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%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "2.21",
%%% date = "08 April 2017",
%%% time = "09:34:07 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 = "60671 38213 189769 1949142",
%%% 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 2.21, 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 String{} abbreviations,
%%% occupying 94.8MB of disk space.
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%%% Numerous errors have been corrected, and TeX
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%%%
%%% 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
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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 $__$
for $w$ in $G$, finite $U$ contained in $G$, where
$____$ is the subgroup of $G$ generated by $U$. They
describe $____$ 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 $____$ ($\lambda$ 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 $____$
for $w$ in finite $U$ contained in $G$, $G \in G$,
where $____$ 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 $____$ 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
$____$. 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 $____$
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
$R=k/H$, 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 $(X_jX_i-c_{ij}X_iX_j:i$,
homogeneous for the graduation defined above and
containing J, is finitely generated; (2) For each
homogeneous ideal $(h_1, \ldots{}, h_s)$ in
$k/J$, 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 $k/J$, 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__