partial differential
                 equations; Symbol manipulation",
}

@InProceedings{Majewski:1995:SEG,
  author =       "Bohdan S. Majewski and George Havas",
  title =        "A solution to the extended gcd problem",
  crossref =     "Levelt:1995:IPI",
  pages =        "248--253",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p248-majewski/",
  abstract =     "An improved method for expressing the greatest common
                 divisor of $n$ numbers as an integer linear combination
                 of the numbers is presented and analyzed, both
                 theoretically and practically. The performance of this
                 algorithm is compared with other methods, indicating
                 substantial improvements in the size of the solution.
                 The results are given in the light of the current
                 knowledge about the complexity of extended gcd
                 computations. Thus, finding optimal sets of multipliers
                 has been proved to be an NP-complete problem. We
                 present a relatively efficient approximation algorithm
                 with excellent performance. This problem is interesting
                 in its own right. Furthermore, it has important
                 applications, for example in computing canonical normal
                 forms of integer matrices.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Queensland Univ., Brisbane,
                 Qld., Australia",
  classification = "C1160 (Combinatorial mathematics); C4240C
                 (Computational complexity); C4260 (Computational
                 geometry)",
  keywords =     "algebraic computation; algorithms; Canonical normal
                 forms; Complexity; Extended gcd problem; Greatest
                 common divisor; Integer linear combination; Integer
                 matrices, ISSAC; NP-complete problem; performance;
                 symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations.",
  thesaurus =    "Computational complexity; Computational geometry",
}

@InProceedings{Marinari:1995:GDM,
  author =       "Maria Grazia Marinari and Teo Mora and Hans Michael
                 M{\"o}ller",
  title =        "{Gr{\"o}bner} Duality and Multiplicities in Polynomial
                 System Solving",
  crossref =     "Levelt:1995:IPI",
  pages =        "167--179",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p167-marinari/",
  abstract =     "This paper deals with the description of the solutions
                 of zero-dimensional systems of polynomial equations.
                 Based on different models for describing solutions, we
                 consider suitable representations of a multiple root,
                 or more precisely suitable descriptions of the primary
                 component of the system at a root. We analyse the
                 complexity of finding the representations. We also
                 discuss the current approach to the representation of
                 real roots.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Genoa Univ., Italy",
  classification = "C1110 (Algebra); C4240C (Computational complexity)",
  keywords =     "Gr{\"o}bner duality; Multiplicities; Polynomial system
                 solving; Zero-dimensional systems; Polynomial
                 equations; Solution description models; Multiple root;
                 Primary component; Complexity; Real roots, ISSAC;
                 symbolic computation; algebraic computation;
                 algorithms; theory; verification",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Representations (general and
                 polynomial). {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
                 Algebraic algorithms. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  thesaurus =    "Computational complexity; Duality [mathematics];
                 Equations; Polynomials",
}

@InProceedings{Marje:1995:NLA,
  author =       "Prabhav Marje",
  title =        "A nearly linear algorithm for {Sylow} subgroups in
                 small-base groups",
  crossref =     "Levelt:1995:IPI",
  pages =        "270--277",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p270-marje/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.2.1} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Combinatorics, Permutations and
                 combinations. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}

@InProceedings{Minkwitz:1995:COI,
  author =       "Torsten Minkwitz",
  title =        "On the Computation of Ordinary Irreducible
                 Representations of Finite Groups",
  crossref =     "Levelt:1995:IPI",
  pages =        "278--284",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p278-minkwitz/",
  abstract =     "This article describes a method to compute ordinary
                 matrix representations afforded by all the irreducible
                 characters of a finite group. It can be shown to work
                 for any solvable group and a number of other classes of
                 groups. However, it is a method to construct
                 irreducible representations $P$ of any finite group
                 $G$, provided that $G$ contains a subgroup $H$ with an
                 irreducible character that is contained with
                 multiplicity one in the character of the restriction of
                 $p$ to $H$. The improvements in comparison with known
                 methods are algorithmic rather than in mathematical
                 principle.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
                 Univ., Germany",
  classification = "B0290H (Linear algebra); C4140 (Linear algebra);
                 C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; Finite groups;
                 Irreducible characters; languages; Mathematical
                 principle, ISSAC; Ordinary irreducible representations;
                 Ordinary matrix representations; performance; Solvable
                 group; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Representations (general and
                 polynomial). {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices.",
  thesaurus =    "Matrix algebra; Symbol manipulation",
}

@InProceedings{Morje:1995:NLA,
  author =       "P. Morje",
  title =        "A nearly linear algorithm for {Sylow} subgroups in
                 small-base groups",
  crossref =     "Levelt:1995:IPI",
  pages =        "270--277",
  year =         "1995",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $G$ be a permutation group acting on a finite set
                 $\Omega$ and assume that no composition factor of $G$
                 is an exceptional group of Lie type. Let $p$ be a
                 prime. New Monte Carlo algorithms are presented for the
                 construction and conjugation of Sylow $p$-subgroups of
                 G. The running time of the algorithms is
                 $O(sn\log^c\bmod{}G\bmod{})$ for some explicitly
                 computable constant $c$ where $n$ is the size of
                 $\Omega$ and $s$ is the number of generators for $G$.
                 This running time is nearly linear for small-base
                 groups. The method employs a reduction to the case of
                 permutation representations of finite simple groups,
                 where we invoke the classification of finite simple
                 groups and design algorithms for the alternating and
                 classical families of simple groups.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Ohio State Univ., Columbus, OH, USA",
  classification = "C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; Finite simple groups; Lie type;
                 Monte Carlo algorithms; Nearly linear algorithm;
                 Permutation group; Permutation representations; Simple
                 groups, ISSAC; Small-base groups; Sylow subgroups;
                 symbolic computation",
  thesaurus =    "Symbol manipulation",
}

@InProceedings{Nam:1995:HSM,
  author =       "Tr{\^{\`a}}n Quo{\^{\'a}}c Nam",
  title =        "A Hybrid Symbolic-Numerical Method for Tracing
                 Surface-to-Surface Intersections",
  crossref =     "Levelt:1995:IPI",
  pages =        "51--58",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p51-nam/",
  abstract =     "We present a hybrid symbolic-numerical algorithm for
                 approximation and representation of surface-to-surface
                 intersections-the fundamental and difficult problem in
                 computer aided geometric design (CAGD) and solid
                 modelling. Reliability and efficiency of intersection
                 algorithms are two basic prerequisites for their
                 effective use in any practical system. Typically, a
                 numerical algorithm is efficient, but it is not fully
                 robust and may fail in certain cases; On the other
                 hand, algorithms based on exact arithmetic are fully
                 robust and accurate, but are normally slow and require
                 a lot of memory space. Perhaps the goals of efficiency
                 and reliability cannot be met simultaneously without
                 some compromises. In this paper, we negotiate those
                 compromises judiciously. The key step of the algorithm
                 is based upon a new technique of the author, namely the
                 `extended Newton method' for determining the roots of
                 an arbitrary system of equations iteratively, where the
                 equations can be nonlinear algebraic or
                 transcendental.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 Univ., Linz, Austria",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C4260
                 (Computational geometry); C6130B (Graphics
                 techniques)",
  keywords =     "algebraic computation; algorithms; Computer aided
                 geometric design; experimentation; Extended Newton
                 method, ISSAC; Hybrid symbolic-numerical method;
                 Intersection algorithms; Memory space; reliability;
                 Solid modelling; Surface-to-surface intersections
                 tracing; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials. {\bf J.6} Computer Applications,
                 COMPUTER-AIDED ENGINEERING, Computer-aided design
                 (CAD).",
  thesaurus =    "Computational geometry; Engineering graphics;
                 Polynomials; Solid modelling",
}

@InProceedings{Quere:1995:ARL,
  author =       "M. P. Qu{\'e}r{\'e} and G. Villard",
  title =        "An algorithm for the reduction of linear {DAE}",
  crossref =     "Levelt:1995:IPI",
  pages =        "223--231",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p223-quere/",
  abstract =     "Studies linear differential algebraic equations (DAE)
                 with time-varying coefficients. Such equations,
                 $B(t)x(t)=A(t)x(t)+f(t)$, have been intensively studied
                 from a numerical point of view. Canonical forms have
                 been proposed to find conditions under which the
                 equation admits a solution, to find the set of
                 consistent initial conditions and to determine
                 conditions under which there is a unique solution.
                 However, since the situation where the system admits
                 infinitely many solutions for one initial value is not
                 really tractable in a numerical framework, few
                 algorithms may be found in this latter case. Among
                 them, we find the method of P. Kunkel and V. Mehrmann
                 (1992), who proposed a new set of local characterizing
                 quantities for the treatment of the system. This leads
                 to a generalization of the global index. Nevertheless,
                 these latter characterizing quantities impose too
                 restrictive conditions on the input equations. We
                 propose new definitions for them that lead to a new
                 algorithm which puts the initial system into a reduced
                 form without making any assumption on it. This allows
                 us to propose a new generalization of the global index
                 and a definition for the singularities of the initial
                 system. The questions of existence and uniqueness of
                 solutions are solved in all intervals which do not
                 contain a singularity. Finally, since from a practical
                 point of view the general case of analytic functions is
                 difficult to handle, we focus on the polynomial case.
                 We propose an effective algorithm that has been
                 implemented and report some experiments.",
  acknowledgement = ack-nhfb,
  affiliation =  "LITP-IBP, Paris VI Univ., France",
  classification = "C1110 (Algebra); C1120 (Mathematical analysis);
                 C4140 (Linear algebra); C4170 (Differential equations);
                 C7310 (Mathematics computing)",
  keywords =     "algebraic computation, Linear differential algebraic
                 equations; algorithms; Analytic functions; Canonical
                 forms; Consistent initial conditions; Equation solution
                 conditions; Global index generalization; Infinitely
                 many solutions; Initial system singularities; ISSAC;
                 Linear DAE reduction algorithm; Local characterizing
                 quantities; Numerical framework; Polynomial; Solution
                 existence; Solution uniqueness; symbolic computation;
                 theory; Time-varying coefficients; Unique solution;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
  thesaurus =    "Differential equations; Initial value problems; Linear
                 algebra; Symbol manipulation",
}

@InProceedings{Rakoczi:1995:FRN,
  author =       "Ferenc R{\'a}k{\'o}czi",
  title =        "Fast Recognition of the Nilpotency of Permutation
                 Groups",
  crossref =     "Levelt:1995:IPI",
  pages =        "265--269",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p265-rakoczi/",
  abstract =     "Let $G$ be a subgroup of the symmetric group on $n$
                 points, given by a set of generators, $S$. We describe
                 algorithms that decide whether or not $G$ is nilpotent,
                 and whether or not $G$ is a $p$-group for some prime
                 $p$. The algorithms utilize the imprimitivity structure
                 of such groups. The running time of the algorithms is
                 $O(\log{}n \alpha (n, 4\bmod{}S\bmod{}n))$, where
                 $\alpha(x,y)$ denotes the time required for $x$ Union
                 and $y$ Find operations in a Union-Find data structure,
                 the asymptotically best implementation of which runs in
                 time $O(y \log* (x+y))$. Standard methods for answering
                 the question require the computation of a point
                 stabilizer series, that takes
                 $O(\bmod{}S\bmod{}n^2+n^5)$ time. Implementation of the
                 algorithms in GAP shows that these algorithms run
                 faster than the built-in ones, except for very small
                 cases. For the nilpotence test this is the case even if
                 we just measure the time after the computation of the
                 point stabilizer series.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. and Inf. Sci., Oregon Univ., Eugene,
                 OR, USA",
  classification = "C6130 (Data handling techniques); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; Asymptotically best
                 implementation; Imprimitivity structure; Nilpotency of
                 permutation groups; P-group; Point stabilizer series,
                 ISSAC; Set of generators; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.2.1} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Combinatorics, Permutations and
                 combinations. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
  thesaurus =    "Symbol manipulation",
}

@InProceedings{Richardson:1995:SMR,
  author =       "Daniel Richardson",
  title =        "A simplified method of recognizing zero among
                 elementary constants",
  crossref =     "Levelt:1995:IPI",
  pages =        "104--109",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p104-richardson/",
  abstract =     "In ISSAC '94, a method was given for deciding whether
                 or not an elementary constant, given as a polynomial
                 image of a solution of a system of exponential
                 polynomial equations, represents the famous object
                 zero. In this article the technique is considerably
                 simplified and-speeded up. The main improvement has
                 been to integrate the numerical and symbolic
                 computations in such a way that unnecessary branches of
                 the symbolic computation are avoided.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Bath Univ., UK",
  classification = "C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Elementary
                 constants; Exponential polynomial equations; symbolic
                 computation; Symbolic computations, ISSAC; theory;
                 verification; Zero",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
  thesaurus =    "Symbol manipulation",
}

@InProceedings{Schwartz:1995:SOO,
  author =       "F. Schwartz",
  title =        "Symmetries of $2^{\mbox{nd}}$ and $3^{\mbox{rd}}$
                 order {ODEs}",
  crossref =     "Levelt:1995:IPI",
  pages =        "16--25",
  year =         "1995",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Starting from Lie's classification of point groups of
                 the plane, all possible symmetry groups of
                 $2^{\mbox{nd}}$ and $3^{\mbox{rd}}$ order ordinary
                 differential equations are determined. It turns out
                 that for a $3^{\mbox{rd}}$ order equation a group of
                 any size within Lie's bound $r=7$ may occur as opposed
                 to $2^{\mbox{nd}}$ order equations. In order to
                 determine the group of a given equation, the Janet
                 bases for the determining system are constructed and
                 studied in detail for two-parameter groups. A theorem
                 is proved which allows one to identify the type of a
                 two-parameter group from the coefficients of the Janet
                 basis for its determining system. This is an important
                 step for finding explicit solutions of the original
                 differential equation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. SCAI, GMD, Sankt Augustin, Germany",
  classification = "B0290P (Differential equations); C4170 (Differential
                 equations)",
  keywords =     "algebraic computation; ISSAC; Janet bases; Lie's
                 classification; Ordinary differential equations; Point
                 groups; symbolic computation; Symmetry groups;
                 Two-parameter group; Two-parameter groups",
  thesaurus =    "Differential equations",
  xxauthor =     "F. Schwarz",
}

@InProceedings{Schwarz:1995:SSS,
  author =       "Fritz Schwarz",
  title =        "Symmetries of {$2^{\em nd}$} and $3^{\rm rd}$ order
                 {ODE}'s",
  crossref =     "Levelt:1995:IPI",
  pages =        "16--25",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p16-schwarz/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.8} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations.
                 {\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
}

@InProceedings{Semmler:1995:NUH,
  author =       "Klaus-Dieter Semmler and Mika Sepp{\"a}l{\"a}",
  title =        "Numerical uniformization of hyperelliptic curves",
  crossref =     "Levelt:1995:IPI",
  pages =        "208--215",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p208-semmler/",
  abstract =     "We develop algorithms which allow us to uniformize
                 numerically any given real hyperelliptic plane M-curve.
                 Starting from an equation for such a curve, we get
                 floating point approximations for the generators of a
                 discontinuous group of Mobius transformations
                 uniformizing the given M-curve. Furthermore, we show
                 how to compute an equation for a Riemann surface given
                 by such a group. For real hyperelliptic plane curves
                 having maximal number of real components, this
                 construction gives a complete answer to the problem of
                 numerical uniformization. Some of the algorithms
                 described have already been coded. The programs are to
                 be made publicly available through the WWW home page of
                 the HCM network `Computational conformal geometry'.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. de Math., Ecole Polytech. Federale de Lausanne,
                 Switzerland",
  classification = "B0290F (Interpolation and function approximation);
                 B0290P (Differential equations); C4130 (Interpolation
                 and function approximation); C4170 (Differential
                 equations); C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Computational
                 conformal geometry, ISSAC; Discontinuous group;
                 Floating point approximations; Generators; HCM network
                 home page; Mobius transformations; Numerical
                 uniformization; Publicly available programs; Real
                 hyperelliptic plane M-curves; Riemann surface equation;
                 symbolic computation; theory; World Wide Web",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Number-theoretic
                 computations. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
  thesaurus =    "Elliptic equations; Floating point arithmetic;
                 Function approximation; Mathematics computing; Public
                 domain software",
  xxauthor =     "Klaus-Dieter Semmler and Mika Se{\"a}l{\"a}",
}

@InProceedings{Soiffer:1995:MTM,
  author =       "Neil Soiffer",
  title =        "Mathematical typesetting in {Mathematica}",
  crossref =     "Levelt:1995:IPI",
  pages =        "140--149",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "Compendex database; http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p140-soiffer/",
  abstract =     "Mathematica's user interface has been significantly
                 enhanced in Mathematica Version 3. This paper focuses
                 on the new mathematical typesetting capabilities in the
                 user interface, with the aim of discussing not only
                 what they are, but also the rationale behind the design
                 and also how the capabilities can be used.",
  acknowledgement = ack-nhfb,
  affiliation =  "Wolfram Res. Inc., Champaign, IL, USA",
  classification = "722.2; 723.1.1; 723.2; 921; 921.1; C6180 (User
                 interfaces); C7108 (Desktop publishing); C7310
                 (Mathematics computing)",
  conference =   "Proceedings of the 1995 International Symposium on
                 Symbolic and Algebraic Computation",
  journalabr =   "Int Symp Symbol Algebraic Comput ISSAC Proc",
  keywords =     "Algebra; algebraic computation; algorithms; Computer
                 programming languages; Data structures; design; Design
                 rationale, ISSAC; Display devices; Encoding (symbols);
                 languages; Mathematica Version 3; Mathematical
                 techniques; Mathematical typesetting; String based
                 systems; symbolic computation; Syntax; Tree based
                 systems; User interface enhancement; User interfaces",
  meetingaddress = "Montreal, Can",
  meetingdate =  "Jul 10--12 1995",
  meetingdate2 = "07/10--12/95",
  subject =      "{\bf G.4} Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Mathematica. {\bf I.7.2} Computing
                 Methodologies, DOCUMENT AND TEXT PROCESSING, Document
                 Preparation, Photocomposition/typesetting. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf H.5.2}
                 Information Systems, INFORMATION INTERFACES AND
                 PRESENTATION, User Interfaces, Interaction styles.",
  thesaurus =    "Computer controlled typesetting; Mathematics
                 computing; Software packages; Symbol manipulation; User
                 interfaces",
}

@InProceedings{Sorenson:1995:ALE,
  author =       "Jonathan Sorenson",
  title =        "An analysis of {Lehmer}'s {Euclidean} {GCD}
                 algorithm",
  crossref =     "Levelt:1995:IPI",
  pages =        "254--258",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p254-sorenson/",
  abstract =     "Let $u$ and $v$ be positive integers. We show that a
                 slightly modified version of D. H. Lehmer's greatest
                 common divisor algorithm will compute $\gcd(u, v)$
                 (with $u>v$) using at most
                 $O((\log{}u\log{}v)/k+k\log{}v+\log{}u+k^2)$ bit
                 operations and $O(\log{}u+k2^{2k})$ space, where $k$ is
                 the number of bits in the multiprecision base of the
                 algorithm. This is faster than Euclid's algorithm by a
                 factor that is roughly proportional to $k$. Letting $n$
                 be the number of bits in $u$ and $v$, and setting
                 $k=((\log{}n)/4)$, we obtain a subquadratic running
                 time of $O(n^2/\log{}n)$ in linear space.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Butler Univ.,
                 Indianapolis, IN, USA",
  classification = "C1160 (Combinatorial mathematics); C4260
                 (Computational geometry)",
  keywords =     "algebraic computation, Lehmer's Euclidean GCD
                 algorithm; algorithms; Greatest common divisor
                 algorithm; ISSAC; Linear space; Multiprecision base;
                 Positive integers; Subquadratic running time; symbolic
                 computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Number-theoretic
                 computations.",
  thesaurus =    "Computational geometry",
}

@InProceedings{Storjohann:1995:PRP,
  author =       "Arne Storjohann and George Labahn",
  title =        "Preconditioning of Rectangular Polynomial Matrices for
                 Efficient {Hermite Normal Form} Computation",
  crossref =     "Levelt:1995:IPI",
  pages =        "119--125",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p119-storjohann/",
  abstract =     "We present a Las Vegas probabalistic algorithm for
                 reducing the computation of Hermite normal forms of
                 rectangular polynomial matrices. In particular, the
                 problem of computing the Hermite normal form of a
                 rectangular m*n matrix (with $m>n$) reduces to that of
                 computing the Hermite normal form of a matrix of size
                 $(n+1)*n$ having entries of similar coefficient size
                 and degree. The main cost of the reduction is the same
                 as the cost of fraction-free Gaussian elimination of an
                 $m*n$ polynomial matrix. As an application, the
                 reduction allows for the efficient computation of
                 one-sided GCDs of two matrix polynomials along with the
                 solution of the matrix diophantine equation associated
                 to such a GCD.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
  classification = "C4140 (Linear algebra); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; Hermite normal form
                 computation; Las Vegas probabalistic algorithm; Matrix
                 diophantine equation, ISSAC; Matrix polynomials;
                 Polynomial matrices; Rectangular polynomial matrices;
                 symbolic computation; theory; verification",
  subject =      "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation, Simplification of expressions. {\bf
                 G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo). {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
  thesaurus =    "Matrix algebra; Polynomial matrices; Symbol
                 manipulation",
}

@InProceedings{vanHoeij:1995:ACW,
  author =       "Mark {van Hoeij}",
  title =        "An algorithm for computing the {Weierstrass} normal
                 form",
  crossref =     "Levelt:1995:IPI",
  pages =        "90--95",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p90-van_hoeij/",
  abstract =     "The paper describes an algorithm for computing a
                 normal form $y^2+x^3+ax+b$ for algebraic curves with
                 genus 1. The corresponding isomorphism of
                 function-fields is also computed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Nijmegen Univ., Netherlands",
  classification = "C1110 (Algebra); C4240 (Programming and algorithm
                 theory); C6130 (Data handling techniques)",
  keywords =     "algebraic computation, Algorithm; Algebraic curves;
                 algorithms; Function field isomorphism; Genus 1; ISSAC;
                 symbolic computation; theory; verification; Weierstrass
                 normal form computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 polynomials.",
  thesaurus =    "Algebra; Algorithm theory; Symbol manipulation",
}

@InProceedings{Wolf:1995:PAS,
  author =       "Thomas Wolf",
  title =        "Programs for applying symmetries of {PDEs}",
  crossref =     "Levelt:1995:IPI",
  pages =        "7--15",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p7-wolf/",
  abstract =     "In this paper the programs APPLYSYM, QUASILINPDE and
                 DETRAFO are described which aim at the utilization of
                 infinitesimal symmetries of differential equations. The
                 purpose of QUASILINPDE is the general solution of
                 quasilinear PDEs. This procedure is used by APPLYSYM
                 for the application of point symmetries for either:
                 calculating similarity variables to perform a point
                 transformation which lowers the order of an ODE or
                 effectively reduces the number of explicitly occurring
                 independent variables in a PDE(-system) or for
                 generalizing given special solutions of ODEs/PDEs with
                 new constant parameters. The program DETRAFO performs
                 arbitrary point- and contact-transformations of
                 ODEs/PDEs and is applied if similarity and symmetry
                 variables have been found. The program APPLYSYM is used
                 in connection with the program LIE-PDE for formulating
                 and solving the conditions for point- and
                 contact-symmetries. The actual problem solving is done
                 in all these programs through a call to the package
                 CRACK for solving overdetermined PDE systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Math. Sci., Queen Mary and Westfield Coll.,
                 London, UK",
  classification = "C4170 (Differential equations); C7310 (Mathematics
                 computing)",
  keywords =     "algebraic computation; algorithms; APPLYSYM; CRACK;
                 DETRAFO; Differential equations; Infinitesimal
                 symmetries; languages; ODEs; Overdetermined PDE
                 systems, ISSAC; PDEs; QUASILINPDE; symbolic
                 computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, REDUCE. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Special-purpose algebraic systems.",
  thesaurus =    "Differential equations; Symbol manipulation",
}

@InProceedings{Yokoyama:1995:FRU,
  author =       "Kazuhiro Yokoyama and Ziming Li and Istv{\'a}n Nemes",
  title =        "Finding Roots of Unity among Quotients of the Roots of
                 an Integral Polynomial",
  crossref =     "Levelt:1995:IPI",
  pages =        "85--89",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p85-yokoyama/",
  abstract =     "We present an efficient algorithm for testing whether
                 a given integral polynomial has two distinct roots
                 $\alpha / \beta$ such that $\alpha / \beta$ is a root
                 of unity. The test is based on results obtained by
                 investigation of the structure of the splitting field
                 of the polynomial. By this investigation, we found also
                 an improved bound for the least common multiple of the
                 orders of roots of unity appearing as quotients of
                 distinct roots.",
  acknowledgement = ack-nhfb,
  affiliation =  "ISIS, Fujitsu Labs. Ltd., Shizuoka, Japan",
  classification = "C1110 (Algebra); C4130 (Interpolation and function
                 approximation); C6130 (Data handling techniques)",
  keywords =     "algebraic computation; algorithms; Distinct roots;
                 Efficient algorithm; experimentation; Integral
                 polynomial root quotient; Root order least common
                 multiple bound, ISSAC; Splitting field; symbolic
                 computation; Testing; theory; Unity roots;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
  thesaurus =    "Polynomials; Sequences; Symbol manipulation",
}

@InProceedings{Zima:1995:SOT,
  author =       "Eugene V. Zima",
  title =        "Simplification and Optimization Transformations of
                 Chains of Recurrences",
  crossref =     "Levelt:1995:IPI",
  pages =        "42--50",
  year =         "1995",
  bibdate =      "Thu Mar 12 08:42:30 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p42-zima/",
  abstract =     "The problem of expediting the evaluation of
                 closed-form functions at regular intervals is
                 considered. The chain of recurrences technique to
                 expedite computations is extended by rational
                 simplifications and examined as a form of internal
                 representation, oriented towards fast evaluation.
                 Optimizing transformations of chains of recurrences are
                 proposed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Math. and Cybern., Moscow State
                 Univ., Russia",
  classification = "B0260 (Optimisation techniques); C1180 (Optimisation
                 techniques); C7310 (Mathematics computing)",
  keywords =     "algebraic computation; algorithms; Chains of
                 recurrences; Closed-form functions; Internal
                 representation, ISSAC; languages; Optimization
                 transformations; Rational simplifications; Regular
                 intervals; symbolic computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Simplification of expressions.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.",
  thesaurus =    "Optimisation; Symbol manipulation",
}

@InProceedings{Abramov:1996:DSI,
  author =       "Sergei A. Abramov and Eugene V. Zima",
  title =        "{D'Alembertian} solutions of inhomogeneous linear
                 equations (differential, difference, and some other)",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "232--240",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p232-abramov/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; languages;
                 SIGNUM; SIGSAM; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.7} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations.
                 {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.",
}

@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}

@InProceedings{Amrhein:1996:CSM,
  author =       "Beatrice Amrhein and Oliver Gloor and Wolfgang
                 K{\"u}chlin",
  title =        "A Case Study of Multi-Threaded {Gr{\"o}bner} Basis
                 Completion",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "95--102",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p95-amrhein/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; experimentation;
                 ISSAC; performance; SIGNUM; SIGSAM; symbolic
                 computation",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems. {\bf D.1.3}
                 Software, PROGRAMMING TECHNIQUES, Concurrent
                 Programming, Parallel programming. {\bf C.1.2} Computer
                 Systems Organization, PROCESSOR ARCHITECTURES, Multiple
                 Data Stream Architectures (Multiprocessors), Parallel
                 processors**.",
}

@InProceedings{Bacher:1996:AGO,
  author =       "Rainer Bacher",
  title =        "Automatic Generation of Optimization Code Based on
                 Symbolic Non-Linear Domain Formulation",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "283--291",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p283-bacher/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; languages;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.3} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse,
                 structured, and very large systems (direct and
                 iterative methods). {\bf G.1.6} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization. {\bf
                 G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS,
                 Graph Theory, Network problems. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple.",
}

@InProceedings{Bachmann:1996:MFD,
  author =       "Olaf Bachmann and Hans Sch{\"o}nemann and Simon Gray",
  title =        "{MPP}: {A} Framework for Distributed Polynomial
                 Computations",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "103--112",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p103-bachmann/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; design; ISSAC;
                 languages; SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms.",
}

@InProceedings{Binder:1996:FCL,
  author =       "Franz Binder",
  title =        "Fast Computations in the Lattice of Polynomial
                 Rational Function Fields",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "43--48",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p43-binder/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Number-theoretic
                 computations.",
}

@InProceedings{Buendgen:1996:MAP,
  author =       "R. Buendgen and M. Goebel and W. Kuechlin",
  title =        "A Master-Slave Approach to Parallel Term Rewriting on
                 a Hierarchical Multiprocessor",
  crossref =     "Calmet:1996:DIS",
  pages =        "183--194",
  year =         "1996",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Caboara:1996:MHF,
  author =       "Massimo Caboara and Gabriel {de Dominicis} and Lorenzo
                 Robbiano",
  title =        "Multigraded {Hilbert} Functions and {Buchberger}
                 Algorithm",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "72--78",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p72-caboara/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; performance;
                 SIGNUM; SIGSAM; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.",
}

@InProceedings{Cesari:1996:PFA,
  author =       "G. Cesari and R. Maeder",
  title =        "Parallel $3$-Primes {FFT} Algorithm",
  crossref =     "Calmet:1996:DIS",
  pages =        "174--182",
  year =         "1996",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Clark:1996:DOO,
  author =       "K. L. Clark and F. G. McCabe",
  title =        "Distributed and Object Oriented Symbolic Programming
                 in {April}",
  crossref =     "Briot:1996:OBP",
  pages =        "104--124",
  year =         "1996",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Collins:1996:TMP,
  author =       "George E. Collins and Werner Krandick",
  title =        "A Tangent-Secant Method for Polynomial Complex Root
                 Calculation",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "137--141",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p137-collins/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; performance;
                 SIGNUM; SIGSAM; symbolic computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General.",
}

@InProceedings{Cooperman:1996:NSP,
  author =       "Gene Cooperman and Michael Tselman",
  title =        "New Sequential and Parallel Algorithms for Generating
                 High Dimension {Hecke} Algebras using the Condensation
                 Technique",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "155--160",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p155-cooperman/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; languages;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General. {\bf E.2} Data, DATA STORAGE
                 REPRESENTATIONS, Hash-table representations.",
}

@InProceedings{Eberly:1996:EDA,
  author =       "W. Eberly and M. Giesbrecht",
  title =        "Efficient Decomposition of Associative Algebras",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "170--178",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p170-eberly/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Erlingsson:1996:GGO,
  author =       "{\'U}lfar Erlingsson and Erich Kaltofen and David
                 Musser",
  title =        "Generic {Gram--Schmidt} Orthogonalization by Exact
                 Division",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "275--282",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p275-erlingsson/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; languages;
                 performance; SIGNUM; SIGSAM; symbolic computation;
                 theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C++. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Fateman:1996:SMS,
  author =       "Richard J. Fateman",
  title =        "Symbolic mathematics system evaluators (extended
                 abstract)",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "86--94",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p86-fateman/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; design; ISSAC; languages;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Evaluation strategies. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, AXIOM. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Mathematica.",
}

@InProceedings{Fujise:1996:PDD,
  author =       "Tetsuro Fujise and Hirokazu Murao",
  title =        "Parallel Distinct Degree Factorization Algorithm",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "18--25",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p18-fujise/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; experimentation;
                 ISSAC; SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms.",
}

@InProceedings{Grigoriev:1996:TSP,
  author =       "D. Grigoriev",
  title =        "Testing Shift-Equivalence of Polynomials Using Quantum
                 Machines",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "49--54",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p49-grigoriev/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.3}
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Probabilistic algorithms (including Monte Carlo). {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields.",
}

@InProceedings{Hong:1996:GBU,
  author =       "Hoon Hong",
  title =        "{Gr{\"o}bner} basis under composition {II}",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "79--85",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p79-hong/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@InProceedings{Hubert:1996:GSO,
  author =       "Evelyne Hubert",
  title =        "The General Solution of an Ordinary Differential
                 Equation",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "189--195",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p189-hubert/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
}

@Article{Kaltofen:1996:ISC,
  author =       "E. Kaltofen",
  title =        "{ISSAC} Steering Committee Bylaws",
  journal =      j-SIGSAM,
  volume =       "30",
  number =       "1",
  pages =        "31--33",
  month =        mar,
  year =         "1996",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  bibdate =      "Fri Sep 06 07:11:07 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:1996:RPT,
  author =       "E. Kaltofen and A. Lobo",
  title =        "On Rank Properties of {Toeplitz} Matrices over Finite
                 Fields",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "241--249",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p241-kaltofen/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Linear systems (direct and
                 iterative methods). {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations in
                 finite fields.",
}

@InProceedings{Karmarkar:1996:APG,
  author =       "N. Karmarkar and {Lakshman Y. N.}",
  title =        "Approximate Polynomial Greatest Common Divisors and
                 Nearest Singular Polynomials",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "35--39",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p35-karmarkar/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
}

@InProceedings{Kavian:1996:MPR,
  author =       "Masoud Kavian and R. G. McLenaghan and K. O. Geddes",
  title =        "{MapleTensor}: Progress Report on a New System for
                 Performing Indicial and Component Tensor Calculations
                 Using Symbolic Computation",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "204--211",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p204-kavian/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; design; ISSAC;
                 languages; SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C++. {\bf I.1.1} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions.",
}

@InProceedings{Koenhagen:1996:OAC,
  author =       "Ulla Koenhagen and Ernst W. Mayr",
  title =        "An optimal algorithm for constructing the reduced
                 {Gr{\"o}bner} basis of binomial ideals",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "55--62",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p55-koppenhagen/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.1.3} Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
                 and Classes, Reducibility and completeness. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Koppenhagen:1996:OAC,
  author =       "U. Koppenhagen and E. W. Mayr",
  title =        "An Optimal Algorithm for Constructing the Reduced
                 {Gr{\"o}bner} Basis of Binomial Ideals",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "55--62",
  year =         "1996",
  bibdate =      "Sat May 10 10:28:09 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; ISSAC; SIGNUM; SIGSAM; symbolic
                 computation",
}

@InProceedings{Kuhnle:1996:ESC,
  author =       "Klaus K{\"u}hnle and Ernst W. Mayr",
  title =        "Exponential space computation of {Gr{\"o}bner} bases",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "63--71",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p63-kuhnle/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@InProceedings{Mikhalev:1996:APE,
  author =       "Alexander A. Mikhalev and Andrej A. Zolotykh",
  title =        "Algorithms for Primitive Elements of Free {Lie}
                 Algebras and {Lie} Superalgebras",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "161--169",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p161-mikhalev/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf J.2} Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Physics. {\bf I.1.0}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
}

@InProceedings{Norman:1996:MTA,
  author =       "Arthur Norman and John Fitch",
  title =        "Memory Tracing of Algebraic Calculations",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "113--119",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p113-norman/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 performance; SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems, REDUCE. {\bf
                 D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and
                 Techniques.",
}

@InProceedings{Pottier:1996:EAD,
  author =       "Lo{\"\i}c Pottier",
  title =        "The {Euclidean} algorithm in dimension $n$",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "40--42",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p40-pottier/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Number-theoretic computations.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
}

@InProceedings{Reinhart:1996:DHD,
  author =       "Georg M. Reinhart and William Sit",
  title =        "Differentially Homogeneous Differential Polynomials",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "212--218",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p212-reinhart/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations.",
}

@InProceedings{Richardson:1996:AEE,
  author =       "Daniel Richardson and Bruno Salvy and John Shackell
                 and Joris {Van der Hoeven}",
  title =        "Asymptotic Expansions of $\exp$--$\log$ Functions",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "309--313",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p309-richardson/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
  xxpages =      "309--312",
}

@InProceedings{Richardson:1996:SES,
  author =       "Daniel Richardson",
  title =        "Solution of elementary systems of equations in a box
                 in {$R^n$}",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "120--126",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p120-richardson/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, General.",
}

@InProceedings{Roach:1996:HFR,
  author =       "Kelly Roach",
  title =        "Hypergeometric Function Representations",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "301--308",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p301-roach/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; languages;
                 SIGNUM; SIGSAM; symbolic computation; theory;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, MACSYMA. {\bf I.1.3} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
                 Systems, Maple. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Mathematica.",
}

@InProceedings{Roy:1996:CCS,
  author =       "Marie-Fran{\c{c}}oise Roy and Nicolai Vorobjov",
  title =        "Computing the complexification of a semi-algebraic
                 set",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "26--34",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p26-roy/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Complexity Measures and Classes.",
}

@InProceedings{Schwarz:1996:JBO,
  author =       "Fritz Schwarz",
  title =        "Janet bases of 2nd order ordinary differential
                 equations",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "179--188",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p179-schwarz/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf G.1.8}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
}

@InProceedings{Stetter:1996:AZC,
  author =       "Hans J. Stetter",
  title =        "Analysis of Zero Clusters in Multivariate Polynomial
                 Systems",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "127--136",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p127-stetter/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
}

@InProceedings{Storjohann:1996:AFC,
  author =       "Arne Storjohann and George Labahn",
  title =        "Asymptotically Fast Computation of the {Hermite Normal
                 Forms} of Integer Matrices",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "259--266",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p259-storjohann/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra.",
}

@InProceedings{Storjohann:1996:NOA,
  author =       "Arne Storjohann",
  title =        "Near optimal algorithms for computing {Smith} normal
                 forms of integer matrices",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "267--274",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p267-storjohann/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices.",
}

@InProceedings{Thomas:1996:SCI,
  author =       "G. Thomas",
  title =        "Symbolic Computation of the Index of Quasilinear
                 Differential-Algebraic Equations",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "196--203",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p196-thomas/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@InProceedings{Thuemmel:1996:CCT,
  author =       "A. Thuemmel",
  title =        "Computing Character Tables of $p$-Groups",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "150--154",
  year =         "1996",
  bibdate =      "Sat May 10 10:28:09 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; ISSAC; SIGNUM; SIGSAM; symbolic
                 computation",
}

@InProceedings{Thummel:1996:CCT,
  author =       "Andreas Th{\"u}mmel",
  title =        "Computing character tables of $p$-groups",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "150--154",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p150-thummel/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous. {\bf F.2.2} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Computations on
                 discrete structures. {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices. {\bf E.1} Data, DATA STRUCTURES, Graphs and
                 networks.",
}

@InProceedings{Tsarev:1996:ACE,
  author =       "S. P. Tsarev",
  title =        "An Algorithm for Complete Enumeration of All
                 Factorizations of a Linear Ordinary Differential
                 Operator",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "226--231",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p226-tsarev/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems.",
}

@InProceedings{vanHoeij:1996:RSM,
  author =       "Mark {van Hoeij}",
  title =        "Rational Solutions of the Mixed Differential Equation
                 and Its Application to Factorization of Differential
                 Operators",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "219--225",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p219-van_hoeij/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General. {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Eigenvalues and eigenvectors (direct and
                 iterative methods). {\bf F.2.1} Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices.",
}

@InProceedings{Villard:1996:CPH,
  author =       "G. Villard",
  title =        "Computing {Popov} and {Hermite} Forms of Polynomial
                 Matrices",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "250--258",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p250-villard/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; SIGNUM;
                 SIGSAM; symbolic computation; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on polynomials.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods).",
}

@InProceedings{VonzurGathen:1996:AFP,
  author =       "Joachim {von zur Gathen} and J{\"u}rgen Gerhard",
  title =        "Arithmetic and factorization of polynomial over {${\bf
                 F}_2$} (extended abstract)",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "1--9",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p1-von_zur_gathen/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; experimentation;
                 ISSAC; performance; SIGNUM; SIGSAM; symbolic
                 computation",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations. {\bf G.1.5}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Polynomials, methods for. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields.",
}

@InProceedings{vonzurGathen:1996:FMP,
  author =       "Joachim {von zur Gathen} and Silke Hartlieb",
  title =        "Factoring modular polynomials (extended abstract)",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "10--17",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p10-von_zur_gathen/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; performance;
                 SIGNUM; SIGSAM; symbolic computation; theory;
                 verification",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations. {\bf G.3} Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo).",
}

@InProceedings{Zhao:1996:MPM,
  author =       "Yanjie Zhao and Tetsuya Sakurai and Hiroshi Sugiura
                 and Tatsuo Torii",
  title =        "A Methodology of Parsing Mathematical Notation for
                 Mathematical Computation",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "292--300",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p292-zhao/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; languages;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Grammars and Other Rewriting
                 Systems, Grammar types. {\bf F.4.2} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Grammars and Other Rewriting Systems, Parsing. {\bf
                 F.4.3} Theory of Computation, MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES, Formal Languages.",
}

@InProceedings{Abate:1997:ADS,
  author =       "Jason Abate and Christian Bischof and Lucas Roh and
                 Alan Carle",
  title =        "Algorithms and design for a second-order automatic
                 differentiation module",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "149--155",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p149-abate/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:1997:MCF,
  author =       "Sergei A. Abramov and Eugene V. Zima",
  title =        "Minimal completely factorable annihilators",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "290--297",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p290-abramov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:1997:MIS,
  author =       "Sergei A. Abramov and Mark {van Hoeij}",
  title =        "A method for the integration of solutions of {{\O}re}
                 equations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "172--175",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p172-abramov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adamchik:1997:CLI,
  author =       "Victor Adamchik",
  title =        "A class of logarithmic integrals",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "1--8",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p1-adamchik/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Andradas:1997:ROR,
  author =       "Carlos Andradas and Tom{\'a}s Recio and J. Rafael
                 Sendra",
  title =        "A relatively optimal rational space curve
                 reparametrization algorithm through canonical
                 divisors",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "349--355",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p349-andradas/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bachmann:1997:PSD,
  author =       "Olaf Bachmann and Hans Sch{\"o}nemann and Simon Gray",
  title =        "A proposal for syntactic data integration math
                 protocols",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "165--175",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p165-bachmann/",
  acknowledgement = ack-nhfb,
  keywords =     "design; languages",
  subject =      "{\bf D.2.6} Software, SOFTWARE ENGINEERING,
                 Programming Environments. {\bf D.2.2} Software,
                 SOFTWARE ENGINEERING, Design Tools and Techniques. {\bf
                 E.1} Data, DATA STRUCTURES, Trees. {\bf I.1.3}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Languages and Systems. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
                 E.1} Data, DATA STRUCTURES, Arrays. {\bf G.1.3}
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra.",
}

@InProceedings{Basu:1997:UQE,
  author =       "Saugata Basu",
  title =        "Uniform quantifier elimination and constraint query
                 processing",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "21--27",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p21-basu/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beckermann:1997:FCM,
  author =       "Bernhard Beckermann and Stan Cabay and George Labahn",
  title =        "Fraction-free computation of matrix {Pad{\'e}}
                 systems",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "125--132",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p125-beckermann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bernardin:1997:MMP,
  author =       "Laurent Bernardin",
  title =        "{Maple} on a massively parallel, distributed memory
                 machine",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "217--222",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p217-bernardin/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; languages; performance",
  subject =      "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
                 {\bf C.1.2} Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Parallel processors**. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{Bonacina:1997:ESS,
  author =       "Maria Paola Bonacina",
  title =        "Experiments with subdivisions of search in distributed
                 theorem proving",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "88--100",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p88-bonacina/",
  acknowledgement = ack-nhfb,
  keywords =     "experimentation; performance; verification",
  subject =      "{\bf I.2.3} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Deduction and Theorem Proving, Deduction.
                 {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
                 theorem proving. {\bf I.1.0} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}

@InProceedings{Bronstein:1997:SPD,
  author =       "Manuel Bronstein and Thom Mulders and Jacques-Arthur
                 Weil",
  title =        "On symmetric powers of differential operators",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "156--163",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p156-bronstein/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Buchberger:1997:STP,
  author =       "Bruno Buchberger and Tudor Jebelean and Franz Kriftner
                 and Mircea Marin and Elena Tomu{\c{t}}a and Daniela
                 V{\=a}saru",
  title =        "A survey of the theorema project",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "384--391",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p384-buchberger/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Caboara:1997:FIS,
  author =       "Massimo Caboara and Lorenzo Robbiano",
  title =        "Families of ideals in statistics",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "404--410",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p404-caboara/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cannon:1997:CCC,
  author =       "John Cannon and Bernd Souvignier",
  title =        "On the computation of conjugacy classes in permutation
                 groups",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "392--399",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p392-cannon/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cesari:1997:CCA,
  author =       "Giovanni Cesari",
  title =        "{CALYPSO}: a computer algebra library for parallel
                 symbolic computation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "204--216",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p204-cesari/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; experimentation",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic.",
}

@InProceedings{Chistov:1997:PTA,
  author =       "Alexander Chistov and G{\'a}bor Ivanyos and Marek
                 Karpinski",
  title =        "Polynomial time algorithms for modules over finite
                 dimensional algebras",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "68--74",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p68-chistov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Colin:1997:RRP,
  author =       "Antoine Colin",
  title =        "Relative resolvents and partition tables in {Galois}
                 group computations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "78--84",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p78-colin/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Corless:1997:RSF,
  author =       "Robert M. Corless and Patrizia M. Gianni and Barry M.
                 Trager",
  title =        "A reordered {Schur} factorization method for
                 zero-dimensional polynomial systems with multiple
                 roots",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "133--140",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p133-corless/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Corless:1997:SSL,
  author =       "Robert M. Corless and David J. Jeffrey and Donald E.
                 Knuth",
  title =        "A sequence of series for the {Lambert} ${W}$
                 function",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "197--204",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p197-corless/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Costa:1997:EPL,
  author =       "V{\'\i}tor Santos Costa and Ricardo Bianchini and
                 In{\^e}s de Castro Dutra",
  title =        "Evaluating parallel logic programming systems on
                 scalable multiprocessors",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "58--67",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p58-santos_costa/",
  acknowledgement = ack-nhfb,
  keywords =     "performance",
  subject =      "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Grammars and Other Rewriting
                 Systems, Parallel rewriting systems. {\bf F.1.2} Theory
                 of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes
                 of Computation, Parallelism and concurrency. {\bf
                 C.1.2} Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Parallel processors**. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms.",
}

@InProceedings{Dalmas:1997:OI,
  author =       "St{\'e}phane Dalmas and Marc Ga{\"e}tano and Stephen
                 Watt",
  title =        "An {OpenMath} 1.0 implementation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "241--248",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p241-dalmas/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dolzmann:1997:GEP,
  author =       "Andreas Dolzmann and Thomas Sturm",
  title =        "Guarded expressions in practice",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "376--383",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p376-dolzmann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dora:1997:ANA,
  author =       "J. Della Dora and F. Richard-Jung",
  title =        "About the {Newton} algorithm for non-linear ordinary
                 differential equations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "298--304",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p298-dora/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eberly:1997:PEP,
  author =       "Wayne Eberly",
  title =        "Processor-efficient parallel matrix inversion over
                 abstract fields: two extensions",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "38--45",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p38-eberly/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.0} Mathematics
                 of Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices.",
}

@InProceedings{Eberly:1997:RLA,
  author =       "Wayne Eberly and Erich Kaltofen",
  title =        "On randomized {Lanczos} algorithms",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "176--183",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p176-eberly/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Edneral:1997:CEC,
  author =       "Victor F. Edneral",
  title =        "Computer evaluation of cyclicity in planar cubic
                 system",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "305--309",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p305-edneral/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Egner:1997:DPC,
  author =       "Sebastian Egner and Markus P{\"u}schel and Thomas
                 Beth",
  title =        "Decomposing a permutation into a conjugated tensor
                 product",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "101--108",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p101-egner/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Emiris:1997:SSR,
  author =       "Ioanis Z. Emiris and Victor Y. Pan",
  title =        "The structure of sparse resultant matrices",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "189--196",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p189-emiris/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Encarnacion:1997:ANM,
  author =       "Mark J. Encarnaci{\'o}n",
  title =        "The average number of modular factors in {Trager}'s
                 polynomial factorization algorithm",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "278--281",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p278-encarnacion/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Encarnacion:1997:FPA,
  author =       "Mark J. Encarnaci{\'o}n",
  title =        "Factoring polynomials over algebraic number fields via
                 norms",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "265--270",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p265-encarnacion/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fang:1997:WCI,
  author =       "Xin Gui Fang and George Havas",
  title =        "On the worst-case complexity of integer {Gaussian}
                 elimination",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "28--31",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p28-fang/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fateman:1997:NSS,
  author =       "Richard J. Fateman",
  title =        "Network servers for symbolic mathematics",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "249--256",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p249-fateman/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fujimura:1997:MSS,
  author =       "Masayo Fujimura and Kiyoko Nishizawa",
  title =        "Moduli spaces and symmetry loci of polynomial maps",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "342--348",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p342-fujimura/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Galligo:1997:NAP,
  author =       "Andr{\'e} Galligo and Stephen Watt",
  title =        "A numerical absolute primality test for bivariate
                 polynomials",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "217--224",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p217-galligo/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gautier:1997:NCG,
  author =       "Thierry Gautier and Jean-Louis Roch",
  title =        "{{\sc NC$^2$}} computation of gcd-free basis and
                 alication to parallel algebraic numbers computation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "31--37",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p31-gautier/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
}

@InProceedings{Gemignani:1997:GPB,
  author =       "Luca Gemignani",
  title =        "{GCD} of polynomials and {B{\'e}zout} matrices",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "271--277",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p271-gemignani/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gianni:1997:ICN,
  author =       "Patrizia Gianni and Barry Trager",
  title =        "Integral closure of {Noetherian} rings",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "212--216",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p212-gianni/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:1997:EPS,
  author =       "Mark Giesbrecht",
  title =        "Efficient parallel solution of sparse systems of
                 linear {Diophantine} equations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "1--10",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p1-giesbrecht/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3} Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Sparse, structured, and very large systems
                 (direct and iterative methods). {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Parallel algorithms. {\bf G.3} Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo).",
}

@InProceedings{Glauert:1997:OGR,
  author =       "John Glauert",
  title =        "Object graph rewriting: an experimental parallel
                 implementation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "119--128",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p119-glauert/",
  acknowledgement = ack-nhfb,
  keywords =     "experimentation; languages",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Parallel programming. {\bf E.1}
                 Data, DATA STRUCTURES, Trees. {\bf F.4.1} Theory of
                 Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
                 Mathematical Logic. {\bf F.4.2} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
                 Other Rewriting Systems. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Standard ML.",
}

@InProceedings{Graaf:1997:CFM,
  author =       "W. A. de Graaf",
  title =        "Constructing faithful matrix representations of {Lie}
                 algebras",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "54--59",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p54-de_graaf/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gupta:1997:EDD,
  author =       "Gopal Gupta and Enrico Pontelli",
  title =        "Extended dynamic dependent {And}-parallelism in
                 {ACE}",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "68--79",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p68-gupta/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; performance",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Parallel programming. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Prolog. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Optimization.",
}

@InProceedings{Haridi:1997:ODD,
  author =       "Seif Haridi and Peter {Van Roy} and Gert Smolka",
  title =        "An overview of the design of {Distributed Oz}",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "176--187",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p176-haridi/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; languages",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Concurrent, distributed, and parallel languages. {\bf
                 D.3.1} Software, PROGRAMMING LANGUAGES, Formal
                 Definitions and Theory, Semantics. {\bf C.2.4} Computer
                 Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
                 Distributed Systems, Distributed applications. {\bf
                 I.3.4} Computing Methodologies, COMPUTER GRAPHICS,
                 Graphics Utilities, Graphics editors.",
}

@InProceedings{Hermenegildo:1997:WSC,
  author =       "M. Hermenegildo",
  title =        "Workshop 19: Symbolic Computation",
  crossref =     "Lengauer:1997:EPP",
  pages =        "1167--1168",
  year =         "1997",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Huang:1997:FRM,
  author =       "Xiaohan Huang and Victor Y. Pan",
  title =        "Fast rectangular matrix multiplications and improving
                 parallel matrix computations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "11--23",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p11-huang/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; performance; theory; verification",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms.",
}

@InProceedings{Jebelean:1997:PID,
  author =       "Tudor Jebelean",
  title =        "Practical integer division with {Karatsuba}
                 complexity",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "339--341",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p339-jebelean/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeffrey:1997:ISP,
  author =       "D. J. Jeffrey and G. Labahn and M. {Von Mohrenschildt}
                 and A. D. Rich",
  title =        "Integration of the signum, piecewise and related
                 functions",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "324--330",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p324-jeffrey/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Johnson:1997:PRR,
  author =       "J. R. Johnson and Werner Krandick",
  title =        "Polynomial real root isolation using approximate
                 arithmetic",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "225--232",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p225-johnson/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:1997:FPF,
  author =       "Erich Kaltofen and Victor Shoup",
  title =        "Fast polynomial factorization over high algebraic
                 extensions of finite fields",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "184--188",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p184-kaltofen/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kapur:1997:EFD,
  author =       "Deepak Kapur and Tushar Saxena",
  title =        "Extraneous factors in the {Dixon} resultant
                 formulation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "141--148",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p141-kapur/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kato:1997:PIC,
  author =       "Shohei Kato and Hirohisa Seki and Hidenori Itoh",
  title =        "A parallel implementation of cost-based abductive
                 reasoning",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "111--118",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p111-kato/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; theory",
  subject =      "{\bf I.2.3} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Deduction and Theorem Proving, Deduction.
                 {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
                 AND FORMAL LANGUAGES, Mathematical Logic. {\bf C.1.2}
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Parallel processors**. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Prolog.",
}

@InProceedings{kavian:1997:AGA,
  author =       "M. kavian and R. G. McLenaghan and K. O. Geddes",
  title =        "Application of genetic algorithms to the algebraic
                 simplification of tensor polynomials",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "93--100",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p93-kavian/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lam:1997:MPP,
  author =       "Monica Lam",
  title =        "Maximizing performance on parallel machines
                 (abstract)",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "129--129",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p129-lam/",
  acknowledgement = ack-nhfb,
  keywords =     "performance",
  subject =      "{\bf C.1.2} Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Parallel processors**. {\bf D.3.4}
                 Software, PROGRAMMING LANGUAGES, Processors,
                 Optimization.",
}

@InProceedings{Lehobey:1997:RCR,
  author =       "Fr{\'e}d{\'e}ric Lehobey",
  title =        "Resolvent computations by resultants without
                 extraneous powers",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "85--92",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p85-lehobey/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:1997:MAC,
  author =       "Ziming Li and Istv{\'a}n Nemes",
  title =        "A modular algorithm for computing greatest common
                 right divisors of {{\O}re} polynomials",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "282--289",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p282-li/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:1997:MGB,
  author =       "Qiang Li and Yi-ke Guo and Tetsuo Ida and John
                 Darlington",
  title =        "The minimised geometric {Buchberger} algorithm: an
                 optimal algebraic algorithm for integer programming",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "331--338",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p331-li/",
  acknowledgement = ack-nhfb,
}

@InProceedings{McKay:1997:FRA,
  author =       "John McKay and Richard Stauduhar",
  title =        "Finding relations among the roots of an irreducible
                 polynomial",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "75--77",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p75-mckay/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:1997:TPM,
  author =       "Michael B. Monagan and Gladys Monagan",
  title =        "A toolbox for program manipulation and efficient code
                 generation with an application to a problem in computer
                 vision",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "257--264",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p257-monagan/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Montelius:1997:EPS,
  author =       "Johan Montelius and Seif Haridi",
  title =        "An evaluation of {Penny}: a system for fine grain
                 implicit parallelism",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "46--57",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p46-montelius/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; performance",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Parallel programming. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Concurrent, distributed, and parallel
                 languages. {\bf C.1.2} Computer Systems Organization,
                 PROCESSOR ARCHITECTURES, Multiple Data Stream
                 Architectures (Multiprocessors), Parallel processors**.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@InProceedings{Murao:1997:TEI,
  author =       "Hirokazu Murao and Tetsuro Fujise",
  title =        "Towards an efficient implementation of a fast
                 algorithm for multipoint polynomial evaluation and its
                 parallel processing",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "24--30",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p24-murao/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf C.1.2}
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Parallel processors**. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}

@InProceedings{Norman:1997:CPP,
  author =       "Arthur Norman and John Fitch",
  title =        "{CABAL}: polynomial and power series algebra on a
                 parallel computer",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "196--203",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p196-norman/",
  acknowledgement = ack-nhfb,
  keywords =     "design; experimentation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf C.1.2} Computer Systems Organization,
                 PROCESSOR ARCHITECTURES, Multiple Data Stream
                 Architectures (Multiprocessors), Parallel processors**.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials.",
}

@InProceedings{Noro:1997:CRF,
  author =       "Masayuki Noro and John McKay",
  title =        "Computation of replicable functions on {Risa\slash
                 Asir}",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "130--138",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p130-noro/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; performance;
                 verification",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf I.1.1} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Simplification of expressions.
                 {\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms.",
}

@InProceedings{Nussbaum:1997:RPP,
  author =       "Doron Nussbaum",
  title =        "Rectilinear $p$-piercing problems",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "316--323",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p316-nussbaum/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ohno:1997:IMC,
  author =       "Kazuhiko Ohno and Masahiko Ikawa and Shin-ichiro Mori
                 and Hiroshi Nakashima and Shinji Tomita and Masahiro
                 Goshima",
  title =        "Improvement of message communication in concurrent
                 logic language",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "156--164",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p156-ohno/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; performance",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Concurrent, distributed, and parallel
                 languages. {\bf F.4.1} Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
                 Logic. {\bf F.3.3} Theory of Computation, LOGICS AND
                 MEANINGS OF PROGRAMS, Studies of Program Constructs,
                 Type structure.",
}

@InProceedings{Pflugel:1997:ACE,
  author =       "Eckhard Pfl{\"u}gel",
  title =        "An algorithm for computing exponential solutions of
                 first order linear differential systems",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "164--171",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p164-pflugel/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pontelli:1997:PSC,
  author =       "E. Pontelli and G. Gupta",
  title =        "Parallel symbolic computation in {ACE}",
  crossref =     "Baral:1997:LPN",
  pages =        "359--396",
  year =         "1997",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reischert:1997:AFC,
  author =       "Daniel Reischert",
  title =        "Asymptotically fast computation of subresultants",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "233--240",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p233-reischert/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Roach:1997:MGF,
  author =       "Kelly Roach",
  title =        "{Meijer} ${G}$ functions representations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "205--211",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p205-roach/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rust:1997:RPD,
  author =       "C. J. Rust and G. J. Reid",
  title =        "Rankings of partial derivatives",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "9--16",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p9-rust/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sims:1997:CSA,
  author =       "Charles C. Sims",
  title =        "Computing with subgroups of automorphism groups of
                 finite groups",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "400--403",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p400-sims/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sperber:1997:DPE,
  author =       "Michael Sperber and Peter Thiemann and Hervert
                 Klaeren",
  title =        "Distributed partial evaluation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "80--87",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p80-sperber/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; experimentation; performance",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Optimization. {\bf D.1.1} Software,
                 PROGRAMMING TECHNIQUES, Applicative (Functional)
                 Programming. {\bf I.2.2} Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Automatic Programming, Program
                 transformation. {\bf D.3.4} Software, PROGRAMMING
                 LANGUAGES, Processors, Compilers.",
}

@InProceedings{Stetter:1997:SPS,
  author =       "Hans J. Stetter",
  title =        "Stabilization of polynomial systems solving with
                 {Gr{\"o}bner} bases",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "117--124",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p117-stetter/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stiller:1997:SCO,
  author =       "Peter F. Stiller",
  title =        "Symbolic computation of object\slash image equations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "359--364",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p359-stiller/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Storjohann:1997:SEG,
  author =       "Arne Storjohann",
  title =        "A solution to the extended {GCD} problem with
                 applications",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "109--116",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p109-storjohann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Szanto:1997:CWR,
  author =       "{\'A}gnes Sz{\'a}nt{\'o}",
  title =        "Complexity of the {Wu--Ritt} decomposition",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "139--149",
  year =         "1997",
  bibdate =      "Fri May 07 12:02:05 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p139-szanto/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials. {\bf I.1.0} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 General.",
}

@InProceedings{Teo:1997:DEP,
  author =       "Yong Meng Teo and Wei-Ngan Chin and Soon Huat Tan",
  title =        "Deriving efficient parallel programs for complex
                 recurrences",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "101--110",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p101-teo/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; languages; performance",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Parallel programming. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Application Builder. {\bf F.2.0}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, General. {\bf E.1} Data, DATA
                 STRUCTURES, Lists, stacks, and queues.",
}

@InProceedings{Tsarev:1997:SMI,
  author =       "S. P. Tsarev",
  title =        "Symbolic manipulation of integrodifferential
                 expressions and factorization of linear ordinary
                 differential operators over transcendental extensions
                 of a differential field",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "310--315",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p310-tsarev/",
  acknowledgement = ack-nhfb,
}

@InProceedings{V:1997:MRP,
  author =       "Eugene V. and Zima",
  title =        "Mixed representation of polynomials oriented towards
                 fast parallel shift",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "150--155",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p150-zima/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf I.1.2}
                 Computing Methodologies, SYMBOLIC AND ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
}

@InProceedings{vanderHoeven:1997:LMF,
  author =       "Joris {van der Hoeven}",
  title =        "Lazy multiplication of formal power series",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "17--20",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p17-van_der_hoeven/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Villard:1997:FAC,
  author =       "G. Villard",
  title =        "Further analysis of {Coppersmith}'s block {Wiedemann}
                 algorithm for the solution of sparse linear systems",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "32--39",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p32-villard/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Volcheck:1997:CDP,
  author =       "Emil Volcheck",
  title =        "On computing the dual of a plane algebraic curve",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "356--358",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p356-volcheck/",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:1997:FAT,
  author =       "Joachim von zur Gathen and J{\"u}rgen Gerhard",
  title =        "Fast algorithms for {Taylor} shifts and certain
                 difference equations",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "40--47",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p40-von_zur_gathen/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:1997:TPD,
  author =       "Paul S. Wang",
  title =        "Tools for parallel\slash distributed mathematical
                 computation",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "188--195",
  year =         "1997",
  bibdate =      "Thu Mar 12 07:28:19 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/266670/p188-wang/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; languages",
  subject =      "{\bf C.1.2} Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Parallel processors**. {\bf D.1.3}
                 Software, PROGRAMMING TECHNIQUES, Concurrent
                 Programming, Parallel programming. {\bf D.3.2}
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, LISP.",
}

@InProceedings{Weispfenning:1997:CUE,
  author =       "Wolker Weispfenning",
  title =        "Complexity and uniformity of elimination in
                 {Presburger} arithmetic",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "48--53",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p48-weispfenning/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zimmer:1997:SCA,
  author =       "Horst G. Zimmer",
  title =        "{SIMATH} --- a computer algebra system for number
                 theoretic applications",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "365--375",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p365-zimmer/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zolotykh:1997:TPD,
  author =       "Andrij A. Zolotykh",
  title =        "Tensor product decomposition and other algorithms for
                 representations of large simple {Lie} algebras",
  crossref =     "Kuchlin:1997:PPS",
  pages =        "60--67",
  year =         "1997",
  bibdate =      "Wed Mar 11 18:24:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p60-zolotykh/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:1998:RSF,
  author =       "S. A. Abramov and M. A. Barkatou",
  title =        "Rational solutions of first order linear difference
                 systems",
  crossref =     "Gloor:1998:IPI",
  pages =        "124--131",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p124-abramov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bachmann:1998:MRG,
  author =       "Olaf Bachmann and Hans Sch{\"o}nemann",
  title =        "Monomial representations for {Gr{\"o}bner} bases
                 computations",
  crossref =     "Gloor:1998:IPI",
  pages =        "309--316",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p309-bachmann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:1998:EPL,
  author =       "M. A. Barkatou and E. Pfl{\"u}gel",
  title =        "On the equivalence problem of linear differential
                 systems and its application for factoring completely
                 reducible systems",
  crossref =     "Gloor:1998:IPI",
  pages =        "268--275",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p268-barkatou/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Basu:1998:CCS,
  author =       "Saugata Basu and Richard Pollack and
                 Marie-Fran{\c{c}}oise Roy",
  title =        "Complexity of computing semi-algebraic descriptions of
                 the connected components of a semi-algebraic set",
  crossref =     "Gloor:1998:IPI",
  pages =        "25--29",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p25-basu/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beringer:1998:SSA,
  author =       "Fr{\'e}d{\'e}ric Beringer and Fran{\c{c}}oise Jung",
  title =        "Solving ``generalized algebraic equations''",
  crossref =     "Gloor:1998:IPI",
  pages =        "222--227",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p222-beringer/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bernardin:1998:BHP,
  author =       "Laurent Bernardin",
  title =        "On bivariate {Hensel} and its parallelization",
  crossref =     "Gloor:1998:IPI",
  pages =        "96--100",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p96-bernardin/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bondyfalat:1998:CIM,
  author =       "Didier Bondyfalat and Bernard Mourrain and Victor Y.
                 Pan",
  title =        "Controlled iterative methods for solving polynomial
                 systems",
  crossref =     "Gloor:1998:IPI",
  pages =        "252--259",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p252-bondyfalat/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Breuer:1998:GTS,
  author =       "Thomas Breuer and Steve Linton",
  title =        "The {GAP 4} type system organising algebraic
                 algorithms",
  crossref =     "Gloor:1998:IPI",
  pages =        "38--45",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p38-breuer/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:1998:STI,
  author =       "Christopher W. Brown",
  title =        "Simplification of truth-invariant cylindrical
                 algebraic decompositions",
  crossref =     "Gloor:1998:IPI",
  pages =        "295--301",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p295-brown/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Caboara:1998:EAI,
  author =       "Massimo Caboara and Carlo Traverso",
  title =        "Efficient algorithms for ideal operations (extended
                 abstract)",
  crossref =     "Gloor:1998:IPI",
  pages =        "147--152",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p147-caboara/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chin:1998:OSA,
  author =       "Paulina Chin and Robert M. Corless and George F.
                 Corliss",
  title =        "Optimization strategies for the approximate {GCD}
                 problem",
  crossref =     "Gloor:1998:IPI",
  pages =        "228--235",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p228-chin/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Diaz:1998:FSM,
  author =       "Angel D{\'\i}az and Erich Kaltofen",
  title =        "{FOXBOX}: a system from manipulating symbolic objects
                 in black box representation",
  crossref =     "Gloor:1998:IPI",
  pages =        "30--37",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p30-diaz/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dolzmann:1998:APQ,
  author =       "Andreas Dolzmann and Oliver Gloor and Thomas Sturm",
  title =        "Approaches to parallel quantifier elimination",
  crossref =     "Gloor:1998:IPI",
  pages =        "88--95",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p88-dolzmann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dooley:1998:CMC,
  author =       "Samuel S. Dooley",
  title =        "Coordinating mathematical content and presentation
                 markup in interactive mathematical documents",
  crossref =     "Gloor:1998:IPI",
  pages =        "54--61",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p54-dooley/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dunstan:1998:LFM,
  author =       "Martin Dunstan and Tom Kelsey and Steve Linton and
                 Ursula Martin",
  title =        "Lightweight formal methods for computer algebra
                 systems",
  crossref =     "Gloor:1998:IPI",
  pages =        "80--87",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p80-dunstan/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Egner:1998:SPR,
  author =       "Sebastian Egner and Markus P{\"u}schel",
  title =        "Solving puzzles related to permutation groups",
  crossref =     "Gloor:1998:IPI",
  pages =        "186--193",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p186-egner/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gerhard:1998:HDS,
  author =       "J{\"u}rgen Gerhard",
  title =        "High degree solutions of low degree equations
                 (extended abstract)",
  crossref =     "Gloor:1998:IPI",
  pages =        "284--289",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p284-gerhard/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:1998:CIS,
  author =       "M. Giesbrecht and A. Lobo and B. D. Saunders",
  title =        "Certifying inconsistency of sparse linear systems",
  crossref =     "Gloor:1998:IPI",
  pages =        "113--119",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p113-giesbrecht/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Grigoriev:1998:PAS,
  author =       "D. Grigoriev and A. Slissenko",
  title =        "Polytime algorithm for the shortest path in a homotopy
                 class amidst semi-algebraic obstacles in the plane",
  crossref =     "Gloor:1998:IPI",
  pages =        "17--24",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p17-grigoriev/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hitz:1998:EAC,
  author =       "Markus A. Hitz and Erich Kaltofen",
  title =        "Efficient algorithms for computing the nearest
                 polynomial with constrained roots",
  crossref =     "Gloor:1998:IPI",
  pages =        "236--243",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p236-hitz/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hulpke:1998:CNS,
  author =       "Alexander Hulpke",
  title =        "Computing normal subgroups",
  crossref =     "Gloor:1998:IPI",
  pages =        "194--198",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p194-hulpke/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Iglio:1998:SCC,
  author =       "Pietro Iglio and Giuseppe Attardi",
  title =        "Software components for computer algebra",
  crossref =     "Gloor:1998:IPI",
  pages =        "62--69",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p62-iglio/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeffrey:1998:RIP,
  author =       "D. J. Jeffrey and A. D. Rich",
  title =        "Recursive integration of piecewise-continuous
                 functions",
  crossref =     "Gloor:1998:IPI",
  pages =        "290--294",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p290-jeffrey/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kirrinnis:1998:FNI,
  author =       "Peter Kirrinnis",
  title =        "Fast numerical improvement of factors of polynomial
                 and of partial fractions",
  crossref =     "Gloor:1998:IPI",
  pages =        "260--267",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p260-kirrinnis/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kislenkov:1998:MCR,
  author =       "V. Kislenkov and V. Mitrofanov and E. Zima",
  title =        "Multidimensional chains of recurrences",
  crossref =     "Gloor:1998:IPI",
  pages =        "199--206",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p199-kislenkov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lakshman:1998:SCU,
  author =       "Y. N. Lakshman and Bruce Char and Jeremy Johnson",
  title =        "Software components using symbolic computation for
                 problem solving environments",
  crossref =     "Gloor:1998:IPI",
  pages =        "46--53",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p46-lakshman/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:1998:STO,
  author =       "Ziming Li",
  title =        "A subresultant theory for {{\O}re} polynomials with
                 applications",
  crossref =     "Gloor:1998:IPI",
  pages =        "132--139",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p132-li/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Maignan:1998:SOT,
  author =       "Aude Maignan",
  title =        "Solving one and two-dimensional exponential polynomial
                 systems",
  crossref =     "Gloor:1998:IPI",
  pages =        "215--221",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p215-maignan/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Minh:1998:CMG,
  author =       "Hoang Ngoc Minh and Michel Petitot and Joris {Van Der
                 Hoeven}",
  title =        "Computation of the monodromy of generalized
                 polylogarithms",
  crossref =     "Gloor:1998:IPI",
  pages =        "276--283",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p276-minh/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mulders:1998:M,
  author =       "Thom Mulders and Arne Storjohann",
  title =        "The modulo {$N$} extended {GCD} problem for the
                 polynomials",
  crossref =     "Gloor:1998:IPI",
  pages =        "105--112",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p105-mulders/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Muller-Quade:1998:DLD,
  author =       "J{\"o}rn M{\"u}ller-Quade and Martin R{\"o}tteler",
  title =        "Deciding linear disjointness of finitely generated
                 fields",
  crossref =     "Gloor:1998:IPI",
  pages =        "153--160",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p153-muller-quade/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Muller:1998:MDM,
  author =       "J{\"u}rgen M{\"u}ller",
  title =        "The 5-modular decomposition matrix of the sporadic
                 simple {Conway} group {Co$_3$}",
  crossref =     "Gloor:1998:IPI",
  pages =        "179--185",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p179-muller/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nordbeck:1998:CSB,
  author =       "Patrik Nordbeck",
  title =        "Canonical subalgebraic bases in non-commutative
                 polynomial rings",
  crossref =     "Gloor:1998:IPI",
  pages =        "140--146",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p140-nordbeck/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Norenberg:1998:CMA,
  author =       "R. N{\"o}renberg",
  title =        "Covering monomial algebras",
  crossref =     "Gloor:1998:IPI",
  pages =        "161--164",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p161-norenberg/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Poloskov:1998:CPP,
  author =       "Igor E. Poloskov",
  title =        "Compound program packages and a nonlinear random
                 fluctuations analysis",
  crossref =     "Gloor:1998:IPI",
  pages =        "70--75",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p70-poloskov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Popova:1998:SSN,
  author =       "E. D. Popova and C. P. Ullrich",
  title =        "Simplification of symbolic-numerical interval
                 expressions",
  crossref =     "Gloor:1998:IPI",
  pages =        "207--214",
  year =         "1998",
  bibdate =      "Mon Oct 05 08:51:27 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p207-popova/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reinert:1998:NNR,
  author =       "Birgit Reinert and Klaus Madlener and Teo Mora",
  title =        "A note on {Nielsen} reduction and coset enumeration",
  crossref =     "Gloor:1998:IPI",
  pages =        "171--178",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p171-reinert/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sasaki:1998:ACE,
  author =       "Tateaki Sasaki and Satoshi Yamaguchi",
  title =        "An analysis of cancellation error in multivariate
                 {Hensel} construction with floating-point number
                 arithmetic",
  crossref =     "Gloor:1998:IPI",
  pages =        "1--8",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p1-sasaki/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sato:1998:NTC,
  author =       "Yosuke Sato",
  title =        "A new type of canonical {Gr{\"o}bner} bases in
                 polynomial rings over {Von Neumann} regular rings",
  crossref =     "Gloor:1998:IPI",
  pages =        "317--321",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p317-sato/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schicho:1998:RPR,
  author =       "Josef Schicho",
  title =        "Rational parametrization of real algebraic surfaces",
  crossref =     "Gloor:1998:IPI",
  pages =        "302--308",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p302-schicho/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sims:1998:FMG,
  author =       "Charles C. Sims",
  title =        "Fast multiplication and growth in groups",
  crossref =     "Gloor:1998:IPI",
  pages =        "165--170",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p165-sims/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stetter:1998:SSP,
  author =       "Hans J. Stetter and G{\"u}nther H. Thallinger",
  title =        "Singular systems of polynomials",
  crossref =     "Gloor:1998:IPI",
  pages =        "9--16",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p9-stetter/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Storjohann:1998:I,
  author =       "Arne Storjohann",
  title =        "An {$O(n^3)$} algorithm for the {Frobenius} normal
                 form",
  crossref =     "Gloor:1998:IPI",
  pages =        "101--105",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p101-storjohann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tran:1998:PCG,
  author =       "Q.-N. Tran",
  title =        "Parallel Computation and {Gr{\"o}bner} Bases: An
                 Application for Converting Bases with the {Gr{\"o}bner}
                 Walk",
  crossref =     "Buchberger:1998:YGB",
  pages =        "519--531",
  year =         "1998",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
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}

@InProceedings{Vakhidov:1998:ACA,
  author =       "Akmal A. Vakhidov and Irina V. Tupikova",
  title =        "Application of computer algebra methods to the
                 construction of an asteroid motion theory based on
                 {Lie} transforms",
  crossref =     "Gloor:1998:IPI",
  pages =        "76--79",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
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                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p76-vakhidov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:1998:RSL,
  author =       "Mark {van Hoeij}",
  title =        "Rational solutions of linear difference equations",
  crossref =     "Gloor:1998:IPI",
  pages =        "120--123",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p120-van_hoeij/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wallack:1998:MMM,
  author =       "Aaron Wallack and Ioannis Z. Emiris and Dinesh
                 Manocha",
  title =        "{MARS}: a {MAPLE\slash MATLAB\slash C} resultant-based
                 solver",
  crossref =     "Gloor:1998:IPI",
  pages =        "244--251",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p244-wallack/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abbott:1999:FDC,
  author =       "John Abbott and Manuel Bronstein and Thom Mulders",
  title =        "Fast deterministic computation of determinants of
                 dense matrices",
  crossref =     "Dooley:1999:IJS",
  pages =        "197--204",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:1999:DLD,
  author =       "Sergei A. Abramov and Mark van Hoeij",
  title =        "Desingularization of linear difference operators with
                 polynomial coefficients",
  crossref =     "Dooley:1999:IJS",
  pages =        "269--275",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adams:1999:ATP,
  author =       "A. A. Adams and H. Gottliebsen and S. A. Linton and U.
                 Martin",
  title =        "Automated theorem proving in support of computer
                 algebra: symbolic definite integration as a case
                 study",
  crossref =     "Dooley:1999:IJS",
  pages =        "253--260",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Andradas:1999:BFR,
  author =       "Carlos Andradas and Taom{\'a}s Recio and J. Refael
                 Sendra",
  title =        "Base field restriction techniques for parametric
                 curves",
  crossref =     "Dooley:1999:IJS",
  pages =        "17--22",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Arsac:1999:DCC,
  author =       "Olivier Arsac and St{\'e}phane Dalmas and Marc
                 Ga{\'e}tano",
  title =        "Design of a customizable component to display and edit
                 formulas",
  crossref =     "Dooley:1999:IJS",
  pages =        "283--290",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:1999:RSM,
  author =       "M. A. Barkatou",
  title =        "Rational solutions of matrix difference equations: the
                 problem of equivalence and factorization",
  crossref =     "Dooley:1999:IJS",
  pages =        "277--282",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beckermann:1999:SNF,
  author =       "Bernhard Beckermann and George Labahn and Gilles
                 Villard",
  title =        "Shifted normal forms of polynomial matrices",
  crossref =     "Dooley:1999:IJS",
  pages =        "189--196",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bernardin:1999:SCJ,
  author =       "Laurent Bernardin and Bruce Char and Erich Kaltofen",
  title =        "Symbolic computation in {Java}: an appraisement",
  crossref =     "Dooley:1999:IJS",
  pages =        "237--244",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boucher:1999:APS,
  author =       "Delphine Boucher",
  title =        "About the polynomial solutions of homogeneous linear
                 differential equations depending on parameters",
  crossref =     "Dooley:1999:IJS",
  pages =        "261--268",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bronstein:1999:SLO,
  author =       "Manuel Bronstein and Anne Fredet",
  title =        "Solving linear ordinary differential equations over
                 {$C(x,e^{\int f(x)\,dx})$}",
  crossref =     "Dooley:1999:IJS",
  pages =        "173--179",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:1999:GSF,
  author =       "Christopher W. Brown",
  title =        "Guaranteed solution formula construction",
  crossref =     "Dooley:1999:IJS",
  pages =        "137--144",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brunick:1999:ECD,
  author =       "Gerard P. Brunick and Edward L. Green and Lenwood S.
                 Heath and Craig A. Struble",
  title =        "Efficient construction of {Drinfel'd} doubles",
  crossref =     "Dooley:1999:IJS",
  pages =        "45--52",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:1999:RNF,
  author =       "Guoting Chen and Jean Della Dora",
  title =        "Rational normal form for dynamical systems by
                 {Carleman} linearization",
  crossref =     "Dooley:1999:IJS",
  pages =        "165--172",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Corless:1999:APD,
  author =       "Robert M. Corless and Mark W. Giesbrecht and David J.
                 Jeffrey",
  title =        "Approximate polynomial decomposition",
  crossref =     "Dooley:1999:IJS",
  pages =        "213--219",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{deGraaf:1999:CBF,
  author =       "W. A. de Graaf and J. Wisliceny",
  title =        "Constructing bases of finitely presented {Lie}
                 algebras using {Gr{\"o}bner} bases in free algebras",
  crossref =     "Dooley:1999:IJS",
  pages =        "37--43",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dolzmann:1999:ACS,
  author =       "Andreas Dolzmann and Thomas Sturm",
  title =        "{$P$}-adic constraint solving",
  crossref =     "Dooley:1999:IJS",
  pages =        "151--158",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Doye:1999:ACA,
  author =       "Nicolas J. Doye",
  title =        "Automated coercion for {Axiom}",
  crossref =     "Dooley:1999:IJS",
  pages =        "229--235",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Elkadi:1999:NAG,
  author =       "Mohamed Elkadi and Bernard Mourrain",
  title =        "A new algorithm for the geometric decomposition of a
                 variety",
  crossref =     "Dooley:1999:IJS",
  pages =        "9--16",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giusti:1999:SSO,
  author =       "Marc Giusti and {\'E}ric Schost",
  title =        "Solving some overdetermined polynomial systems",
  crossref =     "Dooley:1999:IJS",
  pages =        "1--8",
  year =         "1999",
  bibdate =      "Tue Oct 22 15:30:12 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hitz:1999:EAC,
  author =       "Markus A. Hitz and Erich Kaltofen and Y. N. Lakshman",
  title =        "Efficient algorithms for computing the nearest
                 polynomial with a real root and related problems",
  crossref =     "Dooley:1999:IJS",
  pages =        "205--212",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeannerod:1999:RAM,
  author =       "C.-P. Jeannerod and E. Pfl{\"u}gel",
  title =        "A reduction algorithm for matrices depending on a
                 parameter",
  crossref =     "Dooley:1999:IJS",
  pages =        "121--128",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:1999:GMP,
  author =       "Erich Kaltofen and Michael B. Monagan",
  title =        "On the genericity of the modular polynomial {GCD}
                 algorithm",
  crossref =     "Dooley:1999:IJS",
  pages =        "59--66",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kislenkov:1999:HFC,
  author =       "V. Kislenkov and V. Mitrofanov and E. Zima",
  title =        "How fast can we compute products?",
  crossref =     "Dooley:1999:IJS",
  pages =        "75--82",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lamban:1999:SI,
  author =       "Laureano Lamb{\'a}n and Vico Pascual and Julio Rubio",
  title =        "Specifying implementations",
  crossref =     "Dooley:1999:IJS",
  pages =        "245--251",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Le:1999:CSC,
  author =       "Ha Le and Chris Howlett",
  title =        "Client-server communication standards for mathematical
                 computation",
  crossref =     "Dooley:1999:IJS",
  pages =        "299--306",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Macutan:1999:FSS,
  author =       "Y. O. Macutan",
  title =        "Formal solutions of scalar singularly-perturbed linear
                 differential equations",
  crossref =     "Dooley:1999:IJS",
  pages =        "113--120",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{McCallum:1999:PCB,
  author =       "Scott McCallum",
  title =        "On projection in {CAD}-based quantifier elimination
                 with equational constraint",
  crossref =     "Dooley:1999:IJS",
  pages =        "145--149",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Moritsugu:1999:MZS,
  author =       "Schuichi Moritsugu and Kazuko Kuriyama",
  title =        "On multiple zeros of systems of algebraic equations",
  crossref =     "Dooley:1999:IJS",
  pages =        "23--30",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mulders:1999:DLS,
  author =       "Thom Mulders and Arne Storjohann",
  title =        "{Diophantine} linear system solving",
  crossref =     "Dooley:1999:IJS",
  pages =        "181--188",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pak:1999:SGS,
  author =       "Igor Pak and Sergey Bratus",
  title =        "On sampling generating sets of finite groups and
                 product replacement algorithm: extended abstract",
  crossref =     "Dooley:1999:IJS",
  pages =        "91--96",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rust:1999:EUT,
  author =       "C. J. Rust and G. J. Reid and A. D. Wittkopf",
  title =        "Existence and uniqueness theorems for formal power
                 series solutions of analytic differential systems",
  crossref =     "Dooley:1999:IJS",
  pages =        "105--112",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shackell:1999:SPR,
  author =       "John Shackell",
  title =        "Star products and the representation of asymptotic
                 growth",
  crossref =     "Dooley:1999:IJS",
  pages =        "97--104",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shoup:1999:ECM,
  author =       "Victor Shoup",
  title =        "Efficient computation of minimal polynomials in
                 algebraic extensions of finite fields",
  crossref =     "Dooley:1999:IJS",
  pages =        "53--58",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tsarev:1999:FNO,
  author =       "S. P. Tsarev",
  title =        "On factorization of nonlinear ordinary differential
                 equations",
  crossref =     "Dooley:1999:IJS",
  pages =        "159--164",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Villard:1999:AIA,
  author =       "Dominique Villard and Michael B. Monagan",
  title =        "{ADrien}: an implementation of automatic
                 differentiation in {Maple}",
  crossref =     "Dooley:1999:IJS",
  pages =        "221--228",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:1999:CSP,
  author =       "Joachim von zur Gathen and Michael N{\"o}cker",
  title =        "Computing special powers in finite fields: extended
                 abstract",
  crossref =     "Dooley:1999:IJS",
  pages =        "83--90",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:1999:DPI,
  author =       "Paul S. Wang",
  title =        "Design and protocol for {Internet} accessible
                 mathematical computation",
  crossref =     "Dooley:1999:IJS",
  pages =        "291--298",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wavrik:1999:CTE,
  author =       "John J. Wavrik",
  title =        "Commutativity theorems: examples in search of
                 algorithms",
  crossref =     "Dooley:1999:IJS",
  pages =        "31--36",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Weispfenning:1999:MRI,
  author =       "Volker Weispfenning",
  title =        "Mixed real-integer linear quantifier elimination",
  crossref =     "Dooley:1999:IJS",
  pages =        "129--136",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zilic:1999:FMP,
  author =       "Zeljko Zilic and Katarzyna Radecka",
  title =        "On feasible multivariate polynomial interpolations
                 over arbitrary fields",
  crossref =     "Dooley:1999:IJS",
  pages =        "67--74",
  year =         "1999",
  bibdate =      "Sat Mar 11 16:39:42 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abbott:2000:FSP,
  author =       "John Abbott and Victor Shoup and Paul Zimmermann",
  title =        "Factorization in {${\mathbb Z}[x]$}: the searching
                 phase",
  crossref =     "Traverso:2000:IAU",
  pages =        "1--7",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p1-abbott/p1-abbott.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p1-abbott/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2000:HDO,
  author =       "Sergei A. Abramov and Manuel Bronstein",
  title =        "Hypergeometric dispersion and the orbit problem",
  crossref =     "Traverso:2000:IAU",
  pages =        "8--13",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p8-abramov/p8-abramov.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p8-abramov/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Anai:2000:DLT,
  author =       "Hirokazu Anai and Volker Weispfenning",
  title =        "Deciding linear-trigonometric problems",
  crossref =     "Traverso:2000:IAU",
  pages =        "14--22",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p14-anai/p14-anai.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p14-anai/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barendegt:2000:RHM,
  author =       "Henk Barendegt and Arjeh M. Cohen",
  title =        "Representing and handling mathematical concepts by
                 humans and machines",
  crossref =     "Traverso:2000:IAU",
  pages =        "6--??",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/345542/p6-barendegt/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Binder:2000:ANR,
  author =       "Franz Binder and Erhard Aichinger and J{\"u}rgen Ecker
                 and Christof N{\"o}bauer and Peter Mayr",
  title =        "Algorithms for near-rings of non-linear
                 transformations",
  crossref =     "Traverso:2000:IAU",
  pages =        "23--29",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p23-binder/p23-binder.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p23-binder/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bodnar:2000:IAR,
  author =       "G{\'a}bor Bodn{\'a}r and Josef Schicho",
  title =        "An improved algorithm for the resolution of
                 singularities",
  crossref =     "Traverso:2000:IAU",
  pages =        "30--37",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p30-bodnar/p30-bodnar.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p30-bodnar/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boulier:2000:CCR,
  author =       "Fran{\c{c}}ois Boulier and Fran{\c{c}}ois Lemaire",
  title =        "Computing canonical representatives of regular
                 differential ideals",
  crossref =     "Traverso:2000:IAU",
  pages =        "38--47",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p38-boulier/p38-boulier.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p38-boulier/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:2000:IPC,
  author =       "Christopher W. Brown",
  title =        "Improved projection for {CAD}'s of {$R^3$}",
  crossref =     "Traverso:2000:IAU",
  pages =        "48--53",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p48-brown/p48-brown.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p48-brown/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cheng:2000:AME,
  author =       "Howard Cheng and Eugene Zima",
  title =        "On accelerated methods to evaluate sums of products of
                 rational numbers",
  crossref =     "Traverso:2000:IAU",
  pages =        "54--61",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p54-cheng/p54-cheng.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p54-cheng/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chtcherba:2000:CER,
  author =       "Arthur D. Chtcherba and Deepak Kapur",
  title =        "Conditions for exact resultants using the {Dixon}
                 formulation",
  crossref =     "Traverso:2000:IAU",
  pages =        "62--70",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p62-chtcherba/p62-chtcherba.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p62-chtcherba/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Collins:2000:MFP,
  author =       "George E. Collins and Werner Krandick",
  title =        "Multiprecision floating point addition",
  crossref =     "Traverso:2000:IAU",
  pages =        "71--77",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p71-collins/p71-collins.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p71-collins/",
  acknowledgement = ack-nhfb,
  keywords =     "FSUM; interval arithmetic; LEDA; MPADD; MPFUN;
                 polynomial root finding",
}

@InProceedings{Cormier:2000:CGG,
  author =       "Olivier Cormier and Michael F. Singer and Felix
                 Ulmer",
  title =        "Computing the {Galois} group of a polynomial using
                 linear differential equations",
  crossref =     "Traverso:2000:IAU",
  pages =        "78--85",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p78-cormier/p78-cormier.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p78-cormier/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cucker:2000:SPS,
  author =       "Felipe Cucker",
  title =        "Solving polynomial systems: a complexity theory
                 viewpoint",
  crossref =     "Traverso:2000:IAU",
  pages =        "??--??",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/345542/p-cucker/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dolzmann:2000:LQE,
  author =       "Andreas Dolzmann and Volker Weispfenning",
  title =        "Local quantifier elimination",
  crossref =     "Traverso:2000:IAU",
  pages =        "86--94",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p86-dolzmann/p86-dolzmann.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p86-dolzmann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dumas:2000:ISF,
  author =       "Jean-Guillaume Dumas and B. David Saunders and Gilles
                 Villard",
  title =        "Integer {Smith} form via the valence: experience with
                 large sparse matrices from homology",
  crossref =     "Traverso:2000:IAU",
  pages =        "95--105",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p95-dumas/p95-dumas.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p95-dumas/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eberly:2000:BBF,
  author =       "Wayne Eberly",
  title =        "Black box {Frobenius} decompositions over small
                 fields",
  crossref =     "Traverso:2000:IAU",
  pages =        "106--113",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p106-eberly/p106-eberly.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p106-eberly/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fernandez-Ferreiros:2000:MDW,
  author =       "Pilar Fernandez-Ferreiros and Maria de los Angeles
                 Gomez-Molleda",
  title =        "A method for deciding whether the {Galois} group is
                 abelian",
  crossref =     "Traverso:2000:IAU",
  pages =        "114--120",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p114-fernandez-ferreiros/p114-fernandez-ferreiros.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p114-fernandez-ferreiros/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fredet:2000:LDE,
  author =       "Anne Fredet",
  title =        "Linear differential equations, iterative logarithms
                 and orderings on monomial differential extensions",
  crossref =     "Traverso:2000:IAU",
  pages =        "121--128",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p121-fredet/p121-fredet.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p121-fredet/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Green:2000:CER,
  author =       "Edward L. Green and Lenwood S. Heath and Craig A.
                 Struble",
  title =        "Constructing endomorphism rings via duals",
  crossref =     "Traverso:2000:IAU",
  pages =        "129--136",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p129-green/p129-green.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p129-green/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Grigoriev:2000:BNV,
  author =       "Dima Grigoriev and Nicolai Vorobjov",
  title =        "Bounds on numers of vectors of multiplicities for
                 polynomials which are easy to compute",
  crossref =     "Traverso:2000:IAU",
  pages =        "137--146",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p137-grigoriev/p137-grigoriev.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p137-grigoriev/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gupta:2000:FPA,
  author =       "Anshul Gupta and Pankaj Rohatgi and Ramesh Agarwal",
  title =        "Fast practical algorithms for the
                 {Boolean-product-witness-matrix} problem",
  crossref =     "Traverso:2000:IAU",
  pages =        "146--152",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p146-gupta/p146-gupta.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p146-gupta/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Harris:2000:ANM,
  author =       "Jason Harris",
  title =        "Advanced notations in {\em Mathematica\/}",
  crossref =     "Traverso:2000:IAU",
  pages =        "153--160",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p153-harris/p153-harris.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p153-harris/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Holt:2000:CWH,
  author =       "Derek F. Holt",
  title =        "Computation in word-hyperbolic groups",
  crossref =     "Traverso:2000:IAU",
  pages =        "??--??",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/345542/p-holt/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Huang:2000:PMP,
  author =       "Yuzhen Huang and Wenda Wu and Hans J. Stetter and
                 Lihong Zhi",
  title =        "Pseudofactors of multivariate polynomials",
  crossref =     "Traverso:2000:IAU",
  pages =        "161--168",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p161-huang/p161-huang.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p161-huang/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hur:2000:ERA,
  author =       "Namhyun Hur and James H. Davenport",
  title =        "An exact real algebraic arithmetic with equality
                 determination",
  crossref =     "Traverso:2000:IAU",
  pages =        "169--174",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p169-hur/p169-hur.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p169-hur/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ivanyos:2000:FRA,
  author =       "G{\'a}bor Ivanyos",
  title =        "Fast randomized algorithms for the structure of matrix
                 algebras over finite fields (extended abstract)",
  crossref =     "Traverso:2000:IAU",
  pages =        "175--183",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p175-ivanyos/p175-ivanyos.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p175-ivanyos/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeannerod:2000:AEP,
  author =       "Claude-Pierre Jeannerod",
  title =        "An algorithm for the eigenvalue perturbation problem:
                 reduction of a ?-matrix to a {Lidskii} matrix",
  crossref =     "Traverso:2000:IAU",
  pages =        "184--191",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/345542/p184-jeannerod/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2000:ETB,
  author =       "Erich Kaltofen and Wen-shin Lee and Austin A. Lobo",
  title =        "Early termination in {Ben-Or\slash Tiwari} sparse
                 interpolation and a hybrid of {Zippel}'s algorithm",
  crossref =     "Traverso:2000:IAU",
  pages =        "192--201",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p192-kaltofen/p192-kaltofen.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p192-kaltofen/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Landsmann:2000:SPP,
  author =       "G{\"u}nter Landsmann and Josef Schicho and Franz
                 Winkler and Erik Hillgarter",
  title =        "Symbolic parametrization of pipe and canal surfaces",
  crossref =     "Traverso:2000:IAU",
  pages =        "202--208",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/345542/p202-landsmann/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lecerf:2000:CED,
  author =       "Gr{\'e}goire Lecerf",
  title =        "Computing an equidimensional decomposition of an
                 algebraic variety by means of geometric resolutions",
  crossref =     "Traverso:2000:IAU",
  pages =        "209--216",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p209-lecerf/p209-lecerf.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p209-lecerf/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lisonek:2000:MIT,
  author =       "Petr Lison{\u{e}}k and Robert B. Israel",
  title =        "Metric invariants of tetrahedra via polynomial
                 elimination",
  crossref =     "Traverso:2000:IAU",
  pages =        "217--219",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p217-lisonek/p217-lisonek.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p217-lisonek/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Miyamoto:2000:CNP,
  author =       "Izumi Miyamoto",
  title =        "Computing normalizers of permutation groups
                 efficiently using isomorphisms of association schemes",
  crossref =     "Traverso:2000:IAU",
  pages =        "220--224",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p220-miyamoto/p220-miyamoto.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p220-miyamoto/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:2000:DIB,
  author =       "Michael B. Monagan and Allan D. Wittkopf",
  title =        "On the design and implementation of {Brown}'s
                 algorithm over the integers and number fields",
  crossref =     "Traverso:2000:IAU",
  pages =        "225--233",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p225-monagan/p225-monagan.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p225-monagan/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mourrain:2000:SPC,
  author =       "Bernard Mourrain and Philippe Tr{\'e}buchet",
  title =        "Solving projective complete intersection faster",
  crossref =     "Traverso:2000:IAU",
  pages =        "234--241",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p234-mourrain/p234-mourrain.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p234-mourrain/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mulders:2000:RSS,
  author =       "Thom Mulders and Arne Storjohann",
  title =        "Rational solutions of singular linear systems",
  crossref =     "Traverso:2000:IAU",
  pages =        "242--249",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p242-mulders/p242-mulders.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p242-mulders/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nocker:2000:SRP,
  author =       "Michael N{\"o}cker",
  title =        "Some remarks on parallel exponentiation (extended
                 abstract)",
  crossref =     "Traverso:2000:IAU",
  pages =        "250--257",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/345542/p250-nocker/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Norman:2000:FEJ,
  author =       "Arthur C. Norman",
  title =        "Further evaluation of {Java} for symbolic
                 computation",
  crossref =     "Traverso:2000:IAU",
  pages =        "258--265",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p258-norman/p258-norman.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p258-norman/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2000:MSP,
  author =       "Victor Y. Pan",
  title =        "Matrix structure, polynomial arithmetic, and
                 erasure-resilient encoding\slash decoding",
  crossref =     "Traverso:2000:IAU",
  pages =        "266--271",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p266-pan/p266-pan.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p266-pan/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reid:2000:DMS,
  author =       "Gregory J. Reid and Allan D. Wittkopf",
  title =        "Determination of maximal symmetry groups of classes of
                 differential equations",
  crossref =     "Traverso:2000:IAU",
  pages =        "272--280",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p272-reid/p272-reid.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p272-reid/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reinert:2000:SSL,
  author =       "Birgit Reinert",
  title =        "Solving systems of linear one-sided equations in
                 integer monoid and group rings",
  crossref =     "Traverso:2000:IAU",
  pages =        "281--287",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p281-reinert/p281-reinert.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p281-reinert/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rosales:2000:HCI,
  author =       "Jos{\'e} Carlos Rosales and Pedro A.
                 Garc{\'\i}a-S{\'a}nchez and Juan Ignacio
                 Garc{\'\i}a-Garc{\'\i}a",
  title =        "How to check if a finitely generated commutative
                 monoid is a principal ideal commutative monoid",
  crossref =     "Traverso:2000:IAU",
  pages =        "288--291",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p288-rosales/p288-rosales.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p288-rosales/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schicho:2000:PPS,
  author =       "Josef Schicho",
  title =        "Proper parametrization of surfaces with a rational
                 pencil",
  crossref =     "Traverso:2000:IAU",
  pages =        "292--300",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p292-schicho/p292-schicho.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p292-schicho/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhang:2000:RCC,
  author =       "Ming Zhang and Ron Goldman",
  title =        "Rectangular corner cutting and
                 {Sylvester}-resultants",
  crossref =     "Traverso:2000:IAU",
  pages =        "301--308",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p301-zhang/p301-zhang.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p301-zhang/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2001:MDI,
  author =       "Sergei A. Abramov and M. Petkovsek",
  title =        "Minimal decomposition of indefinite hypergeometric
                 sums",
  crossref =     "Mourrain:2001:IJU",
  pages =        "7--14",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2001:SLF,
  author =       "Sergei A. Abramov and Manuel Bronstein",
  title =        "On solutions of linear functional systems",
  crossref =     "Mourrain:2001:IJU",
  pages =        "1--6",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adamchik:2001:BF,
  author =       "V. S. Adamchik",
  title =        "On the {Barnes} function",
  crossref =     "Mourrain:2001:IJU",
  pages =        "15--20",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aguirre:2001:GIM,
  author =       "Edith Aguirre and Abdul Salam Jarrah and Reinhard
                 Laubenbacher",
  title =        "Generic ideals and {Moreno-Soc{\'\i}as} conjecture",
  crossref =     "Mourrain:2001:IJU",
  pages =        "21--23",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Armando:2001:MEP,
  author =       "Alessandro Armando and Clemens Ballarin",
  title =        "{Maple}'s evaluation process as constraint contextual
                 rewriting",
  crossref =     "Mourrain:2001:IJU",
  pages =        "32--37",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boulier:2001:P,
  author =       "Fran{\c{c}}ois Boulier and Fran{\c{c}}ois Lemaire and
                 Marc Moreno Maza",
  title =        "{PARDI}!",
  crossref =     "Mourrain:2001:IJU",
  pages =        "38--47",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Buse:2001:RRP,
  author =       "Laurent Bus{\'e}",
  title =        "Residual resultant over the projective plane and the
                 implicitization problem",
  crossref =     "Mourrain:2001:IJU",
  pages =        "48--55",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Caboara:2001:FET,
  author =       "Massimo Caboara and Lorenzo Robbiano",
  title =        "Families of estimable terms",
  crossref =     "Mourrain:2001:IJU",
  pages =        "56--63",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cheng:2001:CAF,
  author =       "Howard Cheng and George Labahn",
  title =        "Computing all factorizations in {$\mathbb{Z}_N[x]$}",
  crossref =     "Mourrain:2001:IJU",
  pages =        "64--71",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cioffi:2001:CMG,
  author =       "Francesca Cioffi and Ferruccio Orecchia",
  title =        "Computation of minimal generators of ideals of fat
                 points",
  crossref =     "Mourrain:2001:IJU",
  pages =        "72--76",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cooperman:2001:SPC,
  author =       "Gene Cooperman and Victor Grinberg",
  title =        "Scalable parallel coset enumeration using bulk
                 definition",
  crossref =     "Mourrain:2001:IJU",
  pages =        "77--84",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Corless:2001:TFB,
  author =       "Robert M. Corless and Mark W. Giesbrecht and Mark van
                 Hoeij and Ilias S. Kotsireas and Stephen M. Watt",
  title =        "Towards factoring bivariate approximate polynomials",
  crossref =     "Mourrain:2001:IJU",
  pages =        "85--92",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cormier:2001:LSL,
  author =       "Olivier Cormier",
  title =        "On {Liouvillian} solutions of linear differential
                 equations of order $4$ and $5$",
  crossref =     "Mourrain:2001:IJU",
  pages =        "93--100",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{DAndrea:2001:HSR,
  author =       "Carlos D'Andrea and Ioannis Z. Emiris",
  title =        "Hybrid sparse resultant matrices for bivariate
                 systems",
  crossref =     "Mourrain:2001:IJU",
  pages =        "24--31",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dominguez:2001:MIC,
  author =       "C{\'e}sar Dom{\'\i}nguez and Julio Rubio",
  title =        "Modeling inheritance as coercion in a symbolic
                 computation system",
  crossref =     "Mourrain:2001:IJU",
  pages =        "109--115",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dora:2001:HC,
  author =       "Jean Della Dora and Aude Maignan and Mihaela
                 Mirica-Ruse and Sergio Yovine",
  title =        "Hybrid computation",
  crossref =     "Mourrain:2001:IJU",
  pages =        "101--108",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fortuna:2001:CRP,
  author =       "Elisabetta Fortuna and Patrizia Gianni and Barry
                 Trager",
  title =        "Computation of the radical of polynomial ideals over
                 fields of arbitrary characteristic",
  crossref =     "Mourrain:2001:IJU",
  pages =        "116--120",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fortune:2001:PRF,
  author =       "Steven Fortune",
  title =        "Polynomial root finding using iterated eigenvalue
                 computation",
  crossref =     "Mourrain:2001:IJU",
  pages =        "121--128",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Foursov:2001:CAC,
  author =       "Mikhail V. Foursov and Marc Moreno Maza",
  title =        "On computer-assisted classification of coupled
                 integrable equations",
  crossref =     "Mourrain:2001:IJU",
  pages =        "129--136",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Galligo:2001:SND,
  author =       "Andr{\'e} Galligo and David Rupprecht",
  title =        "Semi-numerical determination of irreducible branches
                 of a reduced space curve",
  crossref =     "Mourrain:2001:IJU",
  pages =        "137--142",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gemignani:2001:GGI,
  author =       "Luca Gemignani",
  title =        "A generalized {Graeffe}'s iteration for evaluating
                 polynomials and rational functions",
  crossref =     "Mourrain:2001:IJU",
  pages =        "143--149",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Granvilliers:2001:SIC,
  author =       "Laurent Granvilliers and Eric Monfroy and
                 Fr{\'e}d{\'e}ric Benhamou",
  title =        "Symbolic-interval cooperation in constraint
                 programming",
  crossref =     "Mourrain:2001:IJU",
  pages =        "150--166",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gutierrez:2001:UFT,
  author =       "Jamie Gutierrez and Rosario Rubio and David Sevilla",
  title =        "Unirational fields of transcendence degree one and
                 functional decomposition",
  crossref =     "Mourrain:2001:IJU",
  pages =        "167--174",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hanrot:2001:SRA,
  author =       "G. Hanrot and F. Morain",
  title =        "Solvability by radicals from an algorithmic point of
                 view",
  crossref =     "Mourrain:2001:IJU",
  pages =        "175--182",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hunt:2001:SLR,
  author =       "Harry B. Hunt and Madhav V. Marathe and Richard E.
                 Stearns",
  title =        "Strongly-local reductions and the complexity\slash
                 efficient approximability of algebra and optimization
                 on abstract algebraic structures",
  crossref =     "Mourrain:2001:IJU",
  pages =        "183--191",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jinwang:2001:MPI,
  author =       "Liu Jinwang and Liu Zhuojun and Liu Xiaoqi and Wang
                 Mingsheng",
  title =        "The membership problem for ideals of binomial skew
                 polynomial rings",
  crossref =     "Mourrain:2001:IJU",
  pages =        "192--195",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jurkovic:2001:DCS,
  author =       "Neven Jurkovic",
  title =        "Diagnosing and correcting student's misconceptions in
                 an educational computer algebra system",
  crossref =     "Mourrain:2001:IJU",
  pages =        "195--200",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Khanin:2001:DAC,
  author =       "Raya Khanin",
  title =        "Dimensional analysis in computer algebra",
  crossref =     "Mourrain:2001:IJU",
  pages =        "201--208",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Korelc:2001:HSM,
  author =       "Joze Korelc",
  title =        "Hybrid system for multi-language and multi-environment
                 generation of numerical codes",
  crossref =     "Mourrain:2001:IJU",
  pages =        "209--216",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mansfield:2001:TAW,
  author =       "Elizabeth L. Mansfield and Peter E. Hydon",
  title =        "Towards approximations which preserve integrals",
  crossref =     "Mourrain:2001:IJU",
  pages =        "217--222",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{McCallum:2001:PEC,
  author =       "Scott McCallum",
  title =        "On propagation of equational constraints in
                 {CAD}-based quantifier elimination",
  crossref =     "Mourrain:2001:IJU",
  pages =        "223--231",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Micciancio:2001:LSA,
  author =       "Daniele Micciancio and Bogdan Warinschi",
  title =        "A linear space algorithm for computing the {Hermite}
                 normal form",
  crossref =     "Mourrain:2001:IJU",
  pages =        "231--236",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mingsheng:2001:RGB,
  author =       "Wang Mingsheng and Liu Zhuojun",
  title =        "Remarks on {Gr{\"o}bner} basis for ideals under
                 composition",
  crossref =     "Mourrain:2001:IJU",
  pages =        "237--244",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mulholland:2001:ATP,
  author =       "Jamie Mulholland and Michael Monagan",
  title =        "Algorithms for trigonometric polynomials",
  crossref =     "Mourrain:2001:IJU",
  pages =        "245--252",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2001:UPN,
  author =       "Victor Y. Pan",
  title =        "Univariate polynomials: nearly optimal algorithms for
                 factorization and rootfinding",
  crossref =     "Mourrain:2001:IJU",
  pages =        "253--267",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pericleous:2001:NCB,
  author =       "Savvas Pericleous and Nicolai Vorobjov",
  title =        "New complexity bounds for cylindrical decompositions
                 of sub-{Pfaffian} sets",
  crossref =     "Mourrain:2001:IJU",
  pages =        "268--275",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ruatta:2001:MWI,
  author =       "Olivier Ruatta",
  title =        "A multivariate {Weierstrass} iterative rootfinder",
  crossref =     "Mourrain:2001:IJU",
  pages =        "276--283",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sasaki:2001:AMP,
  author =       "Tateaki Sasaki",
  title =        "Approximate multivariate polynomial factorization
                 based on zero-sum relations",
  crossref =     "Mourrain:2001:IJU",
  pages =        "284--291",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sato:2001:DCG,
  author =       "Yosuke Sato and Akira Suzuki",
  title =        "Discrete comprehensive {Gr{\"o}bner} bases",
  crossref =     "Mourrain:2001:IJU",
  pages =        "292--296",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Saunders:2001:BBM,
  author =       "B. D. Saunders",
  title =        "Black box methods for least squares problems",
  crossref =     "Mourrain:2001:IJU",
  pages =        "297--302",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sedjelmaci:2001:PLE,
  author =       "Sidi Mohammed Sedjelmaci",
  title =        "On a parallel {Lehmer--Euclid GCD} algorithm",
  crossref =     "Mourrain:2001:IJU",
  pages =        "303--308",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sedoglavic:2001:PAT,
  author =       "Alexandre Sedoglavic",
  title =        "A probabilistic algorithm to test local algebraic
                 observability in polynomial time",
  crossref =     "Mourrain:2001:IJU",
  pages =        "309--317",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sendra:2001:CDR,
  author =       "J. Rafael Sendra and Franz Winkler",
  title =        "Computation of the degree of rational maps between
                 curves",
  crossref =     "Mourrain:2001:IJU",
  pages =        "317--322",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Thome:2001:FCL,
  author =       "Emmanuel Thom{\'e}",
  title =        "Fast computation of linear generators for matrix
                 sequences and application to the block {Wiedemann}
                 algorithm",
  crossref =     "Mourrain:2001:IJU",
  pages =        "323--331",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:2001:ITF,
  author =       "Joachim von zur Gathen",
  title =        "Irreducible trinomials over finite fields",
  crossref =     "Mourrain:2001:IJU",
  pages =        "332--336",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2001:IAP,
  author =       "P. Wang and S. Gray and N. Kajler and D. Lin and W.
                 Liao and X. Zou",
  title =        "{IAMC} architecture and prototyping: a progress
                 report",
  crossref =     "Mourrain:2001:IJU",
  pages =        "337--344",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zima:2001:CPC,
  author =       "Eugene V. Zima",
  title =        "On computational properties of chains of recurrences",
  crossref =     "Mourrain:2001:IJU",
  pages =        "345--345",
  year =         "2001",
  bibdate =      "Wed May 15 14:28:03 MDT 2002",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2002:AZA,
  author =       "S. A. Abramov",
  title =        "Applicability of {Zeilberger}'s algorithm to
                 hypergeometric terms",
  crossref =     "Mora:2002:IPI",
  pages =        "1--7",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beckermann:2002:FFR,
  author =       "Bernhard Beckermann and Howard Cheng and George
                 Labahn",
  title =        "Fraction-free row reduction of matrices of skew
                 polynomials",
  crossref =     "Mora:2002:IPI",
  pages =        "8--15",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bradford:2002:TBS,
  author =       "Russell Bradford and James H. Davenport",
  title =        "Towards better simplification of elementary
                 functions",
  crossref =     "Mora:2002:IPI",
  pages =        "16--22",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bronstein:2002:SLO,
  author =       "Manuel Bronstein and S{\'e}bastien Lafaille",
  title =        "Solutions of linear ordinary differential equations in
                 terms of special functions",
  crossref =     "Mora:2002:IPI",
  pages =        "23--28",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chtcherba:2002:EOD,
  author =       "Arthur D. Chtcherba and Deepak Kapur",
  title =        "On the efficiency and optimality of {Dixon}-based
                 resultant methods",
  crossref =     "Mora:2002:IPI",
  pages =        "29--36",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Corless:2002:GNA,
  author =       "Robert M. Corless and Andr{\'e} Galligo and Ilias S.
                 Kotsireas and Stephen M. Watt",
  title =        "A geometric-numeric algorithm for absolute
                 factorization of multivariate polynomials",
  crossref =     "Mora:2002:IPI",
  pages =        "37--45",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dickenstein:2002:MRM,
  author =       "Alicia Dickenstein and Ioannis Z. Emiris",
  title =        "Multihomogeneous resultant matrices",
  crossref =     "Mora:2002:IPI",
  pages =        "46--54",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dooley:2002:EMC,
  author =       "Samuel S. Dooley",
  title =        "Editing mathematical content and presentation markup
                 in interactive mathematical documents",
  crossref =     "Mora:2002:IPI",
  pages =        "55--62",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dumas:2002:FFL,
  author =       "Jean Guillaume Dumas and Thierry Gautier and
                 Cl{\'e}ment Pernet",
  title =        "Finite field linear algebra subroutines",
  crossref =     "Mora:2002:IPI",
  pages =        "63--74",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2002:NEA,
  author =       "Jean Charles Faug{\`e}re",
  title =        "A new efficient algorithm for computing {Gr{\"o}bner}
                 bases without reduction to zero {$(F_5)$}",
  crossref =     "Mora:2002:IPI",
  pages =        "75--83",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fernandez-Ferreiros:2002:PSR,
  author =       "P. Fernandez-Ferreiros and M. A. Gomez-Molleda and L.
                 Gonzalez-Vega",
  title =        "Partial solvability by radicals",
  crossref =     "Mora:2002:IPI",
  pages =        "84--91",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fortuna:2002:CTR,
  author =       "Elisabetta Fortuna and Patrizia Gianni and Paola
                 Parenti and Carlo Traverso",
  title =        "Computing the topology of real algebraic surfaces",
  crossref =     "Mora:2002:IPI",
  pages =        "92--100",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:2002:ACS,
  author =       "Mark Giesbrecht and Erich Kaltofen and Wen-shin Lee",
  title =        "Algorithms for computing the sparsest shifts of
                 polynomials via the {Berlekamp\slash Massey}
                 algorithm",
  crossref =     "Mora:2002:IPI",
  pages =        "101--108",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hoeij:2002:MGA,
  author =       "Mark van Hoeij and Michael Monagan",
  title =        "A modular {GCD} algorithm over number fields presented
                 with multiple extensions",
  crossref =     "Mora:2002:IPI",
  pages =        "109--116",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hoeven:2002:NZT,
  author =       "Joris van der Hoeven",
  title =        "A new zero-test for formal power series",
  crossref =     "Mora:2002:IPI",
  pages =        "117--122",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hossain:2002:SIC,
  author =       "Shahadat Hossain and Trond Steihaug",
  title =        "Sparsity issues in the computation of {Jacobian}
                 matrices",
  crossref =     "Mora:2002:IPI",
  pages =        "123--130",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeannerod:2002:RFP,
  author =       "Claude Pierre Jeannerod",
  title =        "A reduced form for perturbed matrix polynomials",
  crossref =     "Mora:2002:IPI",
  pages =        "131--137",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2002:OSV,
  author =       "Erich Kaltofen",
  title =        "An output-sensitive variant of the baby steps\slash
                 giant steps determinant algorithm",
  crossref =     "Mora:2002:IPI",
  pages =        "138--144",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Khetan:2002:DFC,
  author =       "Amit Khetan",
  title =        "Determinantal formula for the chow form of a toric
                 surface",
  crossref =     "Mora:2002:IPI",
  pages =        "145--150",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kogan:2002:CCF,
  author =       "Irina A. Kogan and Marc Moreno Maza",
  title =        "Computation of canonical forms for ternary cubics",
  crossref =     "Mora:2002:IPI",
  pages =        "151--160",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Le:2002:SDS,
  author =       "Ha Le",
  title =        "Simplification of definite sums of rational functions
                 by creative symmetrizing method",
  crossref =     "Mora:2002:IPI",
  pages =        "161--167",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2002:FZD,
  author =       "Ziming Li and Fritz Schwarz and Serguei P. Tsarev",
  title =        "Factoring zero-dimensional ideals of linear partial
                 differential operators",
  crossref =     "Mora:2002:IPI",
  pages =        "168--175",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Luks:2002:PTN,
  author =       "Eugene M. Luks and Takunari Miyazaki",
  title =        "Polynomial-time normalizers for permutation groups
                 with restricted composition factors",
  crossref =     "Mora:2002:IPI",
  pages =        "176--183",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Matera:2002:DHF,
  author =       "Guillermo Matera and Alexandre Sedoglavic",
  title =        "The differential {Hilbert} function of a differential
                 rational mapping can be computed in polynomial time",
  crossref =     "Mora:2002:IPI",
  pages =        "184--191",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nagasaka:2002:TCI,
  author =       "Kosaku Nagasaka",
  title =        "Towards certified irreducibility testing of bivariate
                 approximate polynomials",
  crossref =     "Mora:2002:IPI",
  pages =        "192--199",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Noro:2002:YAP,
  author =       "Masayuki Noro and Kazuhiro Yokoyama",
  title =        "Yet another practical implementation of polynomial
                 factorization over finite fields",
  crossref =     "Mora:2002:IPI",
  pages =        "200--206",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2002:AEA,
  author =       "Victor Y. Pan and Xinmao Wang",
  title =        "Acceleration of {Euclidean} algorithm and extensions",
  crossref =     "Mora:2002:IPI",
  pages =        "207--213",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Richardson:2002:SOF,
  author =       "Daniel Richardson and Simon Langley",
  title =        "Some observations on familiar numbers",
  crossref =     "Mora:2002:IPI",
  pages =        "214--220",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rioboo:2002:TFR,
  author =       "Renaud Rioboo",
  title =        "Towards faster real algebraic numbers",
  crossref =     "Mora:2002:IPI",
  pages =        "221--228",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schicho:2002:SSP,
  author =       "Josef Schicho",
  title =        "Simplification of surface parametrizations",
  crossref =     "Mora:2002:IPI",
  pages =        "229--237",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schost:2002:DBL,
  author =       "{\'E}ric Schost",
  title =        "Degree bounds and lifting techniques for triangular
                 sets",
  crossref =     "Mora:2002:IPI",
  pages =        "238--245",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Storjohann:2002:HOL,
  author =       "Arne Storjohann",
  title =        "High-order lifting",
  crossref =     "Mora:2002:IPI",
  pages =        "246--254",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Suzuki:2002:AAC,
  author =       "Akira Suzuki and Yosuke Sato",
  title =        "An alternative approach to comprehensive {Gr{\"o}bner}
                 bases",
  crossref =     "Mora:2002:IPI",
  pages =        "255--261",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Traverso:2002:NSS,
  author =       "Carlo Traverso and Alberto Zanoni",
  title =        "Numerical stability and stabilization of {Gr{\"o}bner}
                 basis computation",
  crossref =     "Mora:2002:IPI",
  pages =        "262--269",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Weispfenning:2002:CCG,
  author =       "Volker Weispfenning",
  title =        "Canonical comprehensive {Gr{\"o}bner} bases",
  crossref =     "Mora:2002:IPI",
  pages =        "270--276",
  year =         "2002",
  bibdate =      "Sat Dec 13 18:13:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2003:RCF,
  author =       "S. A. Abramov and H. Q. Le and M. Petkov{\v{s}}ek",
  title =        "Rational canonical forms and efficient representations
                 of hypergeometric terms",
  crossref =     "Senda:2003:IPI",
  pages =        "7--14",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aroca:2003:PSS,
  author =       "F. Aroca and J. Cano and F. Jung",
  title =        "Power series solutions for non-linear {PDE}'s",
  crossref =     "Senda:2003:IPI",
  pages =        "15--22",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barnett:2003:CCA,
  author =       "Michael P. Barnett",
  title =        "Chemistry and computer algebra: past, present,
                 future",
  crossref =     "Senda:2003:IPI",
  pages =        "1--2",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Basiri:2003:COG,
  author =       "Abdolali Basiri and Jean-Charles Faug{\`e}re",
  title =        "Changing the ordering of {Gr{\"o}bner} bases with
                 {LLL}: case of two variables",
  crossref =     "Senda:2003:IPI",
  pages =        "23--29",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beaumont:2003:BSE,
  author =       "James Beaumont and Russell Bradford and James H.
                 Davenport",
  title =        "Better simplification of elementary functions through
                 power series",
  crossref =     "Senda:2003:IPI",
  pages =        "30--36",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2003:TPP,
  author =       "A. Bostan and G. Lecerf and {\'E}. Schost",
  title =        "{Tellegen}'s principle into practice",
  crossref =     "Senda:2003:IPI",
  pages =        "37--44",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boucher:2003:FOL,
  author =       "Delphine Boucher and Philippe Gaillard and Felix
                 Ulmer",
  title =        "Fourth order linear differential equations with
                 imprimitive group",
  crossref =     "Senda:2003:IPI",
  pages =        "45--49",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chapman:2003:EAA,
  author =       "Frederick W. Chapman",
  title =        "An elementary algorithm for the automatic derivation
                 and proof of tensor product identities via computer
                 algebra",
  crossref =     "Senda:2003:IPI",
  pages =        "50--57",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cluzeau:2003:FDS,
  author =       "Thomas Cluzeau",
  title =        "Factorization of differential systems in
                 characteristic {\em p\/}",
  crossref =     "Senda:2003:IPI",
  pages =        "58--65",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cooperman:2003:MBD,
  author =       "Gene Cooperman and Eric Robinson",
  title =        "Memory-based and disk-based algorithms for very high
                 degree permutation groups",
  crossref =     "Senda:2003:IPI",
  pages =        "66--73",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Datta:2003:UCA,
  author =       "Ruchira S. Datta",
  title =        "Using computer algebra to find {Nash} equilibria",
  crossref =     "Senda:2003:IPI",
  pages =        "74--79",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Din:2003:PVC,
  author =       "Mohab Safey El Din and {\'E}ric Schost",
  title =        "Polar varieties and computation of one point in each
                 connected component of a smooth real algebraic set",
  crossref =     "Senda:2003:IPI",
  pages =        "224--231",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eberly:2003:ETS,
  author =       "Wayne Eberly",
  title =        "Early termination over small fields",
  crossref =     "Senda:2003:IPI",
  pages =        "80--87",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fateman:2003:CCR,
  author =       "Richard J. Fateman and Raymond Toy",
  title =        "Converting call-by-reference to call-by-value:
                 {Fortran} and {Lisp} coexisting",
  crossref =     "Senda:2003:IPI",
  pages =        "95--102",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fateman:2003:HLP,
  author =       "Richard Fateman",
  title =        "High-level proofs of mathematical programs using
                 automatic differentiation, simplification, and some
                 common sense",
  crossref =     "Senda:2003:IPI",
  pages =        "88--94",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fredet:2003:FLD,
  author =       "Anne Fredet",
  title =        "Factorization of linear differential operators in
                 exponential extensions",
  crossref =     "Senda:2003:IPI",
  pages =        "103--110",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Geddes:2003:EFH,
  author =       "Keith O. Geddes and Wei Wei Zheng",
  title =        "Exploiting fast hardware floating point in high
                 precision computation",
  crossref =     "Senda:2003:IPI",
  pages =        "111--118",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gerhard:2003:SDP,
  author =       "J. Gerhard and M. Giesbrecht and A. Storjohann and E.
                 V. Zima",
  title =        "Shiftless decomposition and polynomial-time rational
                 summation",
  crossref =     "Senda:2003:IPI",
  pages =        "119--126",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:2003:FDO,
  author =       "Mark Giesbrecht and Yang Zhang",
  title =        "Factoring and decomposing {{\O}re} polynomials over
                 {$\mathcal{F}_q(t)$}",
  crossref =     "Senda:2003:IPI",
  pages =        "127--134",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giorgi:2003:CPM,
  author =       "Pascal Giorgi and Claude-Pierre Jeannerod and Gilles
                 Villard",
  title =        "On the complexity of polynomial matrix computations",
  crossref =     "Senda:2003:IPI",
  pages =        "135--142",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hoeven:2003:RMU,
  author =       "Joris van der Hoeven",
  title =        "Relaxed multiplication using the middle product",
  crossref =     "Senda:2003:IPI",
  pages =        "143--147",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hubert:2003:CPS,
  author =       "E. Hubert and N. Le Roux",
  title =        "Computing power series solutions of a nonlinear {PDE}
                 system",
  crossref =     "Senda:2003:IPI",
  pages =        "148--155",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hulpke:2003:TOS,
  author =       "Alexander Hulpke and Steve Linton",
  title =        "Total ordering on subgroups and cosets",
  crossref =     "Senda:2003:IPI",
  pages =        "156--160",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2003:AIP,
  author =       "Erich Kaltofen and John May",
  title =        "On approximate irreducibility of polynomials in
                 several variables",
  crossref =     "Senda:2003:IPI",
  pages =        "161--168",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2003:PFS,
  author =       "Erich Kaltofen",
  title =        "Polynomial factorization: a success story",
  crossref =     "Senda:2003:IPI",
  pages =        "3--4",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Koepf:2003:PSB,
  author =       "Wolfram Koepf",
  title =        "Power series, {Bieberbach} conjecture and the {de
                 Branges} and {Weinstein} functions",
  crossref =     "Senda:2003:IPI",
  pages =        "169--175",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Laubenbacher:2003:CAA,
  author =       "Reinhard Laubenbacher",
  title =        "A computer algebra approach to biological systems",
  crossref =     "Senda:2003:IPI",
  pages =        "5--6",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Levandovskyy:2003:PCA,
  author =       "Viktor Levandovskyy and Hans Sch{\"o}nemann",
  title =        "Plural: a computer algebra system for noncommutative
                 polynomial algebras",
  crossref =     "Senda:2003:IPI",
  pages =        "176--183",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mansfield:2003:ETD,
  author =       "E. L. Mansfield and A. Szanto",
  title =        "Elimination theory for differential difference
                 polynomials",
  crossref =     "Senda:2003:IPI",
  pages =        "191--198",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{McCallum:2003:OIB,
  author =       "Scott McCallum",
  title =        "On order-invariance of a binomial over a nullifying
                 cell",
  crossref =     "Senda:2003:IPI",
  pages =        "184--190",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Meunier:2003:EAG,
  author =       "Ludovic Meunier and Bruno Salvy",
  title =        "{ESF}: an automatically generated encyclopedia of
                 special functions",
  crossref =     "Senda:2003:IPI",
  pages =        "199--206",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Minimair:2003:FSR,
  author =       "Manfred Minimair",
  title =        "Factoring sparse resultants of linearly combined
                 polynomials",
  crossref =     "Senda:2003:IPI",
  pages =        "207--214",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reid:2003:CSN,
  author =       "Greg Reid and Jianliang Tang and Lihong Zhi",
  title =        "A complete symbolic-numeric linear method for camera
                 pose determination",
  crossref =     "Senda:2003:IPI",
  pages =        "215--223",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sasaki:2003:SCC,
  author =       "Tateaki Sasaki",
  title =        "The subresultant and clusters of close roots",
  crossref =     "Senda:2003:IPI",
  pages =        "232--239",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Seidl:2003:GPO,
  author =       "Andreas Seidl and Thomas Sturm",
  title =        "A generic projection operator for partial cylindrical
                 algebraic decomposition",
  crossref =     "Senda:2003:IPI",
  pages =        "240--247",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shaska:2003:DAG,
  author =       "Tanush Shaska",
  title =        "Determining the automorphism group of a hyperelliptic
                 curve",
  crossref =     "Senda:2003:IPI",
  pages =        "248--254",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Vollmer:2003:NHB,
  author =       "Ulrich Vollmer",
  title =        "A note on the {Hermite} basis computation of large
                 integer matrices",
  crossref =     "Senda:2003:IPI",
  pages =        "255--257",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2003:WTW,
  author =       "Paul S. Wang and Norbert Kajler and Yi Zhou and Xiao
                 Zou",
  title =        "{WME}: towards a {Web for Mathematics Education}",
  crossref =     "Senda:2003:IPI",
  pages =        "258--265",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zeng:2003:MCM,
  author =       "Zhonggang Zeng",
  title =        "A method computing multiple roots of inexact
                 polynomials",
  crossref =     "Senda:2003:IPI",
  pages =        "266--272",
  year =         "2003",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aruliah:2004:NPA,
  author =       "D. A. Aruliah and Robert M. Corless",
  title =        "Numerical parameterization of affine varieties using",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "12--18",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bayer:2004:ODO,
  author =       "Thomas Bayer",
  title =        "Optimal descriptions of orbit spaces and strata of
                 finite groups",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "19--26",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beaumont:2004:PAA,
  author =       "James C. Beaumont and Russell J. Bradford and James H.
                 Davenport and Nalina Phisanbut",
  title =        "A poly-algorithmic approach to simplifying elementary
                 functions",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "27--34",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bodnar:2004:EDR,
  author =       "G{\'a}bor Bodn{\'a}r",
  title =        "Efficient desingularization of reducible algebraic
                 sets",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "35--41",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2004:CIB,
  author =       "A. Bostan and G. Lecerf and B. Salvy and {\'E}. Schost
                 and B. Wiebelt",
  title =        "Complexity issues in bivariate polynomial
                 factorization",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "42--49",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brunat:2004:CIF,
  author =       "Josep M. Brunat and Antonio Montes",
  title =        "The characteristic ideal of a finite, connected,
                 regular graph",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "50--57",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Burger:2004:CFS,
  author =       "Reinhold Burger and George Labahn and Mark van Hoeij",
  title =        "Closed form solutions of linear {ODEs} having elliptic
                 function coefficients",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "58--64",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Buse:2004:IPH,
  author =       "Laurent Bus{\'e} and Carlos D'Andrea",
  title =        "Inversion of parameterized hypersurfaces by means of
                 subresultants",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "65--71",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Carette:2004:UES,
  author =       "Jacques Carette",
  title =        "Understanding expression simplification",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "72--79",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chan:2004:NLS,
  author =       "L. Chan and E. S. Cheb-Terrab",
  title =        "Non-{Liouvillian} solutions for second order linear
                 {ODEs}",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "80--86",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cheze:2004:APF,
  author =       "Guillaume Ch{\`e}ze",
  title =        "Absolute polynomial factorization in two variables and
                 the knapsack problem",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "87--94",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chtcherba:2004:SHR,
  author =       "Arthur D. Chtcherba and Deepak Kapur",
  title =        "Support hull: relating the {Cayley--Dixon} resultant
                 constructions to the support of a polynomial system",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "95--102",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dahan:2004:SET,
  author =       "Xavier Dahan and {\'E}ric Schost",
  title =        "Sharp estimates for triangular sets",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "103--110",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dolzmann:2004:EPO,
  author =       "Andreas Dolzmann and Andreas Seidl and Thomas Sturm",
  title =        "Efficient projection orders for {CAD}",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "111--118",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dumas:2004:FFF,
  author =       "Jean-Guillaume Dumas and Pascal Giorgi and Cl{\'e}ment
                 Pernet",
  title =        "{FFPACK}: finite field linear algebra package",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "119--126",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eberly:2004:RKB,
  author =       "Wayne Eberly",
  title =        "Reliable {Krylov}-based algorithms for matrix null
                 space and rank",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "127--134",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Elkadi:2004:PSH,
  author =       "Mohamed Elkadi and Andr{\'e} Galligo and Thi Ha
                 L{\^e}",
  title =        "Parametrized surfaces in huge {$P^3$} of bidegree
                 $(1,2)$",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "141--148",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eriksson:2004:TIH,
  author =       "Nicholas Eriksson",
  title =        "Toric ideals of homogeneous phylogenetic models",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "149--154",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Feng:2004:RGS,
  author =       "Ruyong Feng and Xiao-shan Gao",
  title =        "Rational general solutions of algebraic ordinary
                 differential equations",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "155--162",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Frandsen:2004:RSE,
  author =       "Gudmund S. Frandsen and Igor E. Shparlinski",
  title =        "On reducing a system of equations to a single
                 equation",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "163--166",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gao:2004:AFM,
  author =       "Shuhong Gao and Erich Kaltofen and John May and
                 Zhengfeng Yang and Lihong Zhi",
  title =        "Approximate factorization of multivariate polynomials
                 via differential equations",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "167--174",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gao:2004:DDP,
  author =       "Xiao-Shan Gao and Mingbo Zhang",
  title =        "Decomposition of differential polynomials with
                 constant coefficients",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "175--182",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Geddes:2004:DRN,
  author =       "Keith Geddes and Ha Le and Ziming Li",
  title =        "Differential rational normal forms and a reduction
                 algorithm for hyperexponential func",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "183--190",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Houari:2004:ARC,
  author =       "Hassan El Houari and M'hammed El Kahoui",
  title =        "Algorithms for recognizing coordinates in two
                 variables over {UFD}'s",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "135--140",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hubert:2004:ITD,
  author =       "Evelyne Hubert",
  title =        "Improvements to a triangulation-decomposition
                 algorithm for ordinary differential systems in higher
                 degree cases",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "191--198",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kauers:2004:CPP,
  author =       "Manuel Kauers",
  title =        "Computer proofs for polynomial identities in arbitrary
                 many variables",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "199--204",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Khetan:2004:SRB,
  author =       "Amit Khetan and Ning Song and Ron Goldman",
  title =        "{Sylvester}-resultants for bivariate polynomials with
                 planar {Newton} polygons",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "205--212",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Labahn:2004:HSF,
  author =       "George Labahn and Ziming Li",
  title =        "Hyperexponential solutions of finite-rank ideals in
                 orthogonal {{\O}re} rings",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "213--220",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2004:SCH,
  author =       "Hongbo Li",
  title =        "Symbolic computation in the homogeneous geometric
                 model with {Clifford} algebra",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "221--228",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Linton:2004:FSI,
  author =       "Steve Linton",
  title =        "Finding the smallest image of a set",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "229--234",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Milowski:2004:CII,
  author =       "R. Alexander Milowski",
  title =        "Computing irredundant irreducible decompositions of
                 large scale monomial ideals",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "235--242",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:2004:MQR,
  author =       "Michael Monagan",
  title =        "Maximal quotient rational reconstruction: an almost
                 optimal algorithm for rational reconstruction",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "243--249",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Orden:2004:PNC,
  author =       "David Orden and Francisco Santos",
  title =        "The polytope of non-crossing graphs on a planar point
                 set",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "250--257",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parrilo:2004:SSP,
  author =       "Pablo A. Parrilo",
  title =        "Sums of squares of polynomials and their
                 applications",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "1--1",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Recio:2004:HU,
  author =       "Tomas Recio and J. Rafael Sendra and Carlos
                 Villarino",
  title =        "From hypercircles to units",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "258--265",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rodriguez-Carbonell:2004:AGP,
  author =       "Enric Rodr{\'\i}guez-Carbonell and Deepak Kapur",
  title =        "Automatic Generation of Polynomial Loop Invariants:
                 Algebraic Foundations",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "266--273",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Salem:2004:FPP,
  author =       "Fatima Abu Salem and Shuhong Gao and Alan G. B.
                 Lauder",
  title =        "Factoring polynomials via polytopes",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "4--11",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Santos:2004:TPA,
  author =       "Francisco Santos",
  title =        "Triangulations of polytopes and algebraic geometry",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "2--2",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Saunders:2004:SNF,
  author =       "David Saunders and Zhendong Wan",
  title =        "{Smith Normal Form} of dense integer matrices fast
                 algorithms into practice",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "274--281",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schneider:2004:SSS,
  author =       "Carsten Schneider",
  title =        "Symbolic summation with single-nested sum extensions",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "282--289",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanderHoeven:2004:TFT,
  author =       "Joris van der Hoeven",
  title =        "The truncated {Fourier} transform and applications",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "290--296",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:2004:APG,
  author =       "Mark van Hoeij and Michael Monagan",
  title =        "Algorithms for polynomial {GCD} computation over
                 algebraic function fields",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "297--304",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Verschelde:2004:NAG,
  author =       "Jan Verschelde",
  title =        "Numerical algebraic geometry and symbolic
                 computation",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "3--3",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yang:2004:EME,
  author =       "Michael Yang and Richard Fateman",
  title =        "Extracting mathematical expressions from {PostScript}
                 documents",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "305--311",
  year =         "2004",
  DOI =          "https://doi.org/10.1145/1005285.1005329",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.ocf.berkeley.edu/~mlyang/papers/MichaelYangPsmath.pdf",
  abstract =     "Full-text indexing of documents containing mathematics
                 cannot be considered a complete success unless the
                 mathematics symbolism is extracted and represented in a
                 standardized form permitting both searching for
                 formulas, and re-use of this information in (for
                 example) computer algebra systems. Most documents
                 produced in the past and subsequently digitally
                 encoded, and even most of those potentially ``born
                 digital'' in current journal production are---at
                 best---encoded in a printer form such as Adobe
                 Postscript [1], in which mathematics is not explicitly
                 marked or easily identifiable. While one might look
                 forward in the future to other document encodings such
                 as MathML, the common journal or textbook product is
                 essentially without semantic content: a jumble of odd
                 characters. Sometimes it is just a jumble of black and
                 white dots! In this paper we demonstrate an approach to
                 decoding, to recognizing and extracting mathematical
                 expressions, from a Postscript document. We can produce
                 a syntactic representation of the extracted expressions
                 which can then be used to generate various forms. For
                 example, if we extract TeX or Presentation MathML, we
                 can re-typeset the expression, but perhaps in a
                 different size or font family. More significantly, if
                 we start from this presentation information, we can
                 hope to combine it with additional contextual
                 processing of the surrounding text and meta-data
                 associated with the document, to assign semantics,(e.g.
                 content MathML), or provide versions in computer
                 algebra system languages such as Maple or Mathematica.
                 Finally, it is possible to use this material to present
                 audio or braille versions of mathematics for the
                 visually disabled. We have previously addressed some
                 aspects of the higher level of processing (parsing TeX
                 for example). In this paper we address the only first
                 stage and concentrate on what may seem to be overly
                 simple, but is in fact difficult to do precisely:
                 extracting the mathematics parts from text.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yokoyama:2004:SAE,
  author =       "Kazuhiro Yokoyama",
  title =        "On systems of algebraic equations with parametric
                 exponents",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "312--319",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zeng:2004:AGI,
  author =       "Zhonggang Zeng and Barry H. Dayton",
  title =        "The approximate {GCD} of inexact polynomials",
  crossref =     "Gutierrez:2004:IJU",
  pages =        "320--327",
  year =         "2004",
  bibdate =      "Fri Oct 21 06:52:53 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2005:GAA,
  author =       "S. A. Abramov and M. Petkov{\v{s}}sek",
  title =        "{Gosper}'s algorithm, accurate summation, and the
                 discrete {Newton--Leibniz} formula",
  crossref =     "Kauers:2005:IJB",
  pages =        "5--12",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adams:2005:SSR,
  author =       "Jeffrey Adams and B. David Saunders and Zhendong Wan",
  title =        "Signature of symmetric rational matrices and the
                 unitary dual of {Lie} groups",
  crossref =     "Kauers:2005:IJB",
  pages =        "13--20",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Anai:2005:SRP,
  author =       "Hirokazu Anai and Shinji Hara and Kazuhiro Yokoyama",
  title =        "Sum of roots with positive real parts",
  crossref =     "Kauers:2005:IJB",
  pages =        "21--28",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aroca:2005:AGS,
  author =       "J. M. Aroca and J. Cano and R. Feng and X. S. Gao",
  title =        "Algebraic general solutions of algebraic ordinary
                 differential equations",
  crossref =     "Kauers:2005:IJB",
  pages =        "29--36",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beaumont:2005:ABT,
  author =       "James C. Beaumont and Russell J. Bradford and James H.
                 Davenport and Nalina Phisanbut",
  title =        "Adherence is better than adjacency: computing the
                 {Riemann} index using {CAD}",
  crossref =     "Kauers:2005:IJB",
  pages =        "37--44",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2005:FAP,
  author =       "Alin Bostan and Thomas Cluzeau and Bruno Salvy",
  title =        "Fast algorithms for polynomial solutions of linear
                 differential equations",
  crossref =     "Kauers:2005:IJB",
  pages =        "45--52",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boucher:2005:NCI,
  author =       "Delphine Boucher",
  title =        "Non complete integrability of a magnetic satellite in
                 circular orbit",
  crossref =     "Kauers:2005:IJB",
  pages =        "53--60",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bretto:2005:SSG,
  author =       "Alain Bretto and Luc Gillibert and Bernard Laget",
  title =        "Symmetric and semisymmetric graphs construction using
                 {G}-graphs",
  crossref =     "Kauers:2005:IJB",
  pages =        "61--67",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bronstein:2005:PVE,
  author =       "Manuel Bronstein and Ziming Li and Min Wu",
  title =        "Picard--Vessiot extensions for linear functional
                 systems",
  crossref =     "Kauers:2005:IJB",
  pages =        "68--75",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:2005:UBE,
  author =       "Christopher W. Brown and Scott McCallum",
  title =        "On using bi-equational constraints in {CAD}
                 construction",
  crossref =     "Kauers:2005:IJB",
  pages =        "76--83",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Buchberger:2005:VFS,
  author =       "Bruno Buchberger",
  title =        "A view on the future of symbolic computation",
  crossref =     "Kauers:2005:IJB",
  pages =        "1--1",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Carvajal:2005:HSN,
  author =       "Orlando A. Carvajal and Frederick W. Chapman and Keith
                 O. Geddes",
  title =        "Hybrid symbolic-numeric integration in multiple
                 dimensions via tensor-product series",
  crossref =     "Kauers:2005:IJB",
  pages =        "84--91",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2005:BBC,
  author =       "Zhuliang Chen and Arne Storjohann",
  title =        "A {BLAS} based {C} library for exact linear algebra on
                 integer matrices",
  crossref =     "Kauers:2005:IJB",
  pages =        "92--99",
  year =         "2005",
  DOI =          "https://doi.org/10.1145/1073884.1073899",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Algorithms for solving linear systems of equations
                 over the integers are designed and implemented. The
                 implementations are based on the highly optimized and
                 portable ATLAS/BLAS library for numerical linear
                 algebra and the GNU Multiple Precision library (GMP)
                 for large integer arithmetic.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Costermans:2005:SAE,
  author =       "C. Costermans and J. Y. Enjalbert and Hoang Ngoc Minh
                 and M. Petitot",
  title =        "Structure and asymptotic expansion of multiple
                 harmonic sums",
  crossref =     "Kauers:2005:IJB",
  pages =        "100--107",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dahan:2005:LTT,
  author =       "Xavier Dahan and Marc Moreno Maza and Eric Schost and
                 Wenyuan Wu and Yuzhen Xie",
  title =        "Lifting techniques for triangular decompositions",
  crossref =     "Kauers:2005:IJB",
  pages =        "108--115",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dayton:2005:CMS,
  author =       "Barry H. Dayton and Zhonggang Zeng",
  title =        "Computing the multiplicity structure in solving
                 polynomial systems",
  crossref =     "Kauers:2005:IJB",
  pages =        "116--123",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{deKleine:2005:ANM,
  author =       "Jennifer de Kleine and Michael Monagan and Allan
                 Wittkopf",
  title =        "Algorithms for the non-monic case of the sparse
                 modular {GCD} algorithm",
  crossref =     "Kauers:2005:IJB",
  pages =        "124--131",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Deng:2005:CBR,
  author =       "Jiansong Deng and Falai Chen and Liyong Shen",
  title =        "Computing {$\mu$}-bases of rational curves and
                 surfaces using polynomial matrix factorization",
  crossref =     "Kauers:2005:IJB",
  pages =        "132--139",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dumas:2005:ECC,
  author =       "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and
                 Zhendong Wan",
  title =        "Efficient computation of the characteristic
                 polynomial",
  crossref =     "Kauers:2005:IJB",
  pages =        "140--147",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Galligo:2005:SBB,
  author =       "Andr{\'e} Galligo and Jean Pascal Pavone",
  title =        "Selfintersections of a {B{\'e}zier} bicubic surface",
  crossref =     "Kauers:2005:IJB",
  pages =        "148--155",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gerhold:2005:PPS,
  author =       "Stefan Gerhold and Manuel Kauers",
  title =        "A procedure for proving special function inequalities
                 involving a discrete parameter",
  crossref =     "Kauers:2005:IJB",
  pages =        "156--162",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Grigoriev:2005:GLD,
  author =       "Dima Grigoriev and Fritz Schwarz",
  title =        "Generalized {Loewy}-decomposition of $d$-modules",
  crossref =     "Kauers:2005:IJB",
  pages =        "163--170",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hitz:2005:CNS,
  author =       "Markus A. Hitz",
  title =        "On computing nearest singular {Hankel} matrices",
  crossref =     "Kauers:2005:IJB",
  pages =        "171--176",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hovinen:2005:RBL,
  author =       "Bradford Hovinen and Wayne Eberly",
  title =        "A reliable block {Lanczos} algorithm over small finite
                 fields",
  crossref =     "Kauers:2005:IJB",
  pages =        "177--184",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Huang:2005:SPS,
  author =       "Fangjian Huang and Shengli Chen",
  title =        "{Schur} partition for symmetric ternary forms and
                 readable proof to inequalities",
  crossref =     "Kauers:2005:IJB",
  pages =        "185--192",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeffrey:2005:ATA,
  author =       "D. J. Jeffrey and Pratibha and K. B. Roach",
  title =        "Affine transformations of algebraic numbers",
  crossref =     "Kauers:2005:IJB",
  pages =        "193--199",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Johnson:2005:AAC,
  author =       "Jeremy R. Johnson and Werner Krandick and Anatole D.
                 Ruslanov",
  title =        "Architecture-aware classical {Taylor} shift by $1$",
  crossref =     "Kauers:2005:IJB",
  pages =        "200--207",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2005:CFB,
  author =       "Erich Kaltofen and Pascal Koiran",
  title =        "On the complexity of factoring bivariate supersparse
                 (Lacunary) polynomials",
  crossref =     "Kauers:2005:IJB",
  pages =        "208--215",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2005:GMM,
  author =       "Erich Kaltofen and Dmitriy Morozov and George Yuhasz",
  title =        "Generic matrix multiplication and memory management in
                 {linBox}",
  crossref =     "Kauers:2005:IJB",
  pages =        "216--223",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2005:EAS,
  author =       "Biao Li and Yong Chen and Qi Wang",
  title =        "Exact analytical solutions to the nonlinear
                 {Schr{\"o}dinger} equation model",
  crossref =     "Kauers:2005:IJB",
  pages =        "224--230",
  year =         "2005",
  DOI =          "https://doi.org/10.1145/1073884.1073916",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A method is developed for constructing a series of
                 exact analytical solutions of the nonlinear
                 Schr{\"o}dinger equation model (NLSE) with varying
                 dispersion, nonlinearity, and gain or absorption. With
                 the help of symbolic computation, a broad class of
                 analytical solutions of NLSE are obtained. From our
                 results, many previous known results of NLSE obtained
                 by some authors can be recovered by means of some
                 suitable selections of the arbitrary functions and
                 arbitrary constants. Further, the formation,
                 interaction and stability of solitons have been
                 investigated.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lichtblau:2005:HGF,
  author =       "Daniel Lichtblau",
  title =        "Half-{GCD} and fast rational recovery",
  crossref =     "Kauers:2005:IJB",
  pages =        "231--236",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mao:2005:AWM,
  author =       "Weibo Mao and Jinzhao Wu",
  title =        "Application of {Wu}'s method to symbolic model
                 checking",
  crossref =     "Kauers:2005:IJB",
  pages =        "237--244",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:2005:PAC,
  author =       "Michael Monagan",
  title =        "Probabilistic algorithms for computing resultants",
  crossref =     "Kauers:2005:IJB",
  pages =        "245--252",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mourrain:2005:GNF,
  author =       "Bernard Mourrain",
  title =        "Generalized normal forms and polynomial system
                 solving",
  crossref =     "Kauers:2005:IJB",
  pages =        "253--260",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Oancea:2005:DEI,
  author =       "Cosmin E. Oancea and Stephen M. Watt",
  title =        "Domains and expressions: an interface between two
                 approaches to computer algebra",
  crossref =     "Kauers:2005:IJB",
  pages =        "261--268",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Perez-Diaz:2005:PDF,
  author =       "Sonia P{\'e}rez-D{\'\i}az and J. Rafael Sendra",
  title =        "Partial degree formulae for rational algebraic
                 surfaces",
  crossref =     "Kauers:2005:IJB",
  pages =        "301--308",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reid:2005:SNC,
  author =       "Greg Reid and Jan Verschelde and Allan Wittkopf and
                 Wenyuan Wu",
  title =        "Symbolic-numeric completion of differential systems by
                 homotopy continuation",
  crossref =     "Kauers:2005:IJB",
  pages =        "269--276",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rondepierre:2005:ASN,
  author =       "Aude Rondepierre and Jean-Guillaume Dumas",
  title =        "Algorithms for symbolic\slash numeric control of
                 affine dynamical systems",
  crossref =     "Kauers:2005:IJB",
  pages =        "277--284",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Salvy:2005:FAA,
  author =       "Bruno Salvy",
  title =        "{$D$}-finiteness: algorithms and applications",
  crossref =     "Kauers:2005:IJB",
  pages =        "2--3",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schneider:2005:FTM,
  author =       "Carsten Schneider",
  title =        "Finding telescopers with minimal depth for indefinite
                 nested sum and product expressions",
  crossref =     "Kauers:2005:IJB",
  pages =        "285--292",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schost:2005:MPS,
  author =       "{\'E}ric Schost",
  title =        "Multivariate power series multiplication",
  crossref =     "Kauers:2005:IJB",
  pages =        "293--300",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Storjohann:2005:CRS,
  author =       "Arne Storjohann and Gilles Villard",
  title =        "Computing the rank and a small nullspace basis of a
                 polynomial matrix",
  crossref =     "Kauers:2005:IJB",
  pages =        "309--316",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tournier:2005:ADS,
  author =       "Laurent Tournier",
  title =        "Approximation of dynamical systems using s-systems
                 theory: application to biological systems",
  crossref =     "Kauers:2005:IJB",
  pages =        "317--324",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tsarev:2005:GLT,
  author =       "Sergey P. Tsarev",
  title =        "Generalized {Laplace} transformations and integration
                 of hyperbolic systems of linear partial differential
                 equations",
  crossref =     "Kauers:2005:IJB",
  pages =        "325--331",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Turner:2005:PSB,
  author =       "William J. Turner",
  title =        "Preconditioners for singular black box matrices",
  crossref =     "Kauers:2005:IJB",
  pages =        "332--339",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vandeWoestijne:2005:DES,
  author =       "Christiaan van de Woestijne",
  title =        "Deterministic equation solving over finite fields",
  crossref =     "Kauers:2005:IJB",
  pages =        "348--353",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:2005:SSO,
  author =       "M. van Hoeij and J.-A. Weil",
  title =        "Solving second order linear differential equations
                 with {Klein}'s theorem",
  crossref =     "Kauers:2005:IJB",
  pages =        "340--347",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2005:SAB,
  author =       "Dongming Wang and Bican Xia",
  title =        "Stability analysis of biological systems with real
                 solution classification",
  crossref =     "Kauers:2005:IJB",
  pages =        "354--361",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wu:2005:FKT,
  author =       "Wen-tsun Wu",
  title =        "On a finite kernel theorem for polynomial-type
                 optimization problems and some of its applications",
  crossref =     "Kauers:2005:IJB",
  pages =        "4--4",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yang:2005:OPM,
  author =       "Lu Yang and Zhenbing Zeng",
  title =        "An open problem on metric invariants of tetrahedra",
  crossref =     "Kauers:2005:IJB",
  pages =        "362--364",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zobnin:2005:AOF,
  author =       "Aleksey Zobnin",
  title =        "Admissible orderings and finiteness criteria for
                 differential standard bases",
  crossref =     "Kauers:2005:IJB",
  pages =        "365--372",
  year =         "2005",
  bibdate =      "Fri Oct 21 06:53:01 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abo:2006:IKC,
  author =       "Hirotachi Abo and Chris Peterson",
  title =        "Implementation of {Kumar}'s correspondence",
  crossref =     "Trager:2006:PIS",
  pages =        "9--16",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2006:SRS,
  author =       "S. A. Abramov",
  title =        "On the summation of {$P$}-recursive sequences",
  crossref =     "Trager:2006:PIS",
  pages =        "17--22",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bigatti:2006:CSC,
  author =       "Anna Bigatti and Lorenzo Robbiano",
  title =        "CoCo{A}: a system for computations in commutative
                 algebra",
  crossref =     "Trager:2006:PIS",
  pages =        "6--6",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Borwein:2006:SCM,
  author =       "Jonathan M. Borwein and Chris H. Hamiltony",
  title =        "Symbolic computation of multidimensional {Fenchel}
                 conjugates",
  crossref =     "Trager:2006:PIS",
  pages =        "23--30",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2006:LCA,
  author =       "A. Bostan and F. Chyzak and B. Salvy and T. Cluzeau",
  title =        "Low complexity algorithms for linear recurrences",
  crossref =     "Trager:2006:PIS",
  pages =        "31--38",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boyle:2006:AHP,
  author =       "Phelim Boyle and Alex Potapchik",
  title =        "Application of high-precision computing for pricing
                 arithmetic {Asian} options",
  crossref =     "Trager:2006:PIS",
  pages =        "39--46",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cheng:2006:CPG,
  author =       "Howard Cheng and George Labahn",
  title =        "On computing polynomial {GCD}s in alternate bases",
  crossref =     "Trager:2006:PIS",
  pages =        "47--54",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chtcherba:2006:CDF,
  author =       "Arthur D. Chtcherba and Deepak Kapur",
  title =        "Conditions for determinantal formula for resultant of
                 a polynomial system",
  crossref =     "Trager:2006:PIS",
  pages =        "55--62",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eberly:2006:SSR,
  author =       "Wayne Eberly and Mark Giesbrecht and Pascal Giorgi and
                 Arne Storjohann and Gilles Villard",
  title =        "Solving sparse rational linear systems",
  crossref =     "Trager:2006:PIS",
  pages =        "63--70",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eigenwillig:2006:ATR,
  author =       "Arno Eigenwillig and Vikram Sharma and Chee K. Yap",
  title =        "Almost tight recursion tree bounds for the {Descartes}
                 method",
  crossref =     "Trager:2006:PIS",
  pages =        "71--78",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farcot:2006:SNA,
  author =       "Etienne Farcot",
  title =        "Symbolic numeric analysis of attractors in randomly
                 generated piecewise affine models of gene networks",
  crossref =     "Trager:2006:PIS",
  pages =        "79--86",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farzan:2006:SRF,
  author =       "Arash Farzan and J. Ian Munro",
  title =        "Succinct representation of finite abelian groups",
  crossref =     "Trager:2006:PIS",
  pages =        "87--92",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Filatei:2006:ITF,
  author =       "Akpodigha Filatei and Xin Li and Marc Moreno Maza and
                 {\'E}ric Schost",
  title =        "Implementation techniques for fast polynomial
                 arithmetic in a high-level programming environment",
  crossref =     "Trager:2006:PIS",
  pages =        "93--100",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gao:2006:RSD,
  author =       "Xiao-Shan Gao and Chun-Ming Yuan",
  title =        "Resolvent systems of difference polynomial ideals",
  crossref =     "Trager:2006:PIS",
  pages =        "101--108",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gaudry:2006:FAC,
  author =       "P. Gaudry and F. Morain",
  title =        "Fast algorithms for computing the eigenvalue in the
                 {Schoof--Elkies--Atkin} algorithm",
  crossref =     "Trager:2006:PIS",
  pages =        "109--115",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:2006:SNS,
  author =       "Mark Giesbrecht and George Labahn and Wen-shin Lee",
  title =        "Symbolic-numeric sparse interpolation of multivariate
                 polynomials",
  crossref =     "Trager:2006:PIS",
  pages =        "116--123",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2006:ERB,
  author =       "Li Guo and William Y. Sit",
  title =        "Enumeration of {Rota--Baxter} words",
  crossref =     "Trager:2006:PIS",
  pages =        "124--131",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Harrison:2006:RPD,
  author =       "Michael Harrison and Josef Schicho",
  title =        "Rational parametrisation for degree $6$ {Del Pezzo}
                 surfaces using {Lie} algebras",
  crossref =     "Trager:2006:PIS",
  pages =        "132--137",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Janovitz-Freireich:2006:ARI,
  author =       "Itnuit Janovitz-Freireich and Lajos R{\'o}nyai and
                 {\'A}gnes Sz{\'a}nt{\'o}",
  title =        "Approximate radical of ideals with clusters of roots",
  crossref =     "Trager:2006:PIS",
  pages =        "146--153",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Johnson:2006:HPI,
  author =       "Jeremy R. Johnson and Werner Krandick and Kevin Lynch
                 and David G. Richardson and Anatole D. Ruslanov",
  title =        "High-performance implementations of the {Descartes}
                 method",
  crossref =     "Trager:2006:PIS",
  pages =        "154--161",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2006:AGC,
  author =       "Erich Kaltofen and Zhengfeng Yang and Lihong Zhi",
  title =        "Approximate greatest common divisors of several
                 polynomials with linearly constrained coefficients and
                 singular polynomials",
  crossref =     "Trager:2006:PIS",
  pages =        "169--176",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2006:FSD,
  author =       "Erich Kaltofen and Pascal Koiran",
  title =        "Finding small degree factors of multivariate
                 supersparse (lacunary) polynomials over algebraic
                 number fields",
  crossref =     "Trager:2006:PIS",
  pages =        "162--168",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2006:HSN,
  author =       "Erich Kaltofen and Lihong Zhi",
  title =        "Hybrid symbolic-numeric computation",
  crossref =     "Trager:2006:PIS",
  pages =        "7--7",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kauers:2006:AUS,
  author =       "Manuel Kauers and Carsten Schneider",
  title =        "Application of unspecified sequences in symbolic
                 summation",
  crossref =     "Trager:2006:PIS",
  pages =        "177--183",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Khodadad:2006:FRF,
  author =       "Sara Khodadad and Michael Monagan",
  title =        "Fast rational function reconstruction",
  crossref =     "Trager:2006:PIS",
  pages =        "184--190",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Laplagne:2006:ACR,
  author =       "Santiago Laplagne",
  title =        "An algorithm for the computation of the radical of an
                 ideal",
  crossref =     "Trager:2006:PIS",
  pages =        "191--195",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lazard:2006:SKC,
  author =       "Daniel Lazard",
  title =        "Solving {Kaltofen}'s challenge on {Zolotarev}'s
                 approximation problem",
  crossref =     "Trager:2006:PIS",
  pages =        "196--203",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Levandovskyy:2006:IIN,
  author =       "Viktor Levandovskyy",
  title =        "Intersection of ideals with non-commutative
                 subalgebras",
  crossref =     "Trager:2006:PIS",
  pages =        "212--219",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2006:RMD,
  author =       "Ziming Li and Michael F. Singer and Min Wu and Dabin
                 Zheng",
  title =        "A recursive method for determining the one-dimensional
                 submodules of {Laurent--{\O}re} modules",
  crossref =     "Trager:2006:PIS",
  pages =        "220--227",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Maza:2006:TDP,
  author =       "Marc Moreno Maza",
  title =        "Triangular decompositions of polynomial systems: from
                 theory to practice",
  crossref =     "Trager:2006:PIS",
  pages =        "8--8",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Minimair:2006:RSC,
  author =       "Manfred Minimair",
  title =        "Resultants of skewly composed polynomials",
  crossref =     "Trager:2006:PIS",
  pages =        "228--233",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Miyamoto:2006:IGN,
  author =       "Izumi Miyamoto",
  title =        "An improvement of {GAP} normalizer function for
                 permutation groups",
  crossref =     "Trager:2006:PIS",
  pages =        "234--238",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:2006:RSM,
  author =       "Michael Monagan and Roman Pearce",
  title =        "Rational simplification modulo a polynomial ideal",
  crossref =     "Trager:2006:PIS",
  pages =        "239--245",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Moroz:2006:CRP,
  author =       "Guillaume Moroz",
  title =        "Complexity of the resolution of parametric systems of
                 polynomial equations and inequations",
  crossref =     "Trager:2006:PIS",
  pages =        "246--253",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Neunhoffer:2006:DSU,
  author =       "Max Neunh{\"o}ffer and {\'A}kos Seress",
  title =        "A data structure for a uniform approach to
                 computations with finite groups",
  crossref =     "Trager:2006:PIS",
  pages =        "254--261",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Noro:2006:MDE,
  author =       "Masayuki Noro",
  title =        "Modular dynamic evaluation",
  crossref =     "Trager:2006:PIS",
  pages =        "262--268",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2006:UGA,
  author =       "Wei Pan and Dongming Wang",
  title =        "Uniform {Gr{\"o}bner} bases for ideals generated by
                 polynomials with parametric exponents",
  crossref =     "Trager:2006:PIS",
  pages =        "269--276",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pascal:2006:COB,
  author =       "Cyril Pascal and {\'E}ric Schost",
  title =        "Change of order for bivariate triangular sets",
  crossref =     "Trager:2006:PIS",
  pages =        "277--284",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Poulisse:2006:CCA,
  author =       "Hennie Poulisse",
  title =        "Computational communicative algebra",
  crossref =     "Trager:2006:PIS",
  pages =        "3--4",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Powers:2006:QPT,
  author =       "Victoria Powers and Bruce Reznick",
  title =        "A quantitative {P{\'o}lya's Theorem} with corner
                 zeros",
  crossref =     "Trager:2006:PIS",
  pages =        "285--289",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Renault:2006:CSF,
  author =       "Gu{\'e}na{\"e}l Renault",
  title =        "Computation of the splitting field of a dihedral
                 polynomial",
  crossref =     "Trager:2006:PIS",
  pages =        "290--297",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Robinson:2006:PAD,
  author =       "Eric Robinson and Gene Cooperman",
  title =        "A parallel architecture for disk-based computing over
                 the {Baby Monster} and other large finite simple
                 groups",
  crossref =     "Trager:2006:PIS",
  pages =        "298--305",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Roux:2006:RRC,
  author =       "Nicolas Le Roux and Moulay Barkatou",
  title =        "Rank reduction of a class of {Pfaffian} systems in two
                 variables",
  crossref =     "Trager:2006:PIS",
  pages =        "204--211",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rubio:2006:NIN,
  author =       "Rosario Rubio and J. Miguel Serradilla and M. Pilar
                 V{\'e}lez",
  title =        "A note on implicitization and normal parametrization
                 of rational curves",
  crossref =     "Trager:2006:PIS",
  pages =        "306--309",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sekigawa:2006:LRM,
  author =       "Hiroshi Sekigawa and Kiyoshi Shirayanagi",
  title =        "Locating real multiple zeros of a real interval
                 polynomial",
  crossref =     "Trager:2006:PIS",
  pages =        "310--317",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sexton:2006:AMS,
  author =       "Alan Sexton and Volker Sorge",
  title =        "Abstract matrices in symbolic computation",
  crossref =     "Trager:2006:PIS",
  pages =        "318--325",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Suzuki:2006:SAC,
  author =       "Akira Suzuki and Yosuke Sato",
  title =        "A simple algorithm to compute comprehensive
                 {Gr{\"o}bner} bases using {Gr{\"o}bner} bases",
  crossref =     "Trager:2006:PIS",
  pages =        "326--331",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Turner:2006:BWR,
  author =       "William J. Turner",
  title =        "A block {Wiedemann} rank algorithm",
  crossref =     "Trager:2006:PIS",
  pages =        "332--339",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Umans:2006:GTA,
  author =       "Christopher Umans",
  title =        "Group-theoretic algorithms for matrix multiplication",
  crossref =     "Trager:2006:PIS",
  pages =        "5--5",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanderHoeven:2006:ERN,
  author =       "Joris van der Hoeven",
  title =        "Effective real numbers in {Mmxlib}",
  crossref =     "Trager:2006:PIS",
  pages =        "138--145",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vandeWoestijne:2006:SPD,
  author =       "Christiaan van de Woestijne",
  title =        "Surface parametrisation without diagonalisation",
  crossref =     "Trager:2006:PIS",
  pages =        "340--344",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:2006:WWW,
  author =       "Joachim von zur Gathen",
  title =        "Who was who in polynomial factorization: 1",
  crossref =     "Trager:2006:PIS",
  pages =        "2--2",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wu:2006:ANA,
  author =       "Wenyuan Wu and Greg Reid",
  title =        "Application of numerical algebraic geometry and
                 numerical linear algebra to {PDE}",
  crossref =     "Trager:2006:PIS",
  pages =        "345--352",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhou:2006:GAB,
  author =       "Meng Zhou and Franz Winkler",
  title =        "{Gr{\"o}bner} bases in difference-differential
                 modules",
  crossref =     "Trager:2006:PIS",
  pages =        "353--360",
  year =         "2006",
  bibdate =      "Wed Aug 23 09:43:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:2007:CSI,
  author =       "Moulay A. Barkatou and Eckhard Pfl{\"u}gel",
  title =        "Computing super-irreducible forms of systems of linear
                 differential equations via {Moser}-reduction: a new
                 approach",
  crossref =     "Brown:2007:PIS",
  pages =        "1--8",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/983065.983067",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bini:2007:SMB,
  author =       "Dario A. Bini and Paola Boito",
  title =        "Structured matrix-based methods for polynomial
                 $\in$-gcd: analysis and comparisons",
  crossref =     "Brown:2007:PIS",
  pages =        "9--16",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/983065.983068",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bodrato:2007:IPM,
  author =       "Marco Bodrato and Alberto Zanoni",
  title =        "Integer and polynomial multiplication: towards optimal
                 {Toom--Cook} matrices",
  crossref =     "Brown:2007:PIS",
  pages =        "17--24",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277552",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Karatsuba and Toom--Cook are well-known methods used
                 to multiply efficiently long integers. There have been
                 different proposal about the interpolating values used
                 to determine the matrix to be inverted and the sequence
                 of operations to invert it. A definitive word about
                 which is the optimal matrix (values) and the (number
                 of) basic operations to invert it seems still not to
                 have been said. In this paper we present some
                 particular examples of useful matrices and a method to
                 generate automatically, by means of optimised
                 exhaustive searches on a graph, the best sequence of
                 basic operations to invert them.",
  acknowledgement = ack-nhfb,
  keywords =     "integer and polynomial multiplication; interpolation;
                 Karatsuba; matrix inversion; squaring; Toom--Cook",
}

@InProceedings{Bostan:2007:DEA,
  author =       "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Bruno
                 Salvy and Gr{\'e}goire Lecerf and {\'E}ric Schost",
  title =        "Differential equations for algebraic functions",
  crossref =     "Brown:2007:PIS",
  pages =        "25--32",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277553",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "It is classical that univariate algebraic functions
                 satisfy linear differential equations with polynomial
                 coefficients. Linear recurrences follow for the
                 coefficients of their power series expansions. We show
                 that the linear differential equation of minimal order
                 has coefficients whose degree is cubic in the degree of
                 the function. We also show that there exists a linear
                 differential equation of order linear in the degree
                 whose coefficients are only of quadratic degree.
                 Furthermore, we prove the existence of recurrences of
                 order and degree close to optimal. We study the
                 complexity of computing these differential equations
                 and recurrences. We deduce a fast algorithm for the
                 expansion of algebraic series.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic series; complexity; computer algebra;
                 creative telescoping; differential resolvents",
}

@InProceedings{Bostan:2007:STV,
  author =       "Alin Bostan and Claude-Pierre Jeannerod and {\'E}ric
                 Schost",
  title =        "Solving {Toeplitz}- and {Vandermonde}-like linear
                 systems with large displacement rank",
  crossref =     "Brown:2007:PIS",
  pages =        "33--40",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277554",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Linear systems with structures such as Toeplitz-,
                 Vandermonde-or Cauchy-likeness can be solved in
                 $O\tilde$ operations, where $n$ is the matrix size,
                 $\alpha$ is its displacement rank, and $O\tilde$
                 denotes the omission of logarithmic factors. We show
                 that for Toeplitz-like and Vandermonde-like matrices,
                 this cost can be reduced to $O(\alpha^{\omega-1} n)$,
                 where $\omega$ is a feasible exponent for matrix
                 multiplication over the base field. The best known
                 estimate for $\omega$ is $\omega O(\alpha^{1.38} n)$.
                 We also present consequences for Hermite--Pad{\'e}
                 approximation and bivariate interpolation.",
  acknowledgement = ack-nhfb,
  keywords =     "dense linear algebra; structured linear algebra",
}

@InProceedings{Bremner:2007:NSP,
  author =       "Murray R. Bremner and Michael J. Hancock and Yunfeng
                 Piao",
  title =        "Nonassociative structures on polynomial algebras
                 arising from bio-operations on formal languages: an
                 application of computer algebra to nonassociative
                 systems",
  crossref =     "Brown:2007:PIS",
  pages =        "41--48",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277555",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider sequential insertion and deletion, and
                 contextual insertion and deletion, on the free monoid
                 $\Sigma$ where $\Sigma = \{ x \}$; in each case the
                 result can be regarded as either a set or a multiset.
                 Over any coefficient field $F$ the vector space with
                 basis $\Sigma*$ is linearly isomorphic to the
                 polynomial algebra $F[x]$; each operation on $\Sigma*$
                 extends bilinearly to give a new algebra structure (not
                 necessarily commutative or associative) on $F[x]$. We
                 determine the polynomial identities of degree $\leq 5$
                 satisfied by these structures.",
  acknowledgement = ack-nhfb,
  keywords =     "bio-operations; computer algebra; DNA computing;
                 finite fields; formal languages; linear systems;
                 nonassociative algebra; polynomial identities",
}

@InProceedings{Bretto:2007:GGC,
  author =       "Alain Bretto and Luc Gillibert",
  title =        "{G}-graphs for the cage problem: a new upper bound",
  crossref =     "Brown:2007:PIS",
  pages =        "49--53",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277556",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Constructing some regular graph with a given girth,a
                 given degree and the fewest possible vertices is a hard
                 problem. This problem is called the cage graph problem
                 and has some links with the error codes theory. In this
                 paper we presents some new graphs, constructed from a
                 group, with a girth of 6 and regular of degree $p$, for
                 any prime number $p$. This graphs are of order $2
                 \times p^2$ when the best upper bound known for the
                 $(p,6)$-cage problem was the Sauer bound, equal to
                 $4(p-1)^3$.",
  acknowledgement = ack-nhfb,
  keywords =     "cage graphs; G-graphs; graphs from group",
}

@InProceedings{Brown:2007:CQE,
  author =       "Christopher W. Brown and James H. Davenport",
  title =        "The complexity of quantifier elimination and
                 cylindrical algebraic decomposition",
  crossref =     "Brown:2007:PIS",
  pages =        "54--60",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277557",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper has two parts. In the first part we give a
                 simple and constructive proof that quantifier
                 elimination in real algebra is doubly exponential, even
                 when there is only one free variable and all
                 polynomials in the quantified input are linear. The
                 general result is not new, but we hope the simple and
                 explicit nature of the proof makes it interesting. The
                 second part of the paper uses the construction of the
                 first part to prove some results on the effects of
                 projection order on CAD construction -- roughly that
                 there are CAD construction problems for which one order
                 produces a constant number of cells and another
                 produces a doubly exponential number of cells, and that
                 there are problems for which all orders produce a
                 doubly exponential number of cells. The second of these
                 results implies that there is a true singly vs. doubly
                 exponential gap between the worst-case running times of
                 several modern quantifier elimination algorithms and
                 CAD-based quantifier elimination when the number of
                 quantifier alternations is constant.",
  acknowledgement = ack-nhfb,
  keywords =     "cylindrical algebraic decomposition; quantifier
                 elimination",
}

@InProceedings{Burgisser:2007:DFC,
  author =       "Peter B{\"u}rgisser and Peter Scheiblechner",
  title =        "Differential forms in computational algebraic
                 geometry",
  crossref =     "Brown:2007:PIS",
  pages =        "61--68",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277558",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We give a uniform method for the two problems \#CC$_C$
                 and \#IC$_C$ of counting connected and irreducible
                 components of complex algebraic varieties,
                 respectively. Our algorithms are purely algebraic,
                 i.e., they use only the field structure of C. They work
                 efficiently in parallel and can be implemented by
                 algebraic circuits of polynomial depth, i.e., in
                 parallel polynomial time. The design of our algorithms
                 relies on the concept of algebraic differential forms.
                 A further important building block is an algorithm of
                 S{\'a}nt{\'o} [40] computing a variant of
                 characteristic sets. The crucial complexity parameter
                 for \#IC$_C$ turns out to be the number of equations.
                 We describe a randomised algorithm solving \#IC$_C$ for
                 a fixed number of rational equations given by
                 straight-line programs (slps), which runs in parallel
                 polylogarithmic time in the length and the degree of
                 the slps.",
  acknowledgement = ack-nhfb,
  keywords =     "complexity; connected components; differential forms;
                 irreducible components",
}

@InProceedings{Buse:2007:IBP,
  author =       "Laurent Bus{\'e} and Marc Dohm",
  title =        "Implicitization of bihomogeneous parametrizations of
                 algebraic surfaces via linear syzygies",
  crossref =     "Brown:2007:PIS",
  pages =        "69--76",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277559",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We show that the implicit equation of a surface in
                 3-dimensional projective space parametrized by
                 bi-homogeneous polynomials of bi-degree $(d,d)$ for a
                 given integer $d \geq $1 can be represented and
                 computed from the linear syzygies of its
                 parametrization if the base points are isolated and
                 form locally a complete intersection.",
  acknowledgement = ack-nhfb,
  keywords =     "approximation complexes; implicitization; linear
                 syzygies",
}

@InProceedings{Carette:2007:CFP,
  author =       "Jacques Carette",
  title =        "A canonical form for piecewise defined functions",
  crossref =     "Brown:2007:PIS",
  pages =        "77--84",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277560",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We define a canonical form for piecewise defined
                 functions. We show that the domains and ranges for
                 which these functions are defined is larger than in
                 previous work. Also, our canonical form algorithm is
                 linear in the number of breakpoints instead of
                 exponential. These results rely on the linear structure
                 of the underlying domain of definition.",
  acknowledgement = ack-nhfb,
  keywords =     "canonical form; normal form; piecewise",
}

@InProceedings{Cheng:2007:CNI,
  author =       "Jin-San Cheng and Xiao-Shan Gao and Chee-Keng Yap",
  title =        "Complete numerical isolation of real zeros in
                 zero-dimensional triangular systems",
  crossref =     "Brown:2007:PIS",
  pages =        "92--99",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277562",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a complete numerical algorithm of isolating
                 all the real zeros of a zero-dimensional triangular
                 polynomial system $F_n Z[x_1 \ldots, x_n]$. Our system
                 $F_n$ is general, with no further assumptions. In
                 particular, our algorithm successfully treat multiple
                 zeros directly in such systems. A key idea is to
                 introduce evaluation bounds and sleeve bounds. We
                 implemented our algorithm and promising experimental
                 results are shown.",
  acknowledgement = ack-nhfb,
  keywords =     "evaluation bound; real zero isolation; sleeve bound;
                 triangular system",
}

@InProceedings{Cheng:2007:TSE,
  author =       "Howard Cheng and Guillaume Hanrot and Emmanuel
                 Thom{\'e} and Paul Zimmermann and Eugene Zima",
  title =        "Time-and space-efficient evaluation of some
                 hypergeometric constants",
  crossref =     "Brown:2007:PIS",
  pages =        "85--91",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277561",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The currently best known algorithms for the numerical
                 evaluation of hypergeometric constants such as
                 $\zeta(3)$ to $d$ decimal digits have time complexity
                 $O(M(d) \log^2 d)$ and space complexity of $O(d \log
                 d)$ or $O(d)$. Following work from Cheng, Gergel, Kim
                 and Zima, we present a new algorithm with the same
                 asymptotic complexity, but more efficient in practice.
                 Our implementation of this algorithm improves over
                 existing programs for the computation of $\Pi$, and we
                 announce a new record of 2 billion digits for
                 \zeta(3).",
  acknowledgement = ack-nhfb,
  keywords =     "high-precision evaluation; hypergeometric constants",
}

@InProceedings{Cicalo:2007:NAG,
  author =       "Serena Cical{\`o} and Willem de Graaf",
  title =        "Non-associative {Gr{\"o}bner} bases,
                 finitely-presented {Lie} rings and the {Engel}
                 condition",
  crossref =     "Brown:2007:PIS",
  pages =        "100--107",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277563",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We give an algorithm for constructing a basis and a
                 multiplication table of a finite-dimensional
                 finitely-presented Lie ring. We apply this to construct
                 the biggest $t$ generator Lie rings that satisfy the
                 $n$-Engel condition, for $(t,n) = (t,2), (2,3), (3,3),
                 (2,4)$.",
  acknowledgement = ack-nhfb,
  keywords =     "Engel condition; Gr{\"o}bner basis; Lie ring",
}

@InProceedings{Corless:2007:JHF,
  author =       "Robert M. Corless and Dawit Assefa",
  title =        "{Jeffery--Hamel} flow with {Maple}: a case study of
                 integration of elliptic functions in a {CAS}",
  crossref =     "Brown:2007:PIS",
  pages =        "108--115",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277564",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper takes a classical problem in
                 two-dimensional fluid flow-namely, flow into or out of
                 a wedge-shaped channel with a sink or source at the
                 vertex, which flow is known as Jeffery--Hamel flow and
                 has `well-known' solutions containing elliptic
                 functions-and tries to duplicate, or even extend, the
                 classical solutions by using a CAS, in this instance
                 Maple. The purposes of this case study include
                 examining just how good CAS can be at elliptic
                 functions; and, more importantly, identifying needs for
                 improvement. Another purpose is to compare the
                 analytical solution with modern numerical solutions.
                 Finally, we believe that this work will motivate
                 improvements to CAS facilities for automatic case
                 analysis. As an aside, we present some simple methods
                 for integration of elliptic functions that seem not to
                 be widely known.",
  acknowledgement = ack-nhfb,
  keywords =     "elliptic functions; integration",
}

@InProceedings{Corless:2007:SEA,
  author =       "Robert M. Corless and Hui Ding and Nicholas J. Higham
                 and David J. Jeffrey",
  title =        "The solution of $s \exp(s) = a$ is not always the
                 {Lambert} ${W}$ function of $a$",
  crossref =     "Brown:2007:PIS",
  pages =        "116--121",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277565",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study the solutions of the matrix equation $S
                 \exp(S) = A$. Our motivation comes from the study of
                 systems of delay differential equations $y'(t) = Ay(t -
                 1)$, which occur in some models of practical interest,
                 especially in mathematical biology. This paper
                 concentrates on the distinction between evaluating a
                 matrix function and solving a matrix equation. In
                 particular, it shows that the matrix Lambert $W$
                 function evaluated at the matrix $A$ does not represent
                 all possible solutions of $S \exp(S) = A$. These
                 results can easily be extended to more general matrix
                 equations.",
  acknowledgement = ack-nhfb,
  keywords =     "Lambert $W$ function; matrix function; nonlinear
                 matrix equation",
}

@InProceedings{Cox:2007:GBS,
  author =       "David A. Cox",
  title =        "{Gr{\"o}bner} bases: a sampler of recent
                 developments",
  crossref =     "Brown:2007:PIS",
  pages =        "387--388",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277601",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This tutorial will explore the theory of Gr{\"o}bner
                 bases. The first part will review classic material on
                 monomial orders, the Buchberger Algorithm, and
                 elimination theory. This will be followed by a
                 discussion of the geometry of elimination, where
                 resultants can be replaced with Gr{\"o}bner bases using
                 ideas of Schauenberg [15]. The tutorial will conclude
                 with a sampler of topics about Gr{\"o}bner bases,
                 including graph theory [11], geometric theorem proving
                 via comprehensive Gr{\"o}bner systems [13, 14], the
                 generic Gr{\"o}bner walk [12], alternatives to the
                 Buchberger algorithm and applications [8, 9, 10], and
                 moduli of quiver representations via Gr{\"o}bner bases
                 [5]. (This list of topics is tentative--the tutorial
                 may cover slightly different topics.)",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner bases; elimination theory",
}

@InProceedings{Dimitrova:2007:GFM,
  author =       "Elena S. Dimitrova and Abdul Salam Jarrah and Reinhard
                 Laubenbacher and Brandilyn Stigler",
  title =        "A {Gr{\"o}bner} fan method for biochemical network
                 modeling",
  crossref =     "Brown:2007:PIS",
  pages =        "122--126",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277566",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Polynomial dynamical systems (PDSs) have been used
                 successfully as a framework for the reconstruction, or
                 reverse engineering of biochemical networks from
                 experimental data. Within this modeling space, a
                 particular PDS is chosen by way of a Gr{\"o}bner basis,
                 and using different monomial orders may result in
                 different polynomial models. In this paper, we present
                 a systematic method for selecting most likely
                 polynomial models for a given data set, using the
                 Gr{\"o}bner fan of the ideal of the input data. We
                 apply the method to reverse engineer two biochemical
                 networks, a Boolean model of lactose metabolism in {\em
                 E. coli} and a protein signal transduction network in
                 {\em S. cerevisiae} and compare our results to those
                 from two published network-reconstruction methods.",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner bases; Gr{\"o}bner fan; computational
                 algebra; model selection; monomial orderings; network
                 inference; polynomial dynamical systems; reverse
                 engineering",
}

@InProceedings{Diochnos:2007:CRS,
  author =       "Dimitrios I. Diochnos and Ioannis Z. Emiris and Elias
                 P. Tsigaridas",
  title =        "On the complexity of real solving bivariate systems",
  crossref =     "Brown:2007:PIS",
  pages =        "127--134",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277567",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider exact real solving of well-constrained,
                 bivariate systems of relatively prime polynomials. The
                 main problem is to compute all common real roots in
                 isolating interval representation, and to determine
                 their intersection multiplicities. We present three
                 algorithms and analyze their asymptotic bit complexity,
                 obtaining a bound of $\tilde{O}_B(N^{14})$ for the
                 purely projection-based method, and
                 $\tilde{O}_B(N^{12})$ for two subresultants-based
                 methods: these ignore polylogarithmic factors, and $N$
                 bounds the degree and the bitsize of the polynomials.
                 The previous record bound was
                 $\tilde{O}_B(N^{14})$.\par

                 Our main tool is signed subresultant sequences,
                 extended to several variables by binary segmentation.
                 We exploit advances on the complexity of univariate
                 root isolation, and extend them to multipoint sign
                 evaluation, sign evaluation of bivariate polynomials
                 over two algebraic numbers, and real root counting over
                 an extension field. Our algorithms apply to the problem
                 of simultaneous inequalities; they also compute the
                 topology of real plane algebraic curves in.\par

                 All algorithms have been implemented in Maple, in
                 conjunction with numeric filtering. We compare them
                 against {\sc FGB\slash RS} and {\sc SYNAPS}; we also
                 consider Maple libraries {\sc INSULATE} and {\sc TOP},
                 which compute curve topology. Our software is among the
                 most robust, and its runtimes are within a small
                 constant factor, with respect to the C/C++ libraries.",
  acknowledgement = ack-nhfb,
  keywords =     "Maple; polynomial system; real algebraic number; real
                 solving; topology of real algebraic curve",
}

@InProceedings{Dridi:2007:TNO,
  author =       "Raouf Dridi and Michel Petitot",
  title =        "Towards a new {ODE} solver based on {Cartan}'s
                 equivalence method",
  crossref =     "Brown:2007:PIS",
  pages =        "135--142",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277568",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The aim of the present paper is to propose an
                 algorithm for a new ODE-solver which should improve the
                 abilities of current solvers to handle second order
                 differential equations. The paper provides also a
                 theoretical result revealing the relationship between
                 the change of coordinates, that maps the generic
                 equation to a given target equation, and the symmetry
                 $D$-groupoid of this target.",
  acknowledgement = ack-nhfb,
  keywords =     "Cartan's equivalence method; differential algebra;
                 equivalence problems; ODE-solver",
}

@InProceedings{Eberly:2007:FIO,
  author =       "Wayne Eberly and Mark Giesbrecht and Pascal Giorgi and
                 Arne Storjohann and Gilles Villard",
  title =        "Faster inversion and other black box matrix
                 computations using efficient block projections",
  crossref =     "Brown:2007:PIS",
  pages =        "143--150",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277569",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Efficient block projections of non-singular matrices
                 have recently been used by the authors in [10] to
                 obtain an efficient algorithm to find rational
                 solutions for sparse systems of linear equations. In
                 particular a bound of $O^~(n^{2.5})$ machine operations
                 is presented for this computation assuming that the
                 input matrix can be multiplied by a vector with
                 constant-sized entries using $O^~(n)$ machine
                 operations. Somewhat more general bounds for black-box
                 matrix computations are also derived. Unfortunately,
                 the correctness of this algorithm depends on the
                 existence of efficient block projections of
                 non-singular matrices, and this was only
                 conjectured.\par

                 In this paper we establish the correctness of the
                 algorithm from [10] by proving the existence of
                 efficient block projections for arbitrary non-singular
                 matrices over sufficiently large fields. We further
                 demonstrate the usefulness of these projections by
                 incorporating them into existing black-box matrix
                 algorithms to derive improved bounds for the cost of
                 several matrix problems. We consider, in particular,
                 matrices that can be multiplied by a vector using
                 $O^~(n)$ field operations: We show how to compute the
                 inverse of any such non-singular matrix over any field
                 using an expected number of $O^~(n^{2.27})$ operations
                 in that field. A basis for the null space of such a
                 matrix, and a certification of its rank, are obtained
                 at the same cost. An application of this technique to
                 Kaltofen and Villard's Baby-Steps\slash Giant-Steps
                 algorithms for the determinant and Smith Form of an
                 integer matrix is also sketched, yielding algorithms
                 requiring $O^~(n^{2.66})$ machine operations. More
                 general bounds involving the number of black-box matrix
                 operations to be used are also obtained.\par

                 The derived algorithms are all probabilistic of the Las
                 Vegas type. They are assumed to be able to generate
                 random elements --- bits or field elements --- at unit
                 cost, and always output the correct answer in the
                 expected time given.",
  acknowledgement = ack-nhfb,
  keywords =     "black box linear algebra; linear system solving;
                 sparse integer matrix; structured integer matrix",
}

@InProceedings{Eigenwillig:2007:FEG,
  author =       "Arno Eigenwillig and Michael Kerber and Nicola
                 Wolpert",
  title =        "Fast and exact geometric analysis of real algebraic
                 plane curves",
  crossref =     "Brown:2007:PIS",
  pages =        "151--158",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277570",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An algorithm is presented for the geometric analysis
                 of an algebraic curve $f(x,y) = 0$ in the real affine
                 plane. It computes a cylindrical algebraic
                 decomposition (CAD) of the plane, augmented with
                 adjacency information. The adjacency information
                 describes the curve's topology by a topologically
                 equivalent planar graph. The numerical data in the CAD
                 gives an embedding of the graph.\par

                 The algorithm is designed to provide the exact result
                 for all inputs but to perform only few symbolic
                 operations for the sake of efficiency. In particular,
                 the roots of $f(\propto,y)$ at a critical
                 $x$-coordinate.\par

                 The algorithm is implemented as C++ library AlciX in
                 the EXACUS project. Running time comparisons with top
                 by Gonzalez-Vega and Necula (2002), and with cad2d by
                 Brown demonstrate its efficiency.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic curves; cylindrical algebraic decomposition;
                 Descartes method; exact geometric computation;
                 Sturm--Habicht sequence; topology computation",
}

@InProceedings{Elkadi:2007:STP,
  author =       "Mohamed Elkadi and Andr{\'e} Galligo",
  title =        "Systems of three polynomials with two separated
                 variables",
  crossref =     "Brown:2007:PIS",
  pages =        "159--166",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277571",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Motivated by the computation of intersection loci in
                 Computer Aided Geometric Design (CAGD), we introduce
                 and study the elimination problem for systems of three
                 bivariate polynomial equations with separated
                 variables. Such systems are simple sparse bivariate
                 ones but resemble to univariate systems of two
                 equations both geometrically and algebraically.
                 Interesting structures for generalized Sylvester and
                 bezoutian matrices can be explicited. Then one can take
                 advantage of these structures to represent the objects
                 and speed up the computations. A corresponding notion
                 of subresultant is presented and related to a
                 Gr{\"o}bner basis of the polynomial system.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; bezoutian; bivariate resultants; bivariate
                 subresultant; CAGD; intersection problem; structured
                 matrix; Sylvester matrix; system with separated
                 variables",
}

@InProceedings{Gaudry:2007:GBI,
  author =       "Pierrick Gaudry and Alexander Kruppa and Paul
                 Zimmermann",
  title =        "A {\tt gmp}-based implementation of
                 {Sch{\"o}nhage--Strassen}'s large integer
                 multiplication algorithm",
  crossref =     "Brown:2007:PIS",
  pages =        "167--174",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277572",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Sch{\"o}nhage--Strassen's algorithm is one of the best
                 known algorithms for multiplying large integers.
                 Implementing it efficiently is of utmost importance,
                 since many other algorithms rely on it as a subroutine.
                 We present here an improved implementation, based on
                 the one distributed within the GMP library. The
                 following ideas and techniques were used or tried:
                 faster arithmetic modulo $2^n + 1$, improved cache
                 locality, Mersenne transforms, Chinese Remainder
                 Reconstruction, the $\sqrt 2$ trick, Harley's and
                 Granlund's tricks, improved tuning.",
  acknowledgement = ack-nhfb,
  keywords =     "integer multiplication; multiprecision arithmetic",
}

@InProceedings{Gemignani:2007:SMM,
  author =       "Luca Gemignani",
  title =        "Structured matrix methods for polynomial
                 root-finding",
  crossref =     "Brown:2007:PIS",
  pages =        "175--180",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277573",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we discuss the use of structured matrix
                 methods for the numerical approximation of the zeros of
                 a univariate polynomial. In particular, it is shown
                 that root-finding algorithms based on floating-point
                 eigenvalue computation can benefit from the structure
                 of the matrix problem to reduce their complexity and
                 memory requirements by an order of magnitude.",
  acknowledgement = ack-nhfb,
  keywords =     "complexity; eigenvalue computation; polynomial
                 root-finding; rank-structured matrices",
}

@InProceedings{Hanke:2007:IPC,
  author =       "Timo Hanke",
  title =        "The isomorphism problem for cyclic algebras and an
                 application",
  crossref =     "Brown:2007:PIS",
  pages =        "181--186",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277574",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The isomorphism problem means to decide if two given
                 finite-dimensional simple algebras with center $K$ are
                 $K$-isomorphic and, if so, to construct a
                 $K$-isomorphism between them. Applications lie in
                 computational aspects of representation theory,
                 algebraic geometry and Brauer group theory. The paper
                 presents an algorithm for cyclic algebras that reduces
                 the isomorphism problem to field theory and thus
                 provides a solution if certain field theoretic problems
                 including norm equations can be solved (this is
                 satisfied over number fields). As an application, we
                 can compute all automorphisms of any given cyclic
                 algebra over a number field. A detailed example is
                 provided which leads to the construction of an explicit
                 noncrossed product division algebra.",
  acknowledgement = ack-nhfb,
  keywords =     "abelian crossed product; bicyclic crossed product;
                 cyclic algebra; extension of automorphism;
                 finite-dimensional central-simple algebra; isomorphism
                 problem; noncrossed product; norm equation",
}

@InProceedings{Javadi:2007:SMG,
  author =       "Seyed Mohammad Mahdi Javadi and Michael Monagan",
  title =        "A sparse modular {GCD} algorithm for polynomials over
                 algebraic function fields",
  crossref =     "Brown:2007:PIS",
  pages =        "187--194",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277575",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a first sparse modular algorithm for
                 computing a greatest common divisor of two polynomials
                 $f_1, f_2 \epsilon L [ x ]$ where $L$ is an algebraic
                 function field in $k \geq 0$ parameters with $r \geq 0$
                 field extensions. Our algorithm extends the dense
                 algorithm of Monagan and van Hoeij from 2004 to support
                 multiple field extensions and to be efficient when the
                 gcd is sparse. Our algorithm is an output sensitive Las
                 Vegas algorithm.\par

                 We have implemented our algorithm in Maple. We provide
                 timings demonstrating the efficiency of our algorithm
                 compared to that of Monagan and van Hoeij and with a
                 primitive fraction-free Euclidean algorithm for both
                 dense and sparse GCD problems.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic function fields; GCD algorithms; sparse
                 interpolation",
}

@InProceedings{Johnson:2007:GSD,
  author =       "Jeremy Johnson and Xu Xu",
  title =        "Generating symmetric {DFTs} and equivariant {FFT}
                 algorithms",
  crossref =     "Brown:2007:PIS",
  pages =        "195--202",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277576",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper presents a code generator which produces
                 efficient implementations of multi-dimensional fast
                 Fourier transform (FFT) algorithms which utilize
                 symmetries in the input data to reduce memory usage and
                 the number of arithmetic operations. The FFT algorithms
                 are constructed using a group theoretic version of the
                 divide and conquer step in the FFT that is compatible
                 with the group of symmetries. The GAP compute algebra
                 system is used to perform the necessary group
                 computations and the generated algorithm is represented
                 as a symbolic matrix factorization, which is translated
                 into efficient code using the SPIRAL system.
                 Performance data is given that shows that the resulting
                 code is significantly faster than state-of-the-art FFT
                 implementations that do not utilize the symmetries.",
  acknowledgement = ack-nhfb,
  keywords =     "code generation; fast Fourier transform; group
                 symmetries; matrix factorization; multi-dimensional
                 discrete Fourier transform",
}

@InProceedings{Kaltofen:2007:EAI,
  author =       "Erich Kaltofen and Zhengfeng Yang",
  title =        "On exact and approximate interpolation of sparse
                 rational functions",
  crossref =     "Brown:2007:PIS",
  pages =        "203--210",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277577",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The black box algorithm for separating the numerator
                 from the denominator of a multivariate rational
                 function can be combined with sparse multivariate
                 polynomial interpolation algorithms to interpolate a
                 sparse rational function. Randomization and early
                 termination strategies are exploited to minimize the
                 number of black box evaluations. In addition, rational
                 number coefficients are recovered from modular images
                 by rational vector recovery. The need for separate
                 numerator and denominator size bounds is avoided via
                 correction, and the modulus is minimized by use of
                 lattice basis reduction, a process that can be applied
                 to sparse rational function vector recovery itself.
                 Finally, one can deploy sparse rational function
                 interpolation algorithm in the hybrid symbolic-numeric
                 setting when the black box for the function returns
                 real and complex values with noise. We present and
                 analyze five new algorithms for the above problems and
                 demonstrate their effectiveness on a mark
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "early termination; hybrid symbolic-numeric
                 computation; lattice basis reduction; rational vector
                 recovery; sparse rational function interpolation",
}

@InProceedings{Kanno:2007:POC,
  author =       "Masaaki Kanno and Kazuhiro Yokoyama and Hirokazu Anai
                 and Shinji Hara",
  title =        "Parametric optimization in control using the sum of
                 roots for parametric polynomial spectral
                 factorization",
  crossref =     "Brown:2007:PIS",
  pages =        "211--218",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277578",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper proposes an algebraic approach for
                 parametric optimization which can be utilized for
                 various problems in signal processing and control. The
                 approach exploits the relationship between the sum of
                 roots and polynomial spectral factorization and solves
                 parametric polynomial spectral factorization by means
                 of the sum of roots and the theory of Gr{\"o}bner
                 basis. This enables us to express quantities such as
                 the optimal cost in terms of parameters and the sum of
                 roots. Furthermore an optimization method over
                 parameters is suggested that makes use of the results
                 from parametric polynomial spectral factorization and
                 also employs quantifier elimination. The proposed
                 approach is demonstrated on a numerical example of a
                 particular control problem.",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner basis; H_2 control; parametric
                 optimization; polynomial spectral factorization;
                 quantifier elimination; sum of roots",
}

@InProceedings{Kauers:2007:SSR,
  author =       "Manuel Kauers and Carsten Schneider",
  title =        "Symbolic summation with radical expressions",
  crossref =     "Brown:2007:PIS",
  pages =        "219--226",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277579",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An extension of Karr's summation algorithm is
                 presented by which symbolic sums involving radical
                 expressions can be simplified. We discuss the
                 construction of appropriate difference fields as well
                 as algorithms for solving difference equations in these
                 fields. The paper is concluded by a list of identities
                 found with an implementation of our techniques.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic functions; difference fields; square roots;
                 symbolic summation",
}

@InProceedings{Khungurn:2007:MCP,
  author =       "Pramook Khungurn and Hiroshi Sekigawa and Kiyoshi
                 Shirayanagi",
  title =        "Minimum converging precision of the {QR}-factorization
                 algorithm for real polynomial {GCD}",
  crossref =     "Brown:2007:PIS",
  pages =        "227--234",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277580",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Shirayanagi and Sweedler proved that a large class of
                 algorithms over the reals can be modified slightly so
                 that they also work correctly on fixed-precision
                 floating-point numbers. Their main theorem states that,
                 for each input, there exists a precision, called the
                 minimum converging precision (MCP), at and beyond which
                 the modified `stabilized' algorithm follows the same
                 sequence of instructions as that of the original
                 `exact' algorithm. Bounding the MCP of any non-trivial
                 and useful algorithm has remained an open
                 problem.\par

                 This paper studies the MCP of an algorithm for finding
                 the GCD of two univariate polynomials based on the
                 QR-factorization. We show that the MCP is generally
                 incomputable. Additionally, we derive a bound on the
                 minimal precision at and beyond which the stabilized
                 algorithm gives a polynomial with the same degree as
                 that of the exact GCD, and another bound on the minimal
                 precision at and beyond which the algorithm gives a
                 polynomial with the same support as that of the exact
                 GCD.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic algorithm stabilization; polynomial greatest
                 common divisor",
}

@InProceedings{Kunkle:2007:TSM,
  author =       "Daniel Kunkle and Gene Cooperman",
  title =        "Twenty-six moves suffice for {Rubik}'s cube",
  crossref =     "Brown:2007:PIS",
  pages =        "235--242",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277581",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The number of moves required to solve any state of
                 Rubik's cube has been a matter of long-standing
                 conjecture for over 25 years -- since Rubik's cube
                 appeared. This number is sometimes called `God's
                 number'. An upper bound of 29 (in the face-turn metric)
                 was produced in the early 1990's, followed by an upper
                 bound of 27 in 2006.\par

                 An improved upper bound of 26 is produced using 8000
                 CPU hours. One key to this result is a new, fast
                 multiplication in the mathematical group of Rubik's
                 cube. Another key is efficient out-of-core (disk-based)
                 parallel computation using terabytes of disk storage.
                 One can use the precomputed data structures to produce
                 such solutions for a specific Rubik's cube position in
                 a fraction of a second. Work in progress will use the
                 new `brute-forcing' technique to further reduce the
                 bound.",
  acknowledgement = ack-nhfb,
  keywords =     "disk-based methods; fast multiplication; permutation
                 groups; Rubik's cube; upper bound",
}

@InProceedings{Kurata:2007:CDC,
  author =       "Yosuke Kurata and Masayuki Noro",
  title =        "Computation of discrete comprehensive {Gr{\"o}bner}
                 bases using modular dynamic evaluation",
  crossref =     "Brown:2007:PIS",
  pages =        "243--250",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277582",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we propose a new algorithm to compute a
                 discrete comprehensive Gr{\"o}bner basis (DCGB) [9, 11]
                 which is a special case of a comprehensive Gr{\"o}bner
                 system. Our new algorithm enables us to compute the
                 quasi-inverse and the idempotent in von Neumann regular
                 rings without computing the prime decomposition of the
                 defining ideal of the parameter space, by using the
                 Modular Dynamic Evaluation [7]. The computation of DCGB
                 is frequently executed in Suzuki-Sato's algorithm for
                 computing CGS and CGB [13], and our new algorithm can
                 improve its practical efficiency.",
  acknowledgement = ack-nhfb,
  keywords =     "comprehensive Gr{\"o}bner bases; comprehensive
                 discrete Gr{\"o}bner bases; comprehensive Gr{\"o}bner
                 systems; dynamic evaluation; modular dynamic
                 evaluation; von Neumann regular rings",
}

@InProceedings{Levin:2007:GBR,
  author =       "Alexander B. Levin",
  title =        "{Gr{\"o}bner} bases with respect to several term
                 orderings and multivariate dimension polynomials",
  crossref =     "Brown:2007:PIS",
  pages =        "251--260",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277583",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let {$D$} be a ring of {\O}re polynomials in $m$
                 variables $ x_1, \ldots {}, x_m $ over a field {$K$}
                 and let a partition of the set $ \{ x_1, \ldots {}, x_m
                 \} $ into $p$ disjoint subsets be fixed, so that {$D$}
                 can be treated as a filtered ring with the natural
                 $p$-dimensional filtration associated with the
                 partition. We introduce a special type of reduction in
                 a finitely generated free {$D$}-module and develop the
                 corresponding Gr{\"o}bner basis technique that allows
                 one to prove the existence and find invariants of a
                 dimension polynomial in $p$ variables associated with a
                 finitely generated {$D$}-module. We also outline a
                 method of computation of such a polynomial and obtain
                 an essential generalization of the Kolchin theorem on
                 the dimension polynomial of a differential field
                 extension.",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner basis; differential field extension;
                 dimension polynomial; {\O}re polynomials;
                 $p$-dimensional filtration",
}

@InProceedings{Li:2007:FAT,
  author =       "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
  title =        "Fast arithmetic for triangular sets: from theory to
                 practice",
  crossref =     "Brown:2007:PIS",
  pages =        "269--276",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277585",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study arithmetic operations for triangular families
                 of polynomials, concentrating on multiplication in
                 dimension zero. By a suitable extension of fast
                 univariate Euclidean division, we obtain theoretical
                 and practical improvements over a direct recursive
                 approach; for a family of special cases, we reach
                 quasi-linear complexity. The main outcome we have in
                 mind is the acceleration of higher-level algorithms, by
                 interfacing our low-level implementation with languages
                 such as AXIOM or Maple We show the potential for huge
                 speed-ups, by comparing two AXIOM implementations of
                 van Hoeij and Monagan's modular GCD algorithm.",
  acknowledgement = ack-nhfb,
  keywords =     "high-performance; multiplication; triangular set",
}

@InProceedings{Li:2007:RSG,
  author =       "Hongbo Li",
  title =        "A recipe for symbolic geometric computing: long
                 geometric product, {BREEFS} and {Clifford}
                 factorization",
  crossref =     "Brown:2007:PIS",
  pages =        "261--268",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277584",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In symbolic computing, a major bottleneck is middle
                 expression swell. Symbolic geometric computing based on
                 invariant algebras can alleviate this difficulty. For
                 example, the size of projective geometric computing
                 based on bracket algebra can often be restrained to two
                 terms, using final polynomials, area method, Cayley
                 expansion,etc. This is the `binomial' feature of
                 projective geometric computing in the language of
                 bracket algebra.\par

                 In this paper we report a stunning discovery in
                 Euclidean geometric computing: the term preservation
                 phenomenon. Input an expression in the language of Null
                 Bracket Algebra (NBA), by the recipe we are to propose
                 in this paper, the computing procedure can often be
                 controlled to within the same number of terms as the
                 input, through to the end. In particular, the
                 conclusions of most Euclidean geometric theorems can be
                 expressed by monomials in NBA, and the expression size
                 in the proving procedure can often be controlled to
                 within one term! Euclidean geometric computing can now
                 be announced as having a `monomial' feature in the
                 language of NBA.\par

                 The recipe is composed of three parts: use long
                 geometric product to represent and compute
                 multiplicatively, use `BREEFS' to control the
                 expression size locally, and use Clifford factorization
                 for term reduction and transition from algebra to
                 geometry.\par

                 By the time this paper is being written, the recipe has
                 been tested by 70+ examples from [1], among which 30+
                 have monomial proofs. Among those outside the scope,
                 the famous Miquel's five circle theorem [2 ], whose
                 analytic proof is straightforward but very difficult
                 for symbolic computing, is discovered to have a
                 3-termed elegant proof with the recipe.",
  acknowledgement = ack-nhfb,
  keywords =     "conformal geometric algebra; geometric invariance;
                 geometric theorem proving; null bracket algebra;
                 symbolic geometric computing",
}

@InProceedings{May:2007:EMR,
  author =       "John P. May and David Saunders and Zhendong Wan",
  title =        "Efficient matrix rank computation with application to
                 the study of strongly regular graphs",
  crossref =     "Brown:2007:PIS",
  pages =        "277--284",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277586",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present algorithms for computing the $p$-rank of
                 integer matrices. They are designed to be particularly
                 effective when $p$ is a small prime, the rank is
                 relatively low, and the matrix itself is large and
                 dense and may exceed virtual memory space. Our
                 motivation comes from the study of difference sets and
                 partial difference sets in algebraic design theory. The
                 $p$-rank of the adjacency matrix of an associated
                 strongly regular graph is a key tool for distinguishing
                 difference set constructions and thus answering various
                 existence questions and conjectures. For the $p$-rank
                 computation, we review several memory efficient
                 methods, and present refinements suitable to the small
                 prime, small rank case. We give a new heuristic
                 approach that is notably effective in practice as
                 applied to the strongly regular graph adjacency
                 matrices. It involves projection to a matrix of order
                 slightly above the rank. The projection is extremely
                 sparse, is chosen according to one of several
                 heuristics, and is combined with a small dense
                 certifying component. Our algorithms and heuristics are
                 implemented in the LinBox library. We also briefly
                 discuss some of the software design issues and we
                 present results of experiments for the Paley and
                 Dickson sequences of strongly regular graphs.",
  acknowledgement = ack-nhfb,
  keywords =     "matrix $p$-rank; out of core methods",
}

@InProceedings{Mihailescu:2007:CES,
  author =       "P. Mihailescu and F. Morain and {\'E}. Schost",
  title =        "Computing the eigenvalue in the
                 {Schoof--Elkies--Atkin} algorithm using {Abelian}
                 lifts",
  crossref =     "Brown:2007:PIS",
  pages =        "285--292",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277587",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The Schoof--Elkies=-Atkin algorithm is the best known
                 method for counting the number of points of an elliptic
                 curve defined over a finite field of large
                 characteristic. We use Abelian properties of division
                 polynomials to design a fast theoretical and practical
                 algorithm for finding the eigenvalue.",
  acknowledgement = ack-nhfb,
  keywords =     "elliptic curves; finite fields; SEA algorithm",
}

@InProceedings{Miyamoto:2007:CSM,
  author =       "Izumi Miyamoto",
  title =        "A computation of some multiply homogeneous
                 superschemes from transitive permutation groups",
  crossref =     "Brown:2007:PIS",
  pages =        "293--298",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277588",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $G$ be a doubly transitive permutation group on a
                 set $X$. A doubly homogeneous superscheme is formed by
                 the orbits on the set of triples of $X$ of $G$. Let
                 $\alpha$ be a point of a set $X$ and let $H$ be a
                 transitive group on $X\{\alpha\}$. Then from the
                 combinatorial structure of the superscheme formed by
                 the orbits of $H$ on $X^3$ ,we may construct some
                 doubly homogeneous superschemes on $X$. We will give a
                 general algorithm to compute such superschemes and show
                 how to implement it practically. In particular if $H =
                 G_\alpha$, the stabilizer of $\alpha$ in $G$, then we
                 can construct a superscheme of which automorphism group
                 is $G$ in the cases of moderate size. Furthermore, even
                 if $H$ is not a stabilizer of a doubly transitive
                 group, we can consider some orbit-like sets of a doubly
                 homogeneous superscheme. We see whether such sets form
                 a design in some cases. As a related combinatorial
                 algorithm we have developed a program to compute the
                 automorphism group of a superscheme which is a kind of
                 a labeled hyper graph.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nabeshima:2007:SAC,
  author =       "Katsusuke Nabeshima",
  title =        "A speed-up of the algorithm for computing
                 comprehensive {Gr{\"o}bner} systems",
  crossref =     "Brown:2007:PIS",
  pages =        "299--306",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277589",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We introduce a new algorithm for computing
                 comprehensive Gr{\"o}bner systems. There exists the
                 Suzuki--Sato algorithm for computing comprehensive
                 Gr{\"o}bner systems. The Suzuki--Sato algorithm often
                 creates overmuch cells of the parameter space for
                 comprehensive Gr{\"o}bner systems. Therefore the
                 computation becomes heavy. However, by using
                 inequations (`not equal zero'), we can obtain different
                 cells. In many cases, this number of cells of parameter
                 space is smaller than that of Suzuki--Sato's.
                 Therefore, our new algorithm is more efficient than
                 Suzuki--Sato's one, and outputs a nice comprehensive
                 Gr{\"o}bner system. Our new algorithm has been
                 implemented in the computer algebra system Risa\slash
                 Asir We compare the runtime of our implementation with
                 the Suzuki--Sato algorithm and find our algorithm
                 superior in many cases.",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner bases; comprehensive Gr{\"o}bner bases",
}

@InProceedings{Pernet:2007:FAC,
  author =       "Cl{\'e}ment Pernet and Arne Storjohann",
  title =        "Faster algorithms for the characteristic polynomial",
  crossref =     "Brown:2007:PIS",
  pages =        "307--314",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277590",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A new randomized algorithm is presented for computing
                 the characteristic polynomial of an $n \times n$ matrix
                 over a field. Over a sufficiently large field the
                 asymptotic expected complexity of the algorithm is
                 $O(n^\theta)$ field operations, improving by a factor
                 of $\log n$ on the worst case complexity of
                 Keller--Gehrig's algorithm [11].",
  acknowledgement = ack-nhfb,
  keywords =     "characteristic polynomial; complexity; Frobenius
                 normal form",
}

@InProceedings{Robinson:2007:DBP,
  author =       "Eric Robinson and J{\"u}rgen M{\"u}ller and Gene
                 Cooperman",
  title =        "A disk-based parallel implementation for direct
                 condensation of large permutation modules",
  crossref =     "Brown:2007:PIS",
  pages =        "315--322",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277591",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Through the use of a new disk-based method for
                 enumerating very large orbits, condensation for orbits
                 with tens of billions of elements can be performed. The
                 algorithm is novel in that it offers efficient access
                 to data using distributed disk-based data structures.
                 This provides fast access to hundreds of gigabytes of
                 data,which allows for computing without worrying about
                 memory limitations.\par

                 The new algorithm is demonstrated on one of the
                 long-standing open problems in the Modular Atlas
                 Project [11]: the Brauer tree of the principal 17-block
                 the sporadic simple Fischer group $Fi_{23}$. The tree
                 is completed by computing three orbit counting matrices
                 for the $Fi_{23}$ orbit of size 11,739,046,176 acting
                 on vectors of dimension 728 over GF(2). The
                 construction of these matrices requires 3-1/2 days on a
                 cluster of 56 computers, and uses 8 GB of disk storage
                 and 800 MB of memory per machine.",
  acknowledgement = ack-nhfb,
  keywords =     "Brauer trees; condensation; disk-based computation;
                 matrix groups; parallel computation; permutation
                 groups; sporadic Fischer group",
}

@InProceedings{Ruffo:2007:SLD,
  author =       "James Ruffo",
  title =        "A straightening law for the {Drinfel'd Lagrangian
                 Grassmannian}",
  crossref =     "Brown:2007:PIS",
  pages =        "323--330",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277592",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The Drinfel'd Lagrangian Grassmannian compacts the
                 space of algebraic maps of fixed degree from the
                 projective line into the Lagrangian Grassmannian. It
                 has a natural projective embedding arising from the
                 highest weight embedding of the ordinary Lagrangian
                 Grassmannian. We show that the defining ideal of any
                 Schubert subvariety is generated by polynomials which
                 give a straightening law on an ordered set.
                 Consequentially, any such subvariety is Cohen--Macaulay
                 and Koszul.",
  acknowledgement = ack-nhfb,
  keywords =     "algebras with straightening law; Drinfel'd ag
                 varieties quasimaps",
}

@InProceedings{Schwarz:2007:LDL,
  author =       "F. Schwarz",
  title =        "{Loewy} decomposition of linear differential
                 equations",
  crossref =     "Brown:2007:PIS",
  pages =        "389--390",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277602",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "D-module; Janet basis; Loewy decomposition",
}

@InProceedings{Sekigawa:2007:RFR,
  author =       "Hiroshi Sekigawa",
  title =        "On real factors of real interval polynomials",
  crossref =     "Brown:2007:PIS",
  pages =        "331--338",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277593",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "For a real multivariate interval polynomial $P$ and a
                 real multivariate polynomial $f$, we provide a rigorous
                 method for deciding whether there exists a polynomial
                 $p$ in $P$ such that $p$ is divisible by $f$. When $P$
                 is univariate, there is a well-known criterion for
                 whether there exists a polynomial $p(\chi)$ in $P$ such
                 that $p(\alpha) = 0$ for a given real number $\alpha$.
                 Since $p(\alpha) = 0$ if and only if $p(\chi)$ is
                 divisible by $\chi - \alpha$, our result is a
                 generalization of the criterion to multivariate
                 polynomials and higher degree factors.",
  acknowledgement = ack-nhfb,
  keywords =     "divisibility; factor; interval polynomial; polytope",
}

@InProceedings{Sharma:2007:CRR,
  author =       "Vikram Sharma",
  title =        "Complexity of real root isolation using continued
                 fractions",
  crossref =     "Brown:2007:PIS",
  pages =        "339--346",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277594",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The efficiency of the continued fraction algorithm for
                 isolating the real roots of a univariate polynomial
                 depends upon computing tight lower bounds on the
                 smallest positive root of a polynomial. The known
                 complexity bounds for the algorithm rely on the
                 impractical assumption that it is possible to
                 efficiently compute the floor of the smallest positive
                 root of a polynomial; without this assumption, the
                 worst case bounds are exponential. In this paper, we
                 derive the first polynomial worst case bound on the
                 algorithm: for a square-free integer polynomial of
                 degree $n$ and coefficients of bit-length $L$, the
                 bit-complexity of the continued fraction algorithm is
                 $\tilde{O}(n^7 L^2)$, using a bound by Hong to compute
                 the floor of the smallest positive root of a
                 polynomial; here $\tilde{O}$ indicates that we are
                 omitting logarithmic factors.",
  acknowledgement = ack-nhfb,
  keywords =     "continued fractions; Davenport-Mahler bound; Descartes
                 rule of signs; polynomial real root isolation",
}

@InProceedings{Smith:2007:ADA,
  author =       "Jacob Smith and Gabriel {Dos Reis} and Jaakko
                 J{\"a}rvi",
  title =        "Algorithmic differentiation in {Axiom}",
  crossref =     "Brown:2007:PIS",
  pages =        "347--354",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277595",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper describes the design and implementation of
                 an algorithmic differentiation framework in the Axiom
                 computer algebra system. Our implementation works by
                 transformations on Spad programs at the level of the
                 typed abstract syntax tree -- Spad is the language for
                 extending Axiom with libraries. The framework
                 illustrates an algebraic theory of algorithmic
                 differentiation, here only for Spad programs, but we
                 suggest that the theory is general. In particular, if
                 it is possible to define a compositional semantics for
                 programs, we define the exact requirements for when a
                 program can be algorithmically differentiated. This
                 leads to a general algorithmic differentiation system,
                 and is not confined to functions which compute with
                 basic data types, such as floating point numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithmic differentiation; axiom; program
                 transformation; symbolic-numeric computation",
}

@InProceedings{vanHoeij:2007:STO,
  author =       "Mark van Hoeij",
  title =        "Solving third order linear differential equations in
                 terms of second order equations",
  crossref =     "Brown:2007:PIS",
  pages =        "355--360",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277596",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper presents a simplified version of a method
                 by Michael Singer for reducing a third order linear ODE
                 to a second order linear ode whenever possible. An
                 implementation is available as well.",
  acknowledgement = ack-nhfb,
  keywords =     "linear differential equations; reduction of order",
}

@InProceedings{Villard:2007:CFL,
  author =       "Gilles Villard",
  title =        "Certification of the {$QR$} factor {$R$} and of
                 lattice basis reducedness",
  crossref =     "Brown:2007:PIS",
  pages =        "361--368",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277597",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Given a lattice basis of $n$ vectors in $Z_n$, we
                 propose an algorithm using $12 n^3 + O(n^2)$ floating
                 point operations for checking whether the basis is
                 $LLL$-reduced. If the basis is reduced then the
                 algorithm will hopefully answer `yes'. If the basis is
                 not reduced, or if the precision used is not sufficient
                 with respect to $n$, and to the numerical properties of
                 the basis, the algorithm will answer `failed'. Hence a
                 positive answer is a rigorous certificate. For
                 implementing the certificate itself, we propose a
                 floating point algorithm for computing (certified)
                 error bounds for the $R$ factor of the $QR$
                 factorization. This algorithm takes into account all
                 possible approximation and rounding errors. The
                 certificate may be implemented using matrix library
                 routines only. We report experiments that show that for
                 a reduced basis of adequate dimension and quality the
                 certificate succeeds, and establish the effectiveness
                 of the certificate. This effectiveness is applied for
                 certifying the output of fastest existing floating
                 point heuristics of $LLL$ reduction, without slowing
                 down the whole process.",
  acknowledgement = ack-nhfb,
  keywords =     "lattice basis reducedness; linear algebra; QR
                 factorization; verification algorithm",
}

@InProceedings{Villard:2007:SRP,
  author =       "Gilles Villard",
  title =        "Some recent progress in exact linear algebra and
                 related questions",
  crossref =     "Brown:2007:PIS",
  pages =        "391--392",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277603",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We describe some major recent progress in exact and
                 symbolic linear algebra. These advances concern the
                 improvement of complexity estimates for fundamental
                 problems such as linear system solution, determinant,
                 inversion and computation of canonical forms. The
                 matrices are over a finite field, the integers, or
                 univariate polynomials. We show how selected techniques
                 are key ingredients for the new solutions:
                 randomization and algebraic conditioning, lifting,
                 subspace approach, divide-double and conquer, minimum
                 matrix polynomial, matrix approximants. These
                 algorithmic progress allow the design of new generation
                 high performance libraries such as LinBox, and open
                 various research directions.\par

                 We refer to [3] for an overview of methods in exact
                 linear algebra, see also [37], [1] (in French), and [7,
                 x2.3]. For fundamentals of computer algebra we refer to
                 [16, 7].",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:2007:CRS,
  author =       "Joachim von zur Gathen",
  title =        "Counting reducible and singular bivariate
                 polynomials",
  crossref =     "Brown:2007:PIS",
  pages =        "369--376",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277598",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Among the bivariate polynomials over a finite field,
                 most are irreducible. We count some classes of special
                 polynomials, namely the reducible ones, those with a
                 square factor, the `relatively irreducible' ones which
                 are irreducible but factor over an extension field, and
                 the singular ones, which have a root at which both
                 partial derivatives vanish.",
  acknowledgement = ack-nhfb,
  keywords =     "bivariate polynomials; combinatorics on polynomials;
                 counting problems; finite fields; reducible
                 polynomials; singular polynomials",
}

@InProceedings{Wu:2007:SNC,
  author =       "Wenyuan Wu and Greg Reid",
  title =        "Symbolic-numeric computation of implicit {Riquier
                 Bases} for {PDE}",
  crossref =     "Brown:2007:PIS",
  pages =        "377--386",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277599",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Riquier Bases for systems of analytic pde are, loosely
                 speaking, a differential analogue of Gr{\"o}bner Bases
                 for polynomial equations. They are determined in the
                 exact case by applying a sequence of prolongations
                 (differentiations) and eliminations to an input system
                 of pde.\par

                 We present a symbolic-numeric method to determine
                 Riquier Bases in implicit form for systems which are
                 dominated by pure derivatives in one of the independent
                 variables and have the same number of pde and
                 unknowns.\par

                 The method is successful provided the prolongations
                 with respect to the dominant independent variable have
                 a block structure which is uncovered by Linear
                 Programming and certain Jacobians are non-singular when
                 evaluated at points on the zero sets defined by the
                 functions of the pde. For polynomially nonlinear pde,
                 homotopy continuation methods from Numerical Algebraic
                 Geometry can be used to compute approximations of the
                 points.\par

                 We give a differential algebraic interpretation of
                 Pryce's method for ode, which generalizes to the pde
                 case. A major aspect of the method's efficiency is that
                 only prolongations with respect to a single (dominant)
                 independent variable are made, possibly after a random
                 change of coordinates. Potentially expensive and
                 numerically unstable eliminations are not made.
                 Examples are given to illustrate theoretical features
                 of the method, including a curtain of Pendula and the
                 control of a crane.",
  acknowledgement = ack-nhfb,
  keywords =     "implicit function theorem; jet spaces; linear
                 programming; numerical algebraic geometry; partial
                 differential equation; ranking; Riquier Bases",
}

@InProceedings{Abramov:2008:PSL,
  author =       "Sergei A. Abramov",
  title =        "Power series and linear difference equations",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "1--2",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390769",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "linear difference equation with polynomial
                 coefficients; power series; sequential solution;
                 subanalytic solution",
}

@InProceedings{Achatz:2008:DPE,
  author =       "Melanie Achatz and Scott McCallum and Volker
                 Weispfenning",
  title =        "Deciding polynomial-exponential problems",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "215--222",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390799",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper presents a decision procedure for a certain
                 class of sentences of first order logic involving
                 integral polynomials and the exponential function in
                 which the variables range over the real numbers. The
                 inputs to the decision procedure are prenex sentences
                 in which only the outermost quantified variable can
                 occur in the exponential function. The decision
                 procedure has been implemented in the computer logic
                 system REDLOG. Closely related work is reported in [2,
                 7, 16, 20, 24].",
  acknowledgement = ack-nhfb,
  keywords =     "decision procedure; exponential polynomials",
}

@InProceedings{Antritter:2008:TCA,
  author =       "Felix Antritter and Jean L{\'e}vine",
  title =        "Towards a computer algebraic algorithm for flat output
                 determination",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "7--14",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390773",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This contribution deals with nonlinear control
                 systems. More precisely, we are interested in the
                 formal computation of a so-called flat output, a
                 particular generalized output whose property is,
                 roughly speaking, that all the integral curves of the
                 system may be expressed as smooth functions of the
                 components of this flat output and their successive
                 time derivatives up to a finite order (to be
                 determined). Recently, a characterization of such flat
                 output has been obtained in the framework of manifolds
                 of jets of infinite order that yields an abstract
                 algorithm for its computation. In this paper it is
                 discussed how these conditions can be checked using
                 computer algebra. All steps of the algorithm are
                 discussed for the simple (but rich enough) example of a
                 non holonomic car.",
  acknowledgement = ack-nhfb,
  keywords =     "control systems; differential flatness",
}

@InProceedings{Aschenbrenner:2008:AFS,
  author =       "Matthias Aschenbrenner and Christopher J. Hillar",
  title =        "An algorithm for finding symmetric {Gr{\"o}bner} bases
                 in infinite dimensional rings",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "117--124",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390787",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A {\em symmetric ideal\/} $I \subset R = K[x_1,
                 x_2,\ldots{}]$ is an ideal that is invariant under the
                 natural action of the infinite symmetric group. We give
                 an explicit algorithm to find Gr{\"o}bner bases for
                 symmetric ideals in the infinite dimensional polynomial
                 ring $R$. This allows for symbolic computation in a new
                 class of rings. In particular, we solve the ideal
                 membership problem for symmetric ideals of $R$.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithm; Gr{\"o}bner basis; invariant ideal; partial
                 ordering; polynomial reduction; symmetric group",
}

@InProceedings{Barkatou:2008:RSL,
  author =       "Moulay A. Barkatou and Gary Broughton and Eckhard
                 Pfl{\"u}gel",
  title =        "Regular systems of linear functional equations and
                 applications",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "15--22",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390774",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The algorithmic classification of singularities of
                 linear differential systems via the computation of
                 Moser- and super-irreducible forms as introduced in
                 [21] and [16] respectively has been widely studied in
                 Computer Algebra ([8, 12, 22, 6, 10]). Algorithms have
                 subsequently been given for other forms of systems such
                 as linear difference systems [4, 3] and the perturbed
                 algebraic eigenvalue problem [18]. In this paper, we
                 extend these concepts to the general class of systems
                 of linear functional equations. We derive a definition
                 of regularity for these type of equations, and an
                 algorithm for recognizing regular systems. When
                 specialised to $q$-difference systems, our results lead
                 to new algorithms for computing polynomial solutions
                 and regular formal solutions.",
  acknowledgement = ack-nhfb,
  keywords =     "computer algebra; Moser-reduction; singularities;
                 super-reduction; systems of linear functional
                 equations",
}

@InProceedings{Bostan:2008:POD,
  author =       "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Nicolas Le
                 Roux",
  title =        "Products of ordinary differential operators by
                 evaluation and interpolation",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "23--30",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390775",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "It is known that multiplication of linear differential
                 operators over ground fields of characteristic zero can
                 be reduced to a constant number of matrix products. We
                 give a new algorithm by evaluation and interpolation
                 which is faster than the previously-known one by a
                 constant factor, and prove that in characteristic zero,
                 multiplication of differential operators and of
                 matrices are computationally equivalent problems. In
                 positive characteristic, we show that differential
                 operators can be multiplied in nearly optimal time.
                 Theoretical results are validated by intensive
                 experiments.",
  acknowledgement = ack-nhfb,
  keywords =     "differential operators; fast algorithms",
}

@InProceedings{Bostan:2008:PSC,
  author =       "Alin Bostan and Bruno Salvy and {\'E}ric Schost",
  title =        "Power series composition and change of basis",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "269--276",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390806",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Efficient algorithms are known for many operations on
                 truncated power series (multiplication, powering,
                 exponential, \ldots{}). Composition is a more complex
                 task. We isolate a large class of power series for
                 which composition can be performed efficiently. We
                 deduce fast algorithms for converting polynomials
                 between various bases, including Euler, Bernoulli,
                 Fibonacci, and the orthogonal Laguerre, Hermite,
                 Jacobi, Krawtchouk, Meixner and Meixner--Pollaczek.",
  acknowledgement = ack-nhfb,
  keywords =     "basis conversion; fast algorithms; orthogonal
                 polynomials; transposed algorithms",
}

@InProceedings{Brickenstein:2008:GFN,
  author =       "Michael Brickenstein and Alexander Dreyer",
  title =        "{Gr{\"o}bner}-free normal forms for {Boolean}
                 polynomials",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "55--62",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390779",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper introduces a new method for interpolation
                 of Boolean functions using Boolean polynomials. It was
                 motivated by some problems arising from computational
                 biology, for reverse engineering the structure of
                 mechanisms in gene regulatory networks. For this
                 purpose polynomial expressions have to be generated,
                 which match known state combinations observed during
                 experiments. Earlier approaches using Gr{\"o}bner
                 techniques have not been powerful enough to treat
                 real-world applications. The proposed method avoids
                 expensive Gr{\"o}bner basis computations completely by
                 directly calculating reduced normal forms. The problem
                 statement can be described by Boolean polynomials,
                 i.e., polynomials with coefficients in $\{0,1\}$ and a
                 degree bound of one. Therefore, the reference
                 implementations mentioned in this work are built on the
                 top of the PolyBoRi framework, which has been designed
                 exclusively for the treatment of this special class of
                 polynomials. A series of randomly generated examples is
                 used to demonstrate the performance of the direct
                 method. It is also compared with other approaches,
                 which incorporate Gr{\"o}bner basis computations.",
  acknowledgement = ack-nhfb,
  keywords =     "Boolean polynomials; Gr{\"o}bner interpolation; normal
                 forms",
}

@InProceedings{Burr:2008:CSA,
  author =       "Michael Burr and Sung Woo Choi and Benjamin Galehouse
                 and Chee K. Yap",
  title =        "Complete subdivision algorithms, {II}: isotopic
                 meshing of singular algebraic curves",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "87--94",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390783",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Given a real function $f(X,Y)$, a box region $B$ and
                 $\epsilon > 0$, we want to compute an
                 $\epsilon$-isotopic polygonal approximation to the
                 curve $C : f(X,Y) = 0$ within $B$. We focus on
                 subdivision algorithms because of their adaptive
                 complexity. Plantinga \& Vegter (2004) gave a numerical
                 subdivision algorithm that is exact when the curve $C$
                 is non-singular. They used a computational model that
                 relies only on function evaluation and interval
                 arithmetic.\par

                 We generalize their algorithm to any (possibly
                 non-simply connected) region $B$ that does not contain
                 singularities of $C$. With this generalization as
                 subroutine, we provide a method to detect isolated
                 algebraic singularities and their branching degree.
                 This appears to be the first complete {\em numerical\/}
                 method to treat implicit algebraic curves with isolated
                 singularities.",
  acknowledgement = ack-nhfb,
  keywords =     "complete numerical algorithm; evaluation bound;
                 implicit algebraic curve; meshing; root bound;
                 singularity; subdivision algorithm",
}

@InProceedings{Caboara:2008:GBP,
  author =       "Massimo Caboara and Fabrizio Caruso and Carlo
                 Traverso",
  title =        "{Gr{\"o}bner} bases for public key cryptography",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "315--324",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390811",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Up to now, any attempt to use Gr{\"o}bner bases in the
                 design of public key cryptosystems has failed, as
                 anticipated by a classical paper of B. Barkee et al.;
                 we show why, and show that the only residual hope is to
                 use binomial ideals, i.e., lattices. We propose two
                 lattice-based cryptosystems that will show the
                 usefulness of multivariate polynomial algebra and
                 Gr{\"o}bner bases in the construction of public key
                 cryptosystems. The first one tries to revive two
                 cryptosystems Polly Cracker and GGH, that have been
                 considered broken, through a hybrid; the second one
                 improves a cryptosystem (NTRU) that only has heuristic
                 and challenged evidence of security, providing evidence
                 that the extension cannot be broken with some of the
                 standard lattice tools that can be used to break some
                 reduced form of NTRU. Because of the bounds on length,
                 we only sketch the construction of these two
                 cryptosystems, and leave many details of the
                 construction of private and public keys, of the proofs
                 and of the security considerations to forthcoming
                 technical papers.",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner basis; Gr{\"o}bner Hermite normal form;
                 lattice; public key cryptosystem",
}

@InProceedings{Daouda:2008:CTN,
  author =       "Diatta Niang Daouda and Bernard Mourrain and Olivier
                 Ruatta",
  title =        "On the computation of the topology of a non-reduced
                 implicit space curve",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "47--54",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390778",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An algorithm is presented for the computation of the
                 topology of a non-reduced space curve defined as the
                 intersection of two implicit algebraic surfaces.\par

                 It computes a Piecewise Linear Structure (PLS) isotopic
                 to the original space curve.\par

                 The algorithm is designed to provide the exact result
                 for all inputs. It's a symbolic-numeric algorithm based
                 on subresultant computation. Simple algebraic criteria
                 are given to certify the output of the
                 algorithm.\par

                 The algorithm uses only one projection of the
                 non-reduced space curve augmented with adjacency
                 information around some 'particular points' of the
                 space curve.\par

                 The algorithm is implemented with the Mathemagix
                 Computer Algebra System (CAS) using the SYNAPS library
                 as a backend.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic curves; exact geometric computation; generic
                 conditions; Sturm--Habicht sequence; subresultants
                 sequence; topology computation",
}

@InProceedings{Debeerst:2008:SDE,
  author =       "Ruben Debeerst and Mark van Hoeij and Wolfram Koepf",
  title =        "Solving differential equations in terms of {Bessel}
                 functions",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "39--46",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390777",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "For differential operators of order 2, this paper
                 presents a new method that combines generalized
                 exponents to find those solutions that can be
                 represented in terms of Bessel functions.",
  acknowledgement = ack-nhfb,
  keywords =     "Bessel functions; differential equations; generalized
                 exponents",
}

@InProceedings{Din:2008:CGO,
  author =       "Mohab Safey El Din",
  title =        "Computing the global optimum of a multivariate
                 polynomial over the reals",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "71--78",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390781",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $f$ be a polynomial in $Q[X_1, \ldots{}, X_n]$ of
                 degree $D$. We provide an efficient algorithm in
                 practice to compute the global supremum $\sup_{x \in
                 R^n} f(x)$ of $f$ (or its infimum $\inf_{x \in R^n}
                 f(x)$). The complexity of our method is bounded by
                 $D^{O(n)}$. In a probabilistic model, a more precise
                 result yields a complexity bounded by $O(n^7 D^{4n})$
                 arithmetic operations in $Q$. Our implementation is
                 more efficient by several orders of magnitude than
                 previous ones based on quantifier elimination.
                 Sometimes, it can tackle problems that numerical
                 techniques do not reach. Our algorithm is based on the
                 computation of generalized critical values of the
                 mapping $x \rightarrow f(x)$, i.e., the set of points
                 \{$c \in C \mid \exists (x_\ell)_{\ell \in N} \subset
                 C^n f(x_\ell) \rightarrow c$, $||x_\ell ||
                 ||d_{x_\ell}f|| \rightarrow 0$ when $\ell \rightarrow
                 \infty$\}. We prove that the global optimum of $f$ lies
                 in its set of generalized critical values and provide
                 an efficient way of deciding which value is the global
                 optimum.",
  acknowledgement = ack-nhfb,
  keywords =     "complexity; global optimization; polynomial system
                 solving; real solutions",
}

@InProceedings{Dumas:2008:QAT,
  author =       "Jean-Guillaume Dumas",
  title =        "{Q}-adic transform revisited",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "63--70",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390780",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present an algorithm to perform a simultaneous
                 modular reduction of several residues. This enables to
                 compress polynomials into integers and perform several
                 modular operations with machine integer arithmetic. The
                 idea is to convert the $X$-adic representation of
                 modular polynomials, with $X$ an indeterminate, to a
                 $q$-adic representation where $q$ is an integer larger
                 than the field characteristic. With some control on the
                 different involved sizes it is then possible to perform
                 some of the $q$-adic arithmetic directly with machine
                 integers or floating points. Depending also on the
                 number of performed numerical operations one can then
                 convert back to the $q$-adic or X-adic representation
                 and eventually mod out high residues. In this note we
                 present a new version of both conversions: more
                 tabulations and a way to reduce the number of divisions
                 involved in the process are presented. The polynomial
                 multiplication is then applied to arithmetic and linear
                 algebra in small finite field extensions.",
  acknowledgement = ack-nhfb,
  keywords =     "DQT (discrete $q$-adic transform); finite field; FQT
                 (fast $q$-adic transform); Kronecker substitution;
                 modular polynomial multiplication; REDQ (simultaneous
                 modular reduction); small extension field",
}

@InProceedings{Faugere:2008:CPT,
  author =       "Jean-Charles Faug{\`e}re and Guillaume Moroz and
                 Fabrice Rouillier and Mohab Safey El Din",
  title =        "Classification of the perspective-three-point problem,
                 discriminant variety and real solving polynomial
                 systems of inequalities",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "79--86",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390782",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Classifying the Perspective-Three-Point problem
                 (abbreviated by P3P in the sequel) consists in
                 determining the number of possible positions of a
                 camera with respect to the apparent position of three
                 points. In the case where the three points form an
                 isosceles triangle, we give a full classification of
                 the P3P. This leads to consider a polynomial system of
                 polynomial equations and inequalities with 4 parameters
                 which is generically zero-dimensional. In the present
                 situation, the parameters represent the apparent
                 position of the three points so that solving the
                 problem means determining all the possible numbers of
                 real solutions with respect to the parameters' values
                 and give a sample point for each of these possible
                 numbers. One way for solving such systems consists
                 first in computing a {\em discriminant variety}. Then,
                 one has to compute at least one point in each connected
                 component of its real complementary in the parameter's
                 space. The last step consists in specializing the
                 parameters appearing in the initial system by these
                 sample points. Many computational tools may be used for
                 implementing such a general method, starting with the
                 well known Cylindrical Algebraic Decomposition (CAD in
                 short), which provides more information than required.
                 In a first stage, we propose a full algorithm based on
                 the straightforward use of some sophisticated software
                 such as FGb (Gr{\"o}bner bases computations) RS (real
                 roots of zero-dimensional systems), DV (Discriminant
                 varieties) and RAGlib (Critical point methods for
                 semi-algebraic systems). We then improve the global
                 algorithm by refining the required computable
                 mathematical objects and related algorithms and finally
                 provide the classification. Three full days of
                 computation were necessary to get this classification
                 which is obtained from more than 40000 points in the
                 parameter's space.",
  acknowledgement = ack-nhfb,
  keywords =     "complexity; computer vision; perspective-three-point
                 problem; polynomial system solving; real solutions",
}

@InProceedings{Fukuda:2008:EAS,
  author =       "Komei Fukuda",
  title =        "Exact algorithms and software in optimization and
                 polyhedral computation",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "333--334",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390814",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this tutorial, we present a new field of research
                 on implementing exact algorithms in optimization and
                 polyhedral computation in exact (arbitrary precision)
                 arithmetic. Such algorithms including those to solve
                 linear programming and convex hull problems have been
                 implemented mostly with floating-point arithmetic. This
                 new field of developing 'exact software' in
                 optimization and polyhedral computation is now at the
                 second stage where new mathematical tools relying on
                 optimization and polyhedral codes are being developed
                 that have not been implemented before. This tutorial is
                 not meant to cover all important developments but to
                 look at some interesting facets.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; convex geometry; exact implementation;
                 optimization; polytopes",
}

@InProceedings{Gerdt:2008:PDA,
  author =       "Vladimir P. Gerdt and Mikhail V. Zinin",
  title =        "A {Pommaret} division algorithm for computing
                 {Gr{\"o}bner} bases in {Boolean} rings",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "95--102",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390784",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper an involutive algorithm for construction
                 of Gr{\"o}bner bases in Boolean rings is presented. The
                 algorithm exploits the Pommaret monomial division as an
                 involutive division. In distinction to other approaches
                 and due to special properties of Pommaret division the
                 algorithm allows to perform the Gr{\"o}bner basis
                 computation directly in a Boolean ring which can be
                 defined as the quotient ring $F_2 [x_1 ,\ldots{},x_n ],
                 1^2 + x_1 ,\ldots{}, x_n^2 + x_n$. Some related
                 cardinality bounds for Pommaret and Gr{\"o}bner bases
                 are derived. Efficiency of our first implementation of
                 the algorithm is illustrated by a number of serial
                 benchmarks.",
  acknowledgement = ack-nhfb,
  keywords =     "Boolean ring; Gr{\"o}bner basis; involutive algorithm;
                 Pommaret division",
}

@InProceedings{Giesbrecht:2008:LPP,
  author =       "Mark Giesbrecht and Daniel S. Roche",
  title =        "On lacunary polynomial perfect powers",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "103--110",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390785",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider the problem of determining whether a
                 $t$-sparse or lacunary polynomial $f$ is a perfect
                 power, that is, $f = h^r$ for some other polynomial $h$
                 and positive integer $r$, and of finding $h$ and $r$
                 should they exist. We show how to determine if $f$ is a
                 perfect power in time polynomial in the size of the
                 lacunary representation. The algorithm works over
                 GF(q)[x] (at least for large characteristic) and over
                 Z[x], where the cost is also polynomial in the log of
                 the infinity norm of $f$. Subject to a conjecture, we
                 show how to find $h$ if it exists via a kind of sparse
                 Newton iteration, again in time polynomial in the size
                 of the sparse representation. Finally, we demonstrate
                 an implementation using the C++ library NTL.",
  acknowledgement = ack-nhfb,
  keywords =     "black box polynomial; lacunary polynomial; perfect
                 power; sparse polynomial",
}

@InProceedings{Grigoriev:2008:LDT,
  author =       "Dima Grigoriev and Fritz Schwarz",
  title =        "{Loewy} decomposition of third-order linear {PDE}'s in
                 the plane",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "277--286",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390807",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Loewy's decomposition of a linear ordinary
                 differential operator as the product of largest
                 completely reducible components is generalized to
                 partial differential operators of order three in two
                 variables. This is made possible by considering the
                 problem in the ring of partial differential operators
                 where both left intersections and right divisors of
                 left ideals are not necessarily principal. Listings of
                 possible decomposition types are given. Many of them
                 are illustrated by worked out examples. Algorithmic
                 questions and questions of uniqueness are discussed in
                 the Summary.",
  acknowledgement = ack-nhfb,
  keywords =     "factorization; linear partial differential equations;
                 Loewy decomposition",
}

@InProceedings{Henrion:2008:PGC,
  author =       "Didier Henrion and Michael Sebek",
  title =        "Plane geometry and convexity of polynomial stability
                 regions",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "111--116",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390786",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The set of controllers stabilizing a linear system is
                 generally non-convex in the parameter space. In the
                 case of two-parameter controller design (e.g. PI
                 control or static output feedback with one input and
                 two outputs), we observe however that quite often for
                 benchmark problem instances, the set of stabilizing
                 controllers seems to be convex. In this note we use
                 elementary techniques from real algebraic geometry
                 (resultants and Bezoutian matrices) to explain this
                 phenomenon. As a byproduct, we derive a convex linear
                 matrix inequality (LMI) formulation of two-parameter
                 fixed-order controller design problem, when possible.",
  acknowledgement = ack-nhfb,
  keywords =     "control theory; convexity; resultants",
}

@InProceedings{Janovitz-Freireich:2008:MMT,
  author =       "Itnuit Janovitz-Freireich and Agnes Sz{\'a}nt{\'o} and
                 Bernard Mourrain and Lajos Ronyai",
  title =        "Moment matrices, trace matrices and the radical of
                 ideals",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "125--132",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390788",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $f_1, \ldots{}, f_s$ be a system of polynomials in
                 $K[x_1,\ldots{}, x_m]$ generating a zero-dimensional
                 ideal $I$ , where $K$ is an arbitrary algebraically
                 closed field. Assume that the factor algebra $A = K[x_
                 , \ldots{}, x_m] / I$ is Gorenstein and that we have a
                 bound $\delta > 0$ such that a basis for $A$ can be
                 computed from multiples of $f_1,\ldots{}, f_s$ of
                 degrees at most $\delta$. We propose a method using
                 Sylvester or Macaulay type resultant matrices of
                 $f_1,\ldots{}, f_s$ and $J$, where $J$ is a polynomial
                 of degree $\delta$ generalizing the Jacobian, to
                 compute moment matrices, and in particular matrices of
                 traces for $A$. These matrices of traces in turn allow
                 us to compute a system of multiplication matrices
                 $\{Mx_i|i = 1,\ldots{}, m\}$ of the radical of $I$,
                 following the approach in the previous work by
                 Janovitz-Freireich, Ronyai and Szanto. Additionally, we
                 give bounds for delta for the case when $I$ has
                 finitely many projective roots.",
  acknowledgement = ack-nhfb,
  keywords =     "matrices of traces; moment matrices; radical ideal;
                 solving polynomial systems",
}

@InProceedings{Kadyrsizova:2008:LRS,
  author =       "Zhibek Kadyrsizova and Valery G. Romanovski",
  title =        "Linearizablity of $1$:$-3$ resonant system with
                 homogeneous cubic nonlinearities",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "255--260",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390804",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study the systems of differential equations of the
                 form $\dot{x} = x + p(x,y)$, $\dot{y} = -3y + q(x,y)$,
                 where $p$ and $q$ are homogeneous polynomials of degree
                 three (either of which may be zero). The necessary and
                 sufficient coefficient conditions for linearization of
                 such systems are obtained.",
  acknowledgement = ack-nhfb,
  keywords =     "normal forms; ordinary differential equations;
                 polynomial ideals; the center and linearizability
                 problems",
}

@InProceedings{Kaltofen:2008:ECG,
  author =       "Erich Kaltofen and Bin Li and Zhengfeng Yang and
                 Lihong Zhi",
  title =        "Exact certification of global optimality of
                 approximate factorizations via rationalizing
                 sums-of-squares with floating point scalars",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "155--164",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390792",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We generalize the technique by Peyrl and Parillo
                 [Proc. SNC 2007] to computing lower bound certificates
                 for several well-known factorization problems in hybrid
                 symbolic-numeric computation. The idea is to transform
                 a numerical sum-of-squares (SOS) representation of a
                 positive polynomial into an exact rational identity.
                 Our algorithms successfully certify accurate rational
                 lower bounds near the irrational global optima for
                 benchmark approximate polynomial greatest common
                 divisors and multivariate polynomial irreducibility
                 radii from the literature, and factor coefficient
                 bounds in the setting of a model problem by Rump (up to
                 $n = 14$, factor degree $= 13$).\par

                 The numeric SOSes produced by the current fixed
                 precision semi-definite programming (SDP) packages
                 (SeDuMi, SOSTOOLS, YALMIP) are usually too coarse to
                 allow successful projection to exact SOSes via Maple
                 11's exact linear algebra. Therefore, before projection
                 we refine the SOSes by rank-preserving Newton
                 iteration. For smaller problems the starting SOSes for
                 Newton can be guessed without SDP (`SDP-free SOS'), but
                 for larger inputs we additionally appeal to sparsity
                 techniques in our SDP formulation.",
  acknowledgement = ack-nhfb,
  keywords =     "approximate factorization; hybrid method; semidefinite
                 programming; sum-of-squares; validated output",
}

@InProceedings{Kaltofen:2008:EFT,
  author =       "Erich Kaltofen and Pascal Koiran",
  title =        "Expressing a fraction of two determinants as a
                 determinant",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "141--146",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390790",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Suppose the polynomials $f$ and $g$ in $K[x_1,
                 \ldots{}, x_r]$ over the field $K$ are determinants of
                 non-singular $m \times m$ and $n \times n$ matrices,
                 respectively, whose entries are in $K \cup x_1,
                 \ldots{}, x_r$. Furthermore, suppose $h = f/g$ is a
                 polynomial in $K[x_1, \ldots{}, x_r]$. We construct an
                 $s \times s$ matrix $C$ whose entries are in $K \cup
                 x_1,\ldots{}, x_r$, such that $h = \det(C)$ and $s =
                 \gamma(m+n)^6$, where $\gamma = O(1)$ if $K$ is an
                 infinite field or if for the finite field $K = F\{q\}$
                 with $q$ elements we have $m = O(q)$, and where $\gamma
                 = (\log_q m)^{1 + o(1)}$ if $q = o(m)$. Our
                 construction utilizes the notion of skew circuits by
                 Toda and WSK circuits by Malod and Portier. Our problem
                 was motivated by resultant formulas derived from Chow
                 forms.\par

                 Additionally, we show that divisions can be removed
                 from formulas that compute polynomials in the input
                 variables over a sufficiently large field within
                 polynomial formula size growth.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic complexity theory; formula complexity;
                 Strassen's removal of divisions; Toda's skew circuits;
                 Valiant's universality of determinants",
}

@InProceedings{Kanno:2008:SOA,
  author =       "Masaaki Kanno and Kazuhiro Yokoyama and Hirokazu Anai
                 and Shinji Hara",
  title =        "Symbolic optimization of algebraic functions",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "147--154",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390791",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper attempts to establish a new framework of
                 symbolic optimization of algebraic functions that is
                 relevant to possibly a wide variety of practical
                 application areas. The crucial aspects of the framework
                 are (i) the suitable use of algebraic methods coupled
                 with the discovery and exploitation of structural
                 properties of the problem in the conversion process
                 into the framework, and (ii) the feasibility of
                 algebraic methods when performing the optimization. As
                 an example an algebraic approach is developed for the
                 discrete-time polynomial spectral factorization problem
                 that illustrates the significance and relevance of the
                 proposed framework. A numerical example of a particular
                 control problem is also included to demonstrate the
                 development.",
  acknowledgement = ack-nhfb,
  keywords =     "Gr{\"o}bner basis; parametric optimization; polynomial
                 spectral factorization; quantifier elimination",
}

@InProceedings{Kauers:2008:IAF,
  author =       "Manuel Kauers",
  title =        "Integration of algebraic functions: a simple heuristic
                 for finding the logarithmic part",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "133--140",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390789",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A new method is proposed for finding the logarithmic
                 part of an integral over an algebraic function. The
                 method uses Groebner bases and is easy to implement. It
                 does not have the feature of finding a closed form of
                 an integral whenever there is one. But it very often
                 does, as we will show by a comparison with the built-in
                 integrators of some computer algebra systems.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic functions; symbolic integration",
}

@InProceedings{Kemper:2008:AIT,
  author =       "Gregor Kemper",
  title =        "Algorithmic invariant theory",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "335--336",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390815",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computational commutative algebra; invariant theory",
}

@InProceedings{Lemaire:2008:WDE,
  author =       "Francois Lemaire and Marc Moreno Maza and Wei Pan and
                 Yuzhen Xie",
  title =        "When does $({T})$ equal {${\rm Sat}(T)$}?",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "207--214",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390798",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Given a regular chain $T$, we aim at finding an
                 efficient way for computing a system of generators of
                 ${\rm Sat}(T)$, the saturated ideal of $T$. A natural
                 idea is to test whether the equality $(T) = {\rm
                 Sat}(T)$ holds, that is, whether $T$ generates its
                 saturated ideal. By generalizing the notion of
                 primitivity from univariate polynomials to regular
                 chains, we establish a necessary and sufficient
                 condition, together with a Gr{\"o}bner basis free
                 algorithm, for testing this equality. Our experimental
                 results illustrate the efficiency of this approach in
                 practice.",
  acknowledgement = ack-nhfb,
  keywords =     "megasquid; primitivity of polynomials; regular chain;
                 saturated ideal",
}

@InProceedings{Levandovskyy:2008:CMT,
  author =       "Viktor Levandovskyy and Jorge Martin Morales",
  title =        "Computational {$D$}-module theory with singular,
                 comparison with other systems and two new algorithms",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "173--180",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390794",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present the new implementation of core functions
                 for the computational $D$-module theory. It is realized
                 as a library {\tt dmod.lib} in the computer algebra
                 system Singular. We show both theoretical advances,
                 such as the LOT and checkRoot algorithms as well as the
                 comparison of our implementation with other packages
                 for $D$-modules in computer algebra systems kan/sm1,
                 Asir and Macaulay. The comparison indicates, that our
                 implementation is among the fastest ones. With our
                 package we are able to solve several challenges in
                 D-module theory and we demonstrate the answers to these
                 problems.",
  acknowledgement = ack-nhfb,
  keywords =     "annihilator; Bernstein--Sato polynomial; D-modules;
                 Gr{\"o}bner bases; intersection with subalgebra;
                 non-commutative Gr{\"o}bner bases; preimage of ideal",
}

@InProceedings{Leykin:2008:NPD,
  author =       "Anton Leykin",
  title =        "Numerical primary decomposition",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "165--172",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390793",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Consider an ideal $I \subset R = C[x_1, \ldots{},
                 x_n]$ defining a complex affine variety $X \subset
                 C^n$. We describe the components associated to $I$ by
                 means of {\em numerical primary decomposition\/} (NPD).
                 The method is based on the construction of {\em
                 deflation ideal\/} $I^{(d)}$ that defines the {\em
                 deflated variety\/} $X^{(d)}$ in a complex space of
                 higher dimension. For every embedded component there
                 exists $d$ and an isolated component $Y^{(d)}$ of
                 $I^{(d)}$ projecting onto $Y$. In turn, $Y^{(d)}$ can
                 be discovered by existing methods for prime
                 decomposition, in particular, the {\em numerical
                 irreducible decomposition}, applied to $X^{(d)}$. The
                 concept of NPD gives a full description of the scheme
                 Spec(R/I) by representing each component with a {\em
                 witness set}. We propose an algorithm to produce a
                 collection of witness sets that contains a NPD and that
                 can be used to solve the {\em ideal membership
                 problem\/} for $I$.",
  acknowledgement = ack-nhfb,
  keywords =     "deflation; numerical algebraic geometry; polynomial
                 homotopy continuation; primary decomposition",
}

@InProceedings{Li:2008:CBB,
  author =       "Hongbo Li and Lei Huang",
  title =        "Complex brackets, balanced complex differences, and
                 applications in symbolic geometric computing",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "181--188",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390795",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In advanced invariant algebras such as null bracket
                 algebra (NBA), symmetries of algebraic operators are
                 the most important devices of encoding and employing
                 syzygies of advanced geometric invariants. The larger
                 the symmetry group, the more powerful the computing
                 devices. In this paper, the largest symmetry group of
                 the two kinds of bracket operators in the NBA of plane
                 geometry is found. An algorithm of complexity $O(N \log
                 N)$ is proposed to reduce a bracket of length $N$ to
                 its normal form, and then decide the congruence of two
                 brackets of length $N$. By writing the two bracket
                 operators as the real and pure imaginary parts of a
                 complex bracket operator, their normal forms can be
                 translated into a class of complex polynomials whose
                 variables are first-order differences, called balanced
                 complex difference (BCD) polynomials. BCD polynomials
                 provide a complex-numbers-based invariant language for
                 advanced algebraic manipulations of geometric problems.
                 A simplification algorithm is proposed for making
                 symbolic geometric computing with NBA and BCD
                 polynomials, with the unique feature of controlling the
                 expression size by avoiding multilinear expansions of
                 the first-order difference variables of complex
                 polynomials.",
  acknowledgement = ack-nhfb,
  keywords =     "bracket algebra; complex numbers method; geometric
                 algebra; graph theory; theorem proving",
}

@InProceedings{Liang:2008:CRC,
  author =       "Songxin Liang and David J. Jeffrey and Marc Moreno
                 Maza",
  title =        "The complete root classification of a parametric
                 polynomial on an interval",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "189--196",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390796",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Given a real parametric polynomial $p(x)$ and an
                 interval $(a,b) \subset R$, the Complete Root
                 Classification (CRC) of $p(x)$ on $(a,b)$ is a
                 collection of all possible cases of its root
                 classification on $(a,b)$, together with the conditions
                 its coefficients must satisfy for each case. In this
                 paper, a new algorithm is proposed for the automatic
                 computation of the complete root classification of a
                 parametric polynomial on an interval. As a direct
                 application, the new algorithm is applied to some real
                 quantifier elimination problems.",
  acknowledgement = ack-nhfb,
  keywords =     "complete root classification; interval; parametric
                 polynomial; real quantifier elimination; real root",
}

@InProceedings{Loera:2008:HNA,
  author =       "J. A. De Loera and J. Lee and P. N. Malkin and S.
                 Margulies",
  title =        "{Hilbert}'s {Nullstellensatz} and an algorithm for
                 proving combinatorial infeasibility",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "197--206",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390797",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Systems of polynomial equations over an
                 algebraically-closed field $K$ can be used to concisely
                 model many combinatorial problems. In this way, a
                 combinatorial problem is feasible (e.g., a graph is
                 3-colorable, Hamiltonian, etc.) if and only if a
                 related system of polynomial equations has a solution
                 over $K$. In this paper, we investigate an algorithm
                 aimed at proving combinatorial infeasibility based on
                 the observed low degree of Hilbert's Nullstellensatz
                 certificates for polynomial systems arising in
                 combinatorics and on large-scale linear-algebra
                 computations over $K$. We report on experiments based
                 on the problem of proving the non-3-colorability of
                 graphs. We successfully solved graph problem instances
                 having thousands of nodes and tens of thousands of
                 edges.",
  acknowledgement = ack-nhfb,
  keywords =     "Nullstellensatz",
}

@InProceedings{Mansfield:2008:DAD,
  author =       "Elizabeth L. Mansfield",
  title =        "Digital atlases and difference forms",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "3--4",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390770",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "When integrating a differential equation numerically,
                 it can be important for the solution method to reflect
                 the geometric properties of the original model. These
                 include conservation laws and first integrals,
                 symmetries, and symplectic or variational structures.
                 Thus there is an increasingly sophisticated subject of
                 'geometric integration' concentrating mostly on local
                 properties of the equation.\par

                 This talk is concerned with ways of ensuring that
                 finite difference schemes accurately mirror {\em
                 global\/} properties. To this end, lattice varieties
                 are introduced on which finite difference schemes
                 amongst others may be defined. There is no assumption
                 of continuity, or that either the lattice variety or
                 the difference systems have a continuum limit; our
                 theory is more general than that of cubical complexes,
                 and the proofs require a different foundation.\par

                 We show that the global structure of a lattice variety
                 can be determined from its digital atlas. This is
                 important for two reasons. First, if the digital atlas
                 has the same 'system of intersections' as that of the
                 smooth model it approximates, you are guaranteed the
                 same global information. Secondly, since our proofs are
                 independent of any continuum limit, global information
                 for inherently discrete models may be obtained. The
                 techniques used are algebraic, specifically homological
                 algebra, which amounts to linear algebra.\par

                 This talk has two meta-messages: (1) Continuity is an
                 illusion. (2) If you want to capture analytic
                 structures in discrete models successfully, cherchez
                 l'alg{\`e}bre.\par

                 No particular expertise is assumed for this talk, which
                 is based on the paper, Difference Forms by Elizabeth L.
                 Mansfield and Peter E. Hydon, to appear in Foundations
                 of Computational Mathematics.",
  acknowledgement = ack-nhfb,
  keywords =     "cohomology; difference chains; difference forms;
                 lattice variety; local difference potentials; local
                 exactness; symbolic numeric methods",
}

@InProceedings{Peternell:2008:GSS,
  author =       "Martin Peternell and Boris Odehnal",
  title =        "On generalized $\ln$-surfaces in $4$-space",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "223--230",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390800",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The present paper investigates a class of
                 two-dimensional rational surfaces &\#966; in {\em
                 R\/}$^4$ whose tangent planes satisfy the following
                 property: For any three-space {\em E\/} in {\em
                 R\/}$^4$ there exists a unique tangent plane {\em T\/}
                 of &\#966; which is parallel to {\em E}. The most
                 interesting families of surfaces are constructed
                 explicitly and geometric properties of these surfaces
                 are derived. Quadratically parameterized surfaces in
                 {\em R\/}$^4$ occur as special cases. This construction
                 generalizes the concept of LN-surfaces in {\em R\/}$^3$
                 to two-dimensional surfaces in {\em R\/}$^4$.",
  acknowledgement = ack-nhfb,
  keywords =     "chordal variety; linear congruence of lines;
                 ln-surface; quadratically parameterized surface;
                 rational parameterization.",
}

@InProceedings{Pfluegel:2008:RDL,
  author =       "Eckhard Pfl{\"u}egel",
  title =        "A rational decomposition-lemma for systems of linear
                 differential-algebraic equations",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "231--238",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390801",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We give a new decomposition lemma for linear
                 differential-algebraic equations (DAEs). This
                 generalises a result which we have given in [12] for
                 singular linear systems of ordinary differential
                 equations to the class of linear DAEs with formal power
                 series coefficients. The results of this paper are a
                 first step towards a formal reduction algorithm for
                 this type of equations.",
  acknowledgement = ack-nhfb,
  keywords =     "computer algebra; linear daes; local reduction;
                 splitting lemma",
}

@InProceedings{Poteaux:2008:GRP,
  author =       "Adrien Poteaux and Marc Rybowicz",
  title =        "Good reduction of {Puiseux} series and complexity of
                 the {Newton--Puiseux} algorithm over finite fields",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "239--246",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390802",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In [12], we sketched a numeric-symbolic method to
                 compute Puiseux series with floating point
                 coefficients. In this paper, we address the symbolic
                 part of our algorithm. We study the reduction of
                 Puiseux series coefficients modulo a prime ideal and
                 prove a good reduction criterion sufficient to preserve
                 the required information, namely Newton polygon trees.
                 We introduce a convenient modification of Newton
                 polygons that greatly simplifies proofs and statements
                 of our results. Finally, we improve complexity bounds
                 for Puiseux series calculations over finite fields, and
                 estimate the bit-complexity of polygon tree
                 computation.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic functions; complexity; finite fields;
                 modular methods; Puiseux series; symbolic-numeric
                 algorithms",
}

@InProceedings{Renault:2008:MMA,
  author =       "Gu{\'e}na{\"e}l Renault and Kazuhiro Yokoyama",
  title =        "Multi-modular algorithm for computing the splitting
                 field of a polynomial",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "247--254",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390803",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $f$ be a univariate monic integral polynomial of
                 degree $n$ and let $(\alpha_1, \ldots{}, \alpha_n)$ be
                 an $n$-tuple of its roots in an algebraic closure $Q$
                 of $Q$. Obtaining an algebraic representation of the
                 splitting field $Q(\alpha_1, \ldots{}, \alpha_n)$ of
                 $f$ is a question of first importance in effective
                 Galois theory. For instance, it allows us to manipulate
                 symbolically the roots of $f$. In this paper, we
                 propose a new method based on multi-modular strategy.
                 Actually, we provide algorithms for this task which
                 return a triangular set encoding the {\em splitting
                 ideal\/} of $f$. We examine the ability\slash
                 practicality of the method by experiments on a real
                 computer and study its complexity.",
  acknowledgement = ack-nhfb,
  keywords =     "Galois theory; splitting field",
}

@InProceedings{Rosenkranz:2008:IDP,
  author =       "Markus Rosenkranz and Georg Regensburger",
  title =        "Integro-differential polynomials and operators",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "261--268",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390805",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We propose two algebraic structures for treating
                 integral operators in conjunction with derivations: The
                 algebra of integro-differential polynomials describes
                 nonlinear integral and differential operators together
                 with initial values. The algebra of
                 integro-differential operators can be used to solve
                 boundary problems for linear ordinary differential
                 equations. In both cases, we describe canonical/normal
                 forms with algorithmic simplifiers.",
  acknowledgement = ack-nhfb,
  keywords =     "Green's operators; integral operators;
                 integro-differential algebras; linear boundary value
                 problems; noncommutative Gr{\"o}bner bases",
}

@InProceedings{Sekigawa:2008:NPZ,
  author =       "Hiroshi Sekigawa",
  title =        "The nearest polynomial with a zero in a given domain
                 from a geometrical viewpoint",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "287--294",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390808",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "For a real univariate polynomial $f$ and a closed
                 complex domain $D$, whose boundary $C$ is a simple
                 curve parameterized by a univariate piecewise rational
                 function, a rigorous method is given for finding a real
                 univariate polynomial $f$ such that $f$ has a zero in
                 $D$ and $||f - \tilde{f}||\infty$ is minimal. First, it
                 is proved that the minimum distance between $f$ and
                 polynomials having a zero at $\alpha \in C$ is a
                 piecewise rational function of the real and imaginary
                 parts of $\alpha$. Thus, on $C$, the minimum distance
                 is a piecewise rational function of a parameter
                 obtained through the parameterization of $C$.
                 Therefore, by using the property that $\tilde{f}$ has a
                 zero on $C$ and computing the minimum distance on $C$,
                 $\tilde{f}$ can be constructed.",
  acknowledgement = ack-nhfb,
  keywords =     "$l\infty$-norm; Davenport--Schinzel sequence;
                 perturbation; polynomial; zero",
}

@InProceedings{Shemyakova:2008:MFL,
  author =       "Ekaterina Shemyakova and Elizabeth L. Mansfield",
  title =        "Moving frames for {Laplace} invariants",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "295--302",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390809",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The development of symbolic methods for the
                 factorization and integration of linear PDEs, many of
                 the methods being generalizations of the Laplace
                 transformations method, requires the finding of
                 complete generating sets of invariants for the
                 corresponding linear operators and their systems with
                 respect to the gauge transformations $L -> g(x,y)^{-1}
                 O L O g(x,y)$. Within the theory of Laplace-like
                 methods, there is no uniform approach to this problem,
                 though some individual invariants for hyperbolic
                 bivariate operators, and complete generating sets of
                 invariants for second- and third-order hyperbolic
                 bivariate ones have been obtained. Here we demonstrate
                 a systematic and much more efficient approach to the
                 same problem by application of moving-frame methods. We
                 give explicit formulae for complete generating sets of
                 invariants for second- and third-order bivariate linear
                 operators, hyperbolic and non-hyperbolic, and also
                 demonstrate the approach for pairs of operators
                 appearing in Darboux transformations.",
  acknowledgement = ack-nhfb,
  keywords =     "gauge transformations; invariants; moving frames;
                 partial differential operators",
}

@InProceedings{Stein:2008:CWC,
  author =       "William A. Stein",
  title =        "Can we create a viable free open source alternative to
                 {Magma}, {Maple}, {Mathematica} and {Matlab}?",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "5--6",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390771",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The goal of the Sage project ({\tt
                 http://sagemath.org}) is to create a truly viable free
                 open source alternative to Magma, Maple, Mathematica
                 and Matlab. Is this possible?",
  acknowledgement = ack-nhfb,
  keywords =     "free; Magma; Maple; Mathematica; Matlab; open source",
}

@InProceedings{Strzebonski:2008:RRI,
  author =       "Adam Strzebonski",
  title =        "Real root isolation for $\exp$-$\log$ functions",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "303--314",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390810",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a real root isolation procedure for
                 univariate functions obtained by composition and
                 rational operations from exp, log, and real constants.
                 We discuss implementation of the procedure and give
                 empirical results. The procedure requires the ability
                 to determine signs of $\exp$-$\log$ functions at simple
                 roots of other $\exp$-$\log$ functions. The currently
                 known method to do this depends on Schanuel's
                 conjecture [6].",
  acknowledgement = ack-nhfb,
  keywords =     "$\exp$-$\log$ functions; real root isolation; solving
                 equations",
}

@InProceedings{Sudan:2008:AAC,
  author =       "Madhu Sudan",
  title =        "Algebraic algorithms and coding theory",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "337--337",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390816",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The associated talk surveys some recent developments
                 in algorithmic coding theory that answer some
                 fundamental questions with algebraic techniques.",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic algorithms; error correcting codes",
}

@InProceedings{Wang:2008:IPQ,
  author =       "Xuhui Wang and Falai Chen and Jiansong Deng",
  title =        "Implicitization and parametrization of quadratic
                 surfaces with one simple base point",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "31--38",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390776",
  bibdate =      "Tue Aug 5 18:10:09 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper discusses implicitization and
                 parametrization of quadratic surfaces with one simple
                 base point. The key point to fulfill the conversion
                 between the implicit and the parametric form is to
                 compute three linearly independent moving planes which
                 we call the weak u-basis of the quadratic surface.
                 Beginning with the parametric form, it is easy to
                 compute the weak u-basis, and then to find its implicit
                 equation. Inversion formulas can also be obtained
                 easily from the weak u-basis. For conversion from the
                 implicit into the parametric form, we present a method
                 based on the observation that there exists one
                 self-intersection line on a quadratic surface with one
                 base point. After computing the self-intersection line,
                 we are able to derive the weak u-basis, from which the
                 parametric equation can be easily obtained. A method is
                 also presented to compute the self-intersection line of
                 a quadratic surface with one base point.",
  acknowledgement = ack-nhfb,
  keywords =     "implicitization; moving plane; parametrization; weak
                 u-basis",
}

@InProceedings{Wu:2008:CMS,
  author =       "Xiaoli Wu and Lihong Zhi",
  title =        "Computing the multiplicity structure from geometric
                 involutive form",
  crossref =     "Jeffrey:2008:PAM",
  pages =        "325--332",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1390768.1390812",
  bibdate =      "Wed Aug 6 09:11:59 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a method based on symbolic-numeric
                 reduction to geometric involutive form to compute the
                 primary component and the differential operators $f$
                 solution of a polynomial ideal. The singular solution
                 can be exact or approximate. If the singular solution
                 is known with limited accuracy, then we propose a new
                 method to refine it to high accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "involutive system; numerical linear algebra",
}

@InProceedings{Andres:2009:PIB,
  author =       "Daniel Andres and Viktor Levandovskyy and Jorge
                 Mart{\`\i}n Morales",
  title =        "Principal intersection and {Bernstein--Sato}
                 polynomial of an affine variety",
  crossref =     "May:2009:PIS",
  pages =        "231--238",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:2009:ARS,
  author =       "Moulay A. Barkatou and Thomas Cluzeau and Carole El
                 Bacha",
  title =        "Algorithms for regular solutions of higher-order
                 linear differential systems",
  crossref =     "May:2009:PIS",
  pages =        "7--14",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beckermann:2009:FFC,
  author =       "Bernhard Beckermann and George Labahn",
  title =        "Fraction-free computation of simultaneous {Pad{\'e}}
                 approximants",
  crossref =     "May:2009:PIS",
  pages =        "15--22",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Benoit:2009:CES,
  author =       "Alexandre Benoit and Bruno Salvy",
  title =        "{Chebyshev} expansions for solutions of linear
                 differential equations",
  crossref =     "May:2009:PIS",
  pages =        "23--30",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bigatti:2009:CSK,
  author =       "Anna M. Bigatti and Eduardo S{\'a}enz-de-Cabez{\'o}n",
  title =        "Computation of the $(n-1)$-st {Koszul Homology} of
                 monomial ideals and related algorithms",
  crossref =     "May:2009:PIS",
  pages =        "31--38",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bihan:2009:FRF,
  author =       "Fr{\'e}d{\'e}ric Bihan and J. Maurice Rojas and Casey
                 E. Stella",
  title =        "Faster real feasibility via circuit discriminants",
  crossref =     "May:2009:PIS",
  pages =        "39--46",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2009:FAD,
  author =       "Alin Bostan and {\'E}ric Schost",
  title =        "Fast algorithms for differential equations in positive
                 characteristic",
  crossref =     "May:2009:PIS",
  pages =        "47--54",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boyer:2009:MES,
  author =       "Brice Boyer and Jean-Guillaume Dumas and Cl{\'e}ment
                 Pernet and Wei Zhou",
  title =        "Memory efficient scheduling of {Strassen--Winograd}'s
                 matrix multiplication algorithm",
  crossref =     "May:2009:PIS",
  pages =        "55--62",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:2009:FST,
  author =       "Christopher W. Brown",
  title =        "Fast simplifications for {Tarski} formulas",
  crossref =     "May:2009:PIS",
  pages =        "63--70",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brownawell:2009:LBZ,
  author =       "W. Dale Brownawell and Chee K. Yap",
  title =        "Lower bounds for zero-dimensional projections",
  crossref =     "May:2009:PIS",
  pages =        "79--86",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cha:2009:LSI,
  author =       "Yongjae Cha and Mark van Hoeij",
  title =        "{Liouvillian} solutions of irreducible linear
                 difference equations",
  crossref =     "May:2009:PIS",
  pages =        "87--94",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2009:CCA,
  author =       "Changbo Chen and Marc Moreno Maza and Bican Xia and Lu
                 Yang",
  title =        "Computing cylindrical algebraic decomposition via
                 triangular decomposition",
  crossref =     "May:2009:PIS",
  pages =        "95--102",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cheng:2009:RIB,
  author =       "Jin-San Cheng and Xiao-Shan Gao and Jia Li",
  title =        "Root isolation for bivariate polynomial systems with
                 local generic position method",
  crossref =     "May:2009:PIS",
  pages =        "103--110",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chyzak:2009:NHS,
  author =       "Fr{\'e}d{\'e}ric Chyzak and Manuel Kauers and Bruno
                 Salvy",
  title =        "A non-holonomic systems approach to special function
                 identities",
  crossref =     "May:2009:PIS",
  pages =        "111--118",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dahan:2009:SCL,
  author =       "Xavier Dahan",
  title =        "Size of coefficients of lexicographical {Gr{\"o}bner}
                 bases: the zero-dimensional, radical and bivariate
                 case",
  crossref =     "May:2009:PIS",
  pages =        "119--126",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dumas:2009:FMC,
  author =       "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and B.
                 David Saunders",
  title =        "On finding multiplicities of characteristic polynomial
                 factors of black-box matrices",
  crossref =     "May:2009:PIS",
  pages =        "135--142",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Emiris:2009:MRF,
  author =       "Ioannis Z. Emiris and Angelos A. Mantzaflaris",
  title =        "Multihomogeneous resultant formulae for systems with
                 scaled support",
  crossref =     "May:2009:PIS",
  pages =        "143--150",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{FaugAre:2009:HOD,
  author =       "Jean-Charles Faug{\`e}re and Ludovic Perret",
  title =        "High order derivatives and decomposition of
                 multivariate polynomials",
  crossref =     "May:2009:PIS",
  pages =        "207--214",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{FaugAre:2009:SSP,
  author =       "Jean-Charles Faug{\`e}re and Sajjad Rahmany",
  title =        "Solving systems of polynomial equations with
                 symmetries using {SAGBI-Gr{\"o}bner} bases",
  crossref =     "May:2009:PIS",
  pages =        "151--158",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2009:IBC,
  author =       "Jean-Charles Faug{\`e}re",
  title =        "Interactions between computer algebra ({Gr{\"o}bner}
                 bases) and cryptology",
  crossref =     "May:2009:PIS",
  pages =        "383--384",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Feo:2009:FAA,
  author =       "Luca De Feo and {\'E}ric Schost",
  title =        "Fast arithmetics in {Artin--Schreier} towers over
                 finite fields",
  crossref =     "May:2009:PIS",
  pages =        "127--134",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giusti:2009:GAF,
  author =       "Marc Giusti",
  title =        "A {Gr{\"o}bner} free alternative to solving and a
                 geometric analogue to {Cook}'s thesis",
  crossref =     "May:2009:PIS",
  pages =        "1--2",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gonzalez-Sanchez:2009:AGB,
  author =       "Jon Gonzalez-Sanchez and Laureano Gonzalez-Vega and
                 Alejandro Pi{\~n}era-Nicolas and Irene Polo-Blanco and
                 Jorge Caravantes and Ignacio F. Rua",
  title =        "Analyzing group based matrix multiplication
                 algorithms",
  crossref =     "May:2009:PIS",
  pages =        "159--166",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Graillat:2009:NAC,
  author =       "Stef Graillat and Philippe Tr{\'e}buchet",
  title =        "A new algorithm for computing certified numerical
                 approximations of the roots of a zero-dimensional
                 system",
  crossref =     "May:2009:PIS",
  pages =        "167--174",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{HalAs:2009:SRD,
  author =       "Miroslav Hal{\'a}s and {\"U}lle Kotta and Ziming Li
                 and Huaifu Wang and Chunming Yuan",
  title =        "Submersive rational difference systems and their
                 accessibility",
  crossref =     "May:2009:PIS",
  pages =        "175--182",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hong:2009:VRQ,
  author =       "Hoon Hong and Mohab Safey El Din",
  title =        "Variant real quantifier elimination: algorithm and
                 application",
  crossref =     "May:2009:PIS",
  pages =        "183--190",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ida:2009:SAM,
  author =       "Tetsuo Ida",
  title =        "Symbolic and algebraic methods in computational
                 origami: invited talk",
  crossref =     "May:2009:PIS",
  pages =        "3--4",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ivanyos:2009:SDP,
  author =       "G{\'a}bor Ivanyos and Marek Karpinski and Nitin
                 Saxena",
  title =        "Schemes for deterministic polynomial factoring",
  crossref =     "May:2009:PIS",
  pages =        "191--198",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Javadi:2009:FMP,
  author =       "Seyed Mohammad Mahdi Javadi and Michael B. Monagan",
  title =        "On factorization of multivariate polynomials over
                 algebraic number and function fields",
  crossref =     "May:2009:PIS",
  pages =        "199--206",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kanno:2009:SAR,
  author =       "Masaaki Kanno and Kazuhiro Yokoyama and Hirokazu Anai
                 and Shinji Hara",
  title =        "Solution of algebraic {Riccati} equations using the
                 sum of roots",
  crossref =     "May:2009:PIS",
  pages =        "215--222",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kunkle:2009:BTF,
  author =       "Daniel Kunkle and Gene Cooperman",
  title =        "Biased tadpoles: a fast algorithm for centralizers in
                 large matrix groups",
  crossref =     "May:2009:PIS",
  pages =        "223--230",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2009:CMR,
  author =       "Xin Li and Marc Moreno Maza and Wei Pan",
  title =        "Computations modulo regular chains",
  crossref =     "May:2009:PIS",
  pages =        "239--246",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{McCallum:2009:DVC,
  author =       "Scott McCallum and Christopher W. Brown",
  title =        "On delineability of varieties in {CAD}-based
                 quantifier elimination with two equational
                 constraints",
  crossref =     "May:2009:PIS",
  pages =        "71--78",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mehlhorn:2009:IRR,
  author =       "Kurt Mehlhorn and Michael Sagraloff",
  title =        "Isolating real roots of real polynomials",
  crossref =     "May:2009:PIS",
  pages =        "247--254",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mevissen:2009:SPS,
  author =       "Martin Mevissen and Kosuke Yokoyama and Nobuki
                 Takayama",
  title =        "Solutions of polynomial systems derived from the
                 steady cavity flow problem",
  crossref =     "May:2009:PIS",
  pages =        "255--262",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monagan:2009:PSP,
  author =       "Michael Monagan and Roman Pearce",
  title =        "Parallel sparse polynomial multiplication using
                 heaps",
  crossref =     "May:2009:PIS",
  pages =        "263--270",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Morel:2009:HLU,
  author =       "Ivan Morel and Damien Stehl{\'e} and Gilles Villard",
  title =        "{H-LLL}: using {Householder} inside {LLL}",
  crossref =     "May:2009:PIS",
  pages =        "271--278",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Orange:2009:CSS,
  author =       "S{\'e}bastien Orange and Gu{\'e}na{\"e}l Renault and
                 Kazuhiro Yokoyama",
  title =        "Computation schemes for splitting fields of
                 polynomials",
  crossref =     "May:2009:PIS",
  pages =        "279--286",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Paschel:2009:ASH,
  author =       "Markus P{\"a}schel",
  title =        "Automatic synthesis of high performance mathematical
                 programs",
  crossref =     "May:2009:PIS",
  pages =        "5--6",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Regensburger:2009:SPA,
  author =       "Georg Regensburger and Markus Rosenkranz and Johannes
                 Middeke",
  title =        "A skew polynomial approach to integro-differential
                 operators",
  crossref =     "May:2009:PIS",
  pages =        "287--294",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Roche:2009:STE,
  author =       "Daniel S. Roche",
  title =        "Space- and time-efficient polynomial multiplication",
  crossref =     "May:2009:PIS",
  pages =        "295--302",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Romero:2009:IBC,
  author =       "Ana Romero and Graham Ellis and Julio Rubio",
  title =        "Interoperating between computer algebra systems:
                 computing homology of groups with {\tt kenzo} and
                 {GAP}",
  crossref =     "May:2009:PIS",
  pages =        "303--310",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sato:2009:CIR,
  author =       "Yosuke Sato and Akira Suzuki",
  title =        "Computation of inverses in residue class rings of
                 parametric polynomial ideals",
  crossref =     "May:2009:PIS",
  pages =        "311--316",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Saunders:2009:LMS,
  author =       "B. David Saunders and Bryan S. Youse",
  title =        "Large matrix, small rank",
  crossref =     "May:2009:PIS",
  pages =        "317--324",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schweighofer:2009:DCS,
  author =       "Markus Schweighofer",
  title =        "Describing convex semialgebraic sets by linear matrix
                 inequalities",
  crossref =     "May:2009:PIS",
  pages =        "385--386",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sexton:2009:CAM,
  author =       "Alan P. Sexton and Volker Sorge and Stephen M. Watt",
  title =        "Computing with abstract matrix structures",
  crossref =     "May:2009:PIS",
  pages =        "325--332",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Storjohann:2009:IMR,
  author =       "Arne Storjohann",
  title =        "Integer matrix rank certification",
  crossref =     "May:2009:PIS",
  pages =        "333--340",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Strzebonski:2009:RRI,
  author =       "Adam Strzebonski",
  title =        "Real root isolation for tame elementary functions",
  crossref =     "May:2009:PIS",
  pages =        "341--350",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Terui:2009:IMC,
  author =       "Akira Terui",
  title =        "An iterative method for calculating approximate {GCD}
                 of univariate polynomials",
  crossref =     "May:2009:PIS",
  pages =        "351--358",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:2009:NDU,
  author =       "Joachim von zur Gathen",
  title =        "The number of decomposable univariate polynomials.
                 extended abstract",
  crossref =     "May:2009:PIS",
  pages =        "359--366",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yap:2009:ENC,
  author =       "Chee K. Yap",
  title =        "Exact numerical computation in algebra and geometry",
  crossref =     "May:2009:PIS",
  pages =        "387--388",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zeng:2009:AIF,
  author =       "Zhonggang Zeng",
  title =        "The approximate irreducible factorization of a
                 univariate polynomial: revisited",
  crossref =     "May:2009:PIS",
  pages =        "367--374",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhou:2009:ECO,
  author =       "Wei Zhou and George Labahn",
  title =        "Efficient computation of order bases",
  crossref =     "May:2009:PIS",
  pages =        "375--382",
  year =         "2009",
  bibdate =      "Tue Aug 11 18:45:25 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2010:SDU,
  author =       "S. A. Abramov",
  title =        "On some decidable and undecidable problems related to
                 $q$-difference equations with parameters",
  crossref =     "Watt:2010:IPI",
  pages =        "311--317",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837993",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Avendano:2010:RNC,
  author =       "Mart{\'\i}n Avenda{\~n}o and Ashraf Ibrahim and J.
                 Maurice Rojas and Korben Rusek",
  title =        "Randomized {NP}-completeness for $p$-adic rational
                 roots of sparse polynomials in one variable",
  crossref =     "Watt:2010:IPI",
  pages =        "331--338",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837997",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:2010:SMS,
  author =       "Moulay A. Barkatou",
  title =        "Symbolic methods for solving systems of linear
                 ordinary differential equations",
  crossref =     "Watt:2010:IPI",
  pages =        "7--8",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837940",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:2010:SRC,
  author =       "Moulay A. Barkatou and Carole El Bacha and Eckhard
                 Pfl{\"u}gel",
  title =        "Simultaneously row- and column-reduced higher-order
                 linear differential systems",
  crossref =     "Watt:2010:IPI",
  pages =        "45--52",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837949",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Berkesch:2010:ABS,
  author =       "Christine Berkesch and Anton Leykin",
  title =        "Algorithms for {Bernstein--Sato} polynomials and
                 multiplier ideals",
  crossref =     "Watt:2010:IPI",
  pages =        "99--106",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837958",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bodrato:2010:SLM,
  author =       "Marco Bodrato",
  title =        "A {Strassen}-like matrix multiplication suited for
                 squaring and higher power computation",
  crossref =     "Watt:2010:IPI",
  pages =        "273--280",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837987",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Strassen's method is not the asymptotically fastest
                 known matrix multiplication algorithm, but it is the
                 most widely used for large matrices. Since his
                 manuscript was published, a number of variants have
                 been proposed with different addition complexities.
                 Here we describe a new one. The new variant is at least
                 as good as those already known for simple matrix
                 multiplication, but can save operations either for
                 chain products or for squaring. Moreover it can be
                 proved optimal for these tasks. The largest saving is
                 shown for nth-power computation, in this scenario the
                 additive complexity can be halved, with respect to
                 original Strassen's.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2010:CCT,
  author =       "Alin Bostan and Shaoshi Chen and Fr{\'e}d{\'e}ric
                 Chyzak and Ziming Li",
  title =        "Complexity of creative telescoping for bivariate
                 rational functions",
  crossref =     "Watt:2010:IPI",
  pages =        "203--210",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837975",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brisebarre:2010:CIP,
  author =       "Nicolas Brisebarre and Mioara Jolde{\c{s}}",
  title =        "{Chebyshev} interpolation polynomial-based tools for
                 rigorous computing",
  crossref =     "Watt:2010:IPI",
  pages =        "147--154",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837966",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Performing numerical computations, yet being able to
                 provide rigorous mathematical statements about the
                 obtained result, is required in many domains like
                 global optimization, ODE solving or integration. Taylor
                 models, which associate to a function a pair made of a
                 Taylor approximation polynomial and a rigorous
                 remainder bound, are a widely used rigorous computation
                 tool. This approach benefits from the advantages of
                 numerical methods, but also gives the ability to make
                 reliable statements about the approximated function.
                 Despite the fact that approximation polynomials based
                 on interpolation at Chebyshev nodes offer a
                 quasi-optimal approximation to a function, together
                 with several other useful features, an analogous to
                 Taylor models, based on such polynomials, has not been
                 yet well-established in the field of validated
                 numerics.\par

                 This paper presents a preliminary work for obtaining
                 such interpolation polynomials together with validated
                 interval bounds for approximating univariate functions.
                 We propose two methods that make practical the use of
                 this: one is based on a representation in Newton basis
                 and the other uses Chebyshev polynomial basis. We
                 compare the quality of the obtained remainders and the
                 performance of the approaches to the ones provided by
                 Taylor models.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:2010:BBW,
  author =       "Christopher W. Brown and Adam Strzebo{\'n}ski",
  title =        "Black-box\slash white-box simplification and
                 applications to quantifier elimination",
  crossref =     "Watt:2010:IPI",
  pages =        "69--76",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837953",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cha:2010:SRR,
  author =       "Yongjae Cha and Mark van Hoeij and Giles Levy",
  title =        "Solving recurrence relations using local invariants",
  crossref =     "Watt:2010:IPI",
  pages =        "303--309",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837992",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2010:TDS,
  author =       "Changbo Chen and James H. Davenport and John P. May
                 and Marc Moreno Maza and Bican Xia and Rong Xiao",
  title =        "Triangular decomposition of semi-algebraic systems",
  crossref =     "Watt:2010:IPI",
  pages =        "187--194",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837972",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Conti:2010:SBL,
  author =       "C. Conti and L. Gemignani and L. Romani",
  title =        "Solving {Bezout}-like polynomial equations for the
                 design of interpolatory subdivision schemes",
  crossref =     "Watt:2010:IPI",
  pages =        "251--256",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837983",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eberly:2010:YAB,
  author =       "Wayne Eberly",
  title =        "Yet another block {Lanczos} algorithm: how to simplify
                 the computation and reduce reliance on preconditioners
                 in the small field case",
  crossref =     "Watt:2010:IPI",
  pages =        "289--296",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837989",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Emiris:2010:DBM,
  author =       "Ioannis Z. Emiris and Bernard Mourrain and Elias P.
                 Tsigaridas",
  title =        "The {DMM} bound: multivariate (aggregate) separation
                 bounds",
  crossref =     "Watt:2010:IPI",
  pages =        "243--250",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837981",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Emiris:2010:RPE,
  author =       "Ioannis Z. Emiris and Andr{\'e} Galligo and Elias P.
                 Tsigaridas",
  title =        "Random polynomials and expected complexity of
                 bisection methods for real solving",
  crossref =     "Watt:2010:IPI",
  pages =        "235--242",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837980",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2010:CLR,
  author =       "Jean-Charles Faug{\`e}re and Mohab Safey {El Din} and
                 Pierre-Jean Spaenlehauer",
  title =        "Computing loci of rank defects of linear matrices
                 using {Gr{\"o}bner} bases and applications to
                 cryptology",
  crossref =     "Watt:2010:IPI",
  pages =        "257--264",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837984",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2010:DGM,
  author =       "Jean-Charles Faug{\`e}re and Joachim von zur Gathen
                 and Ludovic Perret",
  title =        "Decomposition of generic multivariate polynomials",
  crossref =     "Watt:2010:IPI",
  pages =        "131--137",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837963",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gao:2010:NIA,
  author =       "Shuhong Gao and Yinhua Guan and Frank {Volny IV}",
  title =        "A new incremental algorithm for computing
                 {Gr{\"o}bner} bases",
  crossref =     "Watt:2010:IPI",
  pages =        "13--19",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837944",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gerdt:2010:CFD,
  author =       "Vladimir P. Gerdt and Daniel Robertz",
  title =        "Consistency of finite difference approximations for
                 linear {PDE} systems and its algorithmic verification",
  crossref =     "Watt:2010:IPI",
  pages =        "53--59",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837950",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gerhard:2010:AFA,
  author =       "J{\"u}rgen Gerhard",
  title =        "Asymptotically fast algorithms for modern computer
                 algebra",
  crossref =     "Watt:2010:IPI",
  pages =        "9--10",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837941",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The solution of computational tasks from the `real
                 world' requires high performance computations. Not
                 limited to mathematical computing, asymptotically fast
                 algorithms have become one of the major contributing
                 factors in this area. Based on [4], the tutorial will
                 give an introduction to the beauty and elegance of
                 modern computer algebra.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Grigoriev:2010:AFN,
  author =       "D. Grigoriev and F. Schwarz",
  title =        "Absolute factoring of non-holonomic ideals in the
                 plane",
  crossref =     "Watt:2010:IPI",
  pages =        "93--97",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837957",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2010:GOP,
  author =       "Feng Guo and Mohab Safey {El Din} and Lihong Zhi",
  title =        "Global optimization of polynomials using generalized
                 critical values and sums of squares",
  crossref =     "Watt:2010:IPI",
  pages =        "107--114",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837960",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Harvey:2010:PTF,
  author =       "David Harvey and Daniel S. Roche",
  title =        "An in-place truncated {Fourier} transform and
                 applications to polynomial multiplication",
  crossref =     "Watt:2010:IPI",
  pages =        "325--329",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837996",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The truncated Fourier transform (TFT) was introduced
                 by van der Hoeven in 2004 as a means of smoothing the
                 `jumps' in running time of the ordinary FFT algorithm
                 that occur at power-of-two input sizes. However, the
                 TFT still introduces these jumps in memory usage. We
                 describe in-place variants of the forward and inverse
                 TFT algorithms, achieving time complexity $O(n \log n)$
                 with only $O(1)$ auxiliary space. As an application, we
                 extend the second author's results on space-restricted
                 FFT-based polynomial multiplication to polynomials of
                 arbitrary degree.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hubert:2010:AIT,
  author =       "Evelyne Hubert",
  title =        "Algebraic invariants and their differential algebras",
  crossref =     "Watt:2010:IPI",
  pages =        "1--2",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837936",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hutton:2010:CRP,
  author =       "Sharon Hutton and Erich L. Kaltofen and Lihong Zhi",
  title =        "Computing the radius of positive semidefiniteness of a
                 multivariate real polynomial via a dual of
                 {Seidenberg}'s method",
  crossref =     "Watt:2010:IPI",
  pages =        "227--234",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837979",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeannerod:2010:CSG,
  author =       "Claude-Pierre Jeannerod and Christophe Mouilleron",
  title =        "Computing specified generators of structured matrix
                 inverses",
  crossref =     "Watt:2010:IPI",
  pages =        "281--288",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837988",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kapur:2010:NAC,
  author =       "Deepak Kapur and Yao Sun and Dingkang Wang",
  title =        "A new algorithm for computing comprehensive
                 {Gr{\"o}bner} systems",
  crossref =     "Watt:2010:IPI",
  pages =        "29--36",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837946",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kauers:2010:PDB,
  author =       "Manuel Kauers and Carsten Schneider",
  title =        "Partial denominator bounds for partial linear
                 difference equations",
  crossref =     "Watt:2010:IPI",
  pages =        "211--218",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837976",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kauers:2010:WCW,
  author =       "Manuel Kauers and Veronika Pillwein",
  title =        "When can we detect that a {$P$}-finite sequence is
                 positive?",
  crossref =     "Watt:2010:IPI",
  pages =        "195--201",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837974",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Khonji:2010:OSD,
  author =       "Majid Khonji and Cl{\'e}ment Pernet and Jean-Louis
                 Roch and Thomas Roche and Thomas Stalinski",
  title =        "Output-sensitive decoding for redundant residue
                 systems",
  crossref =     "Watt:2010:IPI",
  pages =        "265--272",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837985",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lemaire:2010:MSR,
  author =       "Fran{\c{c}}ois Lemaire and Asli {\"U}rg{\"u}pl{\"u}",
  title =        "A method for semi-rectifying algebraic and
                 differential systems using scaling type {Lie} point
                 symmetries with linear algebra",
  crossref =     "Watt:2010:IPI",
  pages =        "85--92",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837956",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2010:BID,
  author =       "Zijia Li and Zhengfeng Yang and Lihong Zhi",
  title =        "Blind image deconvolution via fast approximate {GCD}",
  crossref =     "Watt:2010:IPI",
  pages =        "155--162",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837967",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Linton:2010:ECS,
  author =       "S. Linton and K. Hammond and A. Konovalov and A. D. Al
                 Zain and P. Trinder and P. Horn and D. Roozemond",
  title =        "Easy composition of symbolic computation software: a
                 new lingua franca for symbolic computation",
  crossref =     "Watt:2010:IPI",
  pages =        "339--346",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837999",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present the results of the first four years of the
                 European research project SCIEnce
                 (www.symbolic-computation.org), which aims to provide
                 key infrastructure for symbolic computation research. A
                 primary outcome of the project is that we have
                 developed a new way of combining computer algebra
                 systems using the Symbolic Computation Software
                 Composability Protocol (SCSCP), in which both protocol
                 messages and data are encoded in the OpenMath format.
                 We describe SCSCP middleware and APIs, outline some
                 implementations for various Computer Algebra Systems
                 (CAS), and show how SCSCP-compliant components may be
                 combined to solve scientific problems that can not be
                 solved within a single CAS, or may be organised into a
                 system for distributed parallel computations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mayr:2010:DBG,
  author =       "Ernst W. Mayr and Stephan Ritscher",
  title =        "Degree bounds for {Gr{\"o}bner} bases of
                 low-dimensional polynomial ideals",
  crossref =     "Watt:2010:IPI",
  pages =        "21--27",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837945",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mezzarobba:2010:NPN,
  author =       "Marc Mezzarobba",
  title =        "{NumGfun}: a package for numerical and analytic
                 computation with {D}-finite functions",
  crossref =     "Watt:2010:IPI",
  pages =        "139--145",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837965",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2010:RCP,
  author =       "Victor Y. Pan and Ai-Long Zheng",
  title =        "Real and complex polynomial root-finding with
                 eigen-solving and preprocessing",
  crossref =     "Watt:2010:IPI",
  pages =        "219--226",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837978",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Roune:2010:SAC,
  author =       "Bjarke Hammersholt Roune",
  title =        "A {Slice} algorithm for corners and
                 {Hilbert--Poincar{\'e}} series of monomial ideals",
  crossref =     "Watt:2010:IPI",
  pages =        "115--122",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837961",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rump:2010:VMR,
  author =       "Siegfried M. Rump",
  title =        "Verification methods: rigorous results using
                 floating-point arithmetic",
  crossref =     "Watt:2010:IPI",
  pages =        "3--4",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837937",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The classical mathematical proof is performed by
                 pencil and paper. However, there are many ways in which
                 computers may be used in a mathematical proof. But
                 `proofs by computers' or even the use of computers in
                 the course of a proof are not so readily accepted (the
                 December 2008 issue of the Notices of the American
                 Mathematical Society is devoted to formal proofs by
                 computers).\par

                 In this talk we discuss how verification methods may
                 assist in achieving a mathematically rigorous result.
                 In particular we emphasize how floating-point
                 arithmetic is used.\par

                 The goal of verification methods is ambitious: For a
                 given problem it is proved, with the aid of a computer,
                 that there exists a (unique) solution within computed
                 bounds. The methods are constructive, and the results
                 are rigorous in every respect. Verification methods
                 apply to data with tolerances as well.\par

                 Rigorous results are the main goal in computer algebra.
                 However, verification methods use solely floating-point
                 arithmetic, so that the total computational effort is
                 not too far from that of a purely (approximate)
                 numerical method. Nontrivial problems have been solved
                 using verification methods. For example:\par

                 Tucker (1999) received the 2004 EMS prize awarded by
                 the European Mathematical Society for (citation)
                 `giving a rigorous proof that the Lorenz attractor
                 exists for the parameter values provided by Lorenz.
                 This was a long standing challenge to the dynamical
                 system community, and was included by Smale in his list
                 of problems for the new millennium. The proof uses
                 computer estimates with rigorous bounds based on higher
                 dimensional interval arithmetics.'\par

                 Sahinidis and Tawaralani (2005) received the 2006
                 Beale-Orchard-Hays Prize for their package BARON which
                 (citation) `incorporates techniques from automatic
                 differentiation, interval arithmetic, and other areas
                 to yield an automatic, modular, and relatively
                 efficient solver for the very difficult area of global
                 optimization'.\par

                 A main goal of this talk is to introduce the principles
                 of how to design verification algorithms, and how these
                 principles differ from those for traditional numerical
                 algorithms.\par

                 We begin with a brief discussion of the working tools
                 of verification methods, in particular floating-point
                 and interval arithmetic. In particular the development
                 and limits of verification methods for finite
                 dimensional problems are discussed in some detail;
                 problems include dense systems of linear equations,
                 sparse linear systems, systems of nonlinear equations,
                 semi-definite programming and other special linear and
                 nonlinear problems including M-matrices, simple and
                 multiple roots of polynomials, bounds for simple and
                 multiple eigenvalues or clusters, and quadrature. We
                 mention that automatic differentiation tools to compute
                 the range of gradients, Hessians, Taylor coefficients,
                 and slopes are necessary. If time permits, verification
                 methods for continuous problems, namely two-point
                 boundary value problems and semilinear elliptic
                 boundary value problems are presented.\par

                 Throughout the talk, a number of examples of the wrong
                 use of interval operations are given. In the past such
                 examples contributed to the dubious reputation of
                 interval arithmetic, whereas they are, in fact, just a
                 misuse.\par

                 Some algorithms are presented in executable
                 Matlab/INTLAB-code. INTLAB, the Matlab toolbox for
                 reliable computing and free for academic use, is
                 developed and written by Rump (1999). It was, for
                 example, used by Bornemann, Laurie, Wagon, and
                 Waldvogel (2004) in the solution of half of the
                 problems of the $10 \times 10$-digit challenge by
                 Trefethen (2002).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rupp:2010:SIC,
  author =       "Karl Rupp",
  title =        "Symbolic integration at compile time in finite element
                 methods",
  crossref =     "Watt:2010:IPI",
  pages =        "347--354",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1838000",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sevilla:2010:PIR,
  author =       "David Sevilla and Daniel Wachsmuth",
  title =        "Polynomial integration on regions defined by a
                 triangle and a conic",
  crossref =     "Watt:2010:IPI",
  pages =        "163--170",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837968",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shi:2010:CSR,
  author =       "Xiaoran Shi and Falai Chen",
  title =        "Computing the singularities of rational space curves",
  crossref =     "Watt:2010:IPI",
  pages =        "171--178",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837970",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Slavici:2010:FML,
  author =       "Vlad Slavici and Xin Dong and Daniel Kunkle and Gene
                 Cooperman",
  title =        "Fast multiplication of large permutations for disk,
                 flash memory and {RAM}",
  crossref =     "Watt:2010:IPI",
  pages =        "355--362",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1838001",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sottile:2010:SSP,
  author =       "Frank Sottile and Ravi Vakil and Jan Verschelde",
  title =        "Solving {Schubert} problems with
                 {Littlewood--Richardson} homotopies",
  crossref =     "Watt:2010:IPI",
  pages =        "179--186",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837971",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Strzebonski:2010:CSS,
  author =       "Adam Strzebo{\'n}ski",
  title =        "Computation with semialgebraic sets represented by
                 cylindrical algebraic formulas",
  crossref =     "Watt:2010:IPI",
  pages =        "61--68",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837952",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sturm:2010:PQS,
  author =       "Thomas Sturm and Christoph Zengler",
  title =        "Parametric quantified {SAT} solving",
  crossref =     "Watt:2010:IPI",
  pages =        "77--84",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837954",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tiwari:2010:TRV,
  author =       "Ashish Tiwari",
  title =        "Theory of reals for verification and synthesis of
                 hybrid dynamical systems",
  crossref =     "Watt:2010:IPI",
  pages =        "5--6",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837938",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tsarev:2010:TFP,
  author =       "S. P. Tsarev",
  title =        "Transformation and factorization of partial
                 differential systems: applications to stochastic
                 systems",
  crossref =     "Watt:2010:IPI",
  pages =        "11--12",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837942",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:2010:FAB,
  author =       "Mark van Hoeij and Quan Yuan",
  title =        "Finding all {Bessel} type solutions for linear
                 differential equations with rational function
                 coefficients",
  crossref =     "Watt:2010:IPI",
  pages =        "37--44",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837948",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A linear differential equation with rational function
                 coefficients has a Bessel type solution when it is
                 solvable in terms of $B_v(f)$, $B_{v+1}(f)$. For second
                 order equations, with rational function coefficients,
                 $f$ must be a rational function or the square root of a
                 rational function. An algorithm was given by Debeerst,
                 van Hoeij, and Koepf, that can compute Bessel type
                 solutions if and only if $f$ is a rational function. In
                 this paper we extend this work to the square root case,
                 resulting in a complete algorithm to find all Bessel
                 type solutions.",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:2010:LSI,
  author =       "Mark van Hoeij and Giles Levy",
  title =        "{Liouvillian} solutions of irreducible second order
                 linear difference equations",
  crossref =     "Watt:2010:IPI",
  pages =        "297--301",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837991",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vonzurGathen:2010:CCP,
  author =       "Joachim von zur Gathen and Mark Giesbrecht and
                 Konstantin Ziegler",
  title =        "Composition collisions and projective polynomials:
                 statement of results",
  crossref =     "Watt:2010:IPI",
  pages =        "123--130",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837962",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zanoni:2010:ITC,
  author =       "Alberto Zanoni",
  title =        "Iterative {Toom--Cook} methods for very unbalanced
                 long integer multiplication",
  crossref =     "Watt:2010:IPI",
  pages =        "319--323",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837995",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider the multiplication of long integers when
                 one factor is much larger than the other one. We
                 describe an iterative approach using Toom--Cook
                 unbalanced methods, which results in the evaluation of
                 the smaller integer only once. The particular case of
                 Toom-2.5 is considered in full detail. A further
                 optimization depending on the parity of the shortest
                 operand evaluation in 1 is also described. A comparison
                 with GMP library is also presented.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ananth:2011:BBD,
  author =       "Prabhanjan Vijendra Ananth and Ambedkar Dukkipati",
  title =        "Border basis detection is {NP-complete}",
  crossref =     "Schost:2011:IPI",
  pages =        "11--18",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993895",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Border basis detection (BBD) is described as follows:
                 given a set of generators of an ideal, decide whether
                 that set of generators is a border basis of the ideal
                 with respect to some order ideal. The motivation for
                 this problem comes from a similar problem related to
                 Gr{\"o}bner bases termed as Gr{\"o}bner basis detection (GBD)
                 which was proposed by Gritzmann and Sturmfels (1993).
                 GBD was shown to be NP-hard by Sturmfels and Wiegelmann
                 (1996). In this paper, we investigate the computational
                 complexity of BBD and show that it is NP-complete.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aparicio-Monforte:2011:FFI,
  author =       "Ainhoa Aparicio-Monforte and Moulay A. Barkatou and
                 Sergi Simon and Jacques-Arthur Weil",
  title =        "Formal first integrals along solutions of differential
                 systems {I}",
  crossref =     "Schost:2011:IPI",
  pages =        "19--26",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993896",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider an analytic vector field x = X (x \right)
                 and study, via a variational approach, whether it may
                 possess analytic first integrals. We assume one
                 solution $ \Gamma $ is known and we study the
                 successive variational equations along $ \Gamma $.
                 Constructions in [MRRS07] show that Taylor expansion
                 coefficients of first integrals appear as rational
                 solutions of the dual linearized variational equations.
                 We show that they also satisfy linear ``filter''
                 conditions. Using this, we adapt the algorithms from
                 [Bar99, vHW97] to design new ones optimized to this
                 effect and demonstrate their use. Part of this work
                 stems from the first author's Ph.D. thesis [AM10].",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bembe:2011:VRR,
  author =       "Daniel Bemb{\'e} and Andr{\'e} Galligo",
  title =        "Virtual roots of a real polynomial and fractional
                 derivatives",
  crossref =     "Schost:2011:IPI",
  pages =        "27--34",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993897",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  abstract =     "After the works of Gonzales-Vega, Lombardi, Mahe [11],
                 and of Coste, Lajous, Lombardi, Roy [6], we consider
                 the virtual roots of a univariate polynomial $f$ with
                 real coefficients. Using fractional derivatives, we
                 associate to $f$ a bivariate polynomial $ P(x, t) $
                 depending on the choice of an origin $a$, then two type
                 of plan curves we call the FDcurve and stem of $f$. We
                 show, in the generic case, how to locate the virtual
                 roots of $f$ on the Budan table and on each of these
                 curves. The paper is illustrated with examples and
                 pictures computed with the computer algebra system
                 Maple.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bernardi:2011:MPD,
  author =       "Alessandra Bernardi and J{\'e}r{\^o}me Brachat and
                 Pierre Comon and Bernard Mourrain",
  title =        "Multihomogeneous polynomial decomposition using moment
                 matrices",
  crossref =     "Schost:2011:IPI",
  pages =        "35--42",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993898",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In the paper, we address the important problem of
                 tensor decomposition which can be seen as a
                 generalisation of Singular Value Decomposition for
                 matrices. We consider general multilinear and
                 multihomogeneous tensors. We show how to reduce the
                 problem to a truncated moment matrix problem and we
                 give a new criterion for flat extension of Quasi-Hankel
                 matrices. We connect this criterion to the commutation
                 characterisation of border bases. A new algorithm is
                 described: it applies for general multihomogeneous
                 tensors, extending the approach of J. J. Sylvester on
                 binary forms. An example illustrates the algebraic
                 operations involved in this approach and how the
                 decomposition can be recovered from eigenvector
                 computation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Borwein:2011:SVG,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "Special values of generalized log-sine integrals",
  crossref =     "Schost:2011:IPI",
  pages =        "43--50",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993899",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  abstract =     "We study generalized log-sine integrals at special
                 values. At $ \pi $ and multiples thereof explicit
                 evaluations are obtained in terms of Nielsen
                 polylogarithms at $ \pm 1 $. For general arguments we
                 present algorithmic evaluations involving Nielsen
                 polylogarithms at related arguments. In particular, we
                 consider log-sine integrals at $ \pi / 3 $ which
                 evaluate in terms of polylogarithms at the sixth root
                 of unity. An implementation of our results for the
                 computer algebra systems Mathematica and SAGE is
                 provided.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bright:2011:VRN,
  author =       "Curtis Bright and Arne Storjohann",
  title =        "Vector rational number reconstruction",
  crossref =     "Schost:2011:IPI",
  pages =        "51--58",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993900",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The final step of some algebraic algorithms is to
                 reconstruct the common denominator $d$ of a collection
                 of rational numbers $ (n_i / d)_{1 \leq i \leq n} $
                 from their images $ (a_i)_{1 \leq i \leq n} \bmod M $,
                 subject to a condition such as $ 0 < d \leq N $ and $
                 N_i \leq N $ for a given magnitude bound $N$. Applying
                 elementwise rational number reconstruction requires
                 that $ M \in \Omega (N^2) $. Using the gradual
                 sublattice reduction algorithm of van Hoeij and
                 Novocin, we show how to perform the reconstruction
                 efficiently even when the modulus satisfies a
                 considerably smaller magnitude bound $ M \in \Omega
                 (N^{1 + 1 / c}) $ for $c$ a small constant, for example
                 $ 2 \leq c \leq 5 $. Assuming $ c \in O(1) $ the cost
                 of the approach is $ O(n (\log M)^3) $ bit operations
                 using the original LLL lattice reduction algorithm, but
                 is reduced to $ O(n (\log M)^2) $ bit operations by
                 incorporating the $ L^2 $ variant of Nguyen and Stehle.
                 As an application, we give a robust method for
                 reconstructing the rational solution vector of a linear
                 system from its image, such as obtained by a solver
                 using $p$-adic lifting.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Burgisser:2011:PAC,
  author =       "Peter B{\"u}rgisser",
  title =        "Probabilistic analysis of condition numbers",
  crossref =     "Schost:2011:IPI",
  pages =        "5--6",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993891",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Condition numbers are well known in numerical linear
                 algebra. It is less known that this concept also plays
                 a crucial part in understanding the efficiency of
                 algorithms in linear programming, convex optimization,
                 and for solving systems of polynomial equations.
                 Indeed, the running time of such algorithms may be
                 often effectively bounded in terms of the condition
                 underlying the problem. ``Smoothed analysis'', as
                 suggested by Spielman and Teng, is a blend of
                 worst-case and average-case probabilistic analysis of
                 algorithms. The goal is to prove that for all inputs
                 (even ill-posed ones), and all slight random
                 perturbations of that input, it is unlikely that the
                 running time (or condition number) will be large. The
                 tutorial will present a unifying view on the notion of
                 condition in linear algebra, convex optimization, and
                 polynomial equations. We will discuss the role of
                 condition for the analysis of algorithms as well as
                 techniques for their probabilistic analysis. For the
                 latter, geometry plays an important role.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Burton:2011:DGV,
  author =       "Benjamin A. Burton",
  title =        "Detecting genus in vertex links for the fast
                 enumeration of $3$-manifold triangulations",
  crossref =     "Schost:2011:IPI",
  pages =        "59--66",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993901",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Enumerating all $3$-manifold triangulations of a given
                 size is a difficult but increasingly important problem
                 in computational topology. A key difficulty for
                 enumeration algorithms is that most combinatorial
                 triangulations must be discarded because they do not
                 represent topological $3$-manifolds. In this paper we
                 show how to preempt bad triangulations by detecting
                 genus in partially-constructed vertex links, allowing
                 us to prune the enumeration tree substantially. The key
                 idea is to manipulate the boundary edges surrounding
                 partial vertex links using expected logarithmic time
                 operations. Practical testing shows the resulting
                 enumeration algorithm to be significantly faster, with
                 up to $ 249 \times $ speed-ups even for small problems
                 where comparisons are feasible. We also discuss
                 parallelisation, and describe new data sets that have
                 been obtained using high-performance computing
                 facilities.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cabarcas:2011:LAC,
  author =       "Daniel Cabarcas and Jintai Ding",
  title =        "Linear algebra to compute syzygies and {Gr{\"o}bner}
                 bases",
  crossref =     "Schost:2011:IPI",
  pages =        "67--74",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993902",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we introduce a new method to avoid zero
                 reductions in Gr{\"o}bner basis computation. We call
                 this method LASyz, which stands for Lineal Algebra to
                 compute Syzygies. LASyz uses exhaustively the
                 information of both principal syzygies and non-trivial
                 syzygies to avoid zero reductions. All computation is
                 done using linear algebra techniques. LASyz is easy to
                 understand and implement. The method does not require
                 to compute Gr{\"o}bner bases of subsequences of
                 generators incrementally and it imposes no restrictions
                 on the reductions allowed. We provide a complete
                 theoretical foundation for the LASyz method and we
                 describe an algorithm to compute Gr{\"o}bner bases for
                 zero dimensional ideals based on this foundation. A
                 qualitative comparison with similar algorithms is
                 provided and the performance of the algorithm is
                 illustrated with experimental data.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2011:ACT,
  author =       "Changbo Chen and Marc Moreno Maza",
  title =        "Algorithms for computing triangular decompositions of
                 polynomial systems",
  crossref =     "Schost:2011:IPI",
  pages =        "83--90",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993904",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  abstract =     "We propose new algorithms for computing triangular
                 decompositions of polynomial systems incrementally.
                 With respect to previous works, our improvements are
                 based on a weakened notion of a polynomial GCD modulo a
                 regular chain, which permits to greatly simplify and
                 optimize the sub-algorithms. Extracting common work
                 from similar expensive computations is also a key
                 feature of our algorithms. In our experimental results
                 the implementation of our new algorithms, realized with
                 the {\tt RegularChains} library in MAPLE, outperforms
                 solvers with similar specifications by several orders
                 of magnitude on sufficiently difficult problems.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2011:CSA,
  author =       "Changbo Chen and James H. Davenport and Marc Moreno
                 Maza and Bican Xia and Rong Xiao",
  title =        "Computing with semi-algebraic sets represented by
                 triangular decomposition",
  crossref =     "Schost:2011:IPI",
  pages =        "75--82",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993903",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This article is a continuation of our earlier work
                 [3], which introduced triangular decompositions of
                 semi-algebraic systems and algorithms for computing
                 them. Our new contributions include theoretical results
                 based on which we obtain practical improvements for
                 these decomposition algorithms. We exhibit new results
                 on the theory of border polynomials of parametric
                 semi-algebraic systems: in particular a geometric
                 characterization of its ``true boundary'' (Definition
                 2). In order to optimize these algorithms, we also
                 propose a technique, that we call relaxation, which can
                 simplify the decomposition process and reduce the
                 number of redundant components in the output. Moreover,
                 we present procedures for basic set-theoretical
                 operations on semi-algebraic sets represented by
                 triangular decomposition. Experimentation confirms the
                 effectiveness of our techniques.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2011:SCR,
  author =       "Shaoshi Chen and Ruyong Feng and Guofeng Fu and Ziming
                 Li",
  title =        "On the structure of compatible rational functions",
  crossref =     "Schost:2011:IPI",
  pages =        "91--98",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993905",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A finite number of rational functions are compatible
                 if they satisfy the compatibility conditions of a
                 first-order linear functional system involving
                 differential, shift and $q$-shift operators. We present
                 a theorem that describes the structure of compatible
                 rational functions. The theorem enables us to decompose
                 a solution of such a system as a product of a rational
                 function, several symbolic powers, a hyperexponential
                 function, a hypergeometric term, and a
                 $q$-hypergeometric term. We outline an algorithm for
                 computing this product, and present an application.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eder:2011:SBA,
  author =       "Christian Eder and John Edward Perry",
  title =        "Signature-based algorithms to compute {Gr{\"o}bner}
                 bases",
  crossref =     "Schost:2011:IPI",
  pages =        "99--106",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993906",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Abstract This paper describes a Buchberger-style
                 algorithm to compute a Gr{\"o}bner basis of a
                 polynomial ideal, allowing for a selection strategy
                 based on ``signatures''. We explain how three recent
                 algorithms can be viewed as different strategies for
                 the new algorithm, and how other selection strategies
                 can be formulated. We describe a fourth as an example.
                 We analyze the strategies both theoretically and
                 empirically, leading to some surprising results.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fang:2011:DSO,
  author =       "Tingting Fang and Mark van Hoeij",
  title =        "$2$-descent for second order linear differential
                 equations",
  crossref =     "Schost:2011:IPI",
  pages =        "107--114",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993907",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $L$ be a second order linear ordinary differential
                 equation with coefficients in $ C(x) $. The goal in
                 this paper is to reduce $L$ to an equation that is
                 easier to solve. The starting point is an irreducible
                 $L$, of order two, and the goal is to decide if $L$ is
                 projectively equivalent to another equation $L$ that is
                 defined over a subfield $ C (f) $ of $ C(x) $. This
                 paper treats the case of $2$-descent, which means
                 reduction to a subfield with index $ [C(x) : C(f)] = 2
                 $. Although the mathematics has already been treated in
                 other papers, a complete implementation could not be
                 given because it involved a step for which we do not
                 have a complete implementation. The contribution of
                 this paper is to give an approach that is fully
                 implementable. Examples illustrate that this algorithm
                 is very useful for finding closed form solutions
                 ($2$-descent, if it exists, reduces the number of true
                 singularities from $n$ to at most $ n / 2 + 2 $).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2011:FAC,
  author =       "Jean-Charles Faug{\`e}re and Chenqi Mou",
  title =        "Fast algorithm for change of ordering of
                 zero-dimensional {Gr{\"o}bner} bases with sparse
                 multiplication matrices",
  crossref =     "Schost:2011:IPI",
  pages =        "115--122",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993908",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $I$ in $ K[x_1, \ldots {}, x_n] $ be a
                 $0$-dimensional ideal of degree $D$ where $K$ is a
                 field. It is well-known that obtaining efficient
                 algorithms for change of ordering of Gr{\"o}bner bases
                 of $I$ is crucial in polynomial system solving. Through
                 the algorithm FGLM, this task is classically tackled by
                 linear algebra operations in $ K[x_1, \ldots {}, x_n] /
                 I $. With recent progress on Gr{\"o}bner bases
                 computations, this step turns out to be the bottleneck
                 of the whole solving process. Our contribution is an
                 algorithm that takes advantage of the sparsity
                 structure of multiplication matrices appearing during
                 the change of ordering. This sparsity structure arises
                 even when the input polynomial system defining $I$ is
                 dense. As a by-product, we obtain an implementation
                 which is able to manipulate $0$-dimensional ideals over
                 a prime field of degree greater than $ 30 \, 000 $. It
                 outperforms the Magma\slash Singular\ldots{} FGb
                 implementations of FGLM. First, we investigate the
                 particular but important shape position case. The
                 obtained algorithm performs the change of ordering
                 within a complexity $ O(D(N i >_1 + n \log (D))) $,
                 where $ N_1 $ is the number of nonzero entries of a
                 multiplication matrix. This almost matches the
                 complexity of computing the minimal polynomial of one
                 multiplication matrix. Then, we address the general
                 case and give corresponding complexity results. Our
                 algorithm is dynamic in the sense that it selects
                 automatically which strategy to use depending on the
                 input. Its key ingredients are the Wiedemann algorithm
                 to handle $1$-dimensional linear recurrence (for the
                 shape position case), and the Berlekamp--Massey-Sakata
                 algorithm from Coding Theory to handle
                 multi-dimensional linearly recurring sequences in the
                 general case.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Giesbrecht:2011:DII,
  author =       "Mark Giesbrecht and Daniel S. Roche",
  title =        "Diversification improves interpolation",
  crossref =     "Schost:2011:IPI",
  pages =        "123--130",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993909",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider the problem of interpolating an unknown
                 multivariate polynomial with coefficients taken from a
                 finite field or as numerical approximations of complex
                 numbers. Building on the recent work of Garg and
                 Schost, we improve on the best-known algorithm for
                 interpolation over large finite fields by presenting a
                 Las Vegas randomized algorithm that uses fewer black
                 box evaluations. Using related techniques, we also
                 address numerical interpolation of sparse polynomials
                 with complex coefficients, and provide the first
                 provably stable algorithm (in the sense of relative
                 error) for this problem, at the cost of modestly more
                 evaluations. A key new technique is a randomization
                 which makes all coefficients of the unknown polynomial
                 distinguishable, producing what we call a diverse
                 polynomial. Another departure from most previous
                 approaches is that our algorithms do not rely on root
                 finding as a subroutine. We show how these improvements
                 affect the practical performance with trial
                 implementations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Greuet:2011:DRI,
  author =       "Aur{\'e}lien Greuet and Mohab Safey {El Din}",
  title =        "Deciding reachability of the infimum of a multivariate
                 polynomial",
  crossref =     "Schost:2011:IPI",
  pages =        "131--138",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993910",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $ f \in Q[X_1, \ l d o t {s}, X_n] $ be of degree
                 $D$. Algorithms for solving the unconstrained global
                 optimization problem $ f *= \inf_x \in R^n f(x) $ are
                 of first importance since this problem appears
                 frequently in numerous applications in engineering
                 sciences. This can be tackled by either designing
                 appropriate quantifier elimination algorithms or by
                 certifying lower bounds on $ f * $ by means of sums of
                 squares decompositions but there is no efficient
                 algorithm for deciding if $ f * $ is a minimum. This
                 paper is dedicated to this important problem. We design
                 a probabilistic algorithm that decides, for a given $f$
                 and the corresponding $ f * $, if $ f * $ is reached
                 over $ R^n $ and computes a point $ x * \in R^n $ such
                 that $ f(x *) = f * $ if such a point exists. This
                 algorithm makes use of algebraic elimination algorithms
                 and real root isolation. If $L$ is the length of a
                 straight-line program evaluating $f$, algebraic
                 elimination steps run in $ O(\log (D - 1) n^6 (n L +
                 n^4) U ((D - 1)^{n + 1})^3) $ arithmetic operations in
                 $Q$ where $ D = \deg (f) $ and $ U(x) = x (\log (x))^2
                 \log \log (x) $. Experiments show its practical
                 efficiency.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2011:ACS,
  author =       "Leilei Guo and Feng Liu",
  title =        "An algorithm for computing set-theoretic generators of
                 an algebraic variety",
  crossref =     "Schost:2011:IPI",
  pages =        "139--146",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993911",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Based on Eisenbud's idea (see [Eisenbud, D., Evans,
                 G., 1973. \booktitle{Every algebraic set in $n$-space
                 is the intersection of $n$ hypersurfaces}. Invent.
                 Math. 19, 107--112]), we present an algorithm for
                 computing set-theoretic generators for any algebraic
                 variety in the affine $n$-space, which consists of at
                 most $n$ polynomials. With minor modifications, this
                 algorithm is also valid for projective algebraic
                 variety in projective $n$-space.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2011:RPL,
  author =       "Li Guo and William Y. Sit and Ronghua Zhang",
  title =        "On {Rota}'s problem for linear operators in
                 associative algebras",
  crossref =     "Schost:2011:IPI",
  pages =        "147--154",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993912",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A long standing problem of Gian-Carlo Rota for
                 associative algebras is the classification of all
                 linear operators that can be defined on them. In the
                 1970s, there were only a few known operators, for
                 example, the derivative operator, the difference
                 operator, the average operator and the Rota--Baxter
                 operator. A few more appeared after Rota posed his
                 problem. However, little progress was made to solve
                 this problem in general. In part, this is because the
                 precise meaning of the problem is not so well
                 understood. In this paper, we propose a formulation of
                 the problem using the framework of operated algebras
                 and viewing an associative algebra with a linear
                 operator as one that satisfies a certain operated
                 polynomial identity. To narrow our focus more on the
                 operators that Rota was interested in, we further
                 consider two particular classes of operators, namely,
                 those that generalize differential or Rota--Baxter
                 operators. With the aid of computer algebra, we are
                 able to come up with a list of these two classes of
                 operators, and provide some evidence that these lists
                 may be complete. Our search have revealed quite a few
                 new operators of these types whose properties are
                 expected to be similar to the differential operator and
                 Rota--Baxter operator respectively. Recently, a more
                 unified approach has emerged in related areas, such as
                 difference algebra and differential algebra, and
                 Rota--Baxter algebra and Nijenhuis algebra. The
                 similarities in these theories can be more efficiently
                 explored by advances on Rota's problem.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gupta:2011:CHF,
  author =       "Somit Gupta and Arne Storjohann",
  title =        "Computing {Hermite} forms of polynomial matrices",
  crossref =     "Schost:2011:IPI",
  pages =        "155--162",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993913",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper presents a new algorithm for computing the
                 Hermite form of a polynomial matrix. Given a
                 nonsingular $ n \times n $ matrix $A$ filled with
                 degree $d$ polynomials with coefficients from a field,
                 the algorithm computes the Hermite form of $A$ using an
                 expected number of $ (n^3 d)^{1 + o(1)} $ field
                 operations. This is the first algorithm that is both
                 softly linear in the degree $d$ and softly cubic in the
                 dimension $n$. The algorithm is randomized of the Las
                 Vegas type.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hart:2011:PPF,
  author =       "William Hart and Mark van Hoeij and Andrew Novocin",
  title =        "Practical polynomial factoring in polynomial time",
  crossref =     "Schost:2011:IPI",
  pages =        "163--170",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993914",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "State of the art factoring in $ Q[x] $ is dominated in
                 theory by a combinatorial reconstruction problem while,
                 excluding some rare polynomials, performance tends to
                 be dominated by Hensel lifting. We present an algorithm
                 which gives a practical improvement (less Hensel
                 lifting) for these more common polynomials. In
                 addition, factoring has suffered from a 25 year
                 complexity gap because the best implementations are
                 much faster in practice than their complexity bounds.
                 We illustrate that this complexity gap can be closed by
                 providing an implementation which is comparable to the
                 best current implementations and for which competitive
                 complexity results can be proved.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2011:QTC,
  author =       "Erich L. Kaltofen and Michael Nehring and B. David
                 Saunders",
  title =        "Quadratic-time certificates in linear algebra",
  crossref =     "Schost:2011:IPI",
  pages =        "171--176",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993915",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present certificates for the positive
                 semidefiniteness of an $n$ by $n$ matrix $A$, whose
                 entries are integers of binary length $ \log || A || $,
                 that can be verified in $ O(n^{(2 + \mu)} (\log || A
                 ||)^{(1 + \mu)}) $ binary operations for any $ \mu > 0
                 $. The question arises in Hilbert\slash Artin-based
                 rational sum-of-squares certificates (proofs) for
                 polynomial inequalities with rational coefficients. We
                 allow certificates that are validated by Monte Carlo
                 randomized algorithms, as in Rusins Freivalds's famous
                 1979 quadratic time certification for the matrix
                 product. Our certificates occupy $ O(n^{(3 + \mu)}
                 (\log || A ||)^{(1 + \mu)}) $ bits, from which the
                 verification algorithm randomly samples a quadratic
                 amount. In addition, we give certificates of the same
                 space and randomized validation time complexity for the
                 Frobenius form, which includes the characteristic and
                 minimal polynomial. For determinant and rank we have
                 certificates of essentially-quadratic binary space and
                 time complexity via Storjohann's algorithms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2011:SBB,
  author =       "Erich L. Kaltofen and Michael Nehring",
  title =        "Supersparse black box rational function
                 interpolation",
  crossref =     "Schost:2011:IPI",
  pages =        "177--186",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993916",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a method for interpolating a supersparse
                 blackbox rational function with rational coefficients,
                 for example, a ratio of binomials or trinomials with
                 very high degree. We input a blackbox rational
                 function, as well as an upper bound on the number of
                 non-zero terms and an upper bound on the degree. The
                 result is found by interpolating the rational function
                 modulo a small prime $p$, and then applying an
                 effective version of Dirichlet's Theorem on primes in
                 an arithmetic progression progressively lift the result
                 to larger primes. Eventually we reach a prime number
                 that is larger than the inputted degree bound and we
                 can recover the original function exactly. In a
                 variant, the initial prime $p$ is large, but the
                 exponents of the terms are known modulo larger and
                 larger factors of $ p - 1 $. The algorithm, as
                 presented, is conjectured to be polylogarithmic in the
                 degree, but exponential in the number of terms.
                 Therefore, it is very effective for rational functions
                 with a small number of non-zero terms, such as the
                 ratio of binomials, but it quickly becomes ineffective
                 for a high number of terms. The algorithm is oblivious
                 to whether the numerator and denominator have a common
                 factor. The algorithm will recover the sparse form of
                 the rational function, rather than the reduced form,
                 which could be dense. We have experimentally tested the
                 algorithm in the case of under 10 terms in numerator
                 and denominator combined and observed its conjectured
                 high efficiency.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaminski:2011:UDC,
  author =       "Jeremy-Yrmeyahu Kaminski and Yann Sepulcre",
  title =        "Using discriminant curves to recover a surface of {$
                 P^4 $} from two generic linear projections",
  crossref =     "Schost:2011:IPI",
  pages =        "187--192",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993917",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study how an irreducible smooth and closed
                 algebraic surface X embedded in CP$^4$, can be
                 recovered using its projections from two points onto
                 embedded projective hyperplanes. The different
                 embeddings are unknown. The only input is the defining
                 equation of each projected surface. We show how both
                 the embeddings and the surface in CP$^4$ can be
                 recovered modulo some action of the group of projective
                 transformations of CP$^4$. We show how in a generic
                 situation, a characteristic matrix of the pair of
                 embeddings can be recovered. Then we use this matrix to
                 recover the class of the couple of maps and as a
                 consequence to recover the surface. For a generic
                 situation, two projections define a surface with two
                 irreducible components. One component has degree d (d
                 -1) and the other has degree d, being the original
                 surface.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kapur:2011:CCG,
  author =       "Deepak Kapur and Yao Sun and Dingkang Wang",
  title =        "Computing comprehensive {Gr{\"o}bner} systems and
                 comprehensive {Gr{\"o}bner} bases simultaneously",
  crossref =     "Schost:2011:IPI",
  pages =        "193--200",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993918",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In Kapur et al (ISSAC, 2010), a new method for
                 computing a comprehensive Gr{\"o}bner system of a
                 parameterized polynomial system was proposed and its
                 efficiency over other known methods was effectively
                 demonstrated. Based on those insights, a new approach
                 is proposed for computing a comprehensive Gr{\"o}bner basis
                 of a parameterized polynomial system. The key new idea
                 is not to simplify a polynomial under various
                 specialization of its parameters, but rather keep track
                 in the polynomial, of the power products whose
                 coefficients vanish; this is achieved by partitioning
                 the polynomial into two parts- nonzero part and zero
                 part for the specialization under consideration. During
                 the computation of a comprehensive Gr{\"o}bner system, for
                 a particular branch corresponding to a specialization
                 of parameter values, nonzero parts of the polynomials
                 dictate the computation, i.e., computing S-polynomials
                 as well as for simplifying a polynomial with respect to
                 other polynomials; but the manipulations on the whole
                 polynomials (including their zero parts) are also
                 performed. Gr{\"o}bner basis computations on such pairs of
                 polynomials can also be viewed as Gr{\"o}bner basis
                 computations on a module. Once a comprehensive Gr{\"o}bner
                 system is generated, both nonzero and zero parts of the
                 polynomials are collected from every branch and the
                 result is a faithful comprehensive Gr{\"o}bner basis, to
                 mean that every polynomial in a comprehensive Gr{\"o}bner
                 basis belongs to the ideal of the original
                 parameterized polynomial system. This technique should
                 be applicable to other algorithms for computing a
                 comprehensive Gr{\"o}bner system as well, thus producing
                 both a comprehensive Gr{\"o}bner system as well as a
                 faithful comprehensive Gr{\"o}bner basis of a parameterized
                 polynomial system simultaneously. The approach is
                 exhibited by adapting the recently proposed method for
                 computing a comprehensive Gr{\"o}bner system in (ISSAC,
                 2010) for computing a comprehensive Gr{\"o}bner basis. The
                 timings on a collection of examples demonstrate that
                 this new algorithm for computing comprehensive Gr{\"o}bner
                 bases has better performance than other existing
                 algorithms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kauers:2011:CT,
  author =       "Manuel Kauers",
  title =        "The concrete tetrahedron",
  crossref =     "Schost:2011:IPI",
  pages =        "7--8",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993892",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We give an overview over computer algebra algorithms
                 for dealing with symbolic sums, recurrence equations,
                 generating functions, and asymptotic estimates, and we
                 will illustrate how to apply these algorithms to
                 problems arising in discrete mathematics.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kauers:2011:RDB,
  author =       "Manuel Kauers and Carsten Schneider",
  title =        "A refined denominator bounding algorithm for
                 multivariate linear difference equations",
  crossref =     "Schost:2011:IPI",
  pages =        "201--208",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993919",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We continue to investigate which polynomials can
                 possibly occur as factors in the denominators of
                 rational solutions of a given partial linear difference
                 equation. In an earlier article we have introduced the
                 distinction between periodic and aperiodic factors in
                 the denominator, and we have given an algorithm for
                 predicting the aperiodic ones. Now we extend this
                 technique towards the periodic case and present a
                 refined algorithm which also finds most of the periodic
                 factors.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kerber:2011:ERR,
  author =       "Michael Kerber and Michael Sagraloff",
  title =        "Efficient real root approximation",
  crossref =     "Schost:2011:IPI",
  pages =        "209--216",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993920",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider the problem of approximating all real
                 roots of a square-free polynomial f. Given isolating
                 intervals, our algorithm refines each of them to a
                 width at most $ 2^{-L} $, that is, each of the roots is
                 approximated to $L$ bits after the binary point. Our
                 method provides a certified answer for arbitrary real
                 polynomials, only requiring finite approximations of
                 the polynomial coefficient and choosing a suitable
                 working precision adaptively. In this way, we get a
                 correct algorithm that is simple to implement and
                 practically efficient. Our algorithm uses the quadratic
                 interval refinement method; we adapt that method to be
                 able to cope with inaccuracies when evaluating $f$,
                 without sacrificing its quadratic convergence behavior.
                 We prove a bound on the bit complexity of our algorithm
                 in terms of degree, coefficient size and discriminant.
                 Our bound improves previous work on integer polynomials
                 by a factor of $ \deg f $ and essentially matches best
                 known theoretical bounds on root approximation which
                 are obtained by very sophisticated algorithms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2011:APF,
  author =       "Yue Li and Gabriel {Dos Reis}",
  title =        "An automatic parallelization framework for algebraic
                 computation systems",
  crossref =     "Schost:2011:IPI",
  pages =        "233--240",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993923",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper proposes a non-intrusive automatic
                 parallelization framework for typeful and
                 property-aware computer algebra systems. Automatic
                 parallelization remains a promising computer program
                 transformation for exploiting ubiquitous concurrency
                 facilities available in modern computers. The framework
                 uses semantics-based static analysis to extract
                 reductions in library components based on algebraic
                 properties. An early implementation shows up to 5 times
                 speed-up for library functions and homotopy-based
                 polynomial system solver. The general framework is
                 applicable to algebraic computation systems and
                 programming languages with advanced type systems that
                 support user-defined axioms or annotation systems.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2011:ARS,
  author =       "Hongbo Li and Ruiyong Sun and Shoubin Yao and Ge Li",
  title =        "Approximate rational solutions torational {ODEs}
                 defined on discrete differentiable curves",
  crossref =     "Schost:2011:IPI",
  pages =        "217--224",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993921",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  abstract =     "In this paper, a new concept is proposed for discrete
                 differential geometry: discrete n-differentiable curve,
                 which is a tangent n-jet on a sequence of space points.
                 A complete method is proposed to solve ODEs of the form
                 n$^{(m)} = F(r, r', \ldots {}, r^{(n)}, n, n', \ldots
                 {}, n^{(m - 1)}, u) / G (r, r', \ldots {}, r^{(n)}, n,
                 n', \ldots {}, n^{(m - 1)}, u)$, where $F$, $G$ are
                 respectively vector-valued and scalar-valued
                 polynomials, where $r$ is a discrete curve obtained by
                 sampling along an unknown smooth curve parametrized by
                 $u$, and where $n$ is the vector field to be computed
                 along the curve. Our Maple-13 program outputs an
                 approximate rational solution with the highest order of
                 approximation for given data and neighborhood size. The
                 method is used to compute rotation minimizing frames of
                 space curves in CAGD. For one-step backward-forward
                 chasing, a 6th-order approximate rational solution is
                 found, and 6 is guaranteed to be the highest order of
                 approximation by rational functions. The theoretical
                 order of approximation is also supported by numerical
                 experiments.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2011:SDR,
  author =       "Wei Li and Xiao-Shan Gao and Cum-Ming Yuan",
  title =        "Sparse differential resultant",
  crossref =     "Schost:2011:IPI",
  pages =        "225--232",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993922",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, the concept of sparse differential
                 resultant for a differentially essential system of
                 differential polynomials is introduced and its
                 properties are proved. In particular, a degree bound
                 for the sparse differential resultant is given. Based
                 on the degree bound, an algorithm to compute the sparse
                 differential resultant is proposed, which is single
                 exponential in terms of the order, the number of
                 variables, and the size of the differentially essential
                 system.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ma:2011:MRG,
  author =       "Yue Ma and Lihong Zhi",
  title =        "The minimum-rank gram matrix completion via modified
                 fixed point continuation method",
  crossref =     "Schost:2011:IPI",
  pages =        "241--248",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993924",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The problem of computing a representation for a real
                 polynomial as a sum of minimum number of squares of
                 polynomials can be casted as finding a symmetric
                 positive semidefinite real matrix of minimum rank
                 subject to linear equality constraints. In this paper,
                 we propose algorithms for solving the minimum-rank Gram
                 matrix completion problem, and show the convergence of
                 these algorithms. Our methods are based on the fixed
                 point continuation method. We also use the
                 Barzilai--Borwein technique and a specific linear
                 combination of two previous iterates to accelerate the
                 convergence of modified fixed point continuation
                 algorithms. We demonstrate the effectiveness of our
                 algorithms for computing approximate and exact rational
                 sum of squares decompositions of polynomials with
                 rational coefficients.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mantzaflaris:2011:DCI,
  author =       "Angelos Mantzaflaris and Bernard Mourrain",
  title =        "Deflation and certified isolation of singular zeros of
                 polynomial systems",
  crossref =     "Schost:2011:IPI",
  pages =        "249--256",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993925",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We develop a new symbolic-numeric algorithm for the
                 certification of singular isolated points, using their
                 associated local ring structure and certified numerical
                 computations. An improvement of an existing method to
                 compute inverse systems is presented, which avoids
                 redundant computation and reduces the size of the
                 intermediate linear systems to solve. We derive a
                 one-step deflation technique, from the description of
                 the multiplicity structure in terms of differentials.
                 The deflated system can be used in Newton-based
                 iterative schemes with quadratic convergence. Starting
                 from a polynomial system and a sufficiently small
                 neighborhood, we obtain a criterion for the existence
                 and uniqueness of a singular root of a given
                 multiplicity structure, applying a well-chosen symbolic
                 perturbation. Standard verification methods, based e.g.
                 on interval arithmetic and a fixed point theorem, are
                 employed to certify that there exists a unique
                 perturbed system with a singular root in the domain.
                 Applications to topological degree computation and to
                 the analysis of real branches of an implicit curve
                 illustrate the method.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mayr:2011:SEG,
  author =       "Ernst W. Mayr and Stephan Ritscher",
  title =        "Space-efficient {Gr{\"o}bner} basis computation
                 without degree bounds",
  crossref =     "Schost:2011:IPI",
  pages =        "257--264",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993926",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The computation of a Gr{\"o}bner basis of a polynomial
                 ideal is known to be exponential space complete. We
                 revisit the algorithm by K{\"u}hnle and Mayr using
                 recent improvements of various degree bounds. The
                 result is an algorithm which is exponential in the
                 ideal dimension (rather than the number of
                 indeterminates). Furthermore, we provide an incremental
                 version of the algorithm which is independent of the
                 knowledge of degree bounds. Employing a space-efficient
                 implementation of Buchberger's S-criterion, the
                 algorithm can be implemented such that the space
                 requirement depends on the representation and
                 Gr{\"o}bner basis degrees of the problem instance
                 (instead of the worst case) and thus is much lower in
                 average.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Miller:2011:CAE,
  author =       "Victor S. Miller",
  title =        "Computational aspects of elliptic curves and modular
                 forms",
  crossref =     "Schost:2011:IPI",
  pages =        "1--2",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993888",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The ultimate motivation for much of the study of
                 Number Theory is the solution of Diophantine Equations
                 --- finding integer solutions to systems of equations.
                 Elliptic curves comprise a large, and important class
                 of such equations. Throughout the history of their
                 study Elliptic Curves have always had a strong
                 algorithmic component. In the early 1960's Birch and
                 Swinnerton-Dyer developed systematic algorithms to
                 automate a generalization of a procedure called
                 ``descent'' which went back to Fermat. The data they
                 obtained was instrumental in formulating their famous
                 conjecture, which is now one of the Clay Mathematical
                 Institute's Millenium prizes.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Moody:2011:DPJ,
  author =       "Dustin Moody",
  title =        "Division polynomials for {Jacobi} quartic curves",
  crossref =     "Schost:2011:IPI",
  pages =        "265--272",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993927",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we find division polynomials for Jacobi
                 quartics. These curves are an alternate model for
                 elliptic curves to the more common Weierstrass
                 equation. Division polynomials for Weierstrass curves
                 are well known, and the division polynomials we find
                 are analogues for Jacobi quartics. Using the division
                 polynomials, we show recursive formulas for the n -th
                 multiple of a point on the quartic curve. As an
                 application, we prove a type of mean-value theorem for
                 Jacobi quartics. These results can be extended to other
                 models of elliptic curves, namely, Jacobi intersections
                 and Huff curves.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nagasaka:2011:CSG,
  author =       "Kosaku Nagasaka",
  title =        "Computing a structured {Gr{\"o}bner} basis
                 approximately",
  crossref =     "Schost:2011:IPI",
  pages =        "273--280",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993928",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "There are several preliminary definitions for a
                 Gr{\"o}bner basis with inexact input since computing
                 such a basis is one of the challenging problems in
                 symbolic-numeric computations for several decades. A
                 structured Gr{\"o}bner basis is such a basis defined
                 from the data mining point of view: how to extract a
                 meaningful result from the given inexact input when the
                 amount of noise is not small or we do not have enough
                 information about the input. However, the known
                 algorithm needs a suitable (unknown) information on
                 terms required for a variant of the Buchberger
                 algorithm. In this paper, we introduce an improved
                 version of the algorithm that does not need any extra
                 information in advance.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2011:RPM,
  author =       "Victor Y. Pan and Guoliang Qian and Ai-Long Zheng",
  title =        "Randomized preconditioning of the {MBA} algorithm",
  crossref =     "Schost:2011:IPI",
  pages =        "281--288",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993929",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "MBA algorithm inverts a structured matrix in nearly
                 linear arithmetic time but requires a serious
                 restriction on the input class. We remove this
                 restriction by means of randomization and extend the
                 progress to some fundamental computations with
                 polynomials, e.g., computing their GCDs and AGCDs,
                 where most effective known algorithms rely on
                 computations with matrices having Toeplitz-like
                 structure. Furthermore, our randomized algorithms fix
                 rank deficiency and ill conditioning of general and
                 structured matrices. At the end we comment on a wide
                 range of other natural extensions of our progress and
                 underlying ideas.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pospelov:2011:FFT,
  author =       "Alexey Pospelov",
  title =        "{Fast Fourier Transforms} over poor fields",
  crossref =     "Schost:2011:IPI",
  pages =        "289--296",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993930",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a new algebraic algorithm for computing the
                 discrete Fourier transform over arbitrary fields. It
                 computes DFTs of infinitely many orders $n$ in $ O(n
                 \log n) $ algebraic operations, while the complexity of
                 a straightforward application of the known FFT
                 algorithms can be $ \Omega (n^{1.5}) $ for such $n$.
                 Our algorithm is a novel combination of the classical
                 FFT algorithms, and is never slower than any of the
                 latter. As an application we come up with an efficient
                 way of computing DFTs of high orders in finite field
                 extensions which can further boost polynomial
                 multiplication algorithms. We relate the complexities
                 of the DFTs of such orders with the complexity of
                 polynomial multiplication.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sagraloff:2011:SEE,
  author =       "Michael Sagraloff and Chee K. Yap",
  title =        "A simple but exact and efficient algorithm for complex
                 root isolation",
  crossref =     "Schost:2011:IPI",
  pages =        "353--360",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993938",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a new exact subdivision algorithm CEVAL for
                 isolating the complex roots of a square-free polynomial
                 in any given box. It is a generalization of a previous
                 real root isolation algorithm called EVAL. Under
                 suitable conditions, our approach is applicable for
                 general analytic functions. CEVAL is based on the
                 simple Bolzano Principle and is easy to implement
                 exactly. Preliminary experiments have shown its
                 competitiveness. We further show that, for the
                 ``benchmark problem'' of isolating all roots of a
                 square-free polynomial with integer coefficients, the
                 asymptotic complexity of both algorithms EVAL and CEVAL
                 matches (up a logarithmic term) that of more
                 sophisticated real root isolation methods which are
                 based on Descartes' Rule of Signs, Continued Fraction
                 or Sturm sequence. In particular, we show that the tree
                 size of EVAL matches that of other algorithms. Our
                 analysis is based on a novel technique called \Delta
                 -clusters from which we expect to see further
                 applications.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sarkar:2011:NRR,
  author =       "Soumojit Sarkar and Arne Storjohann",
  title =        "Normalization of row reduced matrices",
  crossref =     "Schost:2011:IPI",
  pages =        "297--304",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993931",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper gives a deterministic algorithm to
                 transform a row reduced matrix to canonical Popov form.
                 Given as input a row reduced matrix $R$ over $ K[x] $,
                 $ K a $ field, our algorithm computes the Popov form in
                 about the same time as required to multiply together
                 over $ K[x] $ two matrices of the same dimension and
                 degree as $R$. We also show that the problem of
                 transforming a row reduced matrix to Popov form is at
                 least as hard as polynomial matrix multiplication.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Saunders:2011:NSE,
  author =       "B. David Saunders and David Harlan Wood and Bryan S.
                 Youse",
  title =        "Numeric-symbolic exact rational linear system solver",
  crossref =     "Schost:2011:IPI",
  pages =        "305--312",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993932",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An iterative refinement approach is taken to rational
                 linear system solving. Such methods produce, for each
                 entry of the solution vector, a rational approximation
                 with denominator a power of 2. From this the correct
                 rational entry can be reconstructed. Our iteration is a
                 numeric-symbolic hybrid in that it uses an approximate
                 numeric solver at each step together with a symbolic
                 (exact arithmetic) residual computation and symbolic
                 rational reconstruction. The rational solution may be
                 checked symbolically (exactly). However, there is some
                 possibility of failure of convergence, usually due to
                 numeric ill-conditioning. Alternatively, the algorithm
                 may be used to obtain an extended precision floating
                 point approximation of any specified precision. In this
                 case we cannot guarantee the result by rational
                 reconstruction and an exact solution check, but the
                 approach gives evidence (not proof) that the
                 probability of error is extremely small. The chief
                 contributions of the method and implementation are (1)
                 confirmed continuation, (2) improved rational
                 reconstruction, and (3) faster and more robust
                 performance.",
  acknowledgement = ack-nhfb,
}

@InProceedings{She:2011:AAA,
  author =       "Zhikun She and Bai Xue and Zhiming Zheng",
  title =        "Algebraic analysis on asymptotic stability of
                 continuous dynamical systems",
  crossref =     "Schost:2011:IPI",
  pages =        "313--320",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993933",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we propose a mechanisable technique for
                 asymptotic stability analysis of continuous dynamical
                 systems. We start from linearizing a continuous
                 dynamical system, solving the Lyapunov matrix equation
                 and then check whether the solution is positive
                 definite. For the cases that the Jacobian matrix is not
                 a Hurwitz matrix, we first derive an algebraizable
                 sufficient condition for the existence of a Lyapunov
                 function in quadratic form without linearization. Then,
                 we apply a real root classification based method step
                 by step to formulate this derived condition as a
                 semi-algebraic set such that the semi-algebraic set
                 only involves the coefficients of the pre-assumed
                 quadratic form. Finally, we compute a sample point in
                 the resulting semi-algebraic set for the coefficients
                 resulting in a Lyapunov function. In this way, we avoid
                 the use of generic quantifier elimination techniques
                 for efficient computation. We prototypically
                 implemented our algorithm based on DISCOVERER. The
                 experimental results and comparisons demonstrate the
                 feasibility and promise of our approach.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Strzebonski:2011:URR,
  author =       "Adam Strzebonski and Elias Tsigaridas",
  title =        "Univariate real root isolation in an extension field",
  crossref =     "Schost:2011:IPI",
  pages =        "321--328",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993934",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  abstract =     "We present algorithmic, complexity and implementation
                 results for the problem of isolating the real roots of
                 a univariate polynomial in $ B_{\alpha} \in L [y] $,
                 where $ L = Q \alpha $ is a simple algebraic extension
                 of the rational numbers. We revisit two approaches for
                 the problem. In the first approach, using resultant
                 computations, we perform a reduction to a polynomial
                 with integer coefficients and we deduce a bound of $
                 O_B(N^{10}) $ for isolating the real roots of $
                 B_\alpha $, where $N$ is an upper bound on all the
                 quantities (degree and bitsize) of the input
                 polynomials. In the second approach we isolate the real
                 roots working directly on the polynomial of the input.
                 We compute improved separation bounds for the roots and
                 we prove that they are optimal, under mild assumptions.
                 For isolating the real roots we consider a modified
                 Sturm algorithm, and a modified version of Descartes'
                 algorithm introduced by Sagraloff. For the former we
                 prove a complexity bound of $ O_B(N^8) $ and for the
                 latter a bound of $ O_B(N^7) $. We implemented the
                 algorithms in C as part of the core library of
                 Mathematica and we illustrate their efficiency over
                 various data sets. Finally, we present complexity for
                 the general case of the first approach, where the
                 coefficients belong to multiple extensions.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sturm:2011:VSU,
  author =       "Thomas Sturm and Ashish Tiwari",
  title =        "Verification and synthesis using real quantifier
                 elimination",
  crossref =     "Schost:2011:IPI",
  pages =        "329--336",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993935",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present the application of real quantifier
                 elimination to formal verification and synthesis of
                 continuous and switched dynamical systems. Through a
                 series of case studies, we show how first-order
                 formulas over the reals arise when formally analyzing
                 models of complex control systems. Existing
                 off-the-shelf quantifier elimination procedures are not
                 successful in eliminating quantifiers from many of our
                 benchmarks. We therefore automatically combine three
                 established software components: virtual substitution
                 based quantifier elimination in Reduce/Redlog,
                 cylindrical algebraic decomposition implemented in
                 Qepcad, and the simplifier Slfq implemented on top of
                 Qepcad. We use this combination to successfully analyze
                 various models of systems including adaptive cruise
                 control in automobiles, adaptive flight control system,
                 and the classical inverted pendulum problem studied in
                 control theory.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sun:2011:GCS,
  author =       "Yao Sun and Dingkang Wang",
  title =        "A generalized criterion for signature related
                 {Gr{\"o}bner} basis algorithms",
  crossref =     "Schost:2011:IPI",
  pages =        "337--344",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993936",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A generalized criterion for signature related
                 algorithms to compute Gr{\"o}bner basis is proposed in
                 this paper. Signature related algorithms are a popular
                 kind of algorithms for computing Gr{\"o}bner basis,
                 including the famous F5 algorithm, the F5C algorithm,
                 the extended F5 algorithm and the GVW algorithm. The
                 main purpose of current paper is to study in theory
                 what kind of criteria is correct in signature related
                 algorithms and provide a generalized method to develop
                 new criteria. For this purpose, a generalized criterion
                 is proposed. The generalized criterion only relies on a
                 general partial order defined on a set of polynomials.
                 When specializing the partial order to appropriate
                 specific orders, the generalized criterion can
                 specialize to almost all existing criteria of signature
                 related algorithms. For admissible partial orders, a
                 proof is presented for the correctness of the algorithm
                 that is based on this generalized criterion. And the
                 partial orders implied by the criteria of F5 and GVW
                 are also shown to be admissible in this paper. More
                 importantly, the generalized criterion provides an
                 effective method to check whether a new criterion is
                 correct as well as to develop new criteria for
                 signature related algorithms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Szanto:2011:HSN,
  author =       "Agnes Szanto",
  title =        "Hybrid symbolic-numeric methods for the solution of
                 polynomial systems: tutorial overview",
  crossref =     "Schost:2011:IPI",
  pages =        "9--10",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993893",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this tutorial we will focus on the solution of
                 polynomial systems given with inexact coefficients
                 using hybrid symbolic-numeric methods. In particular,
                 we will concentrate on systems that are
                 over-constrained or have roots with multiplicities.
                 These systems are considered ill-posed or
                 ill-conditioned by traditional numerical methods and
                 they try to avoid them. On the other hand, traditional
                 symbolic methods are not designed to handle
                 inexactness. Ill-conditioned polynomial equation
                 systems arise very frequently in many important
                 applications areas such as geometric modeling, computer
                 vision, fluid dynamics, etc.",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:2011:GS,
  author =       "Mark van Hoeij and J{\"u}rgen Kl{\"u}ners and Andrew
                 Novocin",
  title =        "Generating subfields",
  crossref =     "Schost:2011:IPI",
  pages =        "345--352",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993937",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Given a field extension K/k of degree n we are
                 interested in finding the subfields of K containing k.
                 There can be more than polynomially many subfields. We
                 introduce the notion of generating subfields, a set of
                 up to n subfields whose intersections give the rest. We
                 provide an efficient algorithm which uses linear
                 algebra in k or lattice reduction along with
                 factorization. Our implementation shows that previously
                 difficult cases can now be handled.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Villard:2011:RPL,
  author =       "Gilles Villard",
  title =        "Recent progress in linear algebra and lattice basis
                 reduction",
  crossref =     "Schost:2011:IPI",
  pages =        "3--4",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993889",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A general goal concerning fundamental linear algebra
                 problems is to reduce the complexity estimates to
                 essentially the same as that of multiplying two
                 matrices (plus possibly a cost related to the input and
                 output sizes). Among the bottlenecks one usually finds
                 the questions of designing a recursive approach and
                 mastering the sizes of the intermediately computed
                 data. In this talk we are interested in two special
                 cases of lattice basis reduction. We consider bases
                 given by square matrices over $ K[x] $ or $Z$, with,
                 respectively, the notion of reduced form and LLL
                 reduction. Our purpose is to introduce basic tools for
                 understanding how to generalize the Lehmer and
                 Knuth--Sch{\"o}nhage gcd algorithms for basis
                 reduction. Over $ K[x] $ this generalization is a key
                 ingredient for giving a basis reduction algorithm whose
                 complexity estimate is essentially that of multiplying
                 two polynomial matrices. Such a problem relation
                 between integer basis reduction and integer matrix
                 multiplication is not known. The topic receives a lot
                 of attention, and recent results on the subject show
                 that there might be room for progressing on the
                 question.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abramov:2012:VMS,
  author =       "S. A. Abramov and D. E. Khmelnov",
  title =        "On valuations of meromorphic solutions of
                 arbitrary-order linear difference systems with
                 polynomial coefficients",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "12--19",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442836",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Algorithms for computing lower bounds on valuations
                 (e.g., orders of the poles) of the components of
                 meromorphic solutions of arbitrary-order linear
                 difference systems with polynomial coefficients are
                 considered. In addition to algorithms based on ideas
                 which have been already utilized in computer algebra
                 for treating normal first-order systems, a new
                 algorithm using tropical calculations is proposed. It
                 is shown that the latter algorithm is rather fast, and
                 produces the bounds with good accuracy.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adrovic:2012:CPS,
  author =       "Danko Adrovic and Jan Verschelde",
  title =        "Computing {Puiseux} series for algebraic surfaces",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "20--27",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442837",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we outline an algorithmic approach to
                 compute Puiseux series expansions for algebraic sets.
                 The series expansions originate at the intersection of
                 the algebraic set with as many coordinate planes as the
                 dimension of the algebraic set. Our approach starts
                 with a polyhedral method to compute cones of normal
                 vectors to the Newton polytopes of the given polynomial
                 system that defines the algebraic set. If as many
                 vectors in the cone as the dimension of the algebraic
                 set define an initial form system that has isolated
                 solutions, then those vectors are potential tropisms
                 for the initial term of the Puiseux series expansion.
                 Our preliminary methods produce exact representations
                 for solution sets of the cyclic $n$-roots problem, for
                 $n = m^2$, corresponding to a result of Backelin.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Albrecht:2012:MLD,
  author =       "Martin R. Albrecht",
  title =        "The {M4RIE} library for dense linear algebra over
                 small fields with even characteristic",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "28--34",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442838",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We describe algorithms and implementations for linear
                 algebra with dense matrices over $ F_2 e $ for $ 2 \leq
                 e \leq 10 $. Our main contributions are: (1) a
                 specialisation of precomputation tables to $ F_2 e $,
                 called Newton--John tables in this work, to avoid
                 scalar multiplications in Gaussian elimination and
                 matrix multiplication, (2) an efficient implementation
                 of Karatsuba-style multiplication for matrices over
                 extension fields of $ F_2 $ and (3) a description of an
                 open-source library --- called M4RIE --- providing the
                 fastest known implementation of dense linear algebra
                 over $ F_2 e $ with $ 2 \leq e \leq 10 $.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:2012:CCF,
  author =       "M. A. Barkatou and T. Cluzeau and C. {El Bacha} and
                 J.-A. Weil",
  title =        "Computing closed form solutions of integrable
                 connections",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "43--50",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442840",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  abstract =     "We present algorithms for computing rational and
                 hyperexponential solutions of linear $D$-finite partial
                 differential systems written as integrable connections.
                 We show that these types of solutions can be computed
                 recursively by adapting existing algorithms handling
                 ordinary linear differential systems. We provide an
                 arithmetic complexity analysis of the algorithms that
                 we develop. A Maple implementation is available and
                 some examples and applications are given.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Barkatou:2012:SLO,
  author =       "Moulay A. Barkatou and Clemens G. Raab",
  title =        "Solving linear ordinary differential systems in
                 hyperexponential extensions",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "51--58",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442841",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let F be a differential field generated from the
                 rational functions over some constant field by one
                 hyperexponential extension. We present an algorithm to
                 compute the solutions in $F^n$ of systems of $n$
                 first-order linear ODEs. Solutions in $F$ of a scalar ODE
                 of higher order can be determined by an algorithm of
                 Bronstein and Fredet. Our approach avoids reduction to
                 the scalar case. We also give examples to show how this
                 can be applied to integration.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Berthomieu:2012:RPA,
  author =       "J{\'e}r{\'e}my Berthomieu and Romain Lebreton",
  title =        "Relaxed $p$-adic {Hensel} lifting for algebraic
                 systems",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "59--66",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442842",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In a previous article [1], an implementation of lazy p
                 -adic integers with a multiplication of quasi-linear
                 complexity, the so-called relaxed product, was
                 presented. Given a ring $R$ and an element $p$ in $R$,
                 we design a relaxed Hensel lifting for algebraic
                 systems from $R / (p)$ to the $p$-adic completion $R_p$
                 of $R$. Thus, any root of linear and algebraic regular
                 systems can be lifted with a quasi-optimal
                 complexity. We report our implementations in C++ within
                 the computer algebra system Mathemagix and compare them
                 with Newton operator. As an application, we solve
                 linear systems over the integers and compare the
                 running times with Linbox and IML.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bettale:2012:SPS,
  author =       "Luk Bettale and Jean-Charles Faug{\`e}re and Ludovic
                 Perret",
  title =        "Solving polynomial systems over finite fields:
                 improved analysis of the hybrid approach",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "67--74",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442843",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The Polynomial System Solving (PoSSo) problem is a
                 fundamental NP-Hard problem in computer algebra. Among
                 others, PoSSo have applications in area such as coding
                 theory and cryptology. Typically, the security of
                 multivariate public-key schemes (MPKC) such as the UOV
                 cryptosystem of Kipnis, Shamir and Patarin is directly
                 related to the hardness of PoSSo over finite fields.
                 The goal of this paper is to further understand the
                 influence of finite fields on the hardness of PoSSo. To
                 this end, we consider the so-called hybrid approach.
                 This is a polynomial system solving method dedicated to
                 finite fields proposed by Bettale, Faug{\`e}re and
                 Perret (Journal of Mathematical Cryptography, 2009).
                 The idea is to combine exhaustive search with
                 Gr{\"o}bner bases. The efficiency of the hybrid
                 approach is related to the choice of a trade-off
                 between the two methods. We propose here an improved
                 complexity analysis dedicated to quadratic systems.
                 Whilst the principle of the hybrid approach is simple,
                 its careful analysis leads to rather surprising and
                 somehow unexpected results. We prove that the optimal
                 trade-off (i.e. number of variables to be fixed)
                 allowing to minimize the complexity is achieved by
                 fixing a number of variables proportional to the number
                 of variables of the system considered, denoted n. Under
                 some natural algebraic assumption, we show that the
                 asymptotic complexity of the hybrid approach is $
                 2^{(3.31 - 3.62 \log 2 (q) - 1) n} $, where $q$ is the
                 size of the field (under the condition in particular
                 that $ \log (q) \ll n $). This is to date, the best
                 complexity for solving PoSSo over finite fields (when $
                 q > 2 $). We have been able to quantify the gain
                 provided by the hybrid approach compared to a direct
                 Gr{\" o}bner basis method. For quadratic systems, we
                 show (assuming a natural algebraic assumption) that
                 this gain is exponential in the number of variables.
                 Asymptotically, the gain is $ 2^{1.49 n} $ when both
                 $n$ and $q$ grow to infinity and $ \log (q) \ll n $.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beukers:2012:HFC,
  author =       "Frits Beukers",
  title =        "{$A$}-hypergeometric functions: computational
                 aspects",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "1--2",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442830",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Biasse:2012:PTA,
  author =       "Jean-Fran{\c{c}}ois Biasse and Claus Fieker",
  title =        "A polynomial time algorithm for computing the {HNF} of
                 a module over the integers of a number field",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "75--82",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442844",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a variation of the modular algorithm for
                 computing the Hermite Normal Form of an $O_K$-module
                 presented by Cohen [4], where $O_K$ is the ring of
                 integers of a number field $K$. An approach presented in
                 [4] based on reductions modulo ideals was conjectured
                 to run in polynomial time by Cohen, but so far, no such
                 proof was available in the literature. In this paper,
                 we present a modification of the approach of [4] to
                 prevent the coefficient swell and we rigorously assess
                 its complexity with respect to the size of the input
                 and the invariants of the field $K$.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Biscani:2012:PSP,
  author =       "Francesco Biscani",
  title =        "Parallel sparse polynomial multiplication on modern
                 hardware architectures",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "83--90",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442845",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/hash.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a high performance algorithm for the
                 parallel multiplication of sparse multivariate
                 polynomials on modern computer architectures. The
                 algorithm is built on three main concepts: a
                 cache-friendly hash table implementation for the
                 storage of polynomial terms in distributed form, a
                 statistical method for the estimation of the size of
                 the multiplication result, and the use of Kronecker
                 substitution as a homomorphic hash function. The
                 algorithm achieves high performance by promoting data
                 access patterns that favour temporal and spatial
                 locality of reference. We present benchmarks comparing
                 our algorithm to routines of other computer algebra
                 systems, both in sequential and parallel mode.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Blankertz:2012:CCD,
  author =       "Raoul Blankertz and Joachim von zur Gathen and
                 Konstantin Ziegler",
  title =        "Compositions and collisions at degree $ p^2 $",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "91--98",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442846",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A univariate polynomial $f$ over a field is
                 decomposable if $ f = g o h = g (h) $ for nonlinear
                 polynomials $g$ and $h$. In order to count the
                 decomposables, one wants to know the number of
                 equal-degree collisions of the form $ f = g o h = g * o
                 h * $ with $ (g, h) /= (g *, h *) $ and $ \deg g = \deg
                 g * $. Such collisions only occur in the wild case,
                 where the field characteristic $p$ divides $ \deg f $.
                 Reasonable bounds on the number of decomposables over a
                 finite field are known, but they are less sharp in the
                 wild case, in particular for degree $ p^2 $. We provide
                 a classification of all polynomials of degree $ p^2 $
                 with a collision. It yields the exact number of
                 decomposable polynomials of degree $ p^2 $ over a
                 finite field of characteristic $p$. We also present an
                 algorithm that determines whether a given polynomial of
                 degree $ p^2 $ has a collision or not.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2012:FCC,
  author =       "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and Bruno
                 Salvy and Ziming Li",
  title =        "Fast computation of common left multiples of linear
                 ordinary differential operators",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "99--106",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442847",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study tight bounds and fast algorithms for LCLMs of
                 several linear differential operators with polynomial
                 coefficients. We analyse the arithmetic complexity of
                 existing algorithms for LCLMs, as well as the size of
                 their outputs. We propose a new algorithm that recasts
                 the LCLM computation in a linear algebra problem on a
                 polynomial matrix. This algorithm yields sharp bounds
                 on the coefficient degrees of the LCLM, improving by
                 one order of magnitude the best bounds obtained using
                 previous algorithms. The complexity of the new
                 algorithm is almost optimal, in the sense that it
                 nearly matches the arithmetic size of the output.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2012:PSS,
  author =       "Alin Bostan and Bruno Salvy and Muhammad F. I.
                 Chowdhury and {\'E}ric Schost and Romain Lebreton",
  title =        "Power series solutions of singular $ (q)
                 $-differential equations",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "107--114",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442848",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We provide algorithms computing power series solutions
                 of a large class of differential or $q$-differential
                 equations or systems. Their number of arithmetic
                 operations grows linearly with the precision, up to
                 logarithmic terms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bournez:2012:CSI,
  author =       "Olivier Bournez and Daniel S. Gra{\c{c}}a and Amaury
                 Pouly",
  title =        "On the complexity of solving initial value problems",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "115--121",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442849",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we prove that computing the solution of
                 an initial-value problem $ y = p(y) $ with initial
                 condition $ y (t_0) = y_0 \in R^d $ at time $ t_0 + T $
                 with precision $ 2^{- \mu } $ where $p$ is a vector of
                 polynomials can be done in time polynomial in the value
                 of $T$, $ \mu $ and $ Y = [{\rm equation}] $. Contrary
                 to existing results, our algorithm works over any
                 bounded or unbounded domain. Furthermore, we do not
                 assume any Lipschitz condition on the initial-value
                 problem.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2012:ODC,
  author =       "Shaoshi Chen and Manuel Kauers",
  title =        "Order-degree curves for hypergeometric creative
                 telescoping",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "122--129",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442850",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Creative telescoping applied to a bivariate proper
                 hypergeometric term produces linear recurrence
                 operators with polynomial coefficients, called
                 telescopers. We provide bounds for the degrees of the
                 polynomials appearing in these operators. Our bounds
                 are expressed as curves in the $ (r, d) $-plane which
                 assign to every order $r$ a bound on the degree $d$ of
                 the telescopers. These curves are hyperbolas, which
                 reflect the phenomenon that higher order telescopers
                 tend to have lower degree, and vice versa.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2012:TRA,
  author =       "Shaoshi Chen and Manuel Kauers and Michael F. Singer",
  title =        "Telescopers for rational and algebraic functions via
                 residues",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "130--137",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442851",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We show that the problem of constructing telescopers
                 for rational functions of $ m + 1 $ variables is
                 equivalent to the problem of constructing telescopers
                 for algebraic functions of $m$ variables and we present
                 a new algorithm to construct telescopers for algebraic
                 functions of two variables. These considerations are
                 based on analyzing the residues of the input. According
                 to experiments, the resulting algorithm for rational
                 functions of three variables is faster than known
                 algorithms, at least in some examples of combinatorial
                 interest. The algorithm for algebraic functions implies
                 a new bound on the order of the telescopers.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Comer:2012:SPI,
  author =       "Matthew T. Comer and Erich L. Kaltofen and Cl{\'e}ment
                 Pernet",
  title =        "Sparse polynomial interpolation and {Berlekamp\slash
                 Massey} algorithms that correct outlier errors in input
                 values",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "138--145",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442852",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We propose algorithms performing sparse interpolation
                 with errors, based on Prony's--Ben-Or's {\&} Tiwari's
                 algorithm, using a Berlekamp/Massey algorithm with
                 early termination. First, we present an algorithm that
                 can recover a $t$-sparse polynomial $f$ from a sequence
                 of values, where some of the values are wrong, spoiled
                 by either random or misleading errors. Our algorithm
                 requires bounds $ T \geq t $ and $ E \geq e $, where
                 $e$ is the number of evaluation errors. It interpolates
                 $ f(\omega^i) $ for $ i = 1, \ldots {}, 2 T (E + 1) $,
                 where $ \omega $ is a field element at which each
                 non-zero term evaluates distinctly. We also investigate
                 the problem of recovering the minimal linear generator
                 from a sequence of field elements that are linearly
                 generated, but where again $ e \leq E $ elements are
                 erroneous. We show that there exist sequences of $ < 2
                 t (2 e + 1) $ elements, such that two distinct
                 generators of length $t$ satisfy the linear recurrence
                 up to $e$ faults, at least if the field has
                 characteristic $ /= 2 $. Uniqueness can be proven (for
                 any field characteristic) for length $ \geq 2 t (2 e +
                 1) $ of the sequence with e errors. Finally, we present
                 the Majority Rule Berlekamp/Massey algorithm, which can
                 recover the unique minimal linear generator of degree
                 $t$ when given bounds $ T \geq t $ and $ E \geq e $ and
                 the initial sequence segment of $ 2 T (2 E + 1) $
                 elements. Our algorithm also corrects the sequence
                 segment. The Majority Rule algorithm yields a unique
                 sparse interpolant for the first problem. The
                 algorithms are applied to sparse interpolation
                 algorithms with numeric noise, into which we now can
                 bring outlier errors in the values.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Elsheikh:2012:FCS,
  author =       "Mustafa Elsheikh and Mark Giesbrecht and Andy Novocin
                 and B. David Saunders",
  title =        "Fast computation of {Smith} forms of sparse matrices
                 over local rings",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "146--153",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442853",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present algorithms to compute the Smith Normal Form
                 of matrices over two families of local rings. The
                 algorithms use the black-box model which is suitable
                 for sparse and structured matrices. The algorithms
                 depend on a number of tools, such as matrix rank
                 computation over finite fields, for which the
                 best-known time- and memory-efficient algorithms are
                 probabilistic. For an $ n \times n $ matrix $A$ over
                 the ring $ F[z] / (f^e) $, where $ f^e $ is a power of
                 an irreducible polynomial $ f \in F[z] $ of degree $d$,
                 our algorithm requires $ O(\eta d e^2 n) $ operations
                 in $F$, where our black-box is assumed to require $
                 O(\eta) $ operations in $F$ to compute a matrix-vector
                 product by a vector over $ F[z] / (f^e) $ (and $ \eta $
                 is assumed greater than $ n d e $). The algorithm only
                 requires additional storage for $ O(n d e) $ elements
                 of $F$. In particular, if $ \eta = O(n d e) $, then our
                 algorithm requires only $ O(n^2 d^2 e^3) $ operations
                 in $F$, which is an improvement on known dense methods
                 for small $d$ and $e$. For the ring $ Z / p^e Z $,
                 where $p$ is a prime, we give an algorithm which is
                 time- and memory-efficient when the number of
                 nontrivial invariant factors is small. We describe a
                 method for dimension reduction while preserving the
                 invariant factors. The time complexity is essentially
                 linear in $ \mu n r e \log p $, where $ \mu $ is the
                 number of operations in $ Z / p Z $ to evaluate the
                 black-box (assumed greater than $n$) and $r$ is the
                 total number of non-zero invariant factors. To avoid
                 the practical cost of conditioning, we give a Monte
                 Carlo certificate, which at low cost, provides either a
                 high probability of success or a proof of failure. The
                 quest for a time- and memory-efficient solution without
                 restrictions on the number of nontrivial invariant
                 factors remains open. We offer a conjecture which may
                 contribute toward that end.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Emeliyanenko:2012:CSB,
  author =       "Pavel Emeliyanenko and Michael Sagraloff",
  title =        "On the complexity of solving a bivariate polynomial
                 system",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "154--161",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442854",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study the complexity of computing the real
                 solutions of a bivariate polynomial system using the
                 recently presented algorithm Bisolve [2]. Bisolve is an
                 elimination method which, in a first step, projects the
                 solutions of a system onto the $x$- and $y$-axes and,
                 then, selects the actual solutions from the so induced
                 candidate set. However, unlike similar algorithms,
                 Bisolve requires no genericity assumption on the input,
                 and there is no need for any kind of coordinate
                 transformation. Furthermore, extensive benchmarks as
                 presented in [2] confirm that the algorithm is highly
                 practical, that is, a corresponding C++ implementation
                 in Cgal outperforms state of the art approaches by a
                 large factor. In this paper, we focus on the
                 theoretical complexity of Bisolve. For two polynomials
                 $ f, g \in Z[x, y] $ of total degree at most n with
                 integer coefficients bounded by $ 2^\tau $, we show
                 that Bisolve computes isolating boxes for all real
                 solutions of the system $ f = g = 0 $ using $ O(n^8 +
                 n^7 \tau) $ bit operations, thereby improving the
                 previous record bound for the same task by several
                 magnitudes.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2012:CPG,
  author =       "Jean-Charles Faug{\`e}re and Mohab Safey {El Din} and
                 Pierre-Jean Spaenlehauer",
  title =        "Critical points and {Gr{\"o}bner} bases: the unmixed
                 case",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "162--169",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442855",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We consider the problem of computing critical points
                 of the restriction of a polynomial map to an algebraic
                 variety. This is of first importance since the global
                 minimum of such a map is reached at a critical point.
                 Thus, these points appear naturally in non-convex
                 polynomial optimization which occurs in a wide range of
                 scientific applications (control theory, chemistry,
                 economics,\ldots{}). Critical points also play a
                 central role in recent algorithms of effective real
                 algebraic geometry. Experimentally, it has been
                 observed that Gr{\"o}bner basis algorithms are
                 efficient to compute such points. Therefore, recent
                 software based on the so-called Critical Point Method
                 are built on Gr{\"o}bner bases engines. Let $ f_1,
                 \ldots {}, f_p $ be polynomials in $ Q[x_1, \ldots {},
                 x_n] $ of degree $D$, $ V \subset C^n $ be their
                 complex variety and $ \pi_1 $ be the projection map $
                 (x_1, \ldots {}, x_n) \to x_1 $. The critical points of
                 the restriction of $ \pi_1 $ to $V$ are defined by the
                 vanishing of $ f_1, \ldots {}, f_p $ and some maximal
                 minors of the Jacobian matrix associated to $ f_1,
                 \ldots {}, f_p $. Such a system is algebraically
                 structured: the ideal it generates is the sum of a
                 determinantal ideal and the ideal generated by $ f_1,
                 \ldots {}, f_p $. We provide the first complexity
                 estimates on the computation of Gr{\"o}bner bases of
                 such systems defining critical points. We prove that
                 under genericity assumptions on $ f_1, \ldots {}, f_p
                 $, the complexity is polynomial in the generic number
                 of critical points, i.e. $ D^p(D - 1)^{n - p} (n - 1 /
                 p - 1) $. More particularly, in the quadratic case $ D
                 = 2 $, the complexity of such a Gr{\"o}bner basis
                 computation is polynomial in the number of variables
                 $n$ and exponential in $p$. We also give experimental
                 evidence supporting these theoretical results.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2012:SPS,
  author =       "Jean-Charles Faug{\`e}re and Jules Svartz",
  title =        "Solving polynomial systems globally invariant under an
                 action of the symmetric group and application to the
                 equilibria of {$N$} vortices in the plane",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "170--178",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442856",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We propose an efficient algorithm to solve polynomial
                 systems of which equations are globally invariant under
                 an action of the symmetric group G$_N$ acting on the
                 variable x$_i$ with \sigma (x$_i$) = x$_{ \sigma
                 (i)}$ and the number of variables is a multiple of N.
                 For instance, we can assume that swapping two variables
                 (or two pairs of variables) in one equation gives rise
                 to another equation of the system (perhaps changing the
                 sign). The idea is to apply many times divided
                 difference operators to the original system in order to
                 obtain a new system of equations involving only the
                 symmetric functions of a subset of the variables. The
                 next step is to solve the system using Gr{\"o}bner
                 techniques; this is usually several order faster than
                 computing the Gr{\"o}bner basis of the original system
                 since the number of solutions of the corresponding
                 ideal, which is always finite has been divided by at
                 least N!. To illustrate the algorithm and to
                 demonstrate its efficiency, we apply the method to a
                 well known physical problem called equilibria positions
                 of vortices. This problem has been studied for almost
                 150 years and goes back to works by von Helmholtz and
                 Lord Kelvin. Assuming that all vortices have same
                 vorticity, the problem can be reformulated as a system
                 of polynomial equations invariant under an action of
                 G$_N$. Using numerical methods, physicists have been
                 able to compute solutions up to N \leq 7 but it was an
                 open challenge to check whether the set of solution is
                 complete. Direct naive approach of Gr{\"o}bner bases
                 techniques give rise to hard-to-solve polynomial
                 system: for instance, when N = 5, it takes several days
                 to compute the Gr{\"o}bner basis and the number of
                 solutions is 2060. By contrast, applying the new
                 algorithm to the same problem gives rise to a system of
                 17 solutions that can be solved in less than 0.1 sec.
                 Moreover, we are able to compute all equilibria when N
                 \leq 7.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Garcia:2012:RIA,
  author =       "Maria Emilia Alonso Garcia and Andr{\'e} Galligo",
  title =        "A root isolation algorithm for sparse univariate
                 polynomials",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "35--42",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442839",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  abstract =     "We consider a univariate polynomial f with real
                 coefficients having a high degree $N$ but a rather
                 small number $ d + 1 $ of monomials, with $ d \ll N $.
                 Such a sparse polynomial has a number of real root
                 smaller or equal to $d$. Our target is to find for each
                 real root of $f$ an interval isolating this root from
                 the others. The usual subdivision methods, relying
                 either on Sturm sequences or M{\"o}bius transform
                 followed by Descartes' rule of sign, destruct the
                 sparse structure. Our approach relies on the
                 generalized Budan--Fourier theorem of Coste, Lajous,
                 Lombardi, Roy [8] and the techniques developed in
                 Galligo [12]. To such a $f$ is associated a set of $ d
                 + 1 $ $F$-derivatives. The Budan=-Fourier function $
                 V_f(x) $ counts the sign changes in the sequence of
                 $F$-derivatives of the $f$ evaluated at $x$. The values
                 at which this function jumps are called the $F$-virtual
                 roots of $f$, these include the real roots of $f$. We
                 also consider the augmented $F$-virtual roots of $f$
                 and introduce a genericity property which eases our
                 study. We present a real root isolation method and an
                 algorithm which has been implemented in Maple. We rely
                 on an improved generalized Budan--Fourier count applied
                 to both the input polynomial and its reciprocal,
                 together with Newton like approximation steps. The
                 paper is illustrated with examples and pictures.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Garoufalidis:2012:TQH,
  author =       "Stavros Garoufalidis and Christoph Koutschan",
  title =        "Twisting $q$-holonomic sequences by complex roots of
                 unity",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "179--186",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442857",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A sequence $ f_n (q) $ is $q$-holonomic if it
                 satisfies a nontrivial linear recurrence with
                 coefficients polynomials in $q$ and $ q^n $. Our main
                 theorems state that $q$-holonomicity is preserved under
                 twisting, i.e., replacing $q$ by $ \omega q $ where $
                 \omega $ is a complex root of unity, and under the
                 substitution $ q > q^\alpha $ where $ \alpha $ is a
                 rational number. Our proofs are constructive, work in
                 the multivariate setting of \partial -finite sequences
                 and are implemented in the Mathematica package {\tt
                 HolonomicFunctions}. Our results are illustrated by
                 twisting natural $q$-holonomic sequences which appear
                 in quantum topology, namely the colored Jones
                 polynomial of pretzel knots and twist knots. The
                 recurrence of the twisted colored Jones polynomial can
                 be used to compute the asymptotics of the Kashaev
                 invariant of a knot at an arbitrary complex root of
                 unity.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gleixner:2012:IAL,
  author =       "Ambros M. Gleixner and Daniel E. Steffy and Kati
                 Wolter",
  title =        "Improving the accuracy of linear programming solvers
                 with iterative refinement",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "187--194",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442858",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We describe an iterative refinement procedure for
                 computing extended precision or exact solutions to
                 linear programming problems (LPs). Arbitrarily precise
                 solutions can be computed by solving a sequence of
                 closely related LPs with limited precision arithmetic.
                 The LPs solved share the same constraint matrix as the
                 original problem instance and are transformed only by
                 modification of the objective function, right-hand
                 side, and variable bounds. Exact computation is used to
                 compute and store the exact representation of the
                 transformed problems, while numeric computation is used
                 for solving LPs. At all steps of the algorithm the LP
                 bases encountered in the transformed problems
                 correspond directly to LP bases in the original problem
                 description. We demonstrate that this algorithm is
                 effective in practice for computing extended precision
                 solutions and that this leads to direct improvement of
                 the best known methods for solving LPs exactly over the
                 rational numbers.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2012:CIH,
  author =       "Feng Guo and Erich L. Kaltofen and Lihong Zhi",
  title =        "Certificates of impossibility of {Hilbert--Artin}
                 representations of a given degree for definite
                 polynomials and functions",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "195--202",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442859",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We deploy numerical semidefinite programming and
                 conversion to exact rational inequalities to certify
                 that for a positive semidefinite input polynomial or
                 rational function, any representation as a fraction of
                 sums-of-squares of polynomials with real coefficients
                 must contain polynomials in the denominator of degree
                 no less than a given input lower bound. By Artin's
                 solution to Hilbert's 17th problems, such
                 representations always exist for some denominator
                 degree. Our certificates of infeasibility are based on
                 the generalization of Farkas's Lemma to semidefinite
                 programming. The literature has many famous examples of
                 impossibility of SOS representability including
                 Motzkin's, Robinson's, Choi's and Lam's polynomials,
                 and Reznick's lower degree bounds on uniform
                 denominators, e.g., powers of the sum-of-squares of
                 each variable. Our work on exact certificates for
                 positive semidefiniteness allows for non-uniform
                 denominators, which can have lower degree and are often
                 easier to convert to exact identities. Here we
                 demonstrate our algorithm by computing certificates of
                 impossibilities for an arbitrary sum-of-squares
                 denominator of degree 2 and 4 for some symmetric
                 sextics in 4 and 5 variables, respectively. We can also
                 certify impossibility of base polynomials in the
                 denominator of restricted term structure, for instance
                 as in Landau's reduction by one less variable.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hubert:2012:RIS,
  author =       "Evelyne Hubert and George Labahn",
  title =        "Rational invariants of scalings from {Hermite} normal
                 forms",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "219--226",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442862",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Scalings form a class of group actions that have both
                 theoretical and practical importance. A scaling is
                 accurately described by an integer matrix. Tools from
                 linear algebra are exploited to compute a minimal
                 generating set of rational invariants, trivial
                 rewriting and rational sections for such a group
                 action. The primary tools used are Hermite normal forms
                 and their unimodular multipliers. With the same line of
                 ideas, a complete solution to the scaling symmetry
                 reduction of a polynomial system is also presented.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ishikawa:2012:ZHA,
  author =       "Masao Ishikawa and Christoph Koutschan",
  title =        "{Zeilberger}'s holonomic ansatz for {Pfaffians}",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "227--233",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442863",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "A variation of Zeilberger's holonomic ansatz for
                 symbolic determinant evaluations is proposed which is
                 tailored to deal with Pfaffians. The method is also
                 applicable to determinants of skew-symmetric matrices,
                 for which the original approach does not work. As
                 Zeilberger's approach is based on the Laplace expansion
                 (cofactor expansion) of the determinant, we derive our
                 approach from the cofactor expansion of the Pfaffian.
                 To demonstrate the power of our method, we prove, using
                 computer algebra algorithms, some conjectures proposed
                 in the paper ``Pfaffian decomposition and a Pfaffian
                 analogue of q -Catalan Hankel determinants'' by
                 Ishikawa, Tagawa, and Zeng. A minor summation formula
                 related to partitions and Motzkin paths follows as a
                 corollary.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Koiran:2012:UBR,
  author =       "Pascal Koiran",
  title =        "Upper bounds on real roots and lower bounds for the
                 permanent",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "8--8",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442833",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lebreton:2012:AUD,
  author =       "Romain Lebreton and {\'E}ric Schost",
  title =        "Algorithms for the universal decomposition algebra",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "234--241",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442864",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $k$ be a field and let $ f \in k [T] $ be a
                 polynomial of degree $n$. The universal decomposition
                 algebra $A$ is the quotient of $ k[X_1, \ldots {}, X_n]
                 $ by the ideal of symmetric relations (those
                 polynomials that vanish on all permutations of the
                 roots of $f$). We show how to obtain efficient
                 algorithms to compute in $A$. We use a univariate
                 representation of $A$, i.e. an isomorphism of the form
                 $ A k [T] / Q (T) $, since in this representation,
                 arithmetic operations in $A$ are known to be
                 quasi-optimal. We give details for two related
                 algorithms, to find the isomorphism above, and to
                 compute the characteristic polynomial of any element of
                 $A$.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lella:2012:EIA,
  author =       "Paolo Lella",
  title =        "An efficient implementation of the algorithm computing
                 the {Borel}-fixed points of a {Hilbert} scheme",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "242--248",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442865",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Borel-fixed ideals play a key role in the study of
                 Hilbert schemes. Indeed each component and each
                 intersection of components of a Hilbert scheme contains
                 at least one Borel-fixed point, i.e. a point
                 corresponding to a subscheme defined by a Borel-fixed
                 ideal. Moreover Borel-fixed ideals have good
                 combinatorial properties, which make them very
                 interesting in an algorithmic perspective. In this
                 paper, we propose an implementation of the algorithm
                 computing all the saturated Borel-fixed ideals with
                 number of variables and Hilbert polynomial assigned,
                 introduced from a theoretical point of view in the
                 paper ``Segment ideals and Hilbert schemes of points'',
                 Discrete Mathematics 311 (2011).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Levandovskyy:2012:ECA,
  author =       "Viktor Levandovskyy",
  title =        "Elements of computer-algebraic analysis",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "9--10",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442834",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Algebraic Analysis has been coined as a term in the
                 mid 50's by the Japanese group led by Mikio Sato. In
                 recent years many constructions of Algebraic Analysis
                 have been approached from a computer-algebraic point of
                 view, with algorithms and their implementations.
                 Extension of such an interaction from linear
                 differential operators to linear difference, q
                 -difference, q -differential and other linear operators
                 we call Computer-Algebraic Analysis. The major object
                 of study are systems of linear functional equations,
                 their properties, solutions (including those in terms
                 of generalized functions) and behaviour.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ma:2012:CRS,
  author =       "Yue Ma and Lihong Zhi",
  title =        "Computing real solutions of polynomial systems via
                 low-rank moment matrix completion",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "249--256",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442866",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we propose a new algorithm for
                 computing real roots of polynomial equations or a
                 subset of real roots in a given semi-algebraic set
                 described by additional polynomial inequalities. The
                 algorithm is based on using modified fixed point
                 continuation method for solving Lasserre's hierarchy of
                 moment relaxations. We establish convergence properties
                 for our algorithm. For a large-scale polynomial system
                 with only few real solutions in a given area, we can
                 extract them quickly. Moreover, for a polynomial system
                 with an infinite number of real solutions, our
                 algorithm can also be used to find some isolated real
                 solutions or real solutions on the manifolds.",
  acknowledgement = ack-nhfb,
}

@InProceedings{McCarron:2012:SHQ,
  author =       "James McCarron",
  title =        "Small homogeneous quandles",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "257--264",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442867",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We derive an algorithm for computing all the
                 homogeneous quandles of a given order n provided that a
                 list of the transitive permutation groups of degree n
                 are known. We discuss the implementation of the
                 algorithm, and use it to enumerate the number of
                 isomorphism classes of homogeneous quandles up to order
                 23 and compute representatives for each class. We also
                 completely determine the homogeneous quandles of prime
                 order. As a by-product, we are able to confirm an
                 independent calculation of the connected quandles of
                 order at most 30 by Vendramin and, based on this, to
                 compute the number of isomorphism classes of simple
                 quandles to the same order.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mourrain:2012:BBR,
  author =       "Bernard Mourrain and Philippe Tr{\'e}buchet",
  title =        "Border basis representation of a general quotient
                 algebra",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "265--272",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442868",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we generalized the construction of
                 border bases to non-zero dimensional ideals for normal
                 forms compatible with the degree, tackling the
                 remaining obstacle for a general application of border
                 basis methods. First, we give conditions to have a
                 border basis up to a given degree. Next, we describe a
                 new stopping criteria to determine when the reduction
                 with respect to the leading terms is a normal form.
                 This test based on the persistence and regularity
                 theorems of Gotzmann yields a new algorithm for
                 computing a border basis of any ideal, which proceeds
                 incrementally degree by degree until its regularity. We
                 detail it, prove its correctness, present its
                 implementation and report some experimentations which
                 illustrate its practical good behavior.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Oaku:2012:ACD,
  author =       "Toshinori Oaku",
  title =        "An algorithm to compute the differential equations for
                 the logarithm of a polynomial",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "273--280",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442869",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present an algorithm to compute the annihilator of
                 (i.e., the linear differential equations for) the
                 multi-valued analytic function $ f^\lambda (\log f)^m $
                 in the Weyl algebra $ D_n $ for a given non-constant
                 polynomial $f$, a non-negative integer $m$, and a
                 complex number $ \lambda $. This algorithm essentially
                 consists of the differentiation with respect to $s$ of
                 the annihilator of $ f^s $ in the ring $ D_n[s] $ and
                 ideal quotient computation in $ D_n $. The obtained
                 differential equations constitute what is called a
                 holonomic system in $D$-module theory. Hence combined
                 with the integration algorithm for $D$-modules, this
                 enables us to compute a holonomic system for the
                 integral of a function involving the logarithm of a
                 polynomial with respect to some variables.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pauderis:2012:DUC,
  author =       "Colton Pauderis and Arne Storjohann",
  title =        "Deterministic unimodularity certification",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "281--288",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442870",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The asymptotically fastest algorithms for many linear
                 algebra problems on integer matrices, including solving
                 a system of linear equations and computing the
                 determinant, use high-order lifting. Currently,
                 high-order lifting requires the use of a randomized
                 shifted number system to detect and avoid
                 error-producing carries. By interleaving quadratic and
                 linear lifting, we devise a new algorithm for
                 high-order lifting that allows us to work in the usual
                 symmetric range modulo p, thus avoiding randomization.
                 As an application, we give a deterministic algorithm to
                 assay if an n x n integer matrix A is unimodular. The
                 cost of the algorithm is O ((\log n) n$^{ \omega }$
                 M(\log n + \log|| A ||)) bit operations, where || A ||
                 denotes the largest entry in absolute value, and M(t)
                 is the cost of multiplying two integers bounded in bit
                 length by t.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Romero:2012:PBT,
  author =       "Ana Romero and Francis Sergeraert",
  title =        "Programming before theorizing, a case study",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "289--296",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442871",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper relates how a ``simple'' result in
                 combinatorial homotopy eventually led to a totally new
                 understanding of basic theorems in Algebraic Topology,
                 namely the Eilenberg--Zilber theorem, the twisted
                 Eilenberg--Zilber theorem, and finally the
                 Eilenberg-MacLane correspondance between the
                 Classifying Space and Bar constructions. In the last
                 case, it was an amazing lucky consequence of
                 computations based on conjectures not yet proved. The
                 key new tool used in this context is Robin Forman's
                 Discrete Vector Fields theory.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Roune:2012:PGB,
  author =       "Bjarke Hammersholt Roune and Michael Stillman",
  title =        "Practical {Gr{\"o}bner} basis computation",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "203--210",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442860",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We report on our experiences exploring state of the
                 art Gr{\"o}bner basis computation. We investigate
                 signature based algorithms in detail. We also introduce
                 new practical data structures and computational
                 techniques for use in both signature based Gr{\"o}bner
                 basis algorithms and more traditional variations of the
                 classic Buchberger algorithm. Our conclusions are based
                 on experiments using our new freely available open
                 source standalone C++ library.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Roy:2012:CDC,
  author =       "Marie-Fran{\c{c}}oise Roy",
  title =        "Complexity of deciding connectivity in real algebraic
                 sets: recent results and future research directions",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "3--5",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442831",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The number of connected components of a real algebraic
                 set defined in $R^k$ by equations of degree $d$ is
                 $O(d)^k$ which is polynomial in the degree, and singly
                 exponential in the number of variables. Moreover it is
                 very easy to design algebraic sets defined by
                 polynomials of degree $2 d$ in $k$ variables with
                 $O(d)^k$ connected components.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sagraloff:2012:WNM,
  author =       "Michael Sagraloff",
  title =        "When {Newton} meets {Descartes}: a simple and fast
                 algorithm to isolate the real roots of a polynomial",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "297--304",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442872",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We introduce a novel algorithm denoted NewDsc to
                 isolate the real roots of a univariate square-free
                 polynomial f with integer coefficients. The algorithm
                 iteratively subdivides an initial interval which is
                 known to contain all real roots of f and performs exact
                 (rational) operations on the coefficients of f in each
                 step. For the subdivision strategy, we combine
                 Descartes' Rule of Signs and Newton iteration. More
                 precisely, instead of using a fixed subdivision
                 strategy such as bisection in each iteration, a Newton
                 step based on the number of sign variations for an
                 actual interval is considered, and, only if the Newton
                 step fails, we fall back to bisection. Following this
                 approach, quadratic convergence towards the real roots
                 is achieved in most iterations. In terms of complexity,
                 our method induces a recursion tree of almost optimal
                 size $ O (n \cdot \log (n \tau)) $, where $n$ denotes
                 the degree of the polynomial and \tau the bitsize of
                 its coefficients. The latter bound constitutes an
                 improvement by a factor of \tau upon all existing
                 subdivision methods for the task of isolating the real
                 roots. We further provide a detailed complexity
                 analysis which shows that NewDsc needs only $ {\tilde
                 O}(n^3 \tau) $ bit operations to isolate all real roots
                 of f. In comparison to existing asymptotically fast
                 numerical algorithms (e.g. the algorithms by V. Pan and
                 A. Sch{\"o}nhage), NewDsc is much easier to access and,
                 due to its similarities to the classical Descartes
                 method, it seems to be well suited for an efficient
                 implementation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Scheiblechner:2012:ERC,
  author =       "Peter Scheiblechner",
  title =        "Effective {de Rham} cohomology: the hypersurface
                 case",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "305--310",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442873",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We prove an effective bound for the degrees of
                 generators of the algebraic de Rham cohomology of
                 smooth affine hypersurfaces. In particular, we show
                 that the de Rham cohomology $ H^p_{dR}(X) $ of a smooth
                 hypersurface $X$ of degree $d$ in $ C^n $ can be
                 generated by differential forms of degree $ d^{O(pn)}
                 $. This result is relevant for the algorithmic
                 computation of the cohomology, but is also motivated by
                 questions in the theory of ordinary differential
                 equations related to the infinitesimal Hilbert 16th
                 problem.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Seress:2012:CCR,
  author =       "{\'A}kos Seress",
  title =        "Construction of $2$-closed {$M$}-representations",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "311--318",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442874",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The sporadic simple group Monster, denoted by M, acts
                 on the Griess algebra, which is a real vector space of
                 dimension 196,884, equipped with a positive definite
                 scalar product and a bilinear, commutative, and
                 non-associative algebra product. Certain properties of
                 this linear representation of M, together with
                 properties (discovered by Conway and Miyamoto) of
                 idempotents in the Griess algebra that correspond to 2A
                 involutions in M, have been defined by Ivanov as the
                 M-representation of the Monster. This definition
                 enables us to talk about M-representations of arbitrary
                 groups G that are generated by involutions. In general,
                 an M-representation may or may not exist, but if G is
                 isomorphic to a subgroup of the Monster and a
                 representation is isomorphic to the corresponding
                 subalgebra of the Griess algebra then we say that the
                 M-representation is based on an embedding of G in the
                 Monster. In this paper, we describe a generic
                 theoretical procedure to construct M-representations,
                 and a GAP computer program that implements the
                 procedure. It turns out that in many cases the
                 representations are based on embeddings in the Monster,
                 thereby providing a valuable tool of studying
                 subalgebras of the Griess algebra that were
                 unaccessible in the 196,884-dimensional setting.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sharma:2012:NOT,
  author =       "Vikram Sharma and Chee K. Yap",
  title =        "Near optimal tree size bounds on a simple real root
                 isolation algorithm",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "319--326",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442875",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The problem of isolating all real roots of a
                 square-free integer polynomial $ f(X) $ inside any
                 given interval $ I_0 $ is a fundamental problem. EVAL
                 is a simple and practical exact numerical algorithm for
                 this problem: it recursively bisects $ I_0 $, and any
                 sub-interval $ I \subseteq I_0 $, until a certain
                 numerical predicate $ C_0 (I) V C_1 (I) $ holds on each
                 $I$. We prove that the size of the recursion tree is $
                 O(d (L + r + \log d)) $ where $f$ has degree $d$, its
                 coefficients have absolute values $ < 2^L $, and $ I_0
                 $ contains $r$ roots of $f$. In the range $ L \geq d $,
                 our bound is the sharpest known, and provably optimal.
                 Our results are closely paralleled by recent bounds on
                 EVAL by Sagraloff--Yap (ISSAC 2011) and Burr--Krahmer
                 (2012). In the range $ L \leq d $, our bound is
                 incomparable with those of Sagraloff--Yap or
                 Burr--Krahmer. Similar to the Burr--Krahmer proof, we
                 exploit the technique of ``continuous amortization''
                 from Burr--Krahmer--Yap (2009), namely to bound the
                 tree size by an integral $ \int_I O G(x) \, d x $ over
                 a suitable ``charging function'' $ G(x) $. We give an
                 application of this feature to the problem of
                 ray-shooting (i.e., finding smallest root in a given
                 interval).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Slavici:2012:EPM,
  author =       "Vlad Slavici and Daniel Kunkle and Gene Cooperman and
                 Stephen Linton",
  title =        "An efficient programming model for memory-intensive
                 recursive algorithms using parallel disks",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "327--334",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442876",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In order to keep up with the demand for solutions to
                 problems with ever-increasing data sets, both academia
                 and industry have embraced commodity computer clusters
                 with locally attached disks or SANs as an inexpensive
                 alternative to supercomputers. With the advent of tools
                 for parallel disks programming, such as MapReduce,
                 STXXL and Roomy --- that allow the developer to focus
                 on higher-level algorithms --- the programmer
                 productivity for memory-intensive programs has
                 increased many-fold. However, such parallel tools were
                 primarily targeted at iterative programs. We propose a
                 programming model for migrating recursive RAM-based
                 legacy algorithms to parallel disks. Many
                 memory-intensive symbolic algebra algorithms are most
                 easily expressed as recursive algorithms. In this case,
                 the programming challenge is multiplied, since the
                 developer must re-structure such an algorithm with two
                 criteria in mind: converting a naturally recursive
                 algorithm into an iterative algorithm, while
                 simultaneously exposing any potential data parallelism
                 (as needed for parallel disks). This model alleviates
                 the large effort going into the design phase of an
                 external memory algorithm. Research in this area over
                 the past 10 years has focused on per-problem solutions,
                 without providing much insight into the connection
                 between legacy algorithms and out-of-core algorithms.
                 Our method shows how legacy algorithms employing
                 recursion and non-streaming memory access can be more
                 easily translated into efficient parallel disk-based
                 algorithms. We demonstrate the ideas on a largest
                 computation of its kind: the determinization via subset
                 construction and minimization of very large
                 nondeterministic finite set automata (NFA). To our
                 knowledge, this is the largest subset construction
                 reported in the literature. Determinization for large
                 NFA has long been a large computational hurdle in the
                 study of permutation classes defined by token passing
                 networks. The programming model was used to design and
                 implement an efficient NFA determinization algorithm
                 that solves the next stage in analyzing token passing
                 networks representing two stacks in series.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Strassen:2012:ASM,
  author =       "Volker Strassen",
  title =        "Asymptotic spectrum and matrix multiplication",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "6--7",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442832",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The minimal number of arithmetic operations sufficient
                 to multiply matrices of order m by an algebraic circuit
                 has the form m$^{\omega + o(1)}$, where o(1) goes to
                 zero when m tends to infinity. \omega is called the
                 exponent of matrix multiplication. Asymptotically, it
                 controls the complexity of almost all significant
                 computational tasks of linear algebra. The desire to
                 determine \omega has been the main motivation for
                 investigating the complexity of bilinear maps in
                 general.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Strzebonski:2012:SPS,
  author =       "Adam Strzebo{\'n}ski",
  title =        "Solving polynomial systems over semialgebraic sets
                 represented by cylindrical algebraic formulas",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "335--342",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442877",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Cylindrical algebraic formulas are an explicit
                 representation of semialgebraic sets as finite unions
                 of cylindrically arranged disjoint cells bounded by
                 graphs of algebraic functions. We present a version of
                 the Cylindrical Algebraic Decomposition (CAD) algorithm
                 customized for solving systems of polynomial equations
                 and inequalities over semialgebraic sets given in this
                 representation. The algorithm can also be used to solve
                 conjunctions of polynomial conditions in an incremental
                 manner. We show application examples and give an
                 empirical comparison of incremental and direct CAD
                 computation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Strzebonski:2012:URR,
  author =       "Adam Strzebo{\'n}ski and Elias P. Tsigaridas",
  title =        "Univariate real root isolation in multiple extension
                 fields",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "343--350",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442878",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  abstract =     "We present algorithmic, complexity and implementation
                 results for the problem of isolating the real roots of
                 a univariate polynomial in $ B_\alpha \in L [y] $,
                 where $ L = Q(\alpha_1, \ldots {}, \alpha_l) $ is an
                 algebraic extension of the rational numbers. Our bounds
                 are single exponential in $l$ and match the ones
                 presented in [34] for the case $ l = 1 $. We consider
                 two approaches. The first, indirect approach, using
                 multivariate resultants, computes a univariate
                 polynomial with integer coefficients, among the real
                 roots of which are the real roots of $ B_\alpha $. The
                 Boolean complexity of this approach is $ O_B(N^{4 l +
                 4}) $, where $N$ is the maximum of the degrees and the
                 coefficient bitsize of the involved polynomials. The
                 second, direct approach, tries to solve the polynomial
                 directly, without reducing the problem to a univariate
                 one. We present an algorithm that generalizes Sturm
                 algorithm from the univariate case, and modified
                 versions of well known solvers that are either
                 numerical or based on Descartes' rule of sign. We
                 achieve a Boolean complexity of $ O_B $ [equation],
                 respectively. We implemented the algorithms in C as
                 part of the core library of Mathematica and we
                 illustrate their efficiency over various data sets.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sullivant:2012:AS,
  author =       "Seth Sullivant",
  title =        "Algebraic statistics",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "11--11",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442835",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Algebraic statistics advocates polynomial algebra as a
                 tool for addressing problems in statistics and its
                 applications. This connection is based on the fact that
                 most statistical models are defined either
                 parametrically or implicitly via polynomial equations.
                 The idea is summarized by the phrase ``Statistical
                 models are semialgebraic sets''. My tutorial will
                 consist of a detailed study of two examples where the
                 algebra/statistics connection has proven especially
                 useful: in the study of phylogenetic models and in the
                 analysis of contingency tables.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sun:2012:SBA,
  author =       "Yao Sun and Dingkang Wang and Xiaodong Ma and Yang
                 Zhang",
  title =        "A signature-based algorithm for computing
                 {Gr{\"o}bner} bases in solvable polynomial algebras",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "351--358",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442879",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Signature-based algorithms, including F5, F5C, G2V and
                 GVW, are efficient algorithms for computing Gr{\"o}bner
                 bases in commutative polynomial rings. In this paper,
                 we present a signature-based algorithm to compute
                 Gr{\"o}bner bases in solvable polynomial algebras which
                 include usual commutative polynomial rings and some
                 non-commutative polynomial rings like Weyl algebra. The
                 generalized Rewritten Criterion (discussed in Sun and
                 Wang, ISSAC 2011) is used to reject redundant
                 computations. When this new algorithm uses the partial
                 order implied by GVW, its termination is proved without
                 special assumptions on computing orders of critical
                 pairs. Data structures similar to F5 can be used to
                 speed up this new algorithm, and Gr{\"o}bner bases of
                 syzygy modules of input polynomials can be obtained
                 from the outputs easily. Experimental data show that
                 most redundant computations can be avoided in this new
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanderHoeven:2012:CMB,
  author =       "Joris van der Hoeven and Gr{\'e}goire Lecerf",
  title =        "On the complexity of multivariate blockwise polynomial
                 multiplication",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "211--218",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442861",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this article, we study the problem of multiplying
                 two multivariate polynomials which are somewhat but not
                 too sparse, typically like polynomials with convex
                 supports. We design and analyze an algorithm which is
                 based on blockwise decomposition of the input
                 polynomials, and which performs the actual
                 multiplication in an FFT model or some other more
                 general so called ``evaluated model''. If the input
                 polynomials have total degrees at most d, then, under
                 mild assumptions on the coefficient ring, we show that
                 their product can be computed with $O(s^{1.5337})$ ring
                 operations, where $s$ denotes the number of all the
                 monomials of total degree at most $2 d$.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhang:2012:FDO,
  author =       "Mingbo Zhang and Yong Luo",
  title =        "Factorization of differential operators with ordinary
                 differential polynomial coefficients",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "359--365",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442880",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we present an algorithm to factor a
                 differential operator $ L = \sigma^n + c_{n - 1}
                 \sigma^{n - 1} + \cdot \cdot \cdot + c_1 \sigma + c_0 $
                 with coefficients $ c_i $ in $ C \{ y \} $, where $C$
                 is a constant field and $ C \{ y \} $ is the ordinary
                 differential polynomial ring over $C$. Also, we discuss
                 the applications of the algorithm in decomposing
                 nonlinear differential polynomials and factoring
                 differential operators with coefficients in the
                 extension field of $C$.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhou:2012:CMN,
  author =       "Wei Zhou and George Labahn and Arne Storjohann",
  title =        "Computing minimal nullspace bases",
  crossref =     "vanderHoeven:2012:IPI",
  pages =        "366--373",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2442829.2442881",
  bibdate =      "Fri Mar 14 13:49:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we present a deterministic algorithm for
                 the computation of a minimal nullspace basis of an $ m
                 \times n $ input matrix of univariate polynomials over
                 a field $K$ with $ m \eq n $. This algorithm computes a
                 minimal nullspace basis of a degree $d$ input matrix
                 with a cost of $ O \tilde (n_\omega \lceil m d / n
                 \rceil) $ field operations in $K$. Here the soft-$O$
                 notation is Big-$O$ with $ \log $ factors removed while
                 $ \omega $ is the exponent of matrix multiplication.
                 The same algorithm also works in the more general
                 situation on computing a shifted minimal nullspace
                 basis, with a given degree shift [equation] whose
                 entries bound the corresponding column degrees of the
                 input matrix. In this case if $ \rho $ is the sum of
                 the $m$ largest entries of $s$, then a $s$-minimal
                 right nullspace basis can be computed with a cost of $
                 O \tilde (n^\omega \rho / m) $ field operations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Arnold:2013:NTF,
  author =       "Andrew Arnold",
  title =        "A new truncated {Fourier Transform} algorithm",
  crossref =     "Monagan:2013:IPI",
  pages =        "15--22",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465957",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Truncated Fourier Transforms (TFTs), first introduced
                 by van der Hoeven, refer to a family of algorithms that
                 attempt to smooth ``jumps'' in complexity exhibited by
                 FFT algorithms. We present an in-place TFT whose time
                 complexity, measured in terms of ring operations, is
                 asymptotically equivalent to existing not-in-place TFT
                 methods. We also describe a transformation that maps
                 between two families of TFT algorithms that use
                 different sets of evaluation points.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bach:2013:ACS,
  author =       "Eric Bach and Jonathan P. Sorenson",
  title =        "Approximately counting semismooth integers",
  crossref =     "Monagan:2013:IPI",
  pages =        "23--30",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465933",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An integer $n$ is $ (y, z) $-semismooth if $ n = p m $
                 where $m$ is an integer with all prime divisors $ \geq
                 y $ and $p$ is $1$ or a prime $ \geq z $. Large
                 quantities of semismooth integers are utilized in
                 modern integer factoring algorithms, such as the number
                 field sieve, that incorporate the so-called large prime
                 variant. Thus, it is useful for factoring practitioners
                 to be able to estimate the value of $ \Psi (x, y, z) $,
                 the number of $ (y, z) $-semismooth integers up to $x$,
                 so that they can better set algorithm parameters and
                 minimize running times, which could be weeks or months
                 on a cluster supercomputer. In this paper, we explore
                 several algorithms to approximate $ \Psi (x, y, z) $
                 using a generalization of Buchstab's identity with
                 numeric integration.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Basson:2013:EEL,
  author =       "Romain Basson and Reynald Lercier and Christophe
                 Ritzenthaler and Jeroen Sijsling",
  title =        "An explicit expression of the {L{\"u}roth} invariant",
  crossref =     "Monagan:2013:IPI",
  pages =        "31--36",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465507",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this short note, we give an algorithm that returns
                 an explicit expression of the L{\"u}roth invariant in
                 terms of the Dixmier-Ohno invariants of plane quartic
                 curves. We also obtain an explicit factorized
                 expression on the locus of Ciani quartics in terms of
                 the coefficients. After this calculation, we extend our
                 methods to answer two open theoretical questions
                 concerning the sub-locus of singular L{\"u}roth
                 quartics.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Berthe:2013:MGP,
  author =       "Val{\'e}rie Berth{\'e} and Jean Creusefond and
                 Lo{\"\i}ck Lhote and Brigitte Vall{\'e}e",
  title =        "Multiple {GCDs}. {Probabilistic} analysis of the plain
                 algorithm",
  crossref =     "Monagan:2013:IPI",
  pages =        "37--44",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465512",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper provides a probabilistic analysis of an
                 algorithm which computes the gcd of l inputs (with l
                 \geq 2), with a succession of l --- 1 phases, each of
                 them being the Euclid algorithm on two entries. This
                 algorithm is both basic and natural, and two kinds of
                 inputs are studied: polynomials over the finite field
                 F$_q$ and integers. The analysis exhibits the precise
                 probabilistic behaviour of the main parameters, namely
                 the number of iterations in each phase and the
                 evolution of the length of the current gcd along the
                 execution. We first provide an average-case analysis.
                 Then we make it even more precise by a distributional
                 analysis. Our results rigorously exhibit two phenomena:
                 (i) there is a strong difference between the first
                 phase, where most of the computations are done and the
                 remaining phases; (ii) there is a strong similarity
                 between the polynomial and integer cases, as can be
                 expected.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bessonov:2013:ICP,
  author =       "Mariya Bessonov and Alexey Ovchinnikov and Maxwell
                 Shapiro",
  title =        "Integrability conditions for parameterized linear
                 difference equations",
  crossref =     "Monagan:2013:IPI",
  pages =        "45--52",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465942",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We study integrability conditions for systems of
                 parameterized linear difference equations and related
                 properties of linear differential algebraic groups. We
                 show that isomonodromicity of such a system is
                 equivalent to isomonodromicity with respect to each
                 parameter separately under a linearly differentially
                 closed assumption on the field of differential
                 parameters. Due to our result, it is no longer
                 necessary to solve non-linear differential equations to
                 verify isomonodromicity, which will improve efficiency
                 of computation with these systems. Moreover, it is not
                 possible to further strengthen this result by removing
                 the requirement on the parameters, as we show by giving
                 a counterexample. We also discuss the relation between
                 isomonodromicity and the properties of the associated
                 parameterized difference Galois group.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Betten:2013:RCC,
  author =       "Anton Betten",
  title =        "Rainbow cliques and the classification of small
                 {BLT-sets}",
  crossref =     "Monagan:2013:IPI",
  pages =        "53--60",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465508",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In Finite Geometry, a class of objects known as
                 BLT-sets play an important role. They are points on the
                 Q (4, q) quadric satisfying a condition on triples.
                 This paper is a contribution to the difficult problem
                 of classifying these sets up to isomorphism, i.e., up
                 to the action of the automorphism group of the quadric.
                 We reduce the classification problem of these sets to
                 the problem of classifying rainbow cliques in graphs.
                 This allows us to classify BLT-sets for all orders q in
                 the range 31 to 67.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bi:2013:SLR,
  author =       "Jingguo Bi and Qi Cheng and J. Maurice Rojas",
  title =        "Sub-linear root detection, and new hardness results,
                 for sparse polynomials over finite fields",
  crossref =     "Monagan:2013:IPI",
  pages =        "61--68",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465514",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a deterministic $ 2^{O(t)} q^{t - 2 / t - 1
                 + o (1)} $ algorithm to decide whether a univariate
                 polynomial $f$, with exactly $t$ monomial terms and
                 degree $ < q $, has a root in $ F_q $. Our method is
                 the first with complexity sub-linear in $q$ when $t$ is
                 fixed. We also prove a structural property for the
                 nonzero roots in $ F_q $ of any $t$-nomial: the nonzero
                 roots always admit a partition into no more than $ 2
                 \sqrt t - 1 (q - 1)^{t - 2 / t - 1} $ cosets of two
                 subgroups $ S_1 \subseteq S_2 $ of $ F*_q $. This can
                 be thought of as a finite field analogue of Descartes'
                 Rule. A corollary of our results is the first
                 deterministic sub-linear algorithm for detecting common
                 degree one factors of $k$-tuples of $t$-nomials in $
                 F_q[x] $ when $k$ and $t$ are fixed. When $t$ is not
                 fixed we show that, for $p$ prime, detecting roots in $
                 F_p $ for $f$ is NP-hard with respect to
                 BPP-reductions. Finally, we prove that if the
                 complexity of root detection is sub-linear (in a
                 refined sense), relative to the straight-line program
                 encoding, then $ {\rm NEXP} \subseteq P / {\em poly}
                 $.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boady:2013:TRS,
  author =       "Mark Boady and Pavel Grinfeld and Jeremy Johnson",
  title =        "A term rewriting system for the calculus of moving
                 surfaces",
  crossref =     "Monagan:2013:IPI",
  pages =        "69--76",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2466576",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The calculus of moving surfaces (CMS) is an analytic
                 framework that extends the tensor calculus to deforming
                 manifolds. We have applied the CMS to a number of
                 boundary variation problems using a Term Rewrite System
                 (TRS). The TRS is used to convert the initial CMS
                 expression into a form that can be evaluated. The CMS
                 produces expressions that are true for all coordinate
                 spaces. This makes it very powerful but applications
                 remain limited by a rapid growth in the size of
                 expressions. We have extended results on existing
                 problems to orders that had been previously
                 intractable. In this paper, we describe our TRS and our
                 method for evaluating CMS expressions on a specific
                 coordinate system. Our work has already provided new
                 insight into problems of current interest to
                 researchers in the CMS.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2013:CET,
  author =       "Alin Bostan and Fr{\'e}d{\'e}ric Chyzak and {\'E}lie
                 de Panafieu",
  title =        "Complexity estimates for two uncoupling algorithms",
  crossref =     "Monagan:2013:IPI",
  pages =        "85--92",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465941",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Uncoupling algorithms transform a linear differential
                 system of first order into one or several scalar
                 differential equations. We examine two approaches to
                 uncoupling: the cyclic-vector method (CVM) and the
                 Danilevski-Barkatou-Z{\"u}rcher algorithm (DBZ). We
                 give tight size bounds on the scalar equations produced
                 by CVM, and design a fast variant of CVM whose
                 complexity is quasi-optimal with respect to the output
                 size. We exhibit a strong structural link between CVM
                 and DBZ enabling to show that, in the generic case, DBZ
                 has polynomial complexity and that it produces a single
                 equation, strongly related to the output of CVM. We
                 prove that algorithm CVM is faster than DBZ by almost
                 two orders of magnitude, and provide experimental
                 results that validate the theoretical complexity
                 analyses.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2013:CTR,
  author =       "Alin Bostan and Pierre Lairez and Bruno Salvy",
  title =        "Creative telescoping for rational functions using the
                 {Griffiths--Dwork} method",
  crossref =     "Monagan:2013:IPI",
  pages =        "93--100",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465935",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Creative telescoping algorithms compute linear
                 differential equations satisfied by multiple integrals
                 with parameters. We describe a precise and elementary
                 algorithmic version of the Griffiths--Dwork method for
                 the creative telescoping of rational functions. This
                 leads to bounds on the order and degree of the
                 coefficients of the differential equation, and to the
                 first complexity result which is single exponential in
                 the number of variables. One of the important features
                 of the algorithm is that it does not need to compute
                 certificates. The approach is vindicated by a prototype
                 implementation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bostan:2013:HRC,
  author =       "Alin Bostan and Shaoshi Chen and Fr{\'e}d{\'e}ric
                 Chyzak and Ziming Li and Guoce Xin",
  title =        "{Hermite} reduction and creative telescoping for
                 hyperexponential functions",
  crossref =     "Monagan:2013:IPI",
  pages =        "77--84",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465946",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a new reduction algorithm that
                 simultaneously extends Hermite's reduction for rational
                 functions and the Hermite-like reduction for
                 hyperexponential functions. It yields a unique additive
                 decomposition that allows to decide hyperexponential
                 integrability. Based on this reduction algorithm, we
                 design a new algorithm to compute minimal telescopers
                 for bivariate hyperexponential functions. One of its
                 main features is that it can avoid the costly
                 computation of certificates. Its implementation
                 outperforms Maple's function DEtools[Zeilberger]. We
                 also derive an order bound on minimal telescopers that
                 is tighter than the known ones.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boulier:2013:IDF,
  author =       "Fran{\c{c}}ois Boulier and Fran{\c{c}}ois Lemaire and
                 Georg Regensburger and Markus Rosenkranz",
  title =        "On the integration of differential fractions",
  crossref =     "Monagan:2013:IPI",
  pages =        "101--108",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465934",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we provide a differential algebra
                 algorithm for integrating fractions of differential
                 polynomials. It is not restricted to differential
                 fractions that are the derivatives of other
                 differential fractions. The algorithm leads to new
                 techniques for representing differential fractions,
                 which may help converting differential equations to
                 integral equations (as for example used in parameter
                 estimation).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bouzidi:2013:RUR,
  author =       "Yacine Bouzidi and Sylvain Lazard and Marc Pouget and
                 Fabrice Rouillier",
  title =        "Rational univariate representations of bivariate
                 systems and applications",
  crossref =     "Monagan:2013:IPI",
  pages =        "109--116",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465519",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We address the problem of solving systems of two
                 bivariate polynomials of total degree at most d with
                 integer coefficients of maximum bitsize \tau We suppose
                 known a linear separating form (that is a linear
                 combination of the variables that takes different
                 values at distinct solutions of the system) and focus
                 on the computation of a Rational Univariate
                 Representation (RUR). We present an algorithm for
                 computing a RUR with worst-case bit complexity in $
                 {\tilde O}_B (d^7 + d^6 \tau) $ and bound the bitsize
                 of its coefficients by $ {\tilde O}(d^2 + d \tau) $
                 (where $ {\tilde O}_B $ refers to bit complexities and
                 $ {\tilde O} $ to complexities where polylogarithmic
                 factors are omitted). We show in addition that
                 isolating boxes of the solutions of the system can be
                 computed from the RUR with $ {\tilde O}_B (d^8 + d^7
                 \tau) $ bit operations. Finally, we show how a RUR can
                 be used to evaluate the sign of a bivariate polynomial
                 (of degree at most $d$ and bitsize at most $ \tau $)
                 at one real solution of the system in $ {\tilde O}_B
                 (d^8 + d^7 \tau) $ bit operations and at all the $
                 \Theta (d^2) $ solutions in only $ O(d) $ times that
                 for one solution.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bouzidi:2013:SLF,
  author =       "Yacine Bouzidi and Sylvain Lazard and Marc Pouget and
                 Fabrice Rouillier",
  title =        "Separating linear forms for bivariate systems",
  crossref =     "Monagan:2013:IPI",
  pages =        "117--124",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465518",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present an algorithm for computing a separating
                 linear form of a system of bivariate polynomials with
                 integer coefficients, that is a linear combination of
                 the variables that takes different values when
                 evaluated at distinct (complex) solutions of the
                 system. In other words, a separating linear form
                 defines a shear of the coordinate system that sends the
                 algebraic system in generic position, in the sense that
                 no two distinct solutions are vertically aligned. The
                 computation of such linear forms is at the core of most
                 algorithms that solve algebraic systems by computing
                 rational parameterizations of the solutions and,
                 moreover, the computation of a separating linear form
                 is the bottleneck of these algorithms, in terms of
                 worst-case bit complexity. Given two bivariate
                 polynomials of total degree at most $d$ with integer
                 coefficients of bitsize at most $ \tau $, our algorithm
                 computes a separating linear form in $ {\tilde O}_B (d^8
                 + d^7 \tau + d^5 \tau^2) $ bit operations in the worst
                 case, where the previously known best bit complexity
                 for this problem was $ {\tilde O}_B (d^{10} + d^9 \tau)
                 $ (where $ {\tilde O} $ refers to the complexity where
                 polylogarithmic factors are omitted and $ {\tilde O}_B
                 $ refers to the bit complexity)",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bradford:2013:CAD,
  author =       "Russell Bradford and James H. Davenport and Matthew
                 England and Scott McCallum and David Wilson",
  title =        "Cylindrical algebraic decompositions for boolean
                 combinations",
  crossref =     "Monagan:2013:IPI",
  pages =        "125--132",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465516",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  abstract =     "This article makes the key observation that when using
                 cylindrical algebraic decomposition (CAD) to solve a
                 problem with respect to a set of polynomials, it is not
                 always the signs of those polynomials that are of
                 paramount importance but rather the truth values of
                 certain quantifier free formulae involving them. This
                 motivates our definition of a Truth Table Invariant CAD
                 (TTICAD). We generalise the theory of equational
                 constraints to design an algorithm which will
                 efficiently construct a TTICAD for a wide class of
                 problems, producing stronger results than when using
                 equational constraints alone. The algorithm is
                 implemented fully in Maple and we present promising
                 results from experimentation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:2013:CSO,
  author =       "Christopher W. Brown",
  title =        "Constructing a single open cell in a cylindrical
                 algebraic decomposition",
  crossref =     "Monagan:2013:IPI",
  pages =        "133--140",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465952",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper presents an algorithm that, roughly
                 speaking, constructs a single open cell from a
                 cylindrical algebraic decomposition (CAD). The
                 algorithm takes as input a point and a set of
                 polynomials, and computes a description of an open
                 cylindrical cell containing the point in which the
                 input polynomials have constant non-zero sign, provided
                 the point is sufficiently generic. The paper reports on
                 a few example computations carried out by a test
                 implementation of the algorithm, which demonstrate the
                 functioning of the algorithm and illustrate the sense
                 in which it is more efficient than following the usual
                 ``open CAD'' approach. Interest in the problem of
                 computing a single cell from a CAD is motivated by a
                 2012 paper of Jovanovic and de Moura that require
                 solving this problem repeatedly as a key step in NLSAT
                 system. However, the example computations raise the
                 possibility that repeated application of the new method
                 may in fact be more efficient than the usual open CAD
                 approach, both in time and space, for a broad range of
                 problems.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chattopadhyay:2013:FBL,
  author =       "Arkadev Chattopadhyay and Bruno Grenet and Pascal
                 Koiran and Natacha Portier and Yann Strozecki",
  title =        "Factoring bivariate lacunary polynomials without
                 heights",
  crossref =     "Monagan:2013:IPI",
  pages =        "141--148",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465932",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present an algorithm which computes the multilinear
                 factors of bivariate lacunary polynomials. It is based
                 on a new Gap theorem which allows to test whether $
                 P(X) = \Sigma^k_{j = 1} \alpha_j X^{\alpha j}(1 + X)^{
                 = beta j} $ is identically zero in polynomial time. The
                 algorithm we obtain is more elementary than the one by
                 Kaltofen and Koiran (ISSAC'05) since it relies on the
                 valuation of polynomials of the previous form instead
                 of the height of the coefficients. As a result, it can
                 be used to find some linear factors of bivariate
                 lacunary polynomials over a field of large finite
                 characteristic in probabilistic polynomial time.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2013:DEO,
  author =       "Shaoshi Chen and Maximilian Jaroschek and Manuel
                 Kauers and Michael F. Singer",
  title =        "Desingularization explains order-degree curves for ore
                 operators",
  crossref =     "Monagan:2013:IPI",
  pages =        "157--164",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465510",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Desingularization is the problem of finding a left
                 multiple of a given Ore operator in which some factor
                 of the leading coefficient of the original operator is
                 removed. An order-degree curve for a given Ore operator
                 is a curve in the $ (r, d) $-plane such that for all
                 points $ (r, d) $ above this curve, there exists a left
                 multiple of order $r$ and degree $d$ of the given
                 operator. We give a new proof of a desingularization
                 result by Abramov and van Hoeij for the shift case, and
                 show how desingularization implies order-degree curves
                 which are extremely accurate in examples.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2013:NVH,
  author =       "Jingwei Chen and Damien Stehl{\'e} and Gilles
                 Villard",
  title =        "A new view on {HJLS} and {PSLQ}: sums and projections
                 of lattices",
  crossref =     "Monagan:2013:IPI",
  pages =        "149--156",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465936",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The HJLS and PSLQ algorithms are the de facto
                 standards for discovering non-trivial integer relations
                 between a given tuple of real numbers. In this work, we
                 provide a new interpretation of these algorithms, in a
                 more general and powerful algebraic setup: we view them
                 as special cases of algorithms that compute the
                 intersection between a lattice and a vector subspace.
                 Further, we extract from them the first algorithm for
                 manipulating finitely generated additive subgroups of a
                 Euclidean space, including projections of lattices and
                 finite sums of lattices. We adapt the analyses of HJLS
                 and PSLQ to derive correctness and convergence
                 guarantees.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cohn:2013:SES,
  author =       "Henry Cohn",
  title =        "Solving equations with size constraints for the
                 solutions",
  crossref =     "Monagan:2013:IPI",
  pages =        "1--2",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465927",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{DeFeo:2013:FAA,
  author =       "Luca {De Feo} and Javad Doliskani and Eric Schost",
  title =        "Fast algorithms for $l$-adic towers over finite
                 fields",
  crossref =     "Monagan:2013:IPI",
  pages =        "165--172",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465956",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Inspired by previous work of Shoup, Lenstra-De Smit
                 and Couveignes-Lercier, we give fast algorithms to
                 compute in the first levels of the $l$-adic closure of
                 a finite field. In many cases, our algorithms have
                 quasi-linear complexity.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dickenstein:2013:CDR,
  author =       "Alicia Dickenstein and Ioannis Z. Emiris and Vissarion
                 Fisikopoulos",
  title =        "Combinatorics of $4$-dimensional resultant polytopes",
  crossref =     "Monagan:2013:IPI",
  pages =        "173--180",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465937",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The Newton polytope of the resultant, or resultant
                 polytope, characterizes the resultant polynomial more
                 precisely than total degree. The combinatorics of
                 resultant polytopes are known in the Sylvester case
                 [Gelfand et al.90] and up to dimension 3 [Sturmfels
                 94]. We extend this work by studying the combinatorial
                 characterization of 4-dimensional resultant polytopes,
                 which show a greater diversity and involve
                 computational and combinatorial challenges. In
                 particular, our experiments, based on software respol
                 for computing resultant polytopes, establish lower
                 bounds on the maximal number of faces. By studying
                 mixed subdivisions, we obtain tight upper bounds on the
                 maximal number of facets and ridges, thus arriving at
                 the following maximal f-vector: (22,66,66,22), i.e.
                 vector of face cardinalities. Certain general features
                 emerge, such as the symmetry of the maximal f-vector,
                 which are intriguing but still under investigation. We
                 establish a result of independent interest, namely that
                 the f-vector is maximized when the input supports are
                 sufficiently generic, namely full dimensional and
                 without parallel edges. Lastly, we offer a
                 classification result of all possible 4-dimensional
                 resultant polytopes.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dumas:2013:SCR,
  author =       "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and Ziad
                 Sultan",
  title =        "Simultaneous computation of the row and column rank
                 profiles",
  crossref =     "Monagan:2013:IPI",
  pages =        "181--188",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465517",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Gaussian elimination with full pivoting generates a
                 PLUQ matrix decomposition. Depending on the strategy
                 used in the search for pivots, the permutation matrices
                 can reveal some information about the row or the column
                 rank profiles of the matrix. We propose a new pivoting
                 strategy that makes it possible to recover at the same
                 time both row and column rank profiles of the input
                 matrix and of any of its leading sub-matrices. We
                 propose a rank-sensitive and quad-recursive algorithm
                 that computes the latter PLUQ triangular decomposition
                 of an $m \times n$ matrix of rank $r$ in $O(m n
                 r^{\omega - 2})$ field operations, with \omega the
                 exponent of matrix multiplication. Compared to the LEU
                 decomposition by Malashonock, sharing a similar
                 recursive structure, its time complexity is rank
                 sensitive and has a lower leading constant. Over a word
                 size finite field, this algorithm also improves the
                 practical efficiency of previously known
                 implementations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eder:2013:SRG,
  author =       "Christian Eder and Bjarke Hammersholt Roune",
  title =        "Signature rewriting in {Gr{\"o}bner} basis
                 computation",
  crossref =     "Monagan:2013:IPI",
  pages =        "331--338",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465522",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We introduce the RB algorithm for Gr{\"o}bner basis
                 computation, a simpler yet equivalent algorithm to
                 F5GEN. RB contains the original unmodified F5 algorithm
                 as a special case, so it is possible to study and
                 understand F5 by considering the simpler RB. We present
                 simple yet complete proofs of this fact and of F5's
                 termination and correctness. RB is parametrized by a
                 rewrite order and it contains many published algorithms
                 as special cases, including SB. We prove that SB is the
                 best possible instantiation of RB in the following
                 sense. Let X be any instantiation of RB (such as F5).
                 Then the S-pairs reduced by SB are always a subset of
                 the S-pairs reduced by X and the basis computed by SB
                 is always a subset of the basis computed by X.",
  acknowledgement = ack-nhfb,
}

@InProceedings{ElDin:2013:CPM,
  author =       "Mohab Safey {El Din}",
  title =        "Critical point methods and effective real algebraic
                 geometry: new results and trends",
  crossref =     "Monagan:2013:IPI",
  pages =        "5--6",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465928",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2013:CCG,
  author =       "Jean-Charles Faug{\`e}re and Mohab Safey {El Din} and
                 Thibaut Verron",
  title =        "On the complexity of computing {Gr{\"o}bner} bases for
                 quasi-homogeneous systems",
  crossref =     "Monagan:2013:IPI",
  pages =        "189--196",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465943",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let $K$ be a field and $(f_1, \ldots{}, f_n) \subset
                 K[X_1, \ldots{}, X_n]$ be a sequence of
                 quasi-homogeneous polynomials of respective weighted
                 degrees $(d_1, \ldots{}, d_n)$ w.r.t a system of
                 weights ($w_1$, \ldots{}, $w_n$). Such systems are
                 likely to arise from a lot of applications, including
                 physics or cryptography. We design strategies for
                 computing Gr{\"o}bner bases for quasi-homogeneous
                 systems by adapting existing algorithms for homogeneous
                 systems to the quasi-homogeneous case. Overall, under
                 genericity assumptions, we show that for a generic
                 zero-dimensional quasi homogeneous system, the
                 complexity of the full strategy is polynomial in the
                 weighted B{\'e}zout bound $\Pi_{i =1}^n d^i / \Pi _{i
                 =1}^n w^i$. We provide some experimental results based
                 on generic systems as well as systems arising from a
                 cryptography problem. They show that taking advantage
                 of the quasi-homogeneous structure of the systems allow
                 us to solve systems that were out of reach
                 otherwise.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Faugere:2013:GBI,
  author =       "Jean-Charles Faugere and Jules Svartz",
  title =        "{Gr{\"o}bner} bases of ideals invariant under a
                 commutative group: the non-modular case",
  crossref =     "Monagan:2013:IPI",
  pages =        "347--354",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465944",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We propose efficient algorithms to compute the
                 Gr{\"o}bner basis of an ideal I subset k [ x$_1$,\ldots{},
                 x$_n$ ] globally invariant under the action of a
                 commutative matrix group G, in the non-modular case
                 (where char (k) doesn't divide | G |). The idea is to
                 simultaneously diagonalize the matrices in G, and apply
                 a linear change of variables on I corresponding to the
                 base-change matrix of this diagonalization. We can now
                 suppose that the matrices acting on I are diagonal.
                 This action induces a grading on the ring R=k [
                 x$_1$,\ldots{}, x$_n$ ], compatible with the degree, indexed
                 by a group related to G, that we call G -degree. The
                 next step is the observation that this grading is
                 maintained during a Gr{\"o}bner basis computation or
                 even a change of ordering, which allows us to split the
                 Macaulay matrices into | G | submatrices of roughly the
                 same size. In the same way, we are able to split the
                 canonical basis of R/I (the staircase) if I is a
                 zero-dimensional ideal. Therefore, we derive abelian
                 versions of the classical algorithms F$_4$, F$_5$ or
                 FGLM. Moreover, this new variant of F$_4$ / F$_5$
                 allows complete parallelization of the linear algebra
                 steps, which has been successfully implemented. On
                 instances coming from applications (NTRU crypto-system
                 or the Cyclic-n problem), a speed-up of more than 400
                 can be obtained. For example, a Gr{\"o}bner basis of
                 the Cyclic-11 problem can be solved in less than 8
                 hours with this variant of F$_4$. Moreover, using this
                 method, we can identify new classes of polynomial
                 systems that can be solved in polynomial time.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2013:CRS,
  author =       "Qingdong Guo and Mohab Safey {El Din} and Lihong Zhi",
  title =        "Computing rational solutions of linear matrix
                 inequalities",
  crossref =     "Monagan:2013:IPI",
  pages =        "197--204",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465949",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Consider a $ (D \times D) $ symmetric matrix $A$ whose
                 entries are linear forms in $ Q[X^1, \ldots {}, X_k] $
                 with coefficients of bit size $ \leq \tau $. We provide
                 an algorithm which decides the existence of rational
                 solutions to the linear matrix inequality $ A \geq 0 $
                 and outputs such a rational solution if it exists. This
                 problem is of first importance: it can be used to
                 compute algebraic certificates of positivity for
                 multivariate polynomials. Our algorithm runs within $
                 (k < =)^{O(1)} 2^{O(\min (k, D))} D^2 D^O (D^2) $ bit
                 operations; the bit size of the output solution is
                 dominated by $ \tau^{O(1)} 2^{O(\min (k, D))} D^2 $.
                 These results are obtained by designing algorithmic
                 variants of constructions introduced by Klep and
                 Schweighofer. This leads to the best complexity bounds
                 for deciding the existence of sums of squares with
                 rational coefficients of a given polynomial. We have
                 implemented the algorithm; it has been able to tackle
                 Scheiderer's example of a multivariate polynomial that
                 is a sum of squares over the reals but not over the
                 rationals; providing the first computer validation of
                 this counter-example to Sturmfels' conjecture.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hulpke:2013:CST,
  author =       "Alexander J. Hulpke",
  title =        "Calculation of the subgroups of a trivial-fitting
                 group",
  crossref =     "Monagan:2013:IPI",
  pages =        "205--210",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465525",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We describe an algorithm to determine representatives
                 of the conjugacy classes of subgroups of a
                 Trivial-Fitting group, this case being the one prior
                 algorithms reduce to. As a subtask we describe an
                 algorithm for determining conjugacy classes of
                 complements to an arbitrary normal subgroup if the
                 factor group is solvable.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Johansson:2013:FHS,
  author =       "Fredrik Johansson and Manuel Kauers and Marc
                 Mezzarobba",
  title =        "Finding hyperexponential solutions of linear {ODEs} by
                 numerical evaluation",
  crossref =     "Monagan:2013:IPI",
  pages =        "211--218",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465513",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a new algorithm for computing
                 hyperexponential solutions of linear ordinary
                 differential equations with polynomial coefficients.
                 The algorithm relies on interpreting formal series
                 solutions at the singular points as analytic functions
                 and evaluating them numerically at some common ordinary
                 point. The numerical data is used to determine a small
                 number of combinations of the formal series that may
                 give rise to hyperexponential solutions.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaltofen:2013:SMF,
  author =       "Erich L. Kaltofen and Zhengfeng Yang",
  title =        "Sparse multivariate function recovery from values with
                 noise and outlier errors",
  crossref =     "Monagan:2013:IPI",
  pages =        "219--226",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465524",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Error-correcting decoding is generalized to
                 multivariate sparse rational function recovery from
                 evaluations that can be numerically inaccurate and
                 where several evaluations can have severe errors
                 (``outliers''). The generalization of the
                 Berlekamp-Welch decoder to exact Cauchy interpolation
                 of univariate rational functions from values with
                 faults is by Kaltofen and Pernet in 2012. We give a
                 different univariate solution based on structured
                 linear algebra that yields a stable decoder with
                 floating point arithmetic. Our multivariate polynomial
                 and rational function interpolation algorithm combines
                 Zippel's symbolic sparse polynomial interpolation
                 technique [Ph.D. Thesis MIT 1979] with the numeric
                 algorithm by Kaltofen, Yang, and Zhi [Proc. SNC 2007],
                 and removes outliers (``cleans up data'') through
                 techniques from error correcting codes. Our
                 multivariate algorithm can build a sparse model from a
                 number of evaluations that is linear in the sparsity of
                 the model.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kawano:2013:QFT,
  author =       "Yasuhito Kawano and Hiroshi Sekigawa",
  title =        "{Quantum Fourier Transform} over symmetric groups",
  crossref =     "Monagan:2013:IPI",
  pages =        "227--234",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465940",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This paper proposes an O (n$^4$) quantum Fourier
                 transform (QFT) algorithm over symmetric group S$_n$,
                 the fastest QFT algorithm of its kind. We propose a
                 fast Fourier transform algorithm over symmetric group
                 S$_n$, which consists of O (n$^3$) multiplications of
                 unitary matrices, and then transform it into a quantum
                 circuit form. The QFT algorithm can be applied to
                 constructing the standard algorithm of the hidden
                 subgroup problem.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kunwar:2013:SOD,
  author =       "Vijay Jung Kunwar and Mark van Hoeij",
  title =        "Second order differential equations with
                 hypergeometric solutions of degree three",
  crossref =     "Monagan:2013:IPI",
  pages =        "235--242",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465953",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Let L be a second order linear homogeneous
                 differential equation with rational function
                 coefficients. The goal in this paper is to solve L in
                 terms of hypergeometric function 2F1(a,b;c|f) where f
                 is a rational function of degree 3.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lamban:2013:CSM,
  author =       "Laureano Lamb{\'a}n and Francisco J.
                 Mart{\'\i}n-Mateos and Julio Rubio and Jos{\'e}-Luis
                 Ruiz-Reina",
  title =        "Certified symbolic manipulation: bivariate simplicial
                 polynomials",
  crossref =     "Monagan:2013:IPI",
  pages =        "243--250",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465515",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Certified symbolic manipulation is an emerging new
                 field where programs are accompanied by certificates
                 that, suitably interpreted, ensure the correctness of
                 the algorithms. In this paper, we focus on algebraic
                 algorithms implemented in the proof assistant ACL2,
                 which allows us to verify correctness in the same
                 programming environment. The case study is that of
                 bivariate simplicial polynomials, a data structure used
                 to help the proof of properties in Simplicial Topology.
                 Simplicial polynomials can be computationally
                 interpreted in two ways. As symbolic expressions, they
                 can be handled algorithmically, increasing the
                 automation in ACL2 proofs. As representations of
                 functional operators, they help proving properties of
                 categorical morphisms. As an application of this second
                 view, we present the definition in ACL2 of some
                 morphisms involved in the Eilenberg-Zilber reduction, a
                 central part of the Kenzo computer algebra system. We
                 have proved the ACL2 implementations are correct and
                 tested that they get the same results as Kenzo does.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lebreton:2013:CSB,
  author =       "Romain Lebreton and Esmaeil Mehrabi and Eric Schost",
  title =        "On the complexity of solving bivariate systems: the
                 case of non-singular solutions",
  crossref =     "Monagan:2013:IPI",
  pages =        "251--258",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465950",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We give an algorithm for solving bivariate polynomial
                 systems over either k (T)[ X,Y ] or Q [ X,Y ] using a
                 combination of lifting and modular composition
                 techniques.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lenstra:2013:LS,
  author =       "Hendrik Lenstra",
  title =        "Lattices with symmetry",
  crossref =     "Monagan:2013:IPI",
  pages =        "3--4",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465929",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Levandovskyy:2013:ECG,
  author =       "Viktor Levandovskyy and Grischa Studzinski and
                 Benjamin Schnitzler",
  title =        "Enhanced computations of {Gr{\"o}bner} bases in free
                 algebras as a new application of the letterplace
                 paradigm",
  crossref =     "Monagan:2013:IPI",
  pages =        "259--266",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465948",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Recently, the notion of ``letterplace correspondence''
                 between ideals in the free associative algebra KX and
                 certain ideals in the so-called letterplace ring KXP
                 has evolved. We continue this research direction,
                 started by La Scala and Levandovskyy, and present novel
                 ideas, supported by the implementation, for effective
                 computations with ideals in the free algebra by
                 utilizing the generalized letterplace correspondance.
                 In particular, we provide a direct algorithm to compute
                 Gr{\"o}bner bases of non-graded ideals. Surprisingly, we
                 realize its behavior as ``homogenizing without a
                 homogenization variable''. Moreover, we develop new
                 shift-invariant data structures for this family of
                 algorithms and discuss about them. Furthermore we
                 generalize the famous criteria of Gebauer-M{\"o}ller to
                 the non-commutative setting and show the benefits for
                 the computation by allowing to skip unnecessary
                 critical pairs. The methods are implemented in the
                 computer algebra system Singular. We present a
                 comparison of performance of our implementation with
                 the corresponding implementations in the systems Magma
                 [BCP97] and GAP [GAP13] on the representative set of
                 nontrivial examples.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Levin:2013:MDD,
  author =       "Alexander B. Levin",
  title =        "Multivariate difference-differential dimension
                 polynomials and new invariants of
                 difference-differential field extensions",
  crossref =     "Monagan:2013:IPI",
  pages =        "267--274",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465521",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We introduce a method of characteristic sets with
                 respect to several term orderings for
                 difference-differential polynomials. Using this
                 technique, we obtain a method of computation of
                 multivariate dimension polynomials of finitely
                 generated difference-differential field extensions.
                 Furthermore, we find new invariants of such extensions
                 and show how the computation of multivariate
                 difference-differential polynomials is applied to the
                 equivalence problem for systems of algebraic
                 difference-differential equations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2013:SDR,
  author =       "Wei Li and Chun-Ming Yuan and Xiao-Shan Gao",
  title =        "Sparse difference resultant",
  crossref =     "Monagan:2013:IPI",
  pages =        "275--282",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465509",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, the concept of sparse difference
                 resultant for a Laurent transformally essential system
                 of Laurent difference polynomials is introduced and its
                 properties are proved. In particular, order and degree
                 bounds for the sparse difference resultant are given.
                 Based on these bounds, an algorithm to compute the
                 sparse difference resultant is proposed, which is
                 single exponential in terms of the number of variables,
                 the Jacobi number, and the size of the system. Also,
                 the precise order, degree, a determinant
                 representation, and a Poisson-type product formula for
                 the difference resultant are given.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mehlhorn:2013:AFR,
  author =       "Kurt Mehlhorn and Michael Sagraloff and Pengming
                 Wang",
  title =        "From approximate factorization to root isolation",
  crossref =     "Monagan:2013:IPI",
  pages =        "283--290",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465523",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present an algorithm for isolating all roots of an
                 arbitrary complex polynomial $p$ which also works in
                 the presence of multiple roots provided that arbitrary
                 good approximations of the coefficients of $p$ and the
                 number of distinct roots are given. Its output consists
                 of pairwise disjoint disks each containing one of the
                 distinct roots of p, and its multiplicity. The
                 algorithm uses approximate factorization as a
                 subroutine. For the case, where Pan's algorithm [16] is
                 used for the factorization, we derive complexity bounds
                 for the problems of isolating and refining all roots
                 which are stated in terms of the geometric locations of
                 the roots only. Specializing the latter bounds to a
                 polynomial of degree d and with integer coefficients of
                 bitsize less than $ \tau $, we show that $ {\tilde
                 O}(d^3 + d^2 \tau + d \kappa) $ bit operations are
                 sufficient to compute isolating disks of size less than
                 $ 2^- \kappa $ for all roots of p, where $ \kappa $ is
                 an arbitrary positive integer. Our new algorithm has an
                 interesting consequence on the complexity of computing
                 the topology of a real algebraic curve specified as the
                 zero set of a bivariate integer polynomial and for
                 isolating the real solutions of a bivariate system. For
                 input polynomials of degree $n$ and bitsize $ \tau $,
                 the currently best running time improves from $ {\tilde
                 O}(n^9 \tau + n^8 \tau^2) $ (deterministic) to $
                 {\tilde O}(n^6 + n^5 \tau) $ (randomized) for topology
                 computation and from $ {\tilde O}(n^8 + n^7 \tau) $
                 (deterministic) to $ {\tilde O}(n^6 + n^5 \tau) $
                 (randomized) for solving bivariate systems.d",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2013:BCR,
  author =       "Victor Y. Pan and Elias P. Tsigaridas",
  title =        "On the boolean complexity of real root refinement",
  crossref =     "Monagan:2013:IPI",
  pages =        "299--306",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465938",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We assume that a real square-free polynomial $A$ has a
                 degree $d$, a maximum coefficient bitsize \tau and a
                 real root lying in an isolating interval and having no
                 nonreal roots nearby (we quantify this assumption).
                 Then, we combine the Double Exponential Sieve algorithm
                 (also called the Bisection of the Exponents), the
                 bisection, and Newton iteration to decrease the width
                 of this inclusion interval by a factor of $ t = 2^{-L}
                 $. The algorithm has Boolean complexity $ {\tilde O}_B
                 (d^2 \tau + d L) $. Our algorithms support the same
                 complexity bound for the refinement of $r$ roots, for
                 any $ r < = d $.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2013:TFA,
  author =       "Senshan Pan and Yupu Hu and Baocang Wang",
  title =        "The termination of the {$ F5 $} algorithm revisited",
  crossref =     "Monagan:2013:IPI",
  pages =        "291--298",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465520",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The F5 algorithm [8] is generally believed as one of
                 the fastest algorithms for computing Gr{\"o}bner bases.
                 However, its termination problem is still unclear. The
                 crux lies in the non-determinacy of the F5 in selecting
                 which from the critical pairs of the same degree. In
                 this paper, we construct a generalized algorithm F5GEN
                 which contain the F5 as its concrete implementation.
                 Then we prove the correct termination of the F5GEN
                 algorithm. That is to say, for any finite set of
                 homogeneous polynomials, the F5 terminates correctly.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parrilo:2013:CAG,
  author =       "Pablo A. Parrilo",
  title =        "Convex algebraic geometry and semidefinite
                 optimization",
  crossref =     "Monagan:2013:IPI",
  pages =        "9--10",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2466575",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In the past decade there has been a surge of interest
                 in algebraic approaches to optimization problems
                 defined by multivariate polynomials. Fundamental
                 mathematical challenges that arise in this area include
                 understanding the structure of nonnegative polynomials,
                 the interplay between efficiency and complexity of
                 different representations of algebraic sets, and the
                 development of effective algorithms. Remarkably, and
                 perhaps unexpectedly, convexity provides a new
                 viewpoint and a powerful framework for addressing these
                 questions. This naturally brings us to the intersection
                 of algebraic geometry, optimization, and convex
                 geometry, with an emphasis on algorithms and
                 computation. This emerging area has become known as
                 convex algebraic geometry. This tutorial will focus on
                 basic and recent developments in convex algebraic
                 geometry, and the associated computational methods
                 based on semidefinite programming for optimization
                 problems involving polynomial equations and
                 inequalities. There has been much recent progress, by
                 combining theoretical results in real algebraic
                 geometry with semidefinite programming to develop
                 effective computational approaches to these problems.
                 We will make particular emphasis on sum of squares
                 decompositions, general duality properties,
                 infeasibility certificates,
                 approximation/inapproximability results, as well as
                 survey the many exciting developments that have taken
                 place in the last few years.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pauderis:2013:CIS,
  author =       "Colton Pauderis and Arne Storjohann",
  title =        "Computing the invariant structure of integer matrices:
                 fast algorithms into practice",
  crossref =     "Monagan:2013:IPI",
  pages =        "307--314",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465955",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "We present a new heuristic algorithm for computing the
                 determinant of a nonsingular $ n \times n $ integer
                 matrix. Extensive empirical results from a highly
                 optimized implementation show the running time grows
                 approximately as $ n^3 \log n $, even for input
                 matrices with a highly nontrivial Smith invariant
                 structure. We extend the algorithm to compute the
                 Hermite form of the input matrix. Both the determinant
                 and Hermite form algorithm certify correctness of the
                 computed results.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pillwein:2013:TCP,
  author =       "Veronika Pillwein",
  title =        "Termination conditions for positivity proving
                 procedures",
  crossref =     "Monagan:2013:IPI",
  pages =        "315--322",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465945",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Proving positivity of a sequence given by a linear
                 recurrence with polynomial coefficients (P-finite
                 recurrence) is a non-trivial task for both humans and
                 computers. Algorithms dealing with this task are rare
                 or non-existent. One method that was introduced in the
                 last decade by Gerhold and Kauers succeeds on many
                 examples, but termination of this procedure has been
                 proven so far only up to order three for special cases.
                 Here we present an analysis that extends the previously
                 known termination results on recurrences of order
                 three, and also provides termination conditions for
                 recurrences of higher order.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Raab:2013:IUF,
  author =       "Clemens G. Raab",
  title =        "Integration of unspecified functions and families of
                 iterated integrals",
  crossref =     "Monagan:2013:IPI",
  pages =        "323--330",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465939",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "An algorithm for parametric elementary integration
                 over differential fields constructed by a
                 differentially transcendental extension is given. It
                 extends current versions of Risch's algorithm to this
                 setting and is based on some first ideas of Graham H.
                 Campbell transferring his method to more formal grounds
                 and making it parametric, which allows to compute
                 relations among definite integrals. Apart from
                 differentially transcendental functions, such as the
                 gamma function or the zeta function, also unspecified
                 functions and certain families of iterated integrals
                 such as the polylogarithms can be modeled in such
                 differential fields.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Steffy:2013:ELI,
  author =       "Daniel E. Steffy",
  title =        "Exact linear and integer programming: tutorial
                 abstract",
  crossref =     "Monagan:2013:IPI",
  pages =        "11--12",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465931",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This tutorial surveys state-of-the-art algorithms and
                 computational methods for computing exact solutions to
                 linear and mixed-integer programming problems.",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanderHoeven:2013:IMC,
  author =       "Joris van der Hoeven and Gr{\'e}goire Lecerf",
  title =        "Interfacing {{\tt MATHEMAGIX}} with {C++}",
  crossref =     "Monagan:2013:IPI",
  pages =        "363--370",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465511",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we give a detailed description of the
                 interface between the MATHEMAGIX language and C++. In
                 particular, we describe the mechanism which allows us
                 to import a C++ template library (which only permits
                 static instantiation) as a fully generic MATHEMAGIX
                 template library.",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanderHoeven:2013:SFT,
  author =       "Joris van der Hoeven and Romain Lebreton and {\'E}ric
                 Schost",
  title =        "Structured {FFT} and {TFT}: symmetric and lattice
                 polynomials",
  crossref =     "Monagan:2013:IPI",
  pages =        "355--362",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465526",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we consider the problem of efficient
                 computations with structured polynomials. We provide
                 complexity results for computing Fourier Transform and
                 Truncated Fourier Transform of symmetric polynomials,
                 and for multiplying polynomials supported on a
                 lattice.",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanHoeij:2013:CFU,
  author =       "Mark van Hoeij",
  title =        "The complexity of factoring univariate polynomials
                 over the rationals: tutorial abstract",
  crossref =     "Monagan:2013:IPI",
  pages =        "13--14",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2479779",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "This tutorial will explain the algorithm behind the
                 currently fastest implementations for univariate
                 factorization over the rationals. The complexity will
                 be analyzed; it turns out that modifications were
                 needed in order to prove a polynomial time complexity
                 while preserving the best practical performance. The
                 complexity analysis leads to two results: (1) it shows
                 that the practical performance on common inputs can be
                 improved without harming the worst case performance,
                 and (2) it leads to an improved complexity, not only
                 for factoring, but for LLL reduction as well.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wolfram:2013:CAY,
  author =       "Stephen Wolfram",
  title =        "Computer algebra: a $ 32 $-year update",
  crossref =     "Monagan:2013:IPI",
  pages =        "7--8",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465930",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wu:2013:FPR,
  author =       "Wenyuan Wu and Greg Reid",
  title =        "Finding points on real solution components and
                 applications to differential polynomial systems",
  crossref =     "Monagan:2013:IPI",
  pages =        "339--346",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465954",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper we extend complex homotopy methods to
                 finding witness points on the irreducible components of
                 real varieties. In particular we construct such witness
                 points as the isolated real solutions of a constrained
                 optimization problem. First a random hyperplane
                 characterized by its random normal vector is chosen.
                 Witness points are computed by a polyhedral homotopy
                 method. Some of them are at the intersection of this
                 hyperplane with the components. Other witness points
                 are the local critical points of the distance from the
                 plane to components. A method is also given for
                 constructing regular witness points on components, when
                 the critical points are singular. The method is
                 applicable to systems satisfying certain regularity
                 conditions. Illustrative examples are given. We show
                 that the method can be used in the consistent
                 initialization phase of a popular method due to Pryce
                 and Pantelides for preprocessing differential algebraic
                 equations for numerical solution.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yang:2013:VEB,
  author =       "Zhengfeng Yang and Lihong Zhi and Yijun Zhu",
  title =        "Verified error bounds for real solutions of
                 positive-dimensional polynomial systems",
  crossref =     "Monagan:2013:IPI",
  pages =        "371--378",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465951",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "In this paper, we propose two algorithms for verifying
                 the existence of real solutions of positive-dimensional
                 polynomial systems. The first one is based on the
                 critical point method and the homotopy continuation
                 method. It targets for verifying the existence of real
                 roots on each connected component of an algebraic
                 variety $V \cap R^n$ defined by polynomial equations.
                 The second one is based on the low-rank moment matrix
                 completion method and aims for verifying the existence
                 of at least one real roots on $V \cap R^n$. Combined
                 both algorithms with the verification algorithms for
                 zero-dimensional polynomial systems, we are able to
                 find verified real solutions of positive-dimensional
                 polynomial systems very efficiently for a large set of
                 examples.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhou:2013:CCB,
  author =       "Wei Zhou and George Labahn",
  title =        "Computing column bases of polynomial matrices",
  crossref =     "Monagan:2013:IPI",
  pages =        "379--386",
  year =         "2013",
  DOI =          "https://doi.org/10.1145/2465506.2465947",
  bibdate =      "Fri Mar 14 14:33:44 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "Given a matrix of univariate polynomials over a field
                 $K$, its columns generate a $ K[x] $-module. We call
                 any basis of this module a column basis of the given
                 matrix. Matrix gcds and matrix normal forms are
                 examples of such module bases. In this paper we present
                 a deterministic algorithm for the computation of a
                 column basis of an $ m \times n $ input matrix with $ m
                 \leq n $. If $s$ is the average column degree of the
                 input matrix, this algorithm computes a column basis
                 with a cost of $ {\tilde O}(n m^{\omega - 1} s) $ field
                 operations in $K$. Here the soft-$O$ notation is
                 Big-$O$ with log factors removed while $ \omega $ is
                 the exponent of matrix multiplication. Note that the
                 average column degree $s$ is bounded by the commonly
                 used matrix degree that is also the maximum column
                 degree of the input matrix.",
  acknowledgement = ack-nhfb,
}

%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Jenks:1976:SPA,
  editor =       "Richard D. Jenks",
  booktitle =    "{Symsac '76: proceedings of the 1976 ACM Symposium on
                 Symbolic and Algebraic Computation, August 10--12,
                 1976, Yorktown Heights, New York}",
  title =        "{Symsac '76: proceedings of the 1976 ACM Symposium on
                 Symbolic and Algebraic Computation, August 10--12,
                 1976, Yorktown Heights, New York}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "384",
  year =         "1976",
  LCCN =         "QA155.7.E4 A15 1976",
  bibdate =      "Tue Jul 26 09:04:45 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  price =        "US\$20.00",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
}

@Proceedings{Ng:1979:SAC,
  editor =       "Edward W. Ng",
  booktitle =    "{Symbolic and algebraic computation: EUROSAM '79, an
                 International Symposium on Symbolic and Algebraic
                 Manipulation, Marseille, France, June 1979}",
  title =        "{Symbolic and algebraic computation: EUROSAM '79, an
                 International Symposium on Symbolic and Algebraic
                 Manipulation, Marseille, France, June 1979}",
  volume =       "72",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 557",
  year =         "1979",
  CODEN =        "LNCSD9",
  ISBN =         "0-387-09519-5",
  ISBN-13 =      "978-0-387-09519-6",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA155.7.E4 E88 1979",
  bibdate =      "Fri Apr 12 07:14:47 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "algebra --- data processing --- congresses",
}

@Proceedings{Wang:1981:SPA,
  editor =       "Paul S. Wang",
  booktitle =    "{SYMSAC '81: proceedings of the 1981 ACM Symposium on
                 Symbolic and Algebraic Computation, Snowbird, Utah,
                 August 5--7, 1981}",
  title =        "{SYMSAC '81: proceedings of the 1981 ACM Symposium on
                 Symbolic and Algebraic Computation, Snowbird, Utah,
                 August 5--7, 1981}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xi + 249",
  year =         "1981",
  ISBN =         "0-89791-047-8",
  ISBN-13 =      "978-0-89791-047-7",
  LCCN =         "QA155.7.E4 A28 1981",
  bibdate =      "Fri Feb 09 12:29:36 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/macsyma.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  note =         "ACM order no. 505810",
  price =        "US\$23.00",
  acknowledgement = ack-nhfb,
  tableofcontents = "The basis of a computer system for modern algebra /
                 John J. Cannon \\
                 A language for computational algebra / Richard D.
                 Jenks, Barry M. Trager \\
                 Characterization of VAX Macsyma / John K. Foderaro,
                 Richard J. Fateman \\
                 SMP - A Symbolic Manipulation Program / Chris A. Cole,
                 Stephen Wolfram \\
                 An extension of Liouville s theorem on integration in
                 finite terms / M. F. Singer, B. D. Saunders, B. F.
                 Caviness \\
                 Formal solutions of differential equations in the
                 neighborhood of singular points (Regular and Irregular)
                 / J. Della Dora, E. Tournier \\
                 Elementary first integrals of differential equations /
                 M. J. Prelle, M. F. Singer \\
                 A technique for solving ordinary differential equations
                 using Riemann s P-functions / Shunro Watanabe \\
                 Using Lie transformation groups to find closed form
                 solutions to first order ordinary differential
                 equations / Bruce Char \\
                 The computational complexity of continued fractions /
                 V. Strassen \\
                 Newton s iteration and the sparse Hensel algorithm
                 (Extended Abstract) / Richard Zippel \\
                 Automatic generation of finite difference equations and
                 Fourier stability analyses / Michael C. Wirth \\
                 An algorithmic classification of geometries in general
                 relativity / Jan E. Aman, Anders Karlhede \\
                 Formulation of design rules for NMR imaging coil by
                 using symbolic manipulation / John F. Schenck, M. A.
                 Hussain \\
                 Computation for conductance distributions of
                 percolation lattice cells / Rabbe Fogelholm \\
                 Breuer s grow factor algorithm in computer algebra / J.
                 A. van Hulzen \\
                 An implementation of Kovacic s algorithm for solving
                 second order linear homogeneous differential equations
                 / B. David Saunders \\
                 Implementing a polynomial factorization and GCD package
                 / P. M. A. Moore, A. C. Norman \\
                 Note on probabilistic algorithms in integer and
                 polynomial arithmetic / Michael Kaminski \\
                 A case study in interlanguage communication: Fast LISP
                 polynomial operations written in C / Richard J. Fateman
                 \\
                 On the application of Array Processors to symbol
                 manipulation / R. Beardsworth \\
                 The optimization of user programs for an Algebraic
                 Manipulation System / P. D. Pearce, R. J. Hickst \\
                 Views on transportability of Lisp and Lisp-based
                 systems / Richard J. Fateman \\
                 Algebraic constructions for algorithms (Extended
                 Abstract) / S. Winograd \\
                 A cancellation free algorithm, with factoring
                 capabilities, for the efficient solution of large
                 sparse sets of equations / J. Smit \\
                 Efficient Gaussian elimination method for symbolic
                 determinants and linear systems (Extended Abstract) /
                 Tateaki Sasaki, Hirokazu Murao \\
                 Parallelism in algebraic computation and parallel
                 algorithms for symbolic linear systems / Tateaki
                 Sasaki, Yasumasa Kanada \\
                 Algebraic computation for the masses / Joel Moses \\
                 Construction of nilpotent Lie algebras over arbitrary
                 fields / Robert E. Beck, Bernard Kolman \\
                 Algorithms for central extensions of Lie algebras
                 Robert E. Beck, Bernard Kolman \\
                 Computing an invariant subring of $k[X,Y]$ / Rosalind
                 Neuman \\
                 Double cosets and searching small groups / Gregory
                 Butler \\
                 A generalized class of polynomials that are hard to
                 factor / Erich Kaltofen, David R. Musser, B. David
                 Saunders \\
                 Some inequalities about univariate polynomials /
                 Maurice Mignotte \\
                 Factorization over finitely generated fields / James H.
                 Davenport, Barry M. Trager \\
                 On solving systems of algebraic equations via ideal
                 bases and elimination theory / Michael E. Pohst, David
                 Y. Y. Yun \\
                 A p-adic algorithm for univariate partial fractions /
                 Paul S. Wang \\
                 Use of VLSI in algebraic computation: Some suggestions
                 H. T. Kung \\
                 An algebraic front-end for the production and use of
                 numeric programs / Douglas H. Lanam \\
                 Computer algebra and numerical integration / Richard J.
                 Fateman \\
                 Tracing occurrences of patterns in symbolic
                 computations / F. Gardin, J. A. Campbell \\
                 The automatic derivation of periodic solutions to a
                 class of weakly nonlinear differential equations / John
                 Fitch \\
                 User-based integration software / John Fitch.",
}

@Proceedings{Char:1986:PSS,
  editor =       "Bruce W. Char",
  booktitle =    "{Proceedings of the 1986 Symposium on Symbolic and
                 Algebraic Computation: Symsac '86, July 21--23, 1986,
                 Waterloo, Ontario}",
  title =        "{Proceedings of the 1986 Symposium on Symbolic and
                 Algebraic Computation: Symsac '86, July 21--23, 1986,
                 Waterloo, Ontario}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "254",
  year =         "1986",
  ISBN =         "0-89791-199-7 (paperback)",
  ISBN-13 =      "978-0-89791-199-3 (paperback)",
  LCCN =         "QA155.7.E4 A281 1986",
  bibdate =      "Thu Mar 12 07:35:00 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order no. 505860.",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra --- Data processing --- Congresses;
                 Programming languages (Electronic computers) ---
                 Congresses",
}

@Proceedings{Gianni:1989:SAC,
  editor =       "P. (Patrizia) Gianni",
  booktitle =    "{Symbolic and algebraic computation: International
                 Symposium ISSAC '88, Rome, Italy, July 4--8, 1988:
                 proceedings}",
  title =        "{Symbolic and algebraic computation: International
                 Symposium ISSAC '88, Rome, Italy, July 4--8, 1988:
                 proceedings}",
  volume =       "358",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 543",
  year =         "1989",
  ISBN =         "3-540-51084-2",
  ISBN-13 =      "978-3-540-51084-0",
  LCCN =         "QA76.95 .I571 1988",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "Conference held jointly with AAECC-6.",
  series =       ser-LNCS,
  abstract =     "The following topics were dealt with: differential
                 algebra; applications; Gr{\"o}bner bases; differential
                 equations; algorithmic number theory; algebraic
                 geometry; computational geometry; computational logic;
                 systems; and arithmetic.",
  acknowledgement = ack-nhfb,
  classification = "C1110 (Algebra); C4100 (Numerical analysis); C7310
                 (Mathematics)",
  confdate =     "4--8 July 1988",
  conflocation = "Rome, Italy",
  keywords =     "Differential algebra; Applications; Gr{\"o}bner bases;
                 Differential equations; Algorithmic number theory;
                 Algebraic geometry; Computational geometry;
                 Computational logic; Systems; Arithmetic",
  pubcountry =   "West Germany",
  thesaurus =    "Algebra; Computational geometry; Differential
                 equations; Formal logic; Mathematics computing; Theorem
                 proving",
}

@Proceedings{Gonnet:1989:PAI,
  editor =       "Gaston H. Gonnet",
  booktitle =    "{Proceedings of the ACM-SIGSAM 1989 International
                 Symposium on Symbolic and Algebraic Computation: ISSAC
                 '89 / July 17--19, 1989, Portland, Oregon}",
  title =        "{Proceedings of the ACM-SIGSAM 1989 International
                 Symposium on Symbolic and Algebraic Computation: ISSAC
                 '89 / July 17--19, 1989, Portland, Oregon}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "399",
  year =         "1989",
  ISBN =         "0-89791-325-6",
  ISBN-13 =      "978-0-89791-325-6",
  LCCN =         "QA76.95.I59 1989",
  bibdate =      "Thu Sep 26 06:21:35 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number: 505890. English and French.",
  price =        "US\$29.00",
  abstract =     "The following topics were dealt with: differential
                 equations; linear difference equations; functional
                 equivalence; series solutions; factorization; Las Vegas
                 primality test; matrix algebra; rational mappings;
                 Knuth--Bendix procedure and Buchberger algorithm;
                 symbolic algebra; lockup tables; derivations
                 polynomials; Pad{\'e}--Hermite Forms; $p$-adic
                 approximations; nonlinear equations; defect;
                 Sturm--Habicht sequence; MINION; REDUCE; code
                 optimization; IRENA; MACSYMA; GENCRAY; AIPI; Fourier
                 series; functions; integration; education; stability;
                 normal forms; curves; geometry; root isolation;
                 triangle inequalities; parallel algorithms; rewriting
                 systems; and theorem proving.",
  acknowledgement = ack-nhfb,
  classification = "C1110 (Algebra); C1120 (Analysis); C4100 (Numerical
                 analysis); C4200 (Computer theory); C7310
                 (Mathematics)",
  confdate =     "17--19 July 1989",
  conflocation = "Portland, OR, USA",
  confsponsor =  "ACM",
  keywords =     "AIPI; algebra --- data processing --- congresses;
                 Buchberger algorithm; Code optimization; computational
                 complexity --- congresses; Curves; Defect; Derivations;
                 Differential equations; Education; Factorization;
                 Fourier series; Functional equivalence; Functions;
                 GENCRAY; Geometry; Integration; IRENA; Knuth--Bendix
                 procedure; Las Vegas primality test; Linear difference
                 equations; Lockup tables; MACSYMA; Matrix algebra;
                 MINION; Nonlinear equations; Normal forms; P-adic
                 approximations; Pad{\'e}--Hermite Forms; Parallel
                 algorithms; Polynomials; Rational mappings; REDUCE;
                 Rewriting systems; Root isolation; Series solutions;
                 Stability; Sturm--Habicht sequence; Symbolic algebra;
                 Theorem proving, mathematics --- data processing ---
                 congresses; Triangle inequalities",
  pubcountry =   "USA",
  thesaurus =    "Algebra; Computation theory; Functions; Mathematics
                 computing; Numerical analysis; Series [mathematics];
                 Symbol manipulation",
}

@Proceedings{Mora:1989:AAA,
  editor =       "T. Mora",
  booktitle =    "{Applied Algebra, Algebraic Algorithms and
                 Error-Correcting Codes. 6th International Conference,
                 AAECC-6, Rome, Italy, July 4--8, 1988. Proceedings}",
  title =        "{Applied Algebra, Algebraic Algorithms and
                 Error-Correcting Codes. 6th International Conference,
                 AAECC-6, Rome, Italy, July 4--8, 1988. Proceedings}",
  volume =       "357",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 480",
  year =         "1989",
  ISBN =         "3-540-51083-4",
  ISBN-13 =      "978-3-540-51083-3",
  LCCN =         "QA268 .A35 1988",
  bibdate =      "Tue Sep 17 06:46:18 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "Conference held jointly with ISSAC '88.",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
  confdate =     "4--8 July 1988",
  conflocation = "Rome, Italy",
  pubcountry =   "West Germany",
}

@Proceedings{Watanabe:1990:IPI,
  editor =       "Shunro Watanabe and Morio Nagata",
  booktitle =    "{ISSAC '90: proceedings of the International Symposium
                 on Symbolic and Algebraic Computation: August 20--24,
                 1990, Tokyo, Japan}",
  title =        "{ISSAC '90: proceedings of the International Symposium
                 on Symbolic and Algebraic Computation: August 20--24,
                 1990, Tokyo, Japan}",
  publisher =    pub-ACM # " and " # pub-AW,
  address =      pub-ACM:adr # " and " # pub-AW:adr,
  pages =        "ix + 307",
  year =         "1990",
  ISBN =         "0-89791-401-5 (ACM), 0-201-54892-5 (Addison-Wesley)",
  ISBN-13 =      "978-0-89791-401-7 (ACM), 978-0-201-54892-1
                 (Addison-Wesley)",
  LCCN =         "QA76.95 .I57 1990",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The following topics were dealt with: foundations of
                 symbolic computation; computational logics; systems;
                 algorithms on polynomials; integration and differential
                 equations; and algorithms on geometry.",
  acknowledgement = ack-nhfb,
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory)",
  confdate =     "20--24 Aug. 1990",
  conflocation = "Tokyo, Japan",
  confsponsor =  "Inf. Processing Soc. Japan; Japan Soc. Software Sci.
                 Technol.; ACM",
  keywords =     "algebra --- data processing --- congresses;
                 Algorithms; Computational geometry; Computational
                 logics; Differential equations; Geometry; Integration;
                 mathematics --- data processing --- congresses;
                 Polynomials; Symbolic computation; Systems",
  pubcountry =   "USA",
  thesaurus =    "Algorithm theory; Computational geometry; Formal
                 logic; Symbol manipulation",
}

@Proceedings{Watt:1991:IPI,
  editor =       "Stephen M. Watt",
  booktitle =    "{ISSAC '91: proceedings of the 1991 International
                 Symposium on Symbolic and Algebraic Computation, July
                 15--17, 1991, Bonn, Germany}",
  title =        "{ISSAC '91: proceedings of the 1991 International
                 Symposium on Symbolic and Algebraic Computation, July
                 15--17, 1991, Bonn, Germany}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiii + 468",
  year =         "1991",
  ISBN =         "0-89791-437-6",
  ISBN-13 =      "978-0-89791-437-6",
  LCCN =         "QA 76.95 I59 1991",
  bibdate =      "Thu Sep 26 06:00:06 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/magma.bib",
  abstract =     "The following topics were dealt with: algorithms for
                 symbolic mathematical computation; languages, systems
                 and packages; computational geometry, group theory and
                 number theory; automatic theorem proving and
                 programming; interface of symbolics, numerics and
                 graphics; applications in mathematics, science and
                 engineering; and symbolic and algebraic computation in
                 education.",
  acknowledgement = ack-nhfb,
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C4210
                 (Formal logic); C4240 (Programming and algorithm
                 theory); C7310 (Mathematics)",
  confdate =     "15--17 July 1991",
  conflocation = "Bonn, Germany",
  confsponsor =  "ACM",
  keywords =     "algebra --- data processing --- congresses; Algebraic
                 computation; Algorithms; Automatic theorem proving;
                 Computational geometry; Education; Engineering;
                 Graphics; Group theory; Languages; Mathematics;
                 mathematics --- data processing --- congresses; Number
                 theory; Programming; Science; Symbolic mathematical
                 computation; Symbolics",
  pubcountry =   "USA",
  thesaurus =    "Computational complexity; Formal languages;
                 Interpolation; Number theory; Polynomials; Symbol
                 manipulation",
}

@Proceedings{Wang:1992:PII,
  editor =       "Paul S. Wang",
  booktitle =    "{Proceedings of ISSAC '92. International Symposium on
                 Symbolic and Algebraic Computation}",
  title =        "{Proceedings of ISSAC '92. International Symposium on
                 Symbolic and Algebraic Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ix + 406",
  year =         "1992",
  ISBN =         "0-89791-489-9 (soft cover), 0-89791-490-2 (hard
                 cover)",
  ISBN-13 =      "978-0-89791-489-5 (soft cover), 978-0-89791-490-1
                 (hard cover)",
  LCCN =         "QA76.95.I59 1992",
  bibdate =      "Thu Sep 26 05:51:45 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number: 505920.",
  abstract =     "The following topics were dealt with: symbolic
                 computation; differential equations; differs-integral
                 software; algebraic algorithms; algebraic software;
                 real algebraics and root isolation; groups and number
                 theory; systems and interfaces.",
  acknowledgement = ack-nhfb,
  classification = "C6130 (Data handling techniques); C7310
                 (Mathematics)",
  confdate =     "27--29 July 1992",
  conflocation = "Berkeley, CA, USA",
  confsponsor =  "ACM",
  keywords =     "Algebraic algorithms; Algebraic software; Differential
                 equations; Differs-integral software; Groups theory;
                 Interfaces; Number theory; Real algebraics; Root
                 isolation; Symbolic computation",
  pubcountry =   "USA",
  thesaurus =    "Differential equations; Mathematics computing; Symbol
                 manipulation",
}

@Proceedings{ACM:1993:PFA,
  editor =       "{ACM}",
  booktitle =    "{Proceedings of the Fourth ACM SIGPLAN Symposium on
                 Principles and Practice of Parallel Programming, PPOPP:
                 San Diego, California, May 19--22, 1993}",
  title =        "{Proceedings of the Fourth ACM SIGPLAN Symposium on
                 Principles and Practice of Parallel Programming, PPOPP:
                 San Diego, California, May 19--22, 1993}",
  volume =       "28(7)",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ix + 259",
  year =         "1993",
  ISBN =         "0-89791-589-5",
  ISBN-13 =      "978-0-89791-589-2",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  LCCN =         "QA76.642.A27 1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       "ACM SIGPLAN Notices",
  acknowledgement = ack-nhfb,
  sponsor =      "Association for Computing Machinery; Special Interest
                 Group on Programming Languages.",
  standardno =   "1",
}

@Proceedings{Bronstein:1993:IPI,
  editor =       "Manuel Bronstein",
  booktitle =    "{ISSAC'93: proceedings of the 1993 International
                 Symposium on Symbolic and Algebraic Computation, July
                 6--8, 1993, Kiev, Ukraine}",
  title =        "{ISSAC'93: proceedings of the 1993 International
                 Symposium on Symbolic and Algebraic Computation, July
                 6--8, 1993, Kiev, Ukraine}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 321",
  year =         "1993",
  ISBN =         "0-89791-604-2",
  ISBN-13 =      "978-0-89791-604-2",
  LCCN =         "QA 76.95 I59 1993",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number: 505930.",
  abstract =     "The following topics were dealt with: algebraic
                 solutions of equations; computer algebra systems;
                 algorithm theory and complexity; automated theorem
                 proving; polynomials; and matrix algebra.",
  acknowledgement = ack-nhfb,
  classification = "C4210 (Formal logic); C4240 (Programming and
                 algorithm theory); C7310 (Mathematics computing)",
  confdate =     "6--8 July 1993",
  conflocation = "Kiev, Ukraine",
  confsponsor =  "ACM",
  keywords =     "algebra --- data processing --- congresses; Algorithm
                 theory; Automated theorem proving; Complexity; Computer
                 algebra; mathematics --- data processing ---
                 congresses; Matrix algebra; Polynomials",
  pubcountry =   "USA",
  source =       "ISSAC '93",
  sponsor =      "Association for Computing Machinery.",
  thesaurus =    "Computational complexity; Mathematics computing;
                 Matrix algebra; Polynomials; Symbol manipulation;
                 Theorem proving",
}

@Proceedings{Halstead:1993:PSC,
  editor =       "Robert H. Halstead and Takayasu Ito",
  booktitle =    "{Parallel symbolic computing: languages, systems, and
                 applications: US\slash Japan workshop, Cambridge, MA,
                 USA, October 14--17, 1992: proceedings}",
  title =        "{Parallel symbolic computing: languages, systems, and
                 applications: US\slash Japan workshop, Cambridge, MA,
                 USA, October 14--17, 1992: proceedings}",
  number =       "748",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 417",
  year =         "1993",
  ISBN =         "0-387-57396-8, 3-540-57396-8",
  ISBN-13 =      "978-0-387-57396-0, 978-3-540-57396-8",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.58.P3785 1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Proceedings{Sincovec:1993:PSS,
  editor =       "Richard F. Sincovec",
  booktitle =    "{Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, Norfolk, VA,
                 March, 1993}",
  title =        "{Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, Norfolk, VA,
                 March, 1993}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xix + 1041 + iv",
  year =         "1993",
  ISBN =         "0-89871-315-3",
  ISBN-13 =      "978-0-89871-315-2",
  LCCN =         "QA76.58.S55 1993",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
  sponsor =      "Society for Industrial and Applied Mathematics.",
}

@Proceedings{ACM:1994:IPI,
  editor =       "{ACM}",
  booktitle =    "{ISSAC '94: Proceedings of the 1994 International
                 Symposium on Symbolic and Algebraic Computation: July
                 20--22, 1994, Oxford, England, United Kingdom}",
  title =        "{ISSAC '94: Proceedings of the 1994 International
                 Symposium on Symbolic and Algebraic Computation: July
                 20--22, 1994, Oxford, England, United Kingdom}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ix + 359",
  year =         "1994",
  ISBN =         "0-89791-638-7",
  ISBN-13 =      "978-0-89791-638-7",
  LCCN =         "QA76.95.I59 1994",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  confdate =     "20--22 July 1994",
  conflocation = "Oxford, UK",
  confsponsor =  "ACM",
  pubcountry =   "USA",
}

@Proceedings{Adleman:1994:ANT,
  editor =       "L. M. Adleman and M.-D. Huang",
  booktitle =    "{Algorithmic Number Theory. First International
                 Symposium, ANTS-I. Proceedings}",
  title =        "{Algorithmic Number Theory. First International
                 Symposium, ANTS-I. Proceedings}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 322",
  year =         "1994",
  ISBN =         "0-387-58691-1 (New York), 3-540-58691-1 (Berlin)",
  ISBN-13 =      "978-0-387-58691-5 (New York), 978-3-540-58691-3
                 (Berlin)",
  LCCN =         "QA241.A43 1994",
  bibdate =      "Thu Sep 26 05:50:11 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  confdate =     "6--9 May 1994",
  conflocation = "Ithaca, NY, USA",
  pubcountry =   "Germany",
}

@Proceedings{Hong:1994:FIS,
  editor =       "Hoon Hong",
  booktitle =    "{First International Symposium on Parallel Symbolic
                 Computation, PASCO '94, Hagenberg\slash Linz, Austria,
                 September 26--28, 1994}",
  title =        "{First International Symposium on Parallel Symbolic
                 Computation, PASCO '94, Hagenberg\slash Linz, Austria,
                 September 26--28, 1994}",
  volume =       "5",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xiii + 431",
  year =         "1994",
  ISBN =         "981-02-2040-5",
  ISBN-13 =      "978-981-02-2040-2",
  LCCN =         "QA76.642.I58 1994",
  bibdate =      "Thu Mar 12 07:55:38 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       "Lecture notes series in computing",
  acknowledgement = ack-nhfb,
  alttitle =     "Parallel symbolic computation",
  keywords =     "Parallel programming (Computer science) ---
                 Congresses.",
}

@Proceedings{Aityan:1995:PNP,
  editor =       "S. K. Aityan",
  booktitle =    "{Proceedings of neural, parallel and scientific
                 computations: proceedings of the First International
                 Conference on Neural, Parallel and Scientific
                 Computations held at Morehouse College, Atlanta, USA,
                 May 28--31, 1995}",
  title =        "{Proceedings of neural, parallel and scientific
                 computations: proceedings of the First International
                 Conference on Neural, Parallel and Scientific
                 Computations held at Morehouse College, Atlanta, USA,
                 May 28--31, 1995}",
  volume =       "1",
  publisher =    "Dynamic Publishers, Inc",
  address =      "Atlanta, GA",
  pages =        "xi + 506",
  year =         "1995",
  ISBN =         "0-9640398-9-3, 0-9640398-8-5",
  ISBN-13 =      "978-0-9640398-9-6, 978-0-9640398-8-9",
  LCCN =         "QA76.87 .I58 1995",
  bibdate =      "Sat Mar 11 16:48:03 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       "Proceedings of Neural Parallel and Scientific
                 Computations",
  acknowledgement = ack-nhfb,
}

@Proceedings{Ferreira:1995:PAI,
  editor =       "Afonso Ferreira and Jose D. P. Rolim",
  booktitle =    "{Parallel algorithms for irregularly structured
                 problems: second international workshop, IRREGULAR 95,
                 Lyon, France, September 4--6, 1995: proceedings}",
  title =        "{Parallel algorithms for irregularly structured
                 problems: second international workshop, IRREGULAR 95,
                 Lyon, France, September 4--6, 1995: proceedings}",
  volume =       "980",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 409",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISBN =         "3-540-60321-2",
  ISBN-13 =      "978-3-540-60321-4",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.642 .I59 1995",
  bibdate =      "Fri Apr 12 07:41:32 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "computer algorithms --- congresses; parallel
                 programming (computer science) --- congresses",
  xxvolume =     "4005092982",
}

@Proceedings{IEEE:1995:PEI,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the Eighth IEEE Symposium on
                 Computer-Based Medical Systems / June 9--10, 1995,
                 Lubbock, Texas}",
  title =        "{Proceedings of the Eighth IEEE Symposium on
                 Computer-Based Medical Systems / June 9--10, 1995,
                 Lubbock, Texas}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 348",
  year =         "1995",
  ISBN =         "0-8186-7117-3",
  ISBN-13 =      "978-0-8186-7117-3",
  LCCN =         "R858.A2 I155 1995",
  bibdate =      "Thu Sep 26 05:45:15 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "IEEE catalog number 95CH35813.",
  acknowledgement = ack-nhfb,
  confdate =     "9--10 June 1995",
  conflocation = "Lubbock, TX, USA",
  confsponsor =  "IEEE Comput. Soc. Tech. Committee on Comput. Med.;
                 IEEE South Plains Sect.; SPIE - Int. Soc. Opt. Eng.;
                 Texas Tech Univ.; Texas Tech Univ. Health Sci. Center",
  pubcountry =   "USA",
}

@Proceedings{Levelt:1995:IPI,
  editor =       "A. H. M. Levelt",
  booktitle =    "{ISSAC '95: Proceedings of the 1995 International
                 Symposium on Symbolic and Algebraic Computation: July
                 10--12, 1995, Montr{\'e}al, Canada}",
  title =        "{ISSAC '95: Proceedings of the 1995 International
                 Symposium on Symbolic and Algebraic Computation: July
                 10--12, 1995, Montr{\'e}al, Canada}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xviii + 314",
  year =         "1995",
  ISBN =         "0-89791-699-9",
  ISBN-13 =      "978-0-89791-699-8",
  LCCN =         "QA 76.95 I59 1995",
  bibdate =      "Thu Sep 26 05:34:21 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number: 505950",
  series =       "ISSAC -PROCEEDINGS- 1995",
  abstract =     "The following topics were dealt with: differential
                 equations; visualisation; algebraic numbers;
                 algorithms; systems; polynomial and differential
                 algebra; seminumerical methods; greatest common
                 divisors; and.",
  acknowledgement = ack-nhfb,
  classification = "C4100 (Numerical analysis); C4170 (Differential
                 equations); C7310 (Mathematics computing)",
  confdate =     "10--12 July 1995",
  conflocation = "Montr{\'e}al, Que., Canada",
  confsponsor =  "ACM",
  keywords =     "algebra --- data processing --- congresses; Algebraic
                 numbers; Algorithms; Differential algebra; Differential
                 equations; Greatest common divisors; mathematics ---
                 data processing --- congresses; Polynomial;
                 Seminumerical methods; Systems; Visualisation",
  pubcountry =   "USA",
  source =       "ISSAC '95",
  thesaurus =    "Data visualisation; Differential equations; Group
                 theory; Numerical analysis; Symbol manipulation",
}

@Proceedings{Briot:1996:OBP,
  editor =       "Jean-Pierre Briot and Jean-Marc Geib and Akinori
                 Yonezawa",
  booktitle =    "{Object-based parallel and distributed computation:
                 France--Japan Workshop, OBPDC '95, Tokyo, Japan, June
                 21--23, 1995: selected papers}",
  title =        "{Object-based parallel and distributed computation:
                 France--Japan Workshop, OBPDC '95, Tokyo, Japan, June
                 21--23, 1995: selected papers}",
  volume =       "1107",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 348",
  year =         "1996",
  ISBN =         "3-540-61487-7 (softcover)",
  ISBN-13 =      "978-3-540-61487-6 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.64 .F7 1995",
  bibdate =      "Sat Dec 21 16:06:37 MST 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  annote =       "Data parallel programming in the parallel
                 object-oriented language OCore / Hiroki Konaka \ldots{}
                 [et al.] -- Polymorphic matrices in Paladin / Frederic
                 Guidec and Jean-Marc Jezequel -- Programming and
                 debugging for massive parallelism: the case for a
                 parallel object-oriented language A-NETL / Takanobu
                 Baba, Tsutomu Yoshinaga, and Takahiro Furuta --
                 Schematic: a concurrent object-oriented extension to
                 Scheme / Kenjiro Taura and Akinori Yonezawa -- (Thread
                 and object)-oriented distributed programming /
                 Jean-Marc Geib \ldots{} [et al.] -- Distributed and
                 object oriented symbolic programming in April / Keith
                 L. Clark and Frank G. McCabe -- Reactive programming
                 Eiffel// / Denis Caromel and Yves Roudier -- Proofs,
                 concurrent objects, and computations in a FILL
                 framework / Didier Galmiche and Eric Boudinet --
                 Modular description and verification of concurrent
                 objects / Jean-Paul Bahsoun, Stephan Merz, and Corinne
                 Servieres - - CHORUS/COOL: CHORUS object oriented
                 technology / Christian Jacquemot, Peter Strarup Jensen,
                 and Stephane Carrez -- Adaptive operating system design
                 using reflection / Rodger Lea, Yasuhiko Yokote, and
                 Jun-ichiro Itoh -- Isatis: a customizable distributed
                 object-based runtime system / Michel Ban{\^a}tre
                 \ldots{} [et al.] -- Lessons from designing and
                 implementing GARF / Rachid Guerraoui, Benoit Garbinato,
                 and Karim Mazouni -- Design and implementation of DROL
                 runtime environment on real-time Mach kernel / Kazunori
                 Takashio, Hidehisa Shitomi, and Mario Tokoro -- ActNet:
                 the actor model applied to mobile robotic environments
                 / Philippe Darche, Pierre-Guillaume Raverdy, and Eric
                 Commelin -- Component-based programming and application
                 management with Olan / Luc Bellissard \ldots{} [et al.]
                 -- The version management architecture of an
                 object-oriented distributed systems environment: OZ++ /
                 Michiharu Tsukamoto \ldots{} [et al.] -- Formal
                 semantics of agent evolution in language Flage /
                 Yasuyuki Tahara \ldots{} [et al.].",
  keywords =     "Electronic data processing -- Distributed processing;
                 Object-oriented programming (Computer science);
                 Parallel processing (Electronic computers)",
}

@Proceedings{Calmet:1996:DIS,
  editor =       "Jacques Calmet and Carla Limongelli",
  booktitle =    "{Design and implementation of symbolic computation
                 systems: International Symposium, DISCO '96, Karlsruhe,
                 Germany, September 18--20, 1996: proceedings}",
  title =        "{Design and implementation of symbolic computation
                 systems: International Symposium, DISCO '96, Karlsruhe,
                 Germany, September 18--20, 1996: proceedings}",
  volume =       "1128",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 356",
  year =         "1996",
  ISBN =         "3-540-61697-7 (softcover)",
  ISBN-13 =      "978-3-540-61697-9 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.9.S88I576 1996",
  bibdate =      "Thu Mar 12 12:25:22 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "Automatic theorem proving --- Congresses.; Mathematics
                 --- Data processing --- Congresses.; System design ---
                 Congresses.",
}

@Proceedings{LakshmanYN:1996:IPI,
  editor =       "{Lakshman Y. N.}",
  booktitle =    "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  title =        "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xvii + 313",
  year =         "1996",
  ISBN =         "0-89791-796-0",
  ISBN-13 =      "978-0-89791-796-4",
  LCCN =         "QA 76.95 I59 1996",
  bibdate =      "Thu Mar 12 08:00:14 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
  sponsor =      "ACM; Special Interest Group in Symbolic and Algebraic
                 Manipulation (SIGSAM). ACM; Special Interest Group on
                 Numerical Mathematics (SIGNUM).",
}

@Proceedings{Baral:1997:LPN,
  editor =       "C. Baral and V. S. Kreinovich and V. Lifschitz and M.
                 Gelfond",
  booktitle =    "{Logic programming, non-monotonic reasoning and
                 reasoning about actions: Symposium --- November 1995,
                 El Paso, TX}",
  title =        "{Logic programming, non-monotonic reasoning and
                 reasoning about actions: Symposium --- November 1995,
                 El Paso, TX}",
  volume =       "21(2)",
  publisher =    "Baltzer Science",
  address =      "Basel, Switzerland",
  pages =        "????",
  year =         "1997",
  ISSN =         "1012-2443",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       "Annals of Mathematics and Artificial Intelligence",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kuchlin:1997:PPS,
  editor =       "Wolfgang W. K{\"u}chlin",
  booktitle =    "{ISSAC 97: July 21--23, 1997, Maui, Hawaii, USA:
                 proceedings of the 1997 International Symposium on
                 Symbolic and Algebraic Computation}",
  title =        "{ISSAC 97: July 21--23, 1997, Maui, Hawaii, USA:
                 proceedings of the 1997 International Symposium on
                 Symbolic and Algebraic Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xxii + 414",
  year =         "1997",
  ISBN =         "0-89791-875-4",
  ISBN-13 =      "978-0-89791-875-6",
  LCCN =         "QA76.95",
  bibdate =      "Sat Mar 23 12:41:32 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/258726/",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lengauer:1997:EPP,
  editor =       "Christian Lengauer and Martin Griebl and Sergei
                 Gorlatch",
  booktitle =    "{Euro-Par'97, parallel processing: third International
                 Euro-Par Conference, Passau, Germany, August 26--29,
                 1997: proceedings}",
  title =        "{Euro-Par'97, parallel processing: third International
                 Euro-Par Conference, Passau, Germany, August 26--29,
                 1997: proceedings}",
  volume =       "1300",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxx + 1380",
  year =         "1997",
  ISBN =         "3-540-63440-1 (paperback)",
  ISBN-13 =      "978-3-540-63440-9 (paperback)",
  LCCN =         "QA76.58.I5535 1997",
  bibdate =      "Mon Aug 25 10:50:15 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "Parallel processing (Electronic computers) --
                 Congresses.",
}

@Proceedings{Buchberger:1998:YGB,
  editor =       "Bruno Buchberger and Franz Winkler",
  booktitle =    "33 years of Gr{\"o}bner bases: Gr{\"o}bner bases and
                 applications: Conference --- February 1998, Linz,
                 Austria",
  title =        "33 years of Gr{\"o}bner bases: Gr{\"o}bner bases and
                 applications: Conference --- February 1998, Linz,
                 Austria",
  number =       "251",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "viii + 552",
  year =         "1998",
  ISBN =         "0-521-63298-6",
  ISBN-13 =      "978-0-521-63298-0",
  LCCN =         "QA251.3.G76 1998",
  bibdate =      "Thu Mar 12 11:28:58 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  series =       "London Mathematical Society Lecture Note Series",
  acknowledgement = ack-nhfb,
  sponsor =      "Research Institute for Symbolic Computation.",
}

@Proceedings{Gloor:1998:IPI,
  editor =       "Oliver Gloor",
  booktitle =    "{ISSAC 98: Proceedings of the 1998 International
                 Symposium on Symbolic and Algebraic Computation, August
                 13--15, 1998, University of Rostock, Germany}",
  title =        "{ISSAC 98: Proceedings of the 1998 International
                 Symposium on Symbolic and Algebraic Computation, August
                 13--15, 1998, University of Rostock, Germany}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xxii + 327",
  year =         "1998",
  ISBN =         "1-58113-002-3",
  ISBN-13 =      "978-1-58113-002-7",
  LCCN =         "QA155.7.E4 E88 1998",
  bibdate =      "Wed Sep 16 17:13:58 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Dooley:1999:IJS,
  editor =       "Sam Dooley",
  booktitle =    "{ISSAC 99: July 29--31, 1999, Simon Fraser University,
                 Vancouver, BC, Canada: proceedings of the 1999
                 International Symposium on Symbolic and Algebraic
                 Computation}",
  title =        "{ISSAC 99: July 29--31, 1999, Simon Fraser University,
                 Vancouver, BC, Canada: proceedings of the 1999
                 International Symposium on Symbolic and Algebraic
                 Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xxii + 311",
  year =         "1999",
  ISBN =         "1-58113-073-2",
  ISBN-13 =      "978-1-58113-073-7",
  LCCN =         "QA76.95 .I57 1999",
  bibdate =      "Sat Mar 11 16:51:59 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Traverso:2000:IAU,
  editor =       "Carlo Traverso",
  booktitle =    "{ISSAC 2000: 7--9 August 2000, University of St.
                 Andrews, Scotland: proceedings of the 2000
                 International Symposium on Symbolic and Algebraic
                 Computation}",
  title =        "{ISSAC 2000: 7--9 August 2000, University of St.
                 Andrews, Scotland: proceedings of the 2000
                 International Symposium on Symbolic and Algebraic
                 Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 309",
  year =         "2000",
  ISBN =         "1-58113-218-2",
  ISBN-13 =      "978-1-58113-218-2",
  LCCN =         "QA76.95.I59 2000",
  bibdate =      "Tue Apr 17 09:12:53 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number 505000.",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/345542/",
  acknowledgement = ack-nhfb,
}

@Proceedings{Mourrain:2001:IJU,
  editor =       "Bernard Mourrain",
  booktitle =    "{ISSAC 2001: July 22--25, 2001, University of Western
                 Ontario, London, Ontario, Canada: proceedings of the
                 2001 International Symposium on Symbolic and Algebraic
                 Computation}",
  title =        "{ISSAC 2001: July 22--25, 2001, University of Western
                 Ontario, London, Ontario, Canada: proceedings of the
                 2001 International Symposium on Symbolic and Algebraic
                 Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xii + 352",
  year =         "2001",
  ISBN =         "1-58113-417-7",
  ISBN-13 =      "978-1-58113-417-9",
  LCCN =         "QA76.95.I59 2001",
  bibdate =      "Wed May 15 14:30:19 2002",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number 505010.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Mora:2002:IPI,
  editor =       "Teo Mora",
  booktitle =    "{ISSAC 2002: Proceedings of the 2002 International
                 Symposium on Symbolic and Algebraic Computation, July
                 07--10, 2002, Universit{\'e} de Lille, Lille, France}",
  title =        "{ISSAC 2002: Proceedings of the 2002 International
                 Symposium on Symbolic and Algebraic Computation, July
                 07--10, 2002, Universit{\'e} de Lille, Lille, France}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xx + 276",
  year =         "2002",
  ISBN =         "1-58113-484-3",
  ISBN-13 =      "978-1-58113-484-1",
  LCCN =         "QA76.95",
  bibdate =      "Fri Nov 22 16:20:31 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.lifl.fr/ISSAC2002/",
  acknowledgement = ack-nhfb,
}

@Proceedings{Senda:2003:IPI,
  editor =       "J. Rafael Senda",
  booktitle =    "{ISSAC 2003: Proceedings of the 2003 International
                 Symposium on Symbolic and Algebraic Computation, August
                 3--6, 2003, Drexel University, Philadelphia, PA, USA}",
  title =        "{ISSAC 2003: Proceedings of the 2003 International
                 Symposium on Symbolic and Algebraic Computation, August
                 3--6, 2003, Drexel University, Philadelphia, PA, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 273",
  year =         "2003",
  ISBN =         "1-58113-641-2",
  ISBN-13 =      "978-1-58113-641-8",
  LCCN =         "QA76.95",
  bibdate =      "Sat Dec 13 18:18:22 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number 505030.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Gutierrez:2004:IJU,
  editor =       "Jaime Gutierrez",
  booktitle =    "{ISAAC 2004: July 4--7, 2004, University of Cantabria,
                 Santander, Spain: proceedings of the 2004 International
                 Symposium on Symbolic and Algebraic Computation}",
  title =        "{ISAAC 2004: July 4--7, 2004, University of Cantabria,
                 Santander, Spain: proceedings of the 2004 International
                 Symposium on Symbolic and Algebraic Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xii + 328",
  year =         "2004",
  ISBN =         "1-58113-827-X",
  ISBN-13 =      "978-1-58113-827-6",
  LCCN =         "QA76.95 .I57 2004",
  bibdate =      "Fri Oct 21 06:33:01 MDT 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "International Symposium on Symbolic and Algebraic
                 Computation (2004 : Santander, Spain)",
}

@Proceedings{Kauers:2005:IJB,
  editor =       "Manuel Kauers",
  booktitle =    "{ISSAC '05: July 24--27, 2005, Beijing, China:
                 Proceedings of the 2005 International Symposium on
                 Symbolic and Algebraic Computation}",
  title =        "{ISSAC '05: July 24--27, 2005, Beijing, China:
                 Proceedings of the 2005 International Symposium on
                 Symbolic and Algebraic Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiv + 372",
  year =         "2005",
  ISBN =         "1-59593-095-7",
  ISBN-13 =      "978-1-59593-095-8",
  LCCN =         "????",
  bibdate =      "Fri Oct 21 07:01:24 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM Order Number 505050.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Trager:2006:PIS,
  editor =       "Barry Trager",
  booktitle =    "{Proceedings of the 2006 International Symposium on
                 Symbolic and Algebraic Computation, Genoa, Italy July
                 09--12, 2006}",
  title =        "{Proceedings of the 2006 International Symposium on
                 Symbolic and Algebraic Computation, Genoa, Italy July
                 09--12, 2006}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2006",
  ISBN =         "1-59593-276-3",
  ISBN-13 =      "978-1-59593-276-1",
  LCCN =         "????",
  bibdate =      "Wed Aug 23 09:44:27 2006",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number 505060.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Brown:2007:PIS,
  editor =       "C. W. Brown",
  booktitle =    "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  title =        "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
  ISBN-13 =      "978-1-59593-743-8 (print), 978-1-59593-742-1
                 (CD-ROM)",
  LCCN =         "QA76.5 S98 2007",
  bibdate =      "Fri Jun 20 08:53:37 2008",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  note =         "ACM order number 505070.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Jeffrey:2008:PAM,
  editor =       "David Jeffrey",
  booktitle =    "{Proceedings of the 21st annual meeting of the
                 International Symposium on Symbolic Computation, ISSAC
                 2008, July 20--23, 2008, Hagenberg, Austria}",
  title =        "{Proceedings of the 21st annual meeting of the
                 International Symposium on Symbolic Computation, ISSAC
                 2008, July 20--23, 2008, Hagenberg, Austria}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 338",
  year =         "2008",
  ISBN =         "1-59593-904-0",
  ISBN-13 =      "978-1-59593-904-3",
  LCCN =         "????",
  bibdate =      "Fri Jun 20 08:53:37 2008",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{May:2009:PIS,
  editor =       "John P. May",
  booktitle =    "{Proceedings of the 2009 international symposium on
                 Symbolic and algebraic computation, KIAS, Seoul, Korea,
                 July 28--31, 2009}",
  title =        "{Proceedings of the 2009 international symposium on
                 Symbolic and algebraic computation, KIAS, Seoul, Korea,
                 July 28--31, 2009}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xi + 389",
  year =         "2009",
  ISBN =         "1-60558-609-9",
  ISBN-13 =      "978-1-60558-609-0",
  LCCN =         "????",
  bibdate =      "Fri Jun 20 08:53:37 2009",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Watt:2010:IPI,
  editor =       "Stephen M. Watt",
  booktitle =    "{ISSAC 2010: Proceedings of the 2010 International
                 Symposium on Symbolic and Algebraic Computation, July
                 25--28, 2010, Munich, Germany}",
  title =        "{ISSAC 2010: Proceedings of the 2010 International
                 Symposium on Symbolic and Algebraic Computation, July
                 25--28, 2010, Munich, Germany}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiv + 363",
  year =         "2010",
  ISBN =         "1-4503-0150-9",
  ISBN-13 =      "978-1-4503-0150-3",
  LCCN =         "QA76.95 .I59 2010",
  bibdate =      "Fri Jun 17 08:11:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Schost:2011:IPI,
  editor =       "{\'E}ric Schost and Ioannis Z. Emiris",
  booktitle =    "{ISSAC 2011: Proceedings of the 2011 International
                 Symposium on Symbolic and Algebraic Computation, June
                 7--11, 2011, San Jose, CA, USA}",
  title =        "{ISSAC 2011: Proceedings of the 2011 International
                 Symposium on Symbolic and Algebraic Computation, June
                 7--11, 2011, San Jose, CA, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "362 (est.)",
  year =         "2011",
  ISBN =         "1-4503-0675-6",
  ISBN-13 =      "978-1-4503-0675-1",
  LCCN =         "QA76.95 .I59 2011",
  bibdate =      "Fri Mar 14 12:24:11 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{vanderHoeven:2012:IPI,
  editor =       "Joris van der Hoeven and Mark van Hoeij",
  booktitle =    "{ISSAC 2012: Proceedings of the 2012 International
                 Symposium on Symbolic and Algebraic Computation, July
                 22--25, 2012, Grenoble, France}",
  title =        "{ISSAC 2012: Proceedings of the 2012 International
                 Symposium on Symbolic and Algebraic Computation, July
                 22--25, 2012, Grenoble, France}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2012",
  ISBN =         "1-4503-1269-1",
  ISBN-13 =      "978-1-4503-1269-1",
  LCCN =         "QA76.95 .I59 2012",
  bibdate =      "Fri Mar 14 12:24:11 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/hash.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Monagan:2013:IPI,
  editor =       "Michael Monagan and Gene Cooperman and Mark
                 Giesbrecht",
  booktitle =    "{ISSAC 2013: Proceedings of the 2013 International
                 Symposium on Symbolic and Algebraic Computation, June
                 26--29, 2013, Boston, MA, USA}",
  title =        "{ISSAC 2013: Proceedings of the 2013 International
                 Symposium on Symbolic and Algebraic Computation, June
                 26--29, 2013, Boston, MA, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "387 (est.)",
  year =         "2013",
  ISBN =         "1-4503-2059-7",
  ISBN-13 =      "978-1-4503-2059-7",
  LCCN =         "QA76.95 .I59 2013",
  bibdate =      "Fri Mar 14 12:24:11 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  acknowledgement = ack-nhfb,
}