%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "2.20",
%%%     date            = "15 March 2014",
%%%     time            = "06:59:53 MST",
%%%     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        = "18129 38213 189770 1949248",
%%%     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 2.20, 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{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/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{O:1992:CGA,
  author =       "Grant O. and J. r. Cook",
  title =        "Code generation in {ALPAL} using symbolic techniques",
  crossref =     "Wang:1992:PII",
  pages =        "27--35",
  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/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{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: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{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{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 =          "http://dx.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 =