@Preamble{
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi"
#
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi"
}
@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/|"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGSAM = "SIGSAM Bulletin (ACM Special
Interest Group on Symbolic and
Algebraic Manipulation)"}
@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"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@InProceedings{Fateman:1981:CAN,
author = "Richard J. Fateman",
title = "Computer Algebra and Numerical Integration",
crossref = "Wang:1981:SPA",
pages = "228--232",
year = "1981",
bibdate = "Mon Apr 25 07:01:52 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algebraic manipulation systems such as MACSYMA include
algorithms and heuristic procedures for indefinite and
definite integration, yet these system facilities are
not as generally useful as might be thought. Most
isolated definite integration problems are more
efficiently tackled with numerical programs.
Unfortunately, the answers obtained are sometimes
incorrect, in spite of assurances of accuracy;
furthermore, large classes of problems can sometimes be
solved more rapidly by preliminary algebraic
transformations. In this paper we indicate various
directions for improving the usefulness of integration
programs given closed form integrands, via algebraic
manipulation techniques. These include expansions in
partial fractions or Taylor series, detection and
removal of singularities and symmetries, and various
approximation techniques for troublesome problems.",
acknowledgement = ack-nhfb,
}
@Book{Buchberger:1982:CAS,
author = "Bruno Buchberger and George Edward Collins and Rudiger
Loos and R. Albrecht",
title = "Computer algebra: symbolic and algebraic computation",
volume = "4",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 283",
year = "1982",
ISBN = "0-387-81684-4",
ISBN-13 = "978-0-387-81684-5",
LCCN = "QA155.7.E4 C65 1982",
bibdate = "Thu Dec 28 13:48:31 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
series = "Computing. Supplementum",
acknowledgement = ack-nhfb,
keywords = "algorithms; measurement; theory",
subject = "S1 Algebra --- Data processing; S2 Machine theory",
}
@InProceedings{Abbott:1986:BAN,
author = "J. A. Abbott and R. J. Bradford and J. H. Davenport",
title = "The {Bath} algebraic number package",
crossref = "Char:1986:PSS",
pages = "250--253",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p250-abbott/",
acknowledgement = ack-nhfb,
keywords = "design; measurement; performance",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE.",
}
@InProceedings{Abdali:1986:OOA,
author = "S. K. Abdali and Guy W. Cherry and Neil Soiffer",
title = "An object-oriented approach to algebra system design",
crossref = "Char:1986:PSS",
pages = "24--30",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p24-abdali/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.3.3} Software, PROGRAMMING LANGUAGES, Language
Constructs and Features, Abstract data types. {\bf
D.3.4} Software, PROGRAMMING LANGUAGES, Processors,
Run-time environments. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Specialized application languages. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, Very high-level languages.",
}
@InProceedings{Akritis:1986:TNU,
author = "Alkiviadis G. Akritis",
title = "There is no ``{Uspensky}'s method''",
crossref = "Char:1986:PSS",
pages = "88--90",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p88-akritis/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.1.5} Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Polynomials, methods for. {\bf K.2} Computing Milieux,
HISTORY OF COMPUTING, Systems. {\bf G.1.5} Mathematics
of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
Equations, Iterative methods. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Arnborg:1986:ADR,
author = "S. Arnborg and H. Feng",
title = "Algebraic decomposition of regular curves",
crossref = "Char:1986:PSS",
pages = "53--55",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p53-arnborg/",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "{\bf I.1.m} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Miscellaneous.",
}
@InProceedings{Bachmair:1986:CPC,
author = "Leo Bachmair and Nachum Dershowitz",
title = "Critical-pair criteria for the {Knuth--Bendix}
completion procedure",
crossref = "Char:1986:PSS",
pages = "215--217",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p215-bachmair/",
acknowledgement = ack-nhfb,
keywords = "languages; theory; verification",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems, Parallel rewriting systems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions. {\bf F.2.3} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Tradeoffs between Complexity Measures. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Complexity of proof procedures.",
}
@InProceedings{Bajaj:1986:LAS,
author = "Chanderjit Bajaj",
title = "Limitations to algorithm solvability: {Galois} methods
and models of computation",
crossref = "Char:1986:PSS",
pages = "71--76",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p71-bajaj/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.2.m} Mathematics of Computing,
DISCRETE MATHEMATICS, Miscellaneous. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm design and analysis.",
}
@InProceedings{Bayer:1986:DMS,
author = "D. Bayer and M. Stillman",
title = "The design of {Macaulay}: a system for computing in
algebraic geometry and commutative algebra",
crossref = "Char:1986:PSS",
pages = "157--162",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p157-bayer/",
acknowledgement = ack-nhfb,
keywords = "design; performance; theory",
subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
}
@InProceedings{Beck:1986:SAL,
author = "Robert E. Beck and Bernard Kolman",
title = "Symbolic algorithms for {Lie} algebra computation",
crossref = "Char:1986:PSS",
pages = "85--87",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p85-beck/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.2.2} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Automatic Programming. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, MACSYMA. {\bf K.2}
Computing Milieux, HISTORY OF COMPUTING, Systems.",
}
@InProceedings{Bradford:1986:ERD,
author = "R. J. Bradford and A. C. Hearn and J. A. Padget and E.
Schr{\"u}fer",
title = "Enlarging the {REDUCE} domain of computation",
crossref = "Char:1986:PSS",
pages = "100--106",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p100-bradford/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
}
@InProceedings{Bronstein:1986:GFA,
author = "Manuel Bronstein",
title = "Gsolve: a faster algorithm for solving systems of
algebraic equations",
crossref = "Char:1986:PSS",
pages = "247--249",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p247-bronstein/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.4} Mathematics of Computing,
MATHEMATICAL SOFTWARE, Efficiency. {\bf G.1.5}
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Systems of equations. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness.",
}
@InProceedings{Butler:1986:DCC,
author = "Greg Butler",
title = "Divide-and-conquer in computational group theory",
crossref = "Char:1986:PSS",
pages = "59--64",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p59-butler/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.2.0} Mathematics of Computing, DISCRETE
MATHEMATICS, General. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Chaffy:1986:HCM,
author = "C. Chaffy",
title = "How to compute multivariate {Pad{\'e}} approximants",
crossref = "Char:1986:PSS",
pages = "56--58",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p56-chaffy/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation.",
}
@InProceedings{Char:1986:CAU,
author = "B. W. Char and K. O. Geddes and G. H. Gonnet and B. J.
Marshman and P. J. Ponzo",
title = "Computer algebra in the undergraduate mathematics
classroom",
crossref = "Char:1986:PSS",
pages = "135--140",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p135-char/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; documentation; experimentation;
human factors; performance",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION,
Computer Uses in Education, Computer-assisted
instruction (CAI).",
}
@InProceedings{Cooperman:1986:SMC,
author = "Gene Cooperman",
title = "A semantic matcher for computer algebra",
crossref = "Char:1986:PSS",
pages = "132--134",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p132-cooperman/",
acknowledgement = ack-nhfb,
keywords = "experimentation; human factors; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf F.4.1} Theory
of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Evaluation strategies. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Pattern matching. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Representations
(general and polynomial). {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
}
@InProceedings{Czapor:1986:IBA,
author = "S. R. Czapor and K. O. Geddes",
title = "On implementing {Buchberger}'s algorithm for
{Gr{\"o}bner} bases",
crossref = "Char:1986:PSS",
pages = "233--238",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p233-czapor/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
}
@InProceedings{Davenport:1986:PSM,
author = "J. H. Davenport and C. E. Roth",
title = "{PowerMath}: a system for the {Macintosh}",
crossref = "Char:1986:PSS",
pages = "13--15",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p13-davenport/",
acknowledgement = ack-nhfb,
keywords = "design; theory",
subject = "{\bf K.8} Computing Milieux, PERSONAL COMPUTING,
Apple. {\bf I.1.3} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems.",
}
@InProceedings{Dora:1986:FSL,
author = "J. Della Dora and E. Tournier",
title = "Formal solutions of linear difference equations:
method of {Pincherle--Ramis}",
crossref = "Char:1986:PSS",
pages = "192--196",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p192-della_dora/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL
ANALYSIS, Miscellaneous. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computation of transforms.",
}
@InProceedings{Fitch:1986:AIA,
author = "J. Fitch and A. Norman and M. A. Moore",
title = "Alkahest {III}: automatic analysis of periodic weakly
nonlinear {ODEs}",
crossref = "Char:1986:PSS",
pages = "34--38",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p34-fitch/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; human factors; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf D.2.2}
Software, SOFTWARE ENGINEERING, Design Tools and
Techniques, User interfaces.",
}
@InProceedings{Freeman:1986:SMP,
author = "T. Freeman and G. Imirzian and E. Kaltofen",
title = "A system for manipulating polynomials given by
straight-line programs",
crossref = "Char:1986:PSS",
pages = "169--175",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p169-freeman/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; performance; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations, Polynomials, methods
for.",
}
@InProceedings{Furukawa:1986:GBM,
author = "A. Furukawa and T. Sasaki and H. Kobayashi",
title = "The {Gr{\"o}bner} basis of a module over
{KUX1,\ldots{},Xne} and polynomial solutions of a
system of linear equations",
crossref = "Char:1986:PSS",
pages = "222--224",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p222-furukawa/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods).",
}
@InProceedings{Gates:1986:NCG,
author = "Barbara L. Gates",
title = "A numerical code generation facility for {REDUCE}",
crossref = "Char:1986:PSS",
pages = "94--99",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p94-gates/",
acknowledgement = ack-nhfb,
keywords = "design; languages; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Code generation.",
}
@InProceedings{Gebauer:1986:BAS,
author = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
title = "{Buchberger}'s algorithm and staggered linear bases",
crossref = "Char:1986:PSS",
pages = "218--221",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p218-gebauer/",
acknowledgement = ack-nhfb,
keywords = "algorithms; measurement; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions.",
}
@InProceedings{Geddes:1986:NIS,
author = "K. O. Geddes",
title = "Numerical integration in a symbolic context",
crossref = "Char:1986:PSS",
pages = "185--191",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p185-geddes/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design",
subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Golden:1986:OAM,
author = "J. P. Golden",
title = "An operator algebra for {Macsyma}",
crossref = "Char:1986:PSS",
pages = "244--246",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p244-golden/",
acknowledgement = ack-nhfb,
keywords = "design; theory; verification",
subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, MACSYMA. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
}
@InProceedings{Gonnet:1986:IOS,
author = "G. H. Gonnet",
title = "An implementation of operators for symbolic algebra
systems",
crossref = "Char:1986:PSS",
pages = "239--243",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p239-gonnet/",
acknowledgement = ack-nhfb,
keywords = "design; languages; theory",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Representations (general and
polynomial). {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
}
@InProceedings{Gonnet:1986:NRR,
author = "Gaston H. Gonnet",
title = "New results for random determination of equivalence of
expressions",
crossref = "Char:1986:PSS",
pages = "127--131",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p127-gonnet/",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf G.2.m} Mathematics of Computing,
DISCRETE MATHEMATICS, Miscellaneous.",
}
@InProceedings{Hadzikadic:1986:AKB,
author = "M. Hadzikadic and F. Lichtenberger and D. Y. Y. Yun",
title = "An application of knowledge-base technology in
education: a geometry theorem prover",
crossref = "Char:1986:PSS",
pages = "141--147",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p141-hadzikadic/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; human factors; languages;
performance; verification",
subject = "{\bf K.3.1} Computing Milieux, COMPUTERS AND
EDUCATION, Computer Uses in Education,
Computer-assisted instruction (CAI). {\bf F.2.2} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic, Mechanical theorem
proving. {\bf I.2.3} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Deduction and Theorem
Proving.",
}
@InProceedings{Hayden:1986:SBC,
author = "Michael B. Hayden and Edmund A. Lamagna",
title = "Summation of binomial coefficients using
hypergeometric functions",
crossref = "Char:1986:PSS",
pages = "77--81",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p77-hayden/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf I.2.2} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Automatic Programming,
Automatic analysis of algorithms. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Iterative methods.",
}
@InProceedings{Hilali:1986:ACF,
author = "A. Hilali and A. Wazner",
title = "Algorithm for computing formal invariants of linear
differential systems",
crossref = "Char:1986:PSS",
pages = "197--201",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p197-hilali/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Eigenvalues and
eigenvectors (direct and iterative methods). {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Jurkovic:1986:EES,
author = "N. Jurkovic",
title = "Edusym --- educational symbolic manipulator on a
microcomputer",
crossref = "Char:1986:PSS",
pages = "154--156",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p154-jurkovic/",
acknowledgement = ack-nhfb,
keywords = "human factors; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, MuMATH.
{\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION,
Computer Uses in Education, Computer-assisted
instruction (CAI).",
}
@InProceedings{Kaltofen:1986:FPA,
author = "E. Kaltofen and M. Krishnamoorthy and B. D. Saunders",
title = "Fast parallel algorithms for similarity of matrices",
crossref = "Char:1986:PSS",
pages = "65--70",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p65-kaltofen/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
}
@InProceedings{Kapur:1986:GTP,
author = "Deepak Kapur",
title = "Geometry theorem proving using {Hilbert}'s
{Nullstellensatz}",
crossref = "Char:1986:PSS",
pages = "202--208",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p202-kapur/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf I.2.3}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Deduction and Theorem Proving. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Knowles:1986:ILF,
author = "P. H. Knowles",
title = "Integration of {Liouvillian} functions with special
functions",
crossref = "Char:1986:PSS",
pages = "179--184",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p179-knowles/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL
ANALYSIS, Miscellaneous.",
}
@InProceedings{Kobayashi:1986:GBI,
author = "H. Kobayashi and A. Furukawa and T. Sasaki",
title = "Gr{\"o}bner bases of ideals of convergent power
series",
crossref = "Char:1986:PSS",
pages = "225--227",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p225-kobayashi/",
acknowledgement = ack-nhfb,
keywords = "theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf G.m}
Mathematics of Computing, MISCELLANEOUS.",
}
@InProceedings{Kryukov:1986:CRA,
author = "A. P. Kryukov and Y. Rodionov and G. L. Litvinov",
title = "Construction of rational approximations by means of
{REDUCE}",
crossref = "Char:1986:PSS",
pages = "31--33",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p31-kryukov/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Rational approximation. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions.",
}
@InProceedings{Kryukov:1986:DRE,
author = "A. P. Kryukov",
title = "Dialogue in {REDUCE}: experience and development",
crossref = "Char:1986:PSS",
pages = "107--109",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p107-kryukov/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; performance; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.2.2} Software, SOFTWARE ENGINEERING, Design
Tools and Techniques, User interfaces.",
}
@InProceedings{Kryukov:1986:URC,
author = "A. P. Kryukov and A. Y. Rodionov",
title = "Usage of {REDUCE} for computations of
group-theoretical weight of {Feynman} diagrams in
{non-Abelian} gauge theories",
crossref = "Char:1986:PSS",
pages = "91--93",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p91-kryukov/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.2.m} Mathematics of Computing, DISCRETE
MATHEMATICS, Miscellaneous.",
}
@InProceedings{Kutzler:1986:AGT,
author = "B. Kutzler and S. Stifter",
title = "Automated geometry theorem proving using
{Buchberger}'s algorithm",
crossref = "Char:1986:PSS",
pages = "209--214",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p209-kutzler/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf I.2.3} Computing
Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and
Theorem Proving. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Geometrical
problems and computations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
}
@InProceedings{Leff:1986:CSG,
author = "L. Leff and D. Y. Y. Yun",
title = "Constructive solid geometry: a symbolic computation
approach",
crossref = "Char:1986:PSS",
pages = "121--126",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p121-leff/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED
ENGINEERING. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Geometrical
problems and computations. {\bf I.1.m} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Miscellaneous.",
}
@InProceedings{Leong:1986:IDU,
author = "B. L. Leong",
title = "{Iris}: design of an user interface program for
symbolic algebra",
crossref = "Char:1986:PSS",
pages = "1--6",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p1-leong/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf D.2.2} Software, SOFTWARE ENGINEERING,
Design Tools and Techniques, User interfaces. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf H.1.2}
Information Systems, MODELS AND PRINCIPLES,
User/Machine Systems, Human factors.",
}
@InProceedings{Lucks:1986:FIP,
author = "Michael Lucks",
title = "A fast implementation of polynomial factorization",
crossref = "Char:1986:PSS",
pages = "228--232",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p228-lucks/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; experimentation; performance;
theory",
subject = "{\bf G.1.5} Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Polynomials,
methods for. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations.",
}
@InProceedings{Mawata:1986:SDR,
author = "C. P. Mawata",
title = "A sparse distributed representation using prime
numbers",
crossref = "Char:1986:PSS",
pages = "110--114",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p110-mawata/",
acknowledgement = ack-nhfb,
keywords = "experimentation; performance; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial). {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
matrices. {\bf G.4} Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm design and analysis.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms.",
}
@InProceedings{Purtilo:1986:ASI,
author = "J. Purtilo",
title = "Applications of a software interconnection system in
mathematical problem solving environments",
crossref = "Char:1986:PSS",
pages = "16--23",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p16-purtilo/",
acknowledgement = ack-nhfb,
keywords = "design; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
G.m} Mathematics of Computing, MISCELLANEOUS. {\bf
D.2.m} Software, SOFTWARE ENGINEERING, Miscellaneous.",
}
@InProceedings{Renbao:1986:CAS,
author = "Z. Renbao and X. Ling and R. Zhaoyang",
title = "The computer algebra system {CAS1} for the {IBM-PC}",
crossref = "Char:1986:PSS",
pages = "176--178",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p176-renbao/",
acknowledgement = ack-nhfb,
keywords = "design; theory",
subject = "{\bf K.8} Computing Milieux, PERSONAL COMPUTING, IBM
PC. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Simplification of expressions.",
}
@InProceedings{Sasaki:1986:SAE,
author = "Tateaki Sasaki",
title = "Simplification of algebraic expression by multiterm
rewriting rules",
crossref = "Char:1986:PSS",
pages = "115--120",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p115-sasaki/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Grammars and Other Rewriting Systems,
Parallel rewriting systems.",
}
@InProceedings{Seymour:1986:CCM,
author = "Harlan R. Seymour",
title = "Conform: a conformal mapping system",
crossref = "Char:1986:PSS",
pages = "163--168",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p163-seymour/",
acknowledgement = ack-nhfb,
keywords = "design; languages; performance; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP. {\bf D.3.3} Software,
PROGRAMMING LANGUAGES, Language Constructs and
Features.",
}
@InProceedings{Shavlik:1986:CUG,
author = "Jude W. Shavlik and Gerald F. DeJong",
title = "Computer understanding and generalization of symbolic
mathematical calculations: a case study in physics
problem solving",
crossref = "Char:1986:PSS",
pages = "148--153",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p148-shavlik/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; languages; performance; theory;
verification",
subject = "{\bf I.2.6} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Learning. {\bf K.3.1} Computing Milieux,
COMPUTERS AND EDUCATION, Computer Uses in Education,
Computer-assisted instruction (CAI). {\bf I.1.1}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation.
{\bf I.2.1} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Applications and Expert Systems. {\bf
J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics. {\bf G.4} Mathematics of
Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Substitution mechanisms**. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Evaluation
strategies. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
}
@InProceedings{Smith:1986:MUI,
author = "C. J. Smith and N. Soiffer",
title = "{MathScribe}: a user interface for computer algebra
systems",
crossref = "Char:1986:PSS",
pages = "7--12",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p7-smith/",
acknowledgement = ack-nhfb,
keywords = "design; human factors; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and
Techniques, User interfaces.",
}
@InProceedings{Yun:1986:FCF,
author = "D. Y. Y. Yun and C. N. Zhang",
title = "A fast carry-free algorithm and hardware design for
extended integer {GCD} computation",
crossref = "Char:1986:PSS",
pages = "82--84",
year = "1986",
bibdate = "Thu Mar 12 07:38:29 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p82-yun/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm design and analysis. {\bf B.7.1} Hardware,
INTEGRATED CIRCUITS, Types and Design Styles,
Algorithms implemented in hardware.",
}
@InProceedings{A:1989:SSG,
author = "R. A. and J. r. Ravenscroft and E. A. Lamagna",
title = "Symbolic summation with generating functions",
crossref = "Gonnet:1989:PAI",
pages = "228--233",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p228-ravenscroft/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Generating functions. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods).",
}
@InProceedings{Abbot:1989:RAN,
author = "J. Abbot",
title = "Recovery of algebraic numbers from their $p$-adic
approximations",
crossref = "Gonnet:1989:PAI",
pages = "112--120",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author describes three ways to generalize
Lenstra's algebraic integer recovery method. One
direction adapts the algorithm so that rational numbers
are automatically produced given only upper bounds on
the sizes of the numerators and denominators. Another
direction produces a variant which recovers algebraic
numbers as elements of multiple generator algebraic
number fields. The third direction explains how the
method can work if a reducible minimal polynomial had
been given for an algebraic generator. Any two or all
three of the generalisations may be employed
simultaneously.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory)",
keywords = "Algebraic generator; Algebraic integer recovery
method; Algebraic numbers; Computer algebra;
Denominators; Factorisation; Lenstra; Multiple
generator algebraic number fields; Numerators; P-adic
approximations; Rational numbers; Reducible minimal
polynomial; Upper bounds",
thesaurus = "Computation theory; Number theory; Polynomials; Symbol
manipulation",
}
@InProceedings{Abbott:1989:RAN,
author = "John Abbott",
title = "Recovery of algebraic numbers from their $p$-adic
approximations",
crossref = "Gonnet:1989:PAI",
pages = "112--120",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p112-abbott/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Abdali:1989:EQR,
author = "S. K. Abdali and D. S. Wiset",
title = "Experiments with quadtree representation of matrices",
crossref = "Gianni:1989:SAC",
pages = "96--108",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The quadtrees matrix representation has been recently
proposed as an alternative to the conventional linear
storage of matrices. If all elements of a matrix are
zero, then the matrix is represented by an empty tree;
otherwise it is represented by a tree consisting of
four subtrees, each representing, recursively, a
quadrant of the matrix. Using four-way block
decomposition, algorithms on quadtrees accelerate on
blocks entirely of zeros, and thereby offer improved
performance on sparse matrices. The paper reports the
results of experiments done with a quadtree matrix
package implemented in REDUCE to compare the
performance of quadtree representation with REDUCE's
built-in sequential representation of matrices. Tests
on addition, multiplication, and inversion of dense,
triangular, tridiagonal, and diagonal matrices (both
symbolic and numeric) of sizes up to 100*100 show that
the quadtree algorithms perform well in a broad range
of circumstances, sometimes running orders of magnitude
faster than their sequential counterparts.",
acknowledgement = ack-nhfb,
affiliation = "Tektronix Labs., Beaverton, OR, USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4140 (Linear algebra); C6120 (File organisation);
C7310 (Mathematics)",
keywords = "Addition; Dense matrices; Diagonal matrices; Empty
tree; Four-way block decomposition; Inversion;
Multiplication; Performance comparison; Quadrant;
Quadtree algorithms; Quadtree matrix package; Quadtrees
matrix representation; REDUCE; Sparse matrices;
Subtrees; Triangular matrices; Tridiagonal matrices;
Zero elements",
thesaurus = "Data structures; Mathematics computing; Matrix
algebra; Trees [mathematics]",
}
@InProceedings{Abdulrab:1989:EW,
author = "H. Abdulrab",
title = "Equations in words",
crossref = "Gianni:1989:SAC",
pages = "508--520",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The study of equations in words was introduced by
Lentin (1972). There is always a solution for any
equation with no constant. Makanin (1977) showed that
solving equations with constants is decidable. Pecuchet
(1981) unified the two theories of equations with or
without constants and gave a new description of
Makanin's algorithm. This paper describes some new
results in the field of solving equations in words.",
acknowledgement = ack-nhfb,
affiliation = "LITP, Fac. des Sci., Mont Saint Aignan, France",
classification = "C4210 (Formal logic)",
keywords = "Decidable; Equations in words",
thesaurus = "Decidability",
}
@InProceedings{Abhyankar:1989:CAC,
author = "S. S. Abhyankar and C. L. Bajaj",
title = "Computations with algebraic curves",
crossref = "Gianni:1989:SAC",
pages = "274--284",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present a variety of computational
techniques dealing with algebraic curves both in the
plane and in space. The main results are polynomial
time algorithms: (1) to compute the genus of plane
algebraic curves; (2) to compute the rational
parametric equations for implicitly defined rational
plane algebraic curves of arbitrary degree; (3) to
compute birational mappings between points on
irreducible space curves and points on projected plane
curves and thereby to compute the genus and rational
parametric equations for implicitly defined rational
space curves of arbitrary degree; and (4) to check for
the faithfulness (one to one) of parameterizations.",
acknowledgement = ack-nhfb,
affiliation = "Purdue Univ., West Lafayette, IN, USA",
classification = "C4130 (Interpolation and function approximation);
C4190 (Other numerical methods)",
keywords = "Algebraic curves; Birational mappings; Computational
techniques; Irreducible space curves; Polynomial time
algorithms; Rational parametric equations",
thesaurus = "Computational geometry; Polynomials",
}
@InProceedings{Alonso:1989:CAS,
author = "M. E. Alonso and T. Mora and M. Raimondo",
title = "Computing with algebraic series",
crossref = "Gonnet:1989:PAI",
pages = "101--111",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p101-alonso/",
abstract = "The authors develop a computational model for
algebraic formal power series, based on a symbolic
codification of the series by means of the implicit
function theorem: i.e. they consider algebraic series
as the unique solutions of suitable functional
equations. They show that most of the usual local
commutative algebra can be effectively performed on
algebraic series, since they can reduce to the
polynomial case, where the tangent cone algorithm can
be used to effectively perform local algebra. The main
result to the paper is an effective version of
Weierstrass theorems, which allows effective
elimination theory for algebraic series and an
effective noether normalization lemma.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Complutense, Madrid, Spain",
classification = "C1110 (Algebra); C1120 (Analysis); C4150 (Nonlinear
and functional equations); C4240 (Programming and
algorithm theory)",
keywords = "Algebraic formal power series; Algebraic series;
algorithms; Computational model; Elimination theory;
Functional equations; Implicit function theorem; Local
commutative algebra; Noether normalization lemma;
Polynomial; Symbolic codification; Tangent cone
algorithm; theory; Weierstrass theorems",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Computational logic.",
thesaurus = "Computability; Functional equations; Polynomials;
Series [mathematics]; Symbol manipulation",
}
@InProceedings{Arnborg:1989:EPO,
author = "S. Arnborg",
title = "Experiments with a projection operator for algebraic
decomposition",
crossref = "Gianni:1989:SAC",
pages = "177--182",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Reports an experiment with the projection phase of an
algebraic decomposition problem. The decomposition
asked for is a collection of rational sample points, at
least one in each full-dimensional region of a
decomposition, sign-invariant with respect to a set of
polynomials and with a cylindrical structure. Such a
decomposition is less general than a cylindrical
algebraic decomposition, but still useful for purposes
such as solving collision and motion planning problems
in theoretical robotics. Specifically, there is no
information about the structure of less than
full-dimensional regions and intersections between
projections of regions. This makes quantifier
elimination with alternating quantifiers difficult or
impossible.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Numer. Anal. and Comput. Sci., R. Inst. of
Technol., Stockholm, Sweden",
classification = "C1110 (Algebra)",
keywords = "Algebraic decomposition; Cylindrical structure;
Full-dimensional region; Polynomials; Projection
operator; Projection phase; Rational sample points;
Sign-invariant",
thesaurus = "Algebra; Polynomials",
}
@InProceedings{Ausiello:1989:DMP,
author = "G. Ausiello and A. Marchetti Spaccamela and U. Nanni",
title = "Dynamic maintenance of paths and path expressions on
graphs",
crossref = "Gianni:1989:SAC",
pages = "1--12",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In several applications it is necessary to deal with
data structures that may dynamically change during a
sequence of operations. In these cases the classical
worst case analysis of the cost of a single operation
may not adequately describe the behaviour of the
structure but it is rather more meaningful to analyze
the cost of the whole sequence of operations. The paper
first discusses some results on maintaining paths in
dynamic graphs. Besides, it considers paths problems on
dynamic labeled graphs and shows how to maintain path
expressions in the acyclic case when insertions of new
arcs are allowed.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Inf. e Sistemistica, Rome Univ.,
Italy",
classification = "C1160 (Combinatorial mathematics); C4240
(Programming and algorithm theory); C6120 (File
organisation)",
keywords = "Acyclic case; Data structures; Dynamic graphs; Dynamic
labeled graphs; Dynamic maintenance; Insertions; New
arcs; Path expressions; Paths problems",
thesaurus = "Computational complexity; Data structures; Graph
theory",
}
@InProceedings{Avenhaus:1989:URT,
author = "J. Avenhaus and D. Wi{\ss}mann",
title = "Using rewriting techniques to solve the generalized
word problem in polycyclic groups",
crossref = "Gonnet:1989:PAI",
pages = "322--337",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p322-avenhaus/",
abstract = "The authors apply rewriting techniques to the
generalized word problem GWP in polycyclic groups. They
assume the group $G$ to be given by a canonical
polycyclic string-rewriting system $R$ and consider GWP
in $G$ which is defined by $GWP(w,U)$ iff $w$ in $<U>$
for $w$ in $G$, finite $U$ contained in $G$, where
$<U>$ is the subgroup of $G$ generated by $U$. They
describe $<U>$ also by a rewrite system $S$ and define
a rewrite relation $\mbox{implies}_{S,R}$ in such a way
that $w$ implied by * $\mbox{implies}_{S,R} \lambda$
iff $w$ in $<U>$ ($\lambda$ the empty word). For this
rewrite relation the authors develop different critical
pair criteria for $\mbox{implies}_{S,R}$ to be
$\lambda$-confluent, i.e. confluent on the
left-congruence class $(\lambda )$ of implied by *
$\mbox{implies}_{S,R}$. Using any of these
$\lambda$-confluence criteria they construct a
completion procedure which stops for every input $S$
and computes a $\lambda$-confluent rewrite system
equivalent to $S$. This leads to a decision procedure
for GWP in G. Thus the authors give an explicit uniform
algorithm for deciding GWP in polycyclic groups and a
new proof based almost only on rewriting techniques for
the decidability of this problem. Further, they define
a rewrite relation $\mbox{implies}_{LM,U}$ which is
stronger than $\mbox{implies}_{S,R}$. They show that if
$G$ is given by a nilpotent string-rewriting system,
then by a completion procedure the input $U$ can be
transformed into $V$ such that $\mbox{implies}_{LM,V}$
is even confluent, not just $\lambda$-confluent.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany",
classification = "C1110 (Algebra); C4210 (Formal logic)",
keywords = "$\Lambda$-confluent; algorithms; Canonical polycyclic
string-rewriting system; Completion procedure; Critical
pair criteria; Decidability; design; Explicit uniform
algorithm; Generalized word problem; Group theory;
Nilpotent string-rewriting system; Polycyclic groups;
Rewrite relation; Rewriting techniques; theory",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Decidability; Group theory; Rewriting systems; Symbol
manipulation",
}
@InProceedings{Bajaj:1989:FRP,
author = "C. Bajaj and J. Canny and T. Garrity and J. Warren",
title = "Factoring rational polynomials over the complexes",
crossref = "Gonnet:1989:PAI",
pages = "81--90",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p81-bajaj/",
abstract = "The authors give NC algorithms for determining the
number and degrees of the absolute factors (factors
irreducible over the complex numbers $C$) of a
multivariate polynomial with rational coefficients. NC
is the class of functions computable by
logspace-uniform boolean circuits of polynomial size
and polylogarithmic dept. The measures of size of the
input polynomial are its degree $d$, coefficient length
$c$, number of variables $n$, and for sparse
polynomials, the number of nonzero coefficients $s$.
For the general case, the authors give a random
(Monte-Carlo) NC algorithm in these input measures. If
$n$ is fixed, or if the polynomial is dense, they give
a deterministic NC algorithm. The algorithm also works
in random NC for polynomial represented by
straight-line programs, provided the polynomial can be
evaluated at integer points in NC. The authors discuss
a method for obtaining an approximation to the
coefficients of each factor whose running time is
polynomial in the size of the original (dense)
polynomial. These methods rely on the fact that the
connected components of a complex hypersurface
$P(z_1,\ldots{},z_n)=0$ minus its singular points
correspond to the absolute factors of $P$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Purdue Univ., Lafayette, IN,
USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4240 (Programming and algorithm theory)",
keywords = "Absolute factors; algorithms; Complex numbers;
Factorisation; Functions; Logspace-uniform boolean
circuits; measurement; Monte-Carlo; Multivariate
polynomial; NC algorithms; Rational coefficients;
Rational polynomials; Set theory; theory;
verification",
subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Mechanical theorem proving.",
thesaurus = "Approximation theory; Computability; Computational
complexity; Monte Carlo methods; Polynomials; Set
theory; Symbol manipulation",
xxauthor = "C. Bajaj and J. Canny and R. Garrity and J. Warren",
}
@InProceedings{Barkatou:1989:RLS,
author = "M. A. Barkatou",
title = "On the reduction of linear systems of difference
equations",
crossref = "Gonnet:1989:PAI",
pages = "1--6",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p1-barkatou/",
abstract = "The author deals with linear systems of difference
equations whose coefficients admit generalized
factorial series representations at $z=\infty$. He
gives a criterion by which a given system is determined
to have a regular singularity. He gives an algorithm,
implementable in a computer algebra system, which
reduces in a finite number of steps the system of
difference equations on an irreducible form.",
acknowledgement = ack-nhfb,
affiliation = "Lab. TIM3-IMAG, Grenoble, France",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "algorithms; Computer algebra system; Convergence;
Generalized factorial series; Irreducible form; Linear
difference equations; Regular singularity; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods).",
thesaurus = "Convergence; Difference equations; Linear differential
equations; Mathematics computing; Matrix algebra;
Series [mathematics]; Symbol manipulation",
}
@InProceedings{Barkatou:1989:RNA,
author = "M. A. Barkatou",
title = "Rational {Newton} algorithm for computing formal
solutions of linear differential equations",
crossref = "Gianni:1989:SAC",
pages = "183--195",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a new algorithm for solving linear
differential equations in the neighbourhood of an
irregular singular point. This algorithm is based upon
the same principles as the Newton algorithm, however it
has a lower cost and is more suitable for computing
algebra.",
acknowledgement = ack-nhfb,
affiliation = "CNRS, INPG, IMAG, Grenoble, France",
classification = "C1120 (Analysis); C4170 (Differential equations)",
keywords = "Formal solutions; Irregular singular point; Linear
differential equations; Neighbourhood; Rational Newton
algorithm",
thesaurus = "Linear differential equations",
}
@InProceedings{BoydelaTour:1989:FAS,
author = "T. {Boy de la Tour} and R. Caferra",
title = "A formal approach to some usually informal techniques
used in mathematical reasoning",
crossref = "Gianni:1989:SAC",
pages = "402--406",
year = "1989",
bibdate = "Mon Dec 01 16:57:16 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "One of the striking characteristics of mathematical
reasoning is the contrast between the formal aspects of
mathematical truth and the informal character of the
ways to that truth. Among the many important and
usually informal mathematical activities the authors
are interested in proof analogy (i.e. common pattern
between proofs of different theorems) in the context of
interactive theorem proving.",
acknowledgement = ack-nhfb,
affiliation = "LIFIA-INPG, Grenoble, France",
classification = "C4210 (Formal logic)",
keywords = "Formal approach; Informal character; Interactive
theorem proving; Mathematical reasoning; Mathematical
truth; Usually informal techniques",
thesaurus = "Theorem proving",
}
@InProceedings{Bradford:1989:ETC,
author = "R. J. Bradford and J. H. Davenport",
title = "Effective tests for cyclotomic polynomials",
crossref = "Gianni:1989:SAC",
pages = "244--251",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present two efficient tests that determine
if a given polynomial is cyclotomic, or is a product of
cyclotomics. The first method uses the fact that all
the roots of a cyclotomic polynomial are roots of
unity, and the second the fact that the degree of a
cyclotomic polynomial is a value of $\phi (n)$, for
some $n$. The authors also find the cyclotomic factors
of any polynomial.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Cyclotomic polynomials; Roots",
thesaurus = "Polynomials",
}
@InProceedings{Bradford:1989:SRD,
author = "R. Bradford",
title = "Some results on the defect",
crossref = "Gonnet:1989:PAI",
pages = "129--135",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p129-bradford/",
abstract = "The defect of an algebraic number field (or, more
correctly, of a presentation of the field) is the
largest rational integer that divides the denominator
of any algebraic integer in the field when written
using that presentation. Knowing the defect, or
estimating it accurately is extremely valuable in many
algorithms, the factorization of polynomials over
algebraic number fields being a prime example. The
author presents a few results that are a move in the
right direction.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C4240
(Programming and algorithm theory)",
keywords = "Algebraic integer; Algebraic number field; algorithms;
Defect; Factorization; Polynomials; Rational integer;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2}
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation. {\bf G.1.4} Mathematics of Computing,
NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation. {\bf G.1.9} Mathematics of Computing,
NUMERICAL ANALYSIS, Integral Equations.",
thesaurus = "Computation theory; Number theory; Polynomials; Symbol
manipulation",
}
@InProceedings{Bronstein:1989:FRR,
author = "M. Bronstein",
title = "Fast reduction of the {Risch} differential equation",
crossref = "Gianni:1989:SAC",
pages = "64--72",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a weaker definition of weak-normality which:
can always be obtained in a tower of transcendental
elementary extensions, and gives an explicit formula
for the denominator of $y$, so the equation $y'+fy=g$
can be reduced to a polynomial equation in one
reduction step. As a consequence, a new algorithm is
obtained for solving y'+fy=g. The algorithm is very
similar to the one described by Rothstein (1976),
except that the present one uses weak normality to
prevent finite cancellation, rather than having to find
integer roots of polynomials over the constant field of
$K$ in order to detect it.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1120 (Analysis); C4170 (Differential equations)",
keywords = "Denominator; Explicit formula; Fast reduction;
Polynomial equation; Reduction step; Risch differential
equation; Transcendental elementary extensions;
Weak-normality",
thesaurus = "Differential equations",
}
@InProceedings{Bronstein:1989:SRE,
author = "M. Bronstein",
title = "Simplification of real elementary functions",
crossref = "Gonnet:1989:PAI",
pages = "207--211",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p207-bronstein/",
abstract = "The author describes an algorithm, based on Risch's
real structure theorem, that determines explicitly all
the algebraic relations among a given set of real
elementary functions. He provides examples from its
implementation in the scratchpad computer algebra
system that illustrate the advantages over the use of
complex logarithms and exponentials.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown
Heights, NY, USA",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "algorithms; Computer algebra system; Real elementary
functions; Real structure theorem; Scratchpad; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations.",
thesaurus = "Functions; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Brown:1989:SPP,
author = "C. Brown and G. Cooperman and L. Finkelstein",
title = "Solving permutation problems using rewriting systems",
crossref = "Gianni:1989:SAC",
pages = "364--377",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A new approach is described for finding short
expressions for arbitrary elements of a permutation
group in terms of the original generators which uses
rewriting methods. This forms an important component in
a long term plan to find short solutions for `large'
permutation problems (such as Rubik's cube), which are
difficult to solve by existing search techniques. In
order for this methodology to be successful, it is
important to start with a short presentation for a
finite permutation group. A new method is described for
giving a presentation for an arbitrary permutation
group acting on $n$ letters. This can be used to show
that any such permutation group has a presentation with
at most $n-1$ generators and $(n-1)^2$ relations. As an
application of this method, an $O(n^4)$ algorithm is
described for determining if a set of generators for a
permutation group of $n$ letters is a strong generating
set (in the sense of Sims). The `back end' includes a
novel implementation of the Knuth--Bendix technique on
symmetrization classes for groups.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C4210 (Formal logic)",
keywords = "Knuth--Bendix technique; Permutation problems;
Rewriting systems",
thesaurus = "Rewriting systems",
}
@InProceedings{Butler:1989:CVU,
author = "G. Butler and J. Cannon",
title = "{Cayley}, version 4: the user language",
crossref = "Gianni:1989:SAC",
pages = "456--466",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Cayley, version 4, is a proposed knowledge-based
system for modern algebra. The proposal integrates the
existing powerful algorithm base of Cayley with modest
deductive facilities and large sophisticated databases
of groups and related algebraic structures. The outcome
will be a revolutionary computer algebra system. The
user language of Cayley, version 4, is the first stage
of the project to develop a computer algebra system
which integrates algorithmic, deductive, and factual
knowledge. The language plays an important role in
shaping the users' communication of their knowledge to
the system, and in presenting the results to the user.
The very survival of a system depends upon its
acceptance by the users, so the language must be
natural, extensible, and powerful. The major changes in
the language (over version 3) are the definitions of
algebraic structures, set constructors and associated
control structures, the definitions of maps and
homomorphisms, the provision of packages for procedural
abstraction and encapsulation, database facilities, and
other input/output. The motivation for these changes
has been the need to provide facilities for a
knowledge-based system; to allow sets to be defined by
properties; and to remove semantic ambiguities of
structure definitions.",
acknowledgement = ack-nhfb,
affiliation = "Sydney Univ., NSW, Australia",
classification = "C6170 (Expert systems); C7310 (Mathematics)",
keywords = "Algebra; Algebraic structures; Associated control
structures; Cayley; Computer algebra system; Deductive
facilities; Encapsulation; Factual knowledge;
Homomorphisms; Knowledge-based system; Procedural
abstraction; Set constructors; Sophisticated databases;
User language; Version 4",
thesaurus = "Knowledge based systems; Symbol manipulation",
}
@InProceedings{Cabay:1989:FRA,
author = "S. Cabay and G. Labahn",
title = "A fast, reliable algorithm for calculating
{Pad{\'e}--Hermite} forms",
crossref = "Gonnet:1989:PAI",
pages = "95--100",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p95-cabay/",
abstract = "The authors present a new fast algorithm for the
calculation of a Pad{\'e}--Hermite form for a vector of
power series. When the vector of power series is
normal, the algorithm is shown to calculate a
Pad{\'e}--Hermite form of type $(n_0, \ldots{}, n_k)$
in $O(k.(n_0^2+\ldots{} +n_k^2))$ operations. This
complexity is the same as that of other fast algorithms
for computing Pad{\'e}--Hermite approximants. However,
unlike other algorithms, the new algorithm also
succeeds in the nonnormal case, usually with only a
moderate increase in cost.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Alberta Univ., Edmonton, Alta.,
Canada",
classification = "C1120 (Analysis); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Complexity; Iterative methods; Nonnormal
case; Pad{\'e}--Hermite approximants; Pad{\'e}--Hermite
forms; theory; Vector of power series",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf G.1.9} Mathematics of
Computing, NUMERICAL ANALYSIS, Integral Equations.",
thesaurus = "Computational complexity; Iterative methods; Linear
differential equations; Series [mathematics]; Vectors",
}
@InProceedings{Canny:1989:GCP,
author = "J. Canny",
title = "Generalized characteristic polynomials",
crossref = "Gianni:1989:SAC",
pages = "293--299",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author generalises the notion of characteristic
polynomial for a system of linear equations to systems
of multivariate polynomial equations. The
generalization is natural in the sense that it reduces
to the usual definition when all the polynomials are
linear. Whereas the constant coefficient of the
characteristic polynomial of a linear system is the
determinant, the constant coefficient of the general
characteristic polynomial is the resultant of the
system. This construction is applied to solve a
traditional problem with efficient methods for solving
systems of polynomial equations: the presence of
infinitely many solutions `at infinity'. The author
gives a single-exponential time method for finding all
the isolated solution points of a system of
polynomials, even in the presence of infinitely many
solutions at infinity or elsewhere.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Generalised characteristic polynomials; Multivariate
polynomial equations; Single-exponential time method;
System of linear equations",
thesaurus = "Polynomials",
}
@InProceedings{Canny:1989:SSN,
author = "J. F. Canny and E. Kaltofen and L. Yagati",
title = "Solving systems of non-linear polynomial equations
faster",
crossref = "Gonnet:1989:PAI",
pages = "121--128",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p121-canny/",
abstract = "Finding the solution to a system of $n$ non-linear
polynomial equations in $n$ unknowns over a given
field, say the algebraic closure of the coefficient
field, is a classical and fundamental problem in
computational algebra. The authors give a method that
allows the computation of resultants and $u$-resultants
of polynomial systems in essentially linear space and
quadratic time. The algorithm constitutes the first
improvement over Gaussian elimination-based methods for
computing these fundamental invariants.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comp. Sci., California Univ., Berkeley, CA,
USA",
classification = "C1110 (Algebra); C1120 (Analysis); C4130
(Interpolation and function approximation); C4150
(Nonlinear and functional equations); C4240
(Programming and algorithm theory)",
keywords = "Algebraic closure; algorithms; Coefficient field;
Computational algebra; Computational complexity; Linear
space; Nonlinear polynomial equations; Quadratic time;
Resultants; theory; U-resultants",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.1.5}
Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations, Systems of equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf G.1.1} Mathematics of
Computing, NUMERICAL ANALYSIS, Interpolation.",
thesaurus = "Computational complexity; Nonlinear equations;
Polynomials; Symbol manipulation",
}
@InProceedings{Cantone:1989:DPE,
author = "D. Cantone and V. Cutello and A. Ferro",
title = "Decision procedures for elementary sublanguages of set
theory. {XIV}. {Three} languages involving rank related
constructs",
crossref = "Gianni:1989:SAC",
pages = "407--422",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present three decidability results for
some quantifier-free and quantified theories of sets
involving rank related constructs.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Courant Inst. of Math. Sci.,
New York Univ., NY, USA",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic)",
keywords = "Decidability results; Decision procedures; Elementary
sublanguages; Quantified theories; Quantifier-free;
Rank related constructs; Set theory",
thesaurus = "Decidability; Formal logic; Set theory",
}
@InProceedings{Caprasse:1989:CEB,
author = "H. Caprasse and J. Demaret and E. Schrufer",
title = "Can {EXCALC} be used to investigate high-dimensional
cosmological models with nonlinear {Lagrangians}?",
crossref = "Gianni:1989:SAC",
pages = "116--124",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Recent work in cosmology is characterized by the
extension of the traditional four-dimensional general
relativity models in two directions: Kaluza--Klein type
models which have more than four dimensions, and models
with Lagrangians containing nonlinear terms in the
Riemann curvature tensor and its contractions. The
package EXCALC 2 seems particularly well suited to
investigate these models further. The implementation of
all operations of EXTERIOR CALCULUS opens the way to
perform these calculations efficiently. The article
presents the current stage of investigation in this
direction.",
acknowledgement = ack-nhfb,
affiliation = "Inst. de Phys., Liege Univ., Belgium",
classification = "A9575P (Mathematical and computer techniques);
A9880D (Theoretical cosmology); C7350 (Astronomy and
astrophysics)",
keywords = "Contractions; Cosmology; EXCALC 2; Four-dimensional
general relativity models; High-dimensional
cosmological models; Kaluza--Klein type models;
Nonlinear Lagrangians; Package; Riemann curvature
tensor",
thesaurus = "Astronomy computing; Astrophysics computing;
Cosmology; Software packages",
}
@InProceedings{ChaffyCamus:1989:ARA,
author = "C. Chaffy-Camus",
title = "An application of {REDUCE} to the approximation of
$f(x,y)$",
crossref = "Gianni:1989:SAC",
pages = "73--84",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Pad{\'e} approximants are an important tool in
numerical analysis, to evaluate $f(x)$ from its power
series even outside the disk of convergence, or to
locate its singularities. The paper generalizes this
process to the multivariate case and presents two
applications of this method: the approximation of
implicit curves and the approximation of double power
series. Computations are carried out on a computer
algebra system REDUCE.",
acknowledgement = ack-nhfb,
affiliation = "TIM3-INPG, Grenoble, France",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Approximation; Computer algebra system; Convergence;
Double power series; Implicit curves; Multivariate
case; Numerical analysis; Pad{\'e} approximants;
Reduce; Singularities",
thesaurus = "Approximation theory; Convergence of numerical
methods; Mathematics computing; Software packages",
}
@InProceedings{Char:1989:ARA,
author = "B. W. Char",
title = "Automatic reasoning about numerical stability of
rational expressions",
crossref = "Gonnet:1989:PAI",
pages = "234--241",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p234-char/",
abstract = "While numerical (e.g. Fortran) code generation from
computer algebra is nowadays relatively easy to do, the
expressions as they are produced via computer algebra
typically benefit from nontrivial reformulation for
efficiency and numerical stability. To assist in
automatic `expert reformulation', we desire good
automated tools to assess the stability of a particular
form of an expression. The author discusses an approach
to proofs of numerical stability (with respect to
roundoff error) of rational expressions. The proof
technique is based upon the ability to propagate
properties such as sign, exact representability, or a
certain kind of numerical stability, to floating point
results from properties of their antecedents. The
qualitative approach to numerical stability lends
itself to implementation as a backwards-chaining
theorem prover. While it is not a replacement for
alternative forms of stability analysis, it can
sometimes discover stability and explain it
straightforwardly.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
keywords = "algorithms; Backwards-chaining theorem prover; Code
generation; Computer algebra; Floating point; Numerical
stability; Rational expressions; Roundoff error;
theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Code generation.
{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic.",
thesaurus = "Automatic programming; Convergence of numerical
methods; Mathematics computing; Symbol manipulation",
}
@InProceedings{Char:1989:DIC,
author = "B. W. Char and A. R. Macnaughton and P. A. Strooper",
title = "Discovering inequality conditions in the analytical
solutions of optimization problems",
crossref = "Gianni:1989:SAC",
pages = "109--115",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Kuhn--Tucker conditions can provide an analytic
solution to the problem of maximizing or minimizing a
function subject to inequality constraints, if the
artificial variables known as Lagrange multipliers can
be eliminated. The paper describes an automated
reasoning program that assists in the solution process.
The program may also be useful for other problems
involving algebraic reasoning with inequalities.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
classification = "C1180 (Optimisation techniques); C1230 (Artificial
intelligence); C7310 (Mathematics)",
keywords = "Algebraic reasoning; Analytic solution; Artificial
variables; Automated reasoning program; Function
maximization; Function minimization; Inequality
conditions; Inequality constraints; Kuhn--Tucker
conditions; Lagrange multipliers; Optimization
problems",
thesaurus = "Inference mechanisms; Mathematics computing;
Optimisation",
}
@InProceedings{Chen:1989:CNF,
author = "Guoting Chen",
title = "Computing the normal forms of matrices depending on
parameters",
crossref = "Gonnet:1989:PAI",
pages = "242--249",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p242-chen/",
abstract = "The author considers an algorithm for the exact
computation of the Frobenius, Jordan and Arnold's form
of matrices depending holomorphically on parameters.
The problem originates from the problem of formal
resolution of a first order system of differential
equations depending on parameter. This algorithm has
been implemented in Macsyma.",
acknowledgement = ack-nhfb,
affiliation = "Equipe de Calcul Formel et Algorithmique Parallele,
Laboratoire TIM3-IMAG, Grenoble, France",
classification = "C1110 (Algebra); C1120 (Analysis); C4140 (Linear
algebra); C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; design; Differential equations; Formal
resolution; Macsyma; Matrices; Normal forms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations.",
thesaurus = "Differential equations; Mathematics computing; Matrix
algebra; Symbol manipulation",
}
@InProceedings{Collins:1989:PRP,
author = "G. E. Collins and J. R. Johnson",
title = "The probability of relative primality of {Gaussian}
integers",
crossref = "Gianni:1989:SAC",
pages = "252--258",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors generalize, to an arbitrary number field,
the theorem which gives the probability that two
integers are relatively prime. The probability that two
integers are relatively prime is $ 1/ \zeta (2)$, where
$\zeta$ is the Riemann $\zeta$ function and
$1/\zeta(2)=6/\pi^2$. The theorem for an arbitrary
number field states that the probability that two
ideals are relatively prime is the reciprocal of the
$\zeta$ function of the number field evaluated at two.
In particular, since the Gaussian integers are a unique
factorization domain, the authors get the probability
that two Gaussian integers are relatively prime is
$1/\zeta_G(2)$ where $\zeta_G$ is the $\zeta$ function
associated with the Gaussian integers. In order to
calculate the Gaussian probability, they use a theorem
that enables them to factor the $\zeta$ function into a
product of the Riemann $\zeta$ function and a Dirichlet
series called an L-series.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
Columbus, OH, USA",
classification = "C1140 (Probability and statistics); C1160
(Combinatorial mathematics)",
keywords = "Arbitrary number field; Dirichlet series; Gaussian
integers; L-series; Probability; Relative primality;
Riemann $\zeta$ function",
thesaurus = "Number theory; Probability",
}
@InProceedings{Collins:1989:QES,
author = "G. E. Collins and J. R. Johnson",
title = "Quantifier elimination and the sign variation method
for real root isolation",
crossref = "Gonnet:1989:PAI",
pages = "264--271",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p264-collins/",
abstract = "An important aspect of the construction of a
cylindrical algebraic decomposition (CAD) is real root
isolation. Root isolation involves finding disjoint
intervals, each containing a single root, for all of
the real roots of a given polynomial. Root isolation is
used to construct a CAD of the real line, which serves
as the base case in the construction of higher
dimensional CAD's. It is also an essential part of the
extension phase, which lifts an induced CAD to the next
higher dimension. The authors reexamine the sign
variation method of root isolation devised by Collins
and Akritas (1976). A new proof of termination is
given, which more accurately describes the behavior of
the algorithm. This theorem is then sharpened for the
special case of cubic polynomials. The result for cubic
polynomials is obtained with the aid of Collins's CAD
based quantifier elimination algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
Columbus, OH, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation)",
keywords = "algorithms; Cubic polynomials; Cylindrical algebraic
decomposition; design; Disjoint intervals; Polynomial;
Quantifier elimination; Real root isolation; Sign
variation method; Symbol manipulation; theory",
subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED
ENGINEERING. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Cooperman:1989:RGC,
author = "G. Cooperman and L. Finkelstein and E. Luks",
title = "Reduction of group constructions to point
stabilizers",
crossref = "Gonnet:1989:PAI",
pages = "351--356",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p351-cooperman/",
abstract = "The construction of point stabilizer subgroups is a
problem which has been studied intensively. This work
describes a general reduction of certain group
constructions to the point stabilizer problem. Examples
are given for the centralizer, the normal closure, and
a restricted group intersection problem. For the normal
closure problem, this work provides an alternative to
current algorithms, which are limited by the need for
repeated closures under conjugation. For the
centralizer and restricted group intersection problems,
one can use an existing point stabilizer sequence along
with a recent base change algorithm to avoid generating
a new point stabilizer sequence. This reduces the time
complexity by at least an order of magnitude.
Algorithms and theoretical time estimates for the
special case of a small base are also summarized. An
implementation is in progress.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Base change algorithm; Centralizer; Group
constructions; Group intersection; Group theory; Normal
closure; Point stabilizers; theory; Time complexity",
subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Number-theoretic
computations. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving.",
thesaurus = "Computational complexity; Group theory; Symbol
manipulation",
}
@InProceedings{Deprit:1989:MPS,
author = "A. Deprit and E. Deprit",
title = "Massively parallel symbolic computation",
crossref = "Gonnet:1989:PAI",
pages = "308--316",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p308-deprit/",
abstract = "A massively parallel processor proves to be a powerful
tool for manipulating the very large Poisson series
encountered in nonlinear dynamics. Exploiting the
algebraic structure of Poisson series leads quite
naturally to parallel data structures and algorithms
for symbolic manipulation. Exercising the parallel
symbolic processor on the solution of Kepler's equation
reveals the need to reexamine the serial computational
methods traditionally applied to problems in
dynamics.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
USA",
classification = "C1120 (Analysis); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Algebraic structure; algorithms; design; Massively
parallel processor; Nonlinear dynamics; Parallel data
structures; Symbolic manipulation; theory; Very large
Poisson series",
subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf E.1} Data, DATA STRUCTURES. {\bf
G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations. {\bf C.1.3} Computer
Systems Organization, PROCESSOR ARCHITECTURES, Other
Architecture Styles, Stack-oriented processors**.",
thesaurus = "Data structures; Mathematics computing; Nonlinear
equations; Parallel algorithms; Series [mathematics];
Symbol manipulation",
}
@InProceedings{Devitt:1989:UCA,
author = "J. S. Devitt",
title = "Unleashing computer algebra on the mathematics
curriculum",
crossref = "Gonnet:1989:PAI",
pages = "218--227",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author presents examples of the actual use of a
computer algebra system in the mathematics classroom.
These methods and observations are based on the daily
use of symbolic algebra during lectures. The potential
for focusing student energies on the concepts and ideas
of mathematical instead of just mimicking routine
computations is enormous. Considerable work remains to
make such tools widely accessible but the observations
presented will help to make others aware of the great
potential which exists for these and similar methods.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Saskatchewan Univ., Saskatoon, Sask.,
Canada",
classification = "C7310 (Mathematics); C7810C (Computer-aided
instruction)",
keywords = "Computer algebra; Educational computing; Mathematics
curriculum; Symbolic algebra",
thesaurus = "Educational computing; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Dewar:1989:IIS,
author = "M. C. Dewar",
title = "{IRENA}: an integrated symbolic and numerical
computation environment",
crossref = "Gonnet:1989:PAI",
pages = "171--179",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Computer algebra systems provide an extremely
user-friendly and natural problem-solving environment,
but are comparatively slow and limited in the scope of
problems they can treat. Programs which call routines
from numerical software libraries are fast, but require
longer development and testing time, as well as forcing
potential users to describe their problems in what is,
to them, an unnatural form. Both approaches have
advantages and disadvantages, but until now it has been
rather difficult to mix the two. The author describes
IRENA, an interface between the computer algebra system
REDUCE and the NAG numerical subroutine library, which
provides the NAG user with the advantages of a computer
algebra system and the REDUCE user with the facilities
of an extensive library of numerical software. He
discusses how the two methods could be used
side-by-side to solve problems in definite
integration.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics)",
keywords = "Computer algebra system; Definite integration; IRENA;
NAG; Numerical software; Numerical subroutine library;
REDUCE",
thesaurus = "Integration; Mathematics computing; Symbol
manipulation; User interfaces",
}
@InProceedings{Dicrescenzo:1989:AEA,
author = "C. Dicrescenzo and D. Duval",
title = "Algebraic extensions and algebraic closure in
{Scratchpad II}",
crossref = "Gianni:1989:SAC",
pages = "440--446",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Many problems in computer algebra, as well as in
high-school exercises, are such that their statement
only involves integers but their solution involves
complex numbers. For example, the complex numbers
$\sqrt{2}$ and $-\sqrt{2}$ appear in the solutions of
elementary problems in various domains. The authors
describe an implementation of an algebraic closure
domain constructor in the language Scratchpad II. In
the first part they analyze the problem, and in the
second part they describe a solution based on the D5
system.",
acknowledgement = ack-nhfb,
affiliation = "TIM3, INPG, Grenoble, France",
classification = "C7310 (Mathematics)",
keywords = "Algebraic closure domain constructor; D5 system;
Language Scratchpad II",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Edelsbrunner:1989:TPS,
author = "H. Edelsbrunner and F. P. Preparata and D. B. West",
title = "Tetrahedrizing point sets in three dimensions",
crossref = "Gianni:1989:SAC",
pages = "315--331",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper offers combinatorial results on extremum
problems concerning the number of tetrahedra in a
tetrahedrization of $n$ points in general position in
three dimensions, i.e. such that no four points are
coplanar. It also presents an algorithm that in
$O(n\log{}n)$ time constructs a tetrahedrization of a
set of $n$ points consisting of at most $3n-11$
tetrahedra.",
acknowledgement = ack-nhfb,
affiliation = "Illinois Univ., Urbana, IL, USA",
classification = "C4190 (Other numerical methods)",
keywords = "Combinatorial results; Extremum problems; Tetrahedra;
Tetrahedrization",
thesaurus = "Computational geometry",
}
@InProceedings{Einwohner:1989:MPG,
author = "T. H. Einwohner and R. J. Fateman",
title = "A {MACSYMA} package for the generation and
manipulation of {Chebyshev} series",
crossref = "Gonnet:1989:PAI",
pages = "180--185",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p180-einwohner/",
abstract = "Techniques for a MACSYMA package for expanding an
arbitrary univariate expression as a truncated series
in Chebyshev polynomials and manipulating such
expansions are described. A data structure is
introduced to represent a truncated expansion in a set
of orthogonal polynomials which contains the
independent variable, the name of the orthogonal
polynomial set, the number of terms retained, and a
list of the expansion coefficients. The package
converts a given expression into the aforementioned
data structure. Special cases are the conversion of
sums, products, the ratio, or the composition of
truncated Chebyshev expansions. Another special case is
converting an expression free of truncated Chebyshev
expansions. The package generates exact expansion
coefficients whenever possible. In addition to
well-known Chebyshev expansions, such as for
polynomials, the authors provide new methods for
getting exact Chebyshev expansions for reciprocals of
polynomials of degree one or two, meromorphic
functions, arbitrary powers of a first-degree
polynomial, the error-function, and generalized
hypergeometric functions.",
acknowledgement = ack-nhfb,
affiliation = "Lawrence Livermore Lab., California Univ., CA, USA",
classification = "C4130 (Interpolation and function approximation);
C6120 (File organisation); C6130 (Data handling
techniques); C7310 (Mathematics)",
keywords = "algorithms; Chebyshev polynomials; Chebyshev series;
Data structure; MACSYMA; Orthogonal polynomials;
theory; Univariate expression",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
E.1} Data, DATA STRUCTURES. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Chebyshev approximation; Data structures; Mathematics
computing; Polynomials; Series [mathematics]; Software
packages; Symbol manipulation",
}
@InProceedings{Fateman:1989:LTR,
author = "R. J. Fateman",
title = "Lookup tables, recurrences and complexity",
crossref = "Gonnet:1989:PAI",
pages = "68--73",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p68-fateman/",
abstract = "The use of lookup tables can reduce the complexity of
calculation of functions defined typically by
mathematical recurrence relations. Although this
technique has been adopted by several algebraic
manipulation systems, it has not been examined
critically in the literature. While the use of
tabulation or `memoization' seems to be particularly
simple and worthwhile technique in some areas, there
are some negative consequences. Furthermore, the
expansion of this technique to other areas (other than
recurrences) has not been subjected to analysis. The
paper examines some of the assumptions.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "Algebraic manipulation; algorithms; Complexity;
Functions; Lookup tables; Mathematical recurrence
relations; theory",
subject = "{\bf F.1.3} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Complexity Measures and Classes. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Computational complexity; Number theory; Recursive
functions; Symbol manipulation; Table lookup",
}
@InProceedings{Fateman:1989:SSA,
author = "R. J. Fateman",
title = "Series solutions of algebraic and differential
equations: a comparison of linear and quadratic
algebraic convergence",
crossref = "Gonnet:1989:PAI",
pages = "11--16",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p11-fateman/",
abstract = "Speed of convergence of Newton-like iterations in an
algebraic domain can be affected heavily by the
increasing cost of each step, so much so that a
quadratically convergent algorithm with complex steps
may be comparable to a slower one with simple steps.
The author gives two examples: solving algebraic and
first-order ordinary differential equations using the
MACSYMA algebraic manipulation system, demonstrating
this phenomenon. The relevant programs are exhibited in
the hope that they might give rise to more widespread
application of these techniques.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations); C7310 (Mathematics)",
keywords = "Algebraic equations; Algebraic manipulation system;
algorithms; Convergence; Differential equations; Linear
algebraic convergence; MACSYMA; Newton-like iterations;
Polynomials; Quadratic algebraic convergence; Series
solutions; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations, Boundary
value problems. {\bf G.1.4} Mathematics of Computing,
NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Iterative methods. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Convergence of numerical methods; Differential
equations; Iterative methods; Mathematics computing;
Polynomials; Series [mathematics]; Symbol
manipulation",
}
@InProceedings{Fitch:1989:CRB,
author = "J. Fitch",
title = "Can {REDUCE} be run in parallel?",
crossref = "Gonnet:1989:PAI",
pages = "155--162",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p155-fitch/",
abstract = "In order to make a substantial improvement in the
performance of algebra systems it will eventually be
necessary to use a parallel execution system. This
paper considers one approach to detecting parallelism,
an automatic method related to compilation, and applies
it to REDUCE, and to the factoriser in particular.",
acknowledgement = ack-nhfb,
classification = "C6130 (Data handling techniques); C6150C (Compilers,
interpreters and other processors); C7310
(Mathematics)",
keywords = "Algebra systems; algorithms; Automatic method;
Compilation; Factoriser; measurement; Parallel
execution system; Parallelism; REDUCE",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf F.3.2} Theory of Computation, LOGICS
AND MEANINGS OF PROGRAMS, Semantics of Programming
Languages.",
thesaurus = "Mathematics computing; Parallel programming; Program
compilers; Symbol manipulation",
}
@InProceedings{Freire:1989:ASC,
author = "E. Freire and E. Gamero and E. Ponce and L. G.
Franquelo",
title = "An algorithm for symbolic computation of center
manifolds",
crossref = "Gianni:1989:SAC",
pages = "218--230",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A useful technique for the study of local bifurcations
is part of the center manifold theory because a
dimensional reduction is achieved. The computation of
Taylor series approximations of center manifolds gives
rise to several difficulties regarding the operational
complexity and the computational effort. Previous works
proceed in such a way that the computational effort is
not optimized. In the paper an algorithm for center
manifolds well suited to symbolic computation is
presented. The algorithm is organized according to an
iterative scheme making good use of the previous steps,
thereby minimizing the number of operations. The
results of two examples obtained through a REDUCE 3.2
implementation of the algorithm are included.",
acknowledgement = ack-nhfb,
affiliation = "Escuela Superior Ingenieros Ind., Sevilla, Spain",
classification = "C1120 (Analysis); C4130 (Interpolation and function
approximation); C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algorithm; Center manifold theory; Computational
effort; Dimensional reduction; Iterative scheme; Local
bifurcations; Operational complexity; REDUCE 3.2;
Symbolic computation; Taylor series approximations",
thesaurus = "Approximation theory; Differential equations;
Mathematics computing; Symbol manipulation",
}
@InProceedings{Galligo:1989:GEC,
author = "Andr\'e Galligo and Lo{\"\i}c Pottier and Carlo
Traverso",
title = "Greater easy common divisor and standard basis
completion algorithms",
crossref = "Gianni:1989:SAC",
pages = "162--176",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The paper considers arithmetic complexity problems;
the main problem is how to limit the growth of the
coefficients in the algorithms and the complexity of
the field operations involved. The problem is important
with every ground field, with the obvious exception of
finite fields.",
acknowledgement = ack-nhfb,
affiliation = "Nice Univ., France",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "Algorithms; Arithmetic complexity problems;
Coefficients; Field operations; Greater easy common
divisor; Standard basis completion algorithms",
thesaurus = "Computational complexity; Rewriting systems",
}
@InProceedings{Gaonzalez:1989:SS,
author = "L. Gaonzalez and H. Lombardi and T. Recio and M.-F.
Roy",
title = "{Sturm--Habicht} sequence",
crossref = "Gonnet:1989:PAI",
pages = "136--146",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p136-gaonzalez/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations. {\bf F.1.3} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic.",
}
@InProceedings{Geddes:1989:HMO,
author = "K. O. Geddes and G. H. Gonnet and T. J. Smedley",
title = "Heuristic methods for operations with algebraic
numbers",
crossref = "Gianni:1989:SAC",
pages = "475--480",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Algorithms for doing computations involving algebraic
numbers have been known for quite some time and
implementations now exist in many computer algebra
systems. Many of these algorithms have been analysed
and shown to run in polynomial time and space, but in
spite of this many real problems take large amounts of
time and space to solve. The authors describe a
heuristic method which can be used for many operations
involving algebraic numbers. They give specifics for
doing algebraic number inverses, and algebraic number
polynomial exact division and greatest common divisor
calculation. The heuristic will not solve all instances
of these problems, but it returns either the correct
result or with failure very quickly, and succeeds for a
very large number of problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic numbers; Heuristic methods; Polynomial",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Geddes:1989:NAC,
author = "K. O. Geddes and G. H. Gonnet",
title = "A new algorithm for computing symbolic limits using
hierarchical series",
crossref = "Gianni:1989:SAC",
pages = "490--495",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors describe an algorithm for computing
symbolic limits, i.e. limits of expressions in symbolic
form, using hierarchical series. A hierarchical series
consists of two levels: an inner level which uses a
simple generalization of Laurent series with finite
principal part and which captures the behaviour of
subexpressions without essential singularities, and an
outer level which captures the essential singularities.
Once such a series has been computed for an expression
at a given point, the limit of the expression at the
point is determined by looking at the most significant
term of the series. This algorithm solves the limit
problem for a large class of expressions.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
keywords = "Algorithm; Finite principal part; Hierarchical series;
Laurent series; Limit problem; Singularities; Symbolic
form; Symbolic limits",
thesaurus = "Series [mathematics]; Symbol manipulation",
}
@InProceedings{Geddes:1989:RIM,
author = "K. O. Geddes and L. Y. Stefanus",
title = "On the {Risch--Norman} integration method and its
implementation in {MAPLE}",
crossref = "Gonnet:1989:PAI",
pages = "212--217",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p212-geddes/",
abstract = "Unlike the recursive Risch algorithm for the
integration of transcendental elementary functions, the
Risch--Norman method processes the tower of field
extensions directly in one step. In addition to
logarithmic and exponential field extensions, this
method can handle extensions in terms of tangents.
Consequently, it allows trigonometric functions to be
treated without converting them to complex exponential
form. The authors review this method and describe its
implementation in MAPLE. A heuristic enhancement to
this method is also presented.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "C1110 (Algebra); C1120 (Analysis); C4160 (Numerical
integration and differentiation); C7310 (Mathematics)",
keywords = "algorithms; Exponential field extensions; Logarithmic
field extensions; MAPLE; Risch--Norman integration;
Tangents; theory; Transcendental elementary functions;
Trigonometric functions",
subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations. {\bf F.1.3} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative
methods).",
thesaurus = "Functions; Integration; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Gianni:1989:DA,
author = "P. Gianni and V. Miller and B. Trager",
title = "Decomposition of algebras",
crossref = "Gianni:1989:SAC",
pages = "300--308",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors deal with the problem of decomposing
finite commutative Q-algebras as a direct product of
local Q-algebras. They solve this problem by reducing
it to the problem of finding a decomposition of finite
algebras over finite field. They show that it is
possible to define a lifting process that allows to
reconstruct the answer over the rational numbers. This
lifting appears to be very efficient since it is a
quadratic lifting that doesn't require stepwise
inversions. It is easy to see that the
Berlekamp--Hensel algorithm for the factorization of
polynomials is a special case of this argument.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1110 (Algebra); C4190 (Other numerical methods)",
keywords = "Berlekamp--Hensel algorithm; Decomposing finite
commutative Q-algebras; Lifting process",
thesaurus = "Algebra; Computational geometry",
}
@InProceedings{Giusti:1989:ATP,
author = "M. Giusti and D. Lazard and A. Valibouze",
title = "Algebraic transformations of polynomial equations,
symmetric polynomials and elimination",
crossref = "Gianni:1989:SAC",
pages = "309--314",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors define a general transformation of
polynomials and study the following concrete problem:
how to perform such a transformation using a standard
system of computer algebra, providing the usual
algebraic tools.",
acknowledgement = ack-nhfb,
affiliation = "Centre de Math., Ecole Polytech., Palaiseau, France",
classification = "C4130 (Interpolation and function approximation);
C6130 (Data handling techniques); C7310 (Mathematics)",
keywords = "Algebraic tools; Algebraic transformations of
polynomial equations; Computer algebra; Elimination;
Symmetric polynomials",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Giusti:1989:CRC,
author = "M. Giusti",
title = "On the {Castelnuovo} regularity for curves",
crossref = "Gonnet:1989:PAI",
pages = "250--253",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p250-giusti/",
abstract = "Let $k$ be a field of characteristic zero; let us
consider an algebraic subvariety of the projective
space $P_k^n$, defined by a homogeneous ideal I of the
polynomial algebra $R=k(x_o,\ldots{},x_n)$. There
exists different objects measuring the complexity of
this subvariety. Some invariants are naturally
intrinsic: the dimension and the degree of the
subvariety, the Hilbert function and its regularity,
and the Castelnuovo regularity. A natural question is
to study the relationships between the integers, at
least when the dimension is small (less or equal to
one). The author gives a slightly different version of
the Castelnuovo--Gruson--Lazarsfeld--Peskine theorem
(1983), which relates the Castelnuovo regularity and
the degree in the case of curves with more general
hypotheses but unfortunately slightly weaker
conclusion.",
acknowledgement = ack-nhfb,
affiliation = "Centre de Mathematiques, CNRS, Ecole Polytechnique,
Palaiseau, France",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation)",
keywords = "algorithms; Castelnuovo regularity; Complexity;
Curves; design; Hilbert function; measurement;
Polynomial algebra; Polynomials; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Complexity Measures and Classes.",
thesaurus = "Computational complexity; Curve fitting; Polynomials",
}
@InProceedings{Gonzalez:1989:SS,
author = "L. Gonzalez and H. Lombardi and T. Recio and M.-F.
Roy",
title = "{Sturm--Habicht} sequence",
crossref = "Gonnet:1989:PAI",
pages = "136--146",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Formal computations with inequalities is a subject of
general interest in computer algebra. In particular it
is fundamental in the parallelisation of basic
algorithms and quantifier elimination for real closed
fields. The authors give a generalisation of the Sturm
theorem essentially due to Sylvester, which is the key
for formal computations with inequalities. They study
the subresultant sequence, precise some of the
classical definitions in order to avoid problems and
study specialisation properties. They introduce the
Sturm--Habicht sequence, which generalizes Habicht's
work (1948). This new sequence, obtained automatically
from a subresultant sequence, has some remarkable
properties: it gives the same information as the Sturm
sequence, recovered by looking only at its principal
coefficients; it can be computed by ring operations and
exact divisions only, in polynomial time in case of
integer coefficients, eventually by modular methods; it
has good specialisation properties. Some information
about applications and implementation of the
Sturm--Habicht sequence is given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Matematicas, Cantabria Univ., Spain",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory)",
keywords = "Computational complexity; Computer algebra;
Inequalities; Integer coefficients; Modular methods;
Parallelisation; Polynomial time; Quantifier
elimination; Ring operations; Sturm theorem;
Sturm--Habicht sequence",
thesaurus = "Computational complexity; Parallel algorithms;
Polynomials; Series [mathematics]; Symbol
manipulation",
}
@InProceedings{Grigorev:1989:CCC,
author = "D. Yu. Grigor'ev",
title = "Complexity of computing the characters and the genre
of a system of exterior differential equations",
crossref = "Gianni:1989:SAC",
pages = "534--543",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let a system
$(\sum_JA_{J,i}(dX_{j1},\ldots{},dX_{jm})=0)_{m,i}$ of
exterior differential equations be given, where
$A_{J,i}$ are polynomials in $n$ variables
$X_1,\ldots{}, X_n$ of degrees less than $d$ and
skew-symmetric relatively to multiindices
$J=(j_1,\ldots{}, j_m)$, the square brackets denote the
exterior product of the differentials
$dX_{j1},\ldots{}, dX_{jm}$. E. Cartan (1945)
introduced the characters and the genre $h$ of the
system. Cauchy--Kovalevski theorem guarantees the
existence of an integral manifold (and even of the
general form) with the dimension less or equal to $h$
satisfying the given system. An algorithm for computing
the characters and the genre is designed with the
running time polynomial in $L$, $(dn)^n$, herein $L$
denotes the bit-size of the system. The algorithm
involves the subexponential-time procedures for finding
the irreducible components of an algebraic variety.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci.,
Leningrad, USSR",
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations)",
keywords = "Algebraic variety; Cauchy--Kovalevski theorem;
Characters; Exterior differential equations; Integral
manifold; Irreducible components; Polynomials",
thesaurus = "Differential equations; Polynomials",
}
@InProceedings{Grossman:1989:LTE,
author = "R. Grossman and R. G. Larson",
title = "Labeled trees and the efficient computation of
derivations",
crossref = "Gonnet:1989:PAI",
pages = "74--80",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p74-grossman/",
abstract = "The paper is concerned with the effective parallel
symbolic computation of operators under composition.
Examples include differential operators under
composition and vector fields under the Lie bracket. In
general, such operators do not commute. An important
problem is to find efficient algorithms to write
expressions involving noncommuting operators in terms
of operators which do commute. If the original
expression enjoys a certain symmetry, then naive
rewriting requires the computation of terms which in
the end cancel. Previously, the authors gave an
algorithm which in some cases is exponentially faster
than the naive expansion of the noncommutating
operators (1989). In this paper they show how that
algorithm can be naturally parallelized.",
acknowledgement = ack-nhfb,
affiliation = "Illinois Univ., Chicago, IL, USA",
classification = "C1120 (Analysis); C1160 (Combinatorial mathematics);
C4210 (Formal logic); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Computational complexity; Data structures;
Derivations; Differential operators; Labeled trees; Lie
bracket; Noncommuting operators; Operators; Parallel
algorithms; Parallel symbolic computation; theory;
Vector fields",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.2} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Modes of Computation,
Parallelism and concurrency.",
thesaurus = "Computational complexity; Data structures;
Differentiation; Parallel algorithms; Symbol
manipulation; Trees [mathematics]",
}
@InProceedings{Hentzel:1989:VNA,
author = "I. R. Hentzel and D. J. Pokrass",
title = "Verification of non-identities in algebras",
crossref = "Gianni:1989:SAC",
pages = "496--507",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors present a computer assisted algorithm
which establishes whether or not a proposed identity is
a consequence of the defining identities of a variety
of nonassociative algebras. When the nonassociative
polynomial is not an identity, the algorithm produces a
proof called a characteristic function. Like an
ordinary counterexample, the characteristic function
can be used to convince a verifier that the polynomial
is not identically zero. However the characteristic
function appears to be computationally easier to
verify. Also, it reduces or eliminates problems with
characteristic. The authors used this method to obtain
and verify a new result in the theory of nonassociative
algebras. Namely, in a free right alternative algebra
$(a,a,b)^3 \ne 0$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Iowa State Univ., Ames, IA, USA",
classification = "C7310 (Mathematics)",
keywords = "Algebras; Characteristic function; Computer assisted
algorithm; Nonassociative polynomial; Nonidentities
verification",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Juozapavicius:1989:SCW,
author = "A. Juozapavicius",
title = "Symbolic computation for {Witt} rings",
crossref = "Gianni:1989:SAC",
pages = "271--273",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author considers bilinear and quadratic forms over
polynomial rings, such that they can carry linear
discrete orderings. The author defines the notion of
reduced form and presents theorems concerning
equivalence of forms to their reduced presentation. The
proofs of these statements are based on the
Buchberger's algorithms and their modifications to
Gr{\"o}bner bases.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Vilnius State Univ., Lithuanian SSR,
USSR",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Bilinear forms; Symbolic computation; Witt rings;
Quadratic forms; Polynomial rings; Linear discrete
orderings; Reduced form; Gr{\"o}bner bases",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Kaltofen:1989:ISM,
author = "E. Kaltofen and L. Yagati",
title = "Improved sparse multivariate polynomial interpolation
algorithms",
crossref = "Gianni:1989:SAC",
pages = "467--474",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The authors consider the problem of interpolating
sparse multivariate polynomials from their values. They
discuss two algorithms for sparse interpolation, one
due to Ben-Or and Tiwari (1988) and the other due to
Zippel (1988). They present efficient algorithms for
finding the rank of certain special Toeplitz systems
arising in the Ben-Or and Tiwari algorithm and for
solving transposed Vandermonde systems of equations,
the use of which greatly improves the time complexities
of the two interpolation algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Sparse multivariate polynomial interpolation
algorithms; Time complexities; Toeplitz systems;
Transposed Vandermonde systems of equations",
thesaurus = "Interpolation; Polynomials",
}
@InProceedings{Kaltofen:1989:IVP,
author = "E. Kaltofen and T. Valente and N. Yui",
title = "An improved {Las Vegas} primality test",
crossref = "Gonnet:1989:PAI",
pages = "26--33",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p26-kaltofen/",
abstract = "The authors present a modification of the
Goldwasser--Kilian--Atkin primality test, which, when
given an input $n$, outputs either prime or composite,
along with a certificate of correctness which may be
verified in polynomial time. Atkin's method computes
the order of an elliptic curve whose endomorphism ring
is isomorphic to the ring of integers of a given
imaginary quadratic field $Q(\sqrt{-D})$. Once an
appropriate order is found, the parameters of the curve
are computed as a function of a root modulo $n$ of the
Hilbert class equation for the Hilbert class field of
$Q(\sqrt{-D})$. The modification proposed determines
instead a root of the Watson class equation for
$Q(\sqrt{-D})$ and applies a transformation to get a
root of the corresponding Hilbert equation. This is a
substantial improvement, in that the Watson equations
have much smaller coefficients than do the Hilbert
equations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C1160 (Combinatorial mathematics); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Certificate of correctness; Elliptic
curve; Endomorphism ring; Goldwasser--Kilian--Atkin
primality test; Hilbert equation; Imaginary quadratic
field; Las Vegas primality test; Number theory;
Polynomial time; Prime number; Programming theory;
theory; Watson class equation",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Hyperbolic
equations. {\bf G.3} Mathematics of Computing,
PROBABILITY AND STATISTICS. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation.",
thesaurus = "Computational complexity; Mathematics computing;
Number theory; Program verification; Programming
theory",
}
@InProceedings{Kirchner:1989:CER,
author = "C. Kirchner and H. Kirchner",
title = "Constrained equational reasoning",
crossref = "Gonnet:1989:PAI",
pages = "382--389",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p382-kirchner/",
abstract = "The theory of constrained equational reasoning is
outlined. Many questions and prolongations of this work
arise.",
acknowledgement = ack-nhfb,
classification = "C4210 (Formal logic)",
keywords = "algorithms; Constrained equational reasoning; Formal
logic; Theorem proving; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Computational logic.",
thesaurus = "Formal logic; Theorem proving",
}
@InProceedings{Kobayashi:1989:SSA,
author = "H. Kobayashi and S. Moritsugu and R. W. Hogan",
title = "Solving systems of algebraic equations",
crossref = "Gianni:1989:SAC",
pages = "139--149",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Shows an algorithm for computing all the solutions
with their multiplicities of a system of algebraic
equations. The algorithm previously proposed by the
authors for the case where the ideal is
zero-dimensional and radical seems to have practical
efficiency. The authors present a new method for
solving systems which are not necessarily radical. The
set of all solutions is partitioned into subsets each
of which consists of mutually conjugate solutions
having the same multiplicity.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Coll. of Sci. and Technol., Nihon
Univ., Tokyo, Japan",
classification = "C1110 (Algebra); C4210 (Formal logic)",
keywords = "Algebraic equations; Algorithm; Ideal; Multiplicities;
Mutually conjugate solutions; Radical; Subsets;
Zero-dimensional",
thesaurus = "Algebra; Problem solving; Theorem proving",
}
@InProceedings{Kredel:1989:SDC,
author = "H. Kredel",
title = "Software development for computer algebra or from
{ALDES\slash SAC-2} to {WEB\slash Modula-2}",
crossref = "Gianni:1989:SAC",
pages = "447--455",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author defines a new concept for developing
computer algebra software. The development system will
integrate a documentation system, a programming
language, algorithm libraries, and an interactive
calculation facility. The author exemplifies the
workability of this concept by applying it to the well
known ALDES/SAC-2 system. The ALDES Translator is
modified to help in converting ALDES/SAC-2 Code to
Modula-2. The implementation and module setup of the
SAC-2 basic system, list processing system and
arithmetic system in Modula-2 are discussed. An example
gives a first idea of the performance of the system.
The WEB System of Structured Documentation is used to
generate documentation with {\TeX}.",
acknowledgement = ack-nhfb,
affiliation = "Passau Univ., West Germany",
classification = "C6110B (Software engineering techniques); C7310
(Mathematics)",
keywords = "ALDES/SAC-2 system; Algorithm libraries; Computer
algebra software; Documentation system; Interactive
calculation facility; Performance; Programming
language; WEB/Modula-2",
thesaurus = "Mathematics computing; Software engineering; Symbol
manipulation",
}
@InProceedings{Kuhn:1989:MEC,
author = "N. Kuhn and K. Madlener",
title = "A method for enumerating cosets of a group presented
by a canonical system",
crossref = "Gonnet:1989:PAI",
pages = "338--350",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p338-kuhn/",
abstract = "The application of rewriting techniques to enumerate
cosets of subgroups in groups is investigated. Given a
class of groups $G$ having canonical string rewriting
presentations the authors consider the GWP for this
class which is defined by $GWP(w,U)$ iff $w$ in $<U>$
for $w$ in finite $U$ contained in $G$, $G \in G$,
where $<U>$ is the subgroup of $G$ generated by $U$.
They show how to associate to $U$ two rewriting
relations to $-{}_U$ and implies $-{}_U$ on strings
such that $w$ in $<U>$ iff $w$ from $*$ to
$-{}_U\lambda$ iff $w$ implied by
$*\mbox{implies}-_U\lambda$ ($\lambda$ the empty word),
both representing the left congruence generated by
$<U>$. They derive general critical pair criteria for
confluence and $\lambda$-confluence for these
relations. Using these criteria completion procedures
can be constructed which enumerate cosets like the
Todd--Coxeter algorithm without explicit definition of
all cosets. The procedures are shown to be terminating
if the index of the subgroup is finite or for groups
with finite canonical monadic group presentations. If
the completion procedure terminates it returns a prefix
rewriting system which is confluent on $\Sigma *$, thus
deciding the GWP and the index problem for this class
of groups. The normal forms of the rewriting relations
form a minimal Schreier-representative system of $<U>$
in $G$.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany",
classification = "C1110 (Algebra); C4210 (Formal logic)",
keywords = "$\Lambda$-confluence; algorithms; Canonical string
rewriting presentations; Completion procedures;
Confluence; Cosets; Critical pair criteria;
Decidability; Finite canonical monadic group
presentations; Generalized word problem; Group theory;
Minimal Schreier-representative system; Rewriting
relations; Rewriting techniques; Subgroups; theory;
Todd--Coxeter algorithm",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems. {\bf F.4.2} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
Other Rewriting Systems, Decision problems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Decidability; Group theory; Rewriting systems; Symbol
manipulation",
}
@InProceedings{Kutzler:1989:CAT,
author = "B. Kutzler",
title = "Careful algebraic translations of geometry theorems",
crossref = "Gonnet:1989:PAI",
pages = "254--263",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p254-kutzler/",
abstract = "Modern application areas like computer-aided design
and robotics have revived interest in geometry. The
algorithmic techniques of computer algebra are
important tools for solving large classes of nonlinear
geometric problems. However, their application requires
a translation of geometric problems into algebraic
form. So far, this algebraization process has not
gained special attention, since it was considered
`obvious'. In the context of automated geometry theorem
proving, the use of algebraic deduction techniques led
to very promising results, but it seemed to change the
nature of proof problems from deciding the validity of
a theorem to finding nondegeneracy conditions under
which the theorem holds. A careful analysis shows, that
this is mainly due to the `careless' translation
method. A careful translation technique is presented
that resolves this defect. The usefulness of the new
algebraization method is demonstrated on concrete
examples. A practical comparison with the former
`careless' translation is done.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1160 (Combinatorial mathematics); C4190 (Other
numerical methods); C4210 (Formal logic); C4290 (Other
computer theory); C7310 (Mathematics)",
keywords = "Algebraic deduction; algorithms; Automated geometry
theorem proving; Computer algebra; experimentation;
Geometry theorems; Nonlinear geometric problems;
theory",
subject = "{\bf I.2.0} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, General. {\bf G.2.1} Mathematics of
Computing, DISCRETE MATHEMATICS, Combinatorics.",
thesaurus = "Computational geometry; Symbol manipulation; Theorem
proving",
}
@InProceedings{MacCallum:1989:ODE,
author = "M. A. H. MacCallum",
title = "An ordinary differential equation solver for
{REDUCE}",
crossref = "Gianni:1989:SAC",
pages = "196--205",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Progress and plans for the implementation of an
ordinary differential equation solver in REDUCE 3.3 are
reported; the aim is to incorporate the best available
methods for obtaining closed-form solutions, and to aim
at the `best possible' alternative when this fails. It
is hoped that this will become a part of the standard
REDUCE program library. Elementary capabilities have
already been implemented, i.e. methods for first order
differential equations of simple types and linear
equations of any order with constant coefficients. The
further methods to be used include: for first-order
equations, an adaptation of Shtokhamer's MACSYMA
program; for higher-order linear equations,
factorisation of the operator where possible; and for
nonlinear equations, the exploitation of Lie
symmetries.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Queen Mary Coll., London, UK",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Closed-form solutions; Factorisation; First-order
equations; Lie symmetries; MACSYMA program; Nonlinear
equations; Ordinary differential equation solver;
REDUCE 3.3; REDUCE program library",
thesaurus = "Differential equations; Mathematics computing;
Software packages; Subroutines",
}
@InProceedings{Menezes:1989:SCA,
author = "A. J. Menezes and P. C. {van Oorschot} and S. A.
Vanstone",
title = "Some computational aspects of root finding in
${GF}(q^m)$",
crossref = "Gianni:1989:SAC",
pages = "259--270",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "This paper is an implementation report comparing
several variations of a deterministic algorithm for
finding roots of polynomials in finite extension
fields. Running times for problem instances in fields
$\mbox{GF}(2^m)$, including $m>1000$, are given.
Comparisons are made between the variations, and
improvements achieved in running times are discussed.",
acknowledgement = ack-nhfb,
affiliation = "Waterloo Univ., Ont., Canada",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Computational aspects; Root finding; Roots of
polynomials",
thesaurus = "Polynomials",
}
@InProceedings{Miller:1989:PGE,
author = "B. R. Miller",
title = "A program generator for efficient evaluation of
{Fourier} series",
crossref = "Gonnet:1989:PAI",
pages = "199--206",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p199-miller/",
abstract = "Many fields require the evaluation of large
multi-variate Fourier series, but the naive method of
calling sine and cosine for each term can be
prohibitive where computing resources are constrained
or the series are extremely large (30000 terms).
Although the number of such calls can be reduced by
using trigonometric identities, such a reduction is
usually not possible by hand. Indeed, even when it is
carried out by computer, care must be taken to generate
compact programs and avoid generating large numbers of
intermediate terms. The author describes an algorithm
for automatically generating very efficient Fortran
programs directly from the mathematical description of
the series to be evaluated. The resulting Fortran
programs are 5-7 times faster than the naive version
and sometimes significantly more compact.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Inst. of Stand. and Technol., Gaithersbury, MD,
USA",
classification = "C6115 (Programming support); C7310 (Mathematics)",
keywords = "algorithms; design; Fortran programs; Fourier series;
languages; Program generator",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computability
theory. {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Code generation. {\bf D.3.3} Software,
PROGRAMMING LANGUAGES, Language Constructs and
Features, Procedures, functions, and subroutines.",
thesaurus = "Automatic programming; Mathematics computing; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Mora:1989:GBN,
author = "T. Mora",
title = "{Gr{\"o}bner} bases in noncommutative algebras",
crossref = "Gianni:1989:SAC",
pages = "150--161",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author has studied, in 1988, the concept of
standard and Gr{\"o}bner bases and algorithms for their
computation in a very wide algebraic context (graded
structures). It is easy to show that if
$R=k<X_1,\ldots{}, X_n>/H$, where $H$ is the ideal
generated by $(X_jX_j-c_{ij}X_iX_j-p_{ij})$ and
$\deg(p_{ij})<\deg(X_iX_j)$ for each $i,j$, then $R$ is
such a graded structure; so his previous techniques can
be applied to it in order to define a concept of
Gr{\"o}bner basis and to produce an algorithm for their
computation, provided that if $J$ is the ideal
generated by $(X_jX_i-c_{ij}X_iX_j:i<j)$, it holds
that: (1) Each ideal in $k<X_1, \ldots{}, X_n>$,
homogeneous for the graduation defined above and
containing J, is finitely generated; (2) For each
homogeneous ideal $(h_1, \ldots{}, h_s)$ in
$k<X_1,\ldots{},X_n>/J$, it is possible to compute a
finite set of syzygies, which together with the trivial
ones, generate the module of syzygies; and (3) For each
homogeneous ideal $(h_1, \ldots{}, h_s)$ and each
homogeneous element $h$ in $k<X_1,\ldots{}, X_n>/J$, it
is possible to decide whether $h$ in
$(h_1,\ldots{},h_s)$, in which case it is possible to
compute a representation of $h$ in terms of
$(h_1,\ldots{},h_s)$. It turns out that the above
conditions hold whenever for no
$i<j<k,c_{ij}=c_{jk}=0$. The author shows how to solve
problems (2) and (3) in case for no
$i<j<k,C_{ij}=c_{jk}=0$.",
acknowledgement = ack-nhfb,
affiliation = "Genova Univ., Italy",
classification = "C4210 (Formal logic)",
keywords = "Gr{\"o}bner bases; Noncommutative algebras; Graded
structures; Ideal; Homogeneous; Set of syzygies;
Decide",
thesaurus = "Algebra; Decidability; Theorem proving",
}
@InProceedings{Murray:1989:EPD,
author = "N. V. Murray and E. Rosenthal",
title = "Employing path dissolution to shorten tableaux
proofs",
crossref = "Gonnet:1989:PAI",
pages = "373--381",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p373-murray/",
abstract = "Path dissolution is an inferencing mechanism that
generalizes the method of analytic tableaux. The main
result presented is that every nontrivial step in any
tableau proof can be speeded up with the application of
dissolution techniques.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
intelligence); C4210 (Formal logic)",
keywords = "algorithms; Analytic tableaux; Formal logic; Graph
theory; Inferencing mechanism; Path dissolution;
Rewrite operations; Tableau proof; Tableaux proofs;
theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Mathematical Logic.",
thesaurus = "Graph theory; Inference mechanisms; Rewriting systems;
Theorem proving",
}
@InProceedings{Musser:1989:GP,
author = "D. R. Musser and A. A. Stepanov",
title = "Generic programming",
crossref = "Gianni:1989:SAC",
pages = "13--25",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Generic programming centers around the idea of
abstracting from concrete, efficient algorithms to
obtain generic algorithms that can be combined with
different data representations to produce a wide
variety of useful software. Four kinds of
abstraction-data, algorithmic, structural, and
representational-are discussed, with examples of their
use in building an Ada library of software components.
The main topic discussed is generic algorithms and an
approach to their formal specification and
verification, with illustration in terms of a
partitioning algorithm such as is used in the quicksort
algorithm. It is argued that generically programmed
software component libraries offer important advantages
for achieving software productivity and reliability.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C6110 (Systems analysis and programming); C6120
(File organisation)",
keywords = "Abstracting; Ada library; Algorithmic abstraction;
Data abstraction; Data representations; Formal
specification; Formal verification; Generic algorithms;
Generic programming; Generically programmed software
component libraries; Partitioning algorithm; Quicksort
algorithm; Representational abstraction; Software
productivity; Software reliability; Structural
abstraction",
thesaurus = "Data structures; Programming",
}
@InProceedings{OHearn:1989:NTP,
author = "P. O'Hearn and Z. Stachniak",
title = "Note on theorem proving strategies for resolution
counterparts of nonclassical logics",
crossref = "Gonnet:1989:PAI",
pages = "364--372",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p364-o_hearn/",
abstract = "The paper shows that two of the more powerful speed-up
techniques available for the classical first-order
logic, namely the set of support and the polarity
strategies, can be formulated and applied to resolution
proof systems for nonclassical logics. The authors
review background information on propositional logics
and propositional resolution proof systems. They
introduce the set of support and polarity strategies.
They show that resolution counterparts of most
structural propositional logics admit both strategies
preserving their refutational completeness.",
acknowledgement = ack-nhfb,
affiliation = "Queen's Univ., Kingston, Ont., Canada",
classification = "C1160 (Combinatorial mathematics); C1230 (Artificial
intelligence); C4210 (Formal logic)",
keywords = "algorithms; Deductive systems; First-order logic;
Inference rules; Nonclassical logics; Polarity;
Propositional logics; Propositional resolution proof
systems; Resolution counterparts; Resolution proof
systems; Speed-up techniques; Support; Theorem proving;
theory; Trees",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory.",
thesaurus = "Formal logic; Inference mechanisms; Theorem proving;
Trees [mathematics]",
}
@InProceedings{Okada:1989:SNC,
author = "M. Okada",
title = "Strong normalizability for the combined system of the
typed $\lambda$ calculus and an arbitrary convergent
term rewrite system",
crossref = "Gonnet:1989:PAI",
pages = "357--363",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p357-okada/",
abstract = "The author gives a proof of strong normalizability of
the typed $\lambda$-calculus extended by an arbitrary
convergent term rewriting system, which provides the
affirmative answer to the open problem proposed in
Breazu-Tannen (1988). Klop (1980) showed that a
combined system of the untyped $\lambda$-calculus and
convergent term rewriting system is not Church--Rosser
in general, though both are Church--Rosser. It is
well-known that the typed $\lambda$-calculus is
convergent (Church--Rosser and terminating).
Breazu-Tannen showed that a combined system of the
typed $\lambda$-calculus and an arbitrary
Church--Rosser term rewriting system is again
Church--Rosser. The strong normalization result in this
paper shows that the combined system of the typed
$\lambda$-calculus and an arbitrary convergent term
rewriting system is again convergent. The strong
normalizability proof is easily extended to the case of
the second order (polymorphically) typed $\lambda$
calculus and the case in which $\mu$-reduction rule is
added.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Concordia Univ., Montreal,
Que., Canada",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Church--Rosser; Convergent term rewrite
system; design; Polymorphically; Rewriting system;
Strong normalizability; theory; Typed $\lambda$
calculus; Typed $\lambda$-calculus",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Lambda
calculus and related systems. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Computational logic.",
thesaurus = "Convergence; Rewriting systems; Symbol manipulation",
}
@InProceedings{Ollivier:1989:IRM,
author = "F. Ollivier",
title = "Inversibility of rational mappings and structural
identifiability in automatics",
crossref = "Gonnet:1989:PAI",
pages = "43--54",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p43-ollivier/",
abstract = "The author investigates different methods for testing
whether a rational mapping $f$ from $k^n$ to $k^m$
admits a rational inverse, or whether a polynomial
mapping admits a polynomial one. He gives a new
solution, which seems much more efficient in practice
than previously known ones using `tag' variables and
standard basis, and a majoration for the degree of the
standard basis calculations which is valid for both
methods in the case of a polynomial map which is
birational. He shows that a better bound can be given
for the method, under some assumption on the form of
$f$. The method can also extend to check whether a
given polynomial belongs to the subfield generated by a
finite set of fractions. The author illustrates the
algorithm with an application to structural
identifiability. The implementation has been done in
the IBM computer algebra system Scratchpad II.",
acknowledgement = ack-nhfb,
affiliation = "Lab. d'Inf. de l'X, Ecole Polytech., Palaiseau,
France",
classification = "C1110 (Algebra); C1120 (Analysis); C7310
(Mathematics)",
keywords = "algorithms; Computer algebra system; experimentation;
Fractions; IBM; Inversibility; Polynomial inverse;
Polynomial mapping; Rational inverse; Rational
mappings; Scratchpad II; Structural identifiability;
theory",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Inverse problems; Mathematics computing; Polynomials;
Set theory; Symbol manipulation",
}
@InProceedings{Pan:1989:SCD,
author = "Victor Pan",
title = "On some computations with dense structured matrices",
crossref = "Gonnet:1989:PAI",
pages = "34--42",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p34-pan/",
abstract = "The author reduces several computations with Hilbert
and Vandermonde type matrices to matrix computations of
the Hankel--Toeplitz type (and vice versa). This
unifies various known algorithms for computations with
dense structured matrices and allows the extension of
any progress in computations with matrices of one class
to the computations with other classes. This allows the
computation of the inverses and the determinants of
$n*n$ matrices of Vandermonde and Hilbert types for the
cost of $O(n \log^2n)$ arithmetic operations.
Previously, such results were only known for the more
narrow class of Vandermonde and generalized Hilbert
matrices.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., City Univ. of New York, Bronx, NY,
USA",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Computational complexity; Dense structured
matrices; Determinants; Hankel--Toeplitz type; Hilbert;
Inverses; theory; Vandermonde",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra, Matrix inversion.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Computational complexity; Determinants; Inverse
problems; Mathematics computing; Matrix algebra",
}
@InProceedings{Porter:1989:DRA,
author = "S. C. Porter",
title = "Dense representation of affine coordinate rings of
curves with one point at infinity",
crossref = "Gonnet:1989:PAI",
pages = "287--297",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p287-porter/",
abstract = "Traditional methods of representing rational functions
on curves are unwieldy and unsuitable for solution of
many problems. This paper describes a simple and
elegant representation of elements of the affine
coordinate ring of an algebraic curve and describes
efficient, easy to implement algorithms to perform
addition, subtraction, multiplication and polynomial
evaluation. This data structure overcomes many of the
disadvantages of more unwieldy traditional
representations. Elements are represented as vectors of
elements of the ground field in a manner similar to the
representation of polynomials of one variable as an
array of coefficients. This data structure is a
fundamental ingredient in the author's decoding method
for algebraic geometry codes. The rational function
approximation techniques used for decoding could not
have been described with multivariate polynomials or
truncated infinite series.",
acknowledgement = ack-nhfb,
affiliation = "Baise State Univ., ID, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Affine coordinate rings; Algebraic curve; Algebraic
geometry codes; algorithms; Curves; Data structure;
Decoding; Polynomial; Rational function approximation;
Rational functions; theory; Vectors",
subject = "{\bf E.1} Data, DATA STRUCTURES. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation. {\bf E.4}
Data, CODING AND INFORMATION THEORY.",
thesaurus = "Computational geometry; Data structures; Functions;
Mathematics computing; Polynomials; Programming theory;
Symbol manipulation; Vectors",
xxpages = "288--297",
}
@InProceedings{Purtilo:1989:MEO,
author = "J. M. Purtilo",
title = "Minion: an environment to organize mathematical
problem solving",
crossref = "Gonnet:1989:PAI",
pages = "147--154",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p147-purtilo/",
abstract = "Maryland University are constructing a management
assistant that works in conjunction with existing
symbolic computation systems. Called Minion, it allows
users to express simple plans for solving large
problems in the interactive environment, and then
guides the user's interaction according to that plan.
Key features are that plans are easy to construct; the
assistant helps a user visualize progress towards
solving the global problem; and individual steps within
a plan can be executed by arbitrary software tools,
whether symbolic-, numeric- or logic-based in their
implementation. The author briefly portrays the
organizational problem that must be treated, and
motivates the need for structure management tools in
mathematical problem solving environments. He details
features of the Minion prototype. After a brief update
on the status of the existing Polylith system, he
describes how Minion is implemented using an
interconnection resource.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
classification = "C6130 (Data handling techniques); C6180 (User
interfaces); C7310 (Mathematics)",
keywords = "algorithms; Interactive environment; Interconnection
resource; Management assistant; Maryland University;
Mathematical problem solving; Minion; Polylith;
Structure management tools; Symbolic computation
systems; theory; User interfaces",
subject = "{\bf I.3.1} Computing Methodologies, COMPUTER
GRAPHICS, Hardware Architecture. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
thesaurus = "Interactive systems; Mathematics computing; Symbol
manipulation; User interfaces",
}
@InProceedings{Rabinowitz:1989:CSS,
author = "S. Rabinowitz",
title = "On the computer solution of symmetric homogeneous
triangle inequalities",
crossref = "Gonnet:1989:PAI",
pages = "272--286",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p272-rabinowitz/",
abstract = "The article presents an effective systematic algorithm
that one can use to prove inequalities. A computer
algorithm that can prove many inequalities is
presented.",
acknowledgement = ack-nhfb,
affiliation = "Alliant Comput. Syst. Corp., Littleton, MA, USA",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Computer algorithm; Symmetric homogeneous
triangle inequalities; theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
thesaurus = "Equations; Mathematics computing; Programming theory;
Symbol manipulation",
}
@InProceedings{Ravenscroft:1989:SSG,
author = "R. A. {Ravenscroft, Jr.} and E. A. Lamagna",
title = "Symbolic summation with generating functions",
crossref = "Gonnet:1989:PAI",
pages = "228--233",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The generating function technique presented is an
important addition to the area of summation algorithms.
With it, many summations that cannot be evaluated by
existing algorithms can be solved. Among these are
hybrid sums and sums involving special classes of
functions including binomial coefficients, Fibonacci
numbers, and harmonic numbers. However, the method is
not viable for hand calculation since the algebraic
manipulation gets very complex. Fortunately, the steps
used in the procedure are consistent regardless of the
particular generating functions that are involved.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Brown Univ., Providence, RI,
USA",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Generating functions; Hybrid sums; Summation
algorithms; Symbolic summation",
thesaurus = "Computation theory; Functions; Series [mathematics];
Symbol manipulation",
}
@InProceedings{Roch:1989:CAM,
author = "J.-L. Roch and P. Senechaud and F. Siebert-Roch and G.
Villard",
title = "Computer algebra on {MIMD} machine",
crossref = "Gianni:1989:SAC",
pages = "423--439",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "PAC is a computer algebra system, based on MIMD type
parallelism. It uses parallelism as a tool for
processing problems which are too complex for a
sequential treatment. Basic fundamentals of the system
are firstly discussed. Then, different problems are
studied, particularly the implementation of
infinite-precision arithmetic, the solution of linear
systems and of Diophantine equations, the
parallelization of Buchberger's algorithm for
Gr{\"o}bner bases. A prototype of PAC is implemented on
the Floating Point System hypercube Tesseract 20 (16
nodes), and different timing results obtained on this
machine are given.",
acknowledgement = ack-nhfb,
affiliation = "TIM3, INPG, Grenoble, France",
classification = "C7310 (Mathematics)",
keywords = "MIMD machine; PAC; Computer algebra system;
Infinite-precision arithmetic; Solution of linear
systems; Diophantine equations; Parallelization;
Gr{\"o}bner bases; Floating Point System hypercube
Tesseract 20; Timing results",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Rolletschek:1989:SDC,
author = "H. Rolletschek",
title = "Shortest division chains in imaginary quadratic number
fields",
crossref = "Gianni:1989:SAC",
pages = "231--243",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Let $O_d$ be the set of algebraic integers in an
imaginary quadratic number field $Q(\sqrt{d})$, $d<0$,
where $d$ is the discriminant of $O_d$. Consider the
Euclidean Algorithm (EA), applied to algebraic integers
$\xi$, $\eta$ in $O_d$. It consists in computing a
sequence of remainders
$\rho_0=\xi,\rho_1=\eta,\rho_2,\ldots{},\rho_{n+1}=0$,
where $\rho_{i+1}=\rho_{i-1}-\gamma_i\rho_i$ for
algebraic integers $\gamma _i \in K, i=1, \ldots{}, n$.
It is shown that except for $d=-11$ the number of
divisions to be carried out is always minimized by
choosing each $\gamma_i$ such that
$N(\rho_{i-1}-\gamma_i\rho_i)$, the norm of
$\rho_{i-1}-\gamma_i\rho_i$, is minimal. This result
has been proven previously in special cases. It also
applies to those imaginary quadratic number rings which
are not Euclidean; in this case the division chains may
be infinite. For $d=-7,-8$ the methods applied so far
must be modified somewhat, and for $d=-11$ a
counterexample is provided and a theorem which
partially answers the question, how shortest division
chains can be obtained.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kent State Univ., OH, USA",
classification = "C1160 (Combinatorial mathematics)",
keywords = "Algebraic integers; Discriminant; Divisions; EA;
Euclidean Algorithm; Imaginary quadratic number fields;
Norm; Remainders; Set; Shortest division chains",
thesaurus = "Number theory",
}
@InProceedings{Saunders:1989:PIC,
author = "B. D. Saunders and H. R. Lee and S. K. Abdali",
title = "A parallel implementation of the cylindrical algebraic
decomposition algorithm",
crossref = "Gonnet:1989:PAI",
pages = "298--307",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p298-saunders/",
abstract = "The authors describe a parallelization scheme for
Collins's cylindrical algebraic decomposition algorithm
for quantifier elimination in the theory of real closed
fields. They discuss a parallel implementation of the
computer algebra system SAC2 in which a complete
sequential implementation of Collins's algorithm
already exists. They report some initial results on the
speedup obtained, drawing on a suite of examples
previously given by Arnon.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Delaware Univ.,
Newark, DE, USA",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Computer algebra system; Cylindrical
algebraic decomposition algorithm; Parallel
implementation; Parallelization; Polynomials;
Quantifier elimination; Real closed fields; SAC2;
theory",
subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Parallelism and
concurrency. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems.",
thesaurus = "Mathematics computing; Parallel algorithms;
Polynomials; Programming theory; Symbol manipulation",
}
@InProceedings{Schwarz:1989:FAL,
author = "F. Schwarz",
title = "A factorization algorithm for linear ordinary
differential equations",
crossref = "Gonnet:1989:PAI",
pages = "17--25",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p17-schwarz/",
abstract = "The reducibility and factorization of linear
homogeneous differential equations are of great
theoretical and practical importance in mathematics.
Although it has been known for a long time that
factorization is in principle a decision procedure, its
use in an automatic differential equation solver
requires a more detailed analysis of the various steps
involved. Especially important are certain auxiliary
equations, the so-called associated equations. An upper
bound for the degree of its coefficients is derived.
Another important ingredient is the computation of
optimal estimates for the size of polynomial and
rational solutions of certain differential equations
with rotational coefficients. Applying these results,
the design of the factorization algorithm LODEF and its
implementation in the Scratchpad II Computer Algebra
System is described.",
acknowledgement = ack-nhfb,
affiliation = "GMD, Inst. F1, St. Augustin, West Germany",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "algorithms; Associated equations; Automatic
differential equation solver; Factorization algorithm;
Linear ordinary differential equations; LODEF; Optimal
estimates; Polynomial solutions; Rational solutions;
Rotational coefficients; Scratchpad II Computer Algebra
System; theory; Upper bound",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods). {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
thesaurus = "Linear differential equations; Mathematics computing;
Polynomials; Symbol manipulation",
}
@InProceedings{Sergeraert:1989:NRN,
author = "F. Sergeraert",
title = "From a noncomputability result to new interesting
definitions and computability results",
crossref = "Gianni:1989:SAC",
pages = "26--32",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Examines the strange situation encountered in
algebraic topology: on one hand no general algorithm is
able to decide whether some topological space is simply
connected; this is an easy consequence of the
undecidability of the word problem. On the other hand
most of the important results in algebraic topology
assume that the spaces under consideration are simply
connected. So that one can ask for algorithms that use
some method or other, and always compute something, in
such a way that if the space given is simply connected,
then the result obtained is the good one. The problem
is to explain what is something in general. The paper
explains that a solution can be found for the computing
problems of the homotopy groups. Then something is a
K-theory group. It obtains in this way a new
understanding of the algebraic K-theory groups and
positive results about their computability.",
acknowledgement = ack-nhfb,
affiliation = "Inst. Fourier, St. Martin d'Heres, France",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "Algebraic K-theory groups; Algebraic topology;
Computability; Homotopy groups; Simply connected;
Topological space; Undecidability; Word problem",
thesaurus = "Group theory; Topology",
}
@InProceedings{Shackell:1989:AEO,
author = "J. Shackell",
title = "Asymptotic estimation of oscillating functions using
an interval calculus",
crossref = "Gianni:1989:SAC",
pages = "481--489",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author considers the problem of estimating the
asymptotic growth of functions defined by expressions
involving exponentials, logarithms, algebraic
operations and also sine functions. Modulo the
assumption that zero-equivalence can be decided on the
set of constant terms, an algorithm exists for the case
when there are no trigonometric functions in the
expression.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Math., Kent Univ., Canterbury, UK",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic operations; Asymptotic estimation;
Asymptotic growth; Exponentials; Interval calculus;
Logarithms; Oscillating functions; Sine functions;
Zero-equivalence",
thesaurus = "Approximation theory; Estimation theory; Symbol
manipulation",
}
@InProceedings{Shackell:1989:DAF,
author = "J. Shackell",
title = "A differential-equations approach to functional
equivalence",
crossref = "Gonnet:1989:PAI",
pages = "7--10",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "To seek algebraic dependencies between functions is to
ask whether there exists a polynomial in them which is
functionally equivalent to zero. The methods outlined
work directly with the given expression, which is
regarded as a polynomial in a top-level basic function
with coefficients in a function field containing the
other basic functions. The top-level function is
defined by a differential equation over the coefficient
field. The techniques are entirely elementary and
involve differentiation, substitution and calculation
of GCDs. The methods decide zero-equivalence in fields
built using arithmetic operations and functional
composition with functions defined as solutions of
algebraic differential equations. The paper treats only
first-order, first-degree equations.",
acknowledgement = ack-nhfb,
affiliation = "Kent Univ., Canterbury, UK",
classification = "C1110 (Algebra); C1120 (Analysis); C4130
(Interpolation and function approximation); C4170
(Differential equations)",
keywords = "Algebraic dependencies; Differential-equations;
Differentiation; Functional equivalence; Functions;
Polynomial; Substitution; Zero-equivalence",
thesaurus = "Differential equations; Functions; Polynomials",
}
@InProceedings{Shackle:1989:DAF,
author = "J. Shackle",
title = "A differential-equations approach to functional
equivalence",
crossref = "Gonnet:1989:PAI",
pages = "7--10",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p7-shackle/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
}
@InProceedings{Sharma:1989:SDA,
author = "N. Sharma and P. S. Wang",
title = "Symbolic derivation and automatic generation of
parallel routines for finite element analysis",
crossref = "Gianni:1989:SAC",
pages = "33--56",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Describes some initial results of a joint research
project involving engineering and computer science.
Based on earlier work on the automatic derivation and
generation of numeric code for finite element analysis,
the authors are conducting research into the mapping of
finite element computations on parallel architectures.
Software is being developed to automatically derive and
generate parallel code that can be used with existing
sequential code to improve speed. They are developing
techniques to derive parallel procedures, based on
high-level user input, to exploit parallel computer
architectures. An experimental software system called
P-FINGER is under development to derive key finite
element routines for the Warp systolic array computer.
A separate parallel code generation package is used to
render the symbolically derived parallel procedures
into code for the Warp parallel computer.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Kent State Univ., OH, USA",
classification = "C4100 (Numerical analysis); C7400 (Engineering)",
keywords = "Automatic derivation; Automatic generation; Computer
science; Engineering; Experimental software system;
Finite element analysis; Finite element computations;
Finite element routines; P-FINGER; Parallel
architectures; Parallel code; Parallel code generation
package; Parallel computer architectures; Parallel
procedures; Parallel routines; Symbolic derivation;
Symbolically derived parallel procedures; Warp parallel
computer; Warp systolic array computer",
thesaurus = "Engineering computing; Finite element analysis;
Parallel processing",
}
@InProceedings{Siebert-Roch:1989:PAH,
author = "F. Siebert-Roch",
title = "Parallel algorithms for {Hermite} normal form of an
integer matrix",
crossref = "Gonnet:1989:PAI",
pages = "317--321",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p317-siebert-roch/",
abstract = "The main problem in integral matrices
triangularization is the `intermediate coefficients
swell'. This aspect limits the dimension of treated
matrices. The lliopoulos algorithm computes the Hermite
normal form of an integer matrix controlling the
coefficients growth by means of the determinant. The
author presents two parallelizations of this algorithm
and their implementations on a MIMD machine, with 16
processors.",
acknowledgement = ack-nhfb,
affiliation = "Laboratoire TIM3-IMAG, Grenoble, France",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Determinant; Hermite normal form; Integer
matrix; Integral matrices triangularization;
Intermediate coefficients swell; Lliopoulos algorithm;
MIMD; Parallel algorithms; Parallelizations; theory",
subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL
ANALYSIS, Integral Equations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Determinants; Mathematics
computing; Matrix algebra; Parallel algorithms; Symbol
manipulation",
}
@InProceedings{Singer:1989:LFI,
author = "M. F. Singer",
title = "{Liouvillian} first integrals of differential
equations",
crossref = "Gianni:1989:SAC",
pages = "57--63",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The system of differential equations
$x=P(x,y),y=Q(x,y)$ has a Liouvillian first integral if
and only if the differential form $Q(x,y)dx-P(x,y)dy$
has an integrating factor of the form
$R(x,y)=exp(\int{}U(x,y)dx+V(x,y)dy)$ where $U$ and $V$
are rational functions and $U_y=V_x$. This theorem
shows that if a Liouvillian first integral exists, then
there is a Liouvillian first integral of a very special
form, but it does not show how to find one. Before
turning to this latter question, the author discusses
how this theorem is placed in the setting of
differential algebra and the tools used to prove it.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
classification = "C1120 (Analysis); C4170 (Differential equations);
C4180 (Integral equations)",
keywords = "Differential algebra; Differential equations;
Differential form; Integrating factor; Liouvillian
first integrals; Rational functions",
thesaurus = "Differential equations; Integral equations",
}
@InProceedings{Smedley:1989:NMA,
author = "T. J. Smedley",
title = "A new modular algorithm for computation of algebraic
number polynomial gcds",
crossref = "Gonnet:1989:PAI",
pages = "91--94",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p91-smedley/",
abstract = "Euclid's algorithm for finding the greatest common
divisor of two polynominals when applied to polynomials
over an algebraic extension field, tends to be very
slow. In the case of polynomials with integer
coefficients, one approach to solving this problem is
to use a modular algorithm. This approach has been
extended to algebraic number fields by Langemyr and
McCallum (1987). Another approach for algebraic numbers
is to use a heuristic method (Geddes, Gonnett and
Smedley, 1988). The paper shows that this heuristic
method can be made into an algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci. Waterloo Univ., Ont., Canada",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory)",
keywords = "Algebraic number polynomial gcds; algorithms; Euclid;
Heuristic method; Integer coefficients; Modular
algorithm; Symbol manipulation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Computation theory; Polynomials; Symbol manipulation",
}
@InProceedings{Stifter:1989:GRM,
author = "S. Stifter",
title = "A generalization of the {Roider} method to solve the
robot collision problem in {3D}",
crossref = "Gianni:1989:SAC",
pages = "332--343",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The Roider method is a method to test by means of
computational geometry whether two convex, compact
objects, say $A$ and $B$, in two dimensions intersect.
Roughly, this iterative method constructs a witness to
disjointness (a wedge formed by a pair of
touching-lines from some $P(\in A)$ to $B$ that
separates $A$ and $B$) if the objects are disjoint. If
the objects intersect then a witness to intersection,
i.e. a point in common to both objects, is constructed.
The author generalizes the Roider method in two
aspects: Firstly, he generalizes the algorithm such
that it is also applicable to convex, compact objects
in three dimensions. Secondly, he generalizes the
method such that it can be used to test whether a
non-moving object A collides with a moving object
$B$.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Keples
Univ., Linz, Austria",
classification = "C3120C (Spatial variables); C4190 (Other numerical
methods)",
keywords = "3D; Computational geometry; Disjointness; Iterative
method; Robot collision problem; Roider method",
thesaurus = "Computational geometry; Position control",
}
@InProceedings{Teitelbaum:1989:CCR,
author = "J. Teitelbaum",
title = "On the computational complexity of the resolution of
plane curve singularities",
crossref = "Gianni:1989:SAC",
pages = "285--292",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author describes an algorithm which computes the
resolution of a plane curve singularity-that is, a
singularity at the origin defined by a formal power
series $F$ in two variables $x$ and $y$ over a field
$k$. The algorithm requires that $k$ be of
characteristic zero (or at least of `large'
characteristic) but this hypothesis can certainly be
removed at the expense of some complications. The
algorithm obtains explicit equations for the blowing-up
of the singularity, and therefore yields all of the
interesting invariants of the singularity, such as its
conductor and its Milnor number. The author also
provides upper bounds for the number of $k$-operations
needed for the operation of the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Michigan Univ., Ann Arbor, MI, USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Computational complexity; Formal power series;
Resolution of plane curve singularities",
thesaurus = "Computational complexity; Series [mathematics]",
}
@InProceedings{Todd:1989:SAP,
author = "P. H. Todd and G. W. Cherry",
title = "Symbolic analysis of planar drawings",
crossref = "Gianni:1989:SAC",
pages = "344--355",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A method is described for performing a symbolic
analysis of planar drawings. The method takes input in
the form of a dimensioned (i.e. labeled) drawing and
determines whether the coordinates of all of the points
in the drawing can be uniquely written in terms of the
specified labels. If it is possible to determine the
coordinates of the points (i.e. the drawing is
consistently dimensioned), then they are calculated.
Otherwise the algorithm returns a flag specifying
whether the drawing is underdimensioned or
overdimensioned. The method employs standard
constructions from geometry such as the construction of
a line from two distinct points or the construction of
a line from a given line, a point and an angle. In
order to determine whether some sequence of given
constructions can be used to calculate the coordinates
of each point the authors construct and analyse an
undirected graph called the dimension graph of the
drawing. If such a sequence exists, then the
calculations are performed by calling symbolic routines
which correspond to the various constructions. An
implementation is described and examples are given.",
acknowledgement = ack-nhfb,
affiliation = "Tektronix Labs., Beaverton, OR, USA",
classification = "C1160 (Combinatorial mathematics); C4190 (Other
numerical methods); C6130 (Data handling techniques)",
keywords = "Coordinates; Dimension graph; Geometry; Labeled
drawing; Planar drawings; Symbolic analysis; Symbolic
routines; Undirected graph",
thesaurus = "Computational geometry; Graph theory; Symbol
manipulation",
}
@InProceedings{Traverso:1989:EGB,
author = "C. Traverso and L. Donati",
title = "Experimenting the {Gr{\"o}bner} basis algorithm with
the {A1PI} system",
crossref = "Gonnet:1989:PAI",
pages = "192--198",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p192-traverso/",
abstract = "The AlPI (Algoritmi Pisa) system is a small polynomial
algebra system. It was designed and implemented by the
first author in MuLISP-86. It is now (almost) ported by
the second author in lucid COMMON-LISP, in such a way
that only a few macros are needed to transport it in
any COMMON-LISP dialect (MuLISP included). Its main aim
is the experimentation on the Buchberger Gr{\"o}bner
basis completion algorithm with its different versions,
and on the Mora tangent cone algorithm. It is driven by
a menu, and has a series of facilities to manipulate
lists of polynomials. After a description of the system
and of the versions of the algorithms presently
implemented, the authors give a series of experimental
results (for the MuLISP version). These results, and
results of the same kind to obtain with further
experimentation, can give suggestions on the versions
of the algorithm to choose as default for other
implementations of the algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dipartmento di Matematica, Pisa Univ., Italy",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "algorithms; experimentation; theory; User interfaces;
Gr{\"o}bner basis algorithm; AlPI system; Algoritmi
Pisa; Polynomial algebra system; MuLISP-86; Macros;
Buchberger Gr{\"o}bner basis; Completion algorithm;
Mora tangent cone algorithm",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Mathematics computing; Polynomials; Symbol
manipulation",
xxtitle = "Experimenting the {Gr{\"o}bner} basis algorithm with
the {AlPI} system",
}
@InProceedings{Traverso:1989:GTA,
author = "C. Traverso",
title = "{Gr{\"o}bner} trace algorithms",
crossref = "Gianni:1989:SAC",
pages = "125--138",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Practical computing experience on Gr{\"o}bner bases
has shown that computing with rational numbers or
integers, very frequently one has very large
coefficients in the intermediate computations, and that
often the final result is of more moderate size.
Sometimes it happens that the size of these numbers,
which have to be kept up to the end, is such that
memory overflow or excessive paging occurs. The
author's approach gives a series of algorithms, based
on the concept of Gr{\"o}bner trace; these algorithms
are mainly probabilistic (Monte Carlo); they include a
series of tests (still probabilistic) to check the
probable correctness; he also describes deterministic
tests that unfortunately are sometimes as costly as a
direct Gr{\"o}bner basis computation, but sometimes
instead very rapid.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Pisa Univ., Italy",
classification = "C1140G (Monte Carlo methods); C4210 (Formal logic)",
keywords = "Gr{\"o}bner trace algorithms; Gr{\"o}bner bases;
Rational numbers; Integers; Probabilistic; Monte Carlo;
Probable correctness; Deterministic tests",
thesaurus = "Monte Carlo methods; Rewriting systems",
}
@InProceedings{Valibouze:1989:RSF,
author = "A. Valibouze",
title = "Resolvents and symmetric functions",
crossref = "Gonnet:1989:PAI",
pages = "390--399",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p390-valibouze/",
abstract = "A model of transformations of polynomial equations
(direct image model) is studied. The model expresses
some minimal polynomials and some resolvents relative
to the Galois group of a polynomial in order to use a
general algorithm of resolution. This algorithm can be
effectively computed in MACSYMA with the extension SYM
that manipulates symmetric polynomials. Examples
obtained by specializing the general algorithm for the
Galois resolvent are given.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Pierre et Marie Curie, Paris, France",
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C7310 (Mathematics)",
keywords = "algorithms; Direct image model; Galois group; MACSYMA;
Minimal polynomials; Polynomial equations; Resolution;
Resolvents; SYM; Symmetric polynomials; theory;
Transformations",
language = "French",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Functions; Mathematics computing; Polynomials; Symbol
manipulation",
}
@InProceedings{vanHulzen:1989:COP,
author = "J. A. {van Hulzen} and B. J. A. Hulshof and B. L.
Gates and M. C. {van Heerwaarden}",
title = "A code optimization package for {REDUCE}",
crossref = "Gonnet:1989:PAI",
pages = "163--170",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p163-van_hulzen/",
abstract = "A survey of the strategy behind and the facilities of
a code optimization package for REDUCE are given. The
authors avoid a detailed discussion of the different
algorithms and concentrate on the user aspects of the
package. Examples of straightforward and more advanced
usage are shown.",
acknowledgement = ack-nhfb,
affiliation = "Twente Univ., Dept. of Comput. Sci., Enschede,
Netherlands",
classification = "C6130 (Data handling techniques); C6150C (Compilers,
interpreters and other processors); C7310
(Mathematics)",
keywords = "algorithms; Code optimization package; Compilers;
REDUCE; theory; User aspects",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.2.2} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Automatic Programming. {\bf D.3.4}
Software, PROGRAMMING LANGUAGES, Processors,
Compilers.",
thesaurus = "Mathematics computing; Optimisation; Program
compilers; Symbol manipulation",
}
@InProceedings{Vinette:1989:USC,
author = "F. Vinette and J. Cizek",
title = "The use of symbolic computation in solving some
nonrelativistic quantum mechanical problems",
crossref = "Gianni:1989:SAC",
pages = "85--95",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Stresses the importance of symbolic computation
languages as a new research tool in applied
mathematics. The treatment of some non-relativistic
quantum mechanical problems are presented as
illustrations of the use of the symbolic computation
language MAPLE developed at the University of Waterloo.
Emphasis is given on the possibility to manipulate
expressions symbolically, to perform rapidly tedious
operations as well as to work in rational arithmetic.
Another important feature will consist in the interface
of MAPLE and FORTRAN.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Waterloo Univ., Ont., Canada",
classification = "A0365D (Functional analytical methods); C7320
(Physics and Chemistry)",
keywords = "Applied mathematics; Expression manipulation; FORTRAN;
Interface; MAPLE; Nonrelativistic quantum mechanical
problems; Symbolic computation languages; Symbolic
manipulation",
thesaurus = "High level languages; Physics computing; Quantum
theory; Symbol manipulation",
}
@InProceedings{Watt:1989:FPM,
author = "S. M. Watt",
title = "A fixed point method for power series computation",
crossref = "Gianni:1989:SAC",
pages = "206--217",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a novel technique for manipulating structures
which represent infinite power series. The technique
described allows a power series to be defined in a very
natural but computationally inefficient way and
transforms it to an equivalent, efficient form. This is
achieved by using a fixed point operator on the delayed
part to remove redundant calculations. The paper
describes this fixed point method and the class of
problems to which it is applicable. It has been used in
Scratchpad II to improve the performance of a number of
operations on infinite series, including division,
reversion, special functions and the solution of linear
and non-linear ordinary differential equations. A few
examples are given of the method and of the speed up
obtained. To illustrate, the computation of the first
$n$ terms of $\exp(u)$ for a dense, infinite series $u$
is reduced from $O(n^4)$ to $O(n^2)$ coefficient
operations, the same as required by the standard
on-line algorithms.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Delayed part; Fixed point method; Fixed point
operator; Infinite power series; Power series
computation; Redundant calculations; Scratchpad II",
thesaurus = "Computational complexity; Mathematics computing",
}
@InProceedings{Weerawarana:1989:GPC,
author = "S. Weerawarana and P. S. Wang",
title = "{GENCRAY}: a portable code generator for {Cray}
{Fortran}",
crossref = "Gonnet:1989:PAI",
pages = "186--191",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p186-weerawarana/",
abstract = "The authors have applied these concepts to finite
element analysis. Their research resulted in the
software systems FINGER and GENTRAN, both written in
Franz LISP. FINGER, derives element strain-displacement
matrices and stiffness matrices based on user-supplied
parameters. The derived codes involve declarations,
expressions, arrays, functions and subroutines. These
quantities are represented by LISP internal data
structures that must be generated into numerical code
by a code translation process. This is the function of
GENTRAN which can translate MACSYMA representations
into f77, ratfor, or C. GENCRAY is a code generation
package similar to GENTRAN but different in many
respects. The output of GENCRAY is f77 or Cray
Fortran-77 (CFT77) code. CFT77 is a superset of f77 and
is the standard Fortran used on Cray supercomputers.
The authors present the design of GENCRAY, the steps of
code translation, its implementation, features for
generating vectorizable and parallel code for the Cray,
and how a user can customize GENCRAY to suite different
purposes.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Kent State Univ., OH, USA",
classification = "C6115 (Programming support); C6130 (Data handling
techniques); C6150C (Compilers, interpreters and other
processors); C7310 (Mathematics)",
keywords = "algorithms; Code generation package; Code translation;
Cray Fortran; Data structures; FINGER; Finite element
analysis; GENCRAY; GENTRAN; Portable code generator;
Supercomputers; theory",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Finite
element methods. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Code generation. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Automatic programming; Finite element analysis;
Mathematics computing; Parallel programming; Program
interpreters; Software portability; Symbol
manipulation",
}
@InProceedings{Weispfenning:1989:EDP,
author = "V. Weispfenning",
title = "Efficient decision procedures for locally finite
theories. {II}",
crossref = "Gianni:1989:SAC",
pages = "262--273",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "For pt. I, see AECC-3, Grenoble, Springer LNCS, vol.
229.",
abstract = "Let $T$ be a finitely axiomatized, universal theory in
a finite, first-order language $L$, and suppose $T$ has
a model companion $T'$ with only finitely many
countable models. $T$ is uniformly locally finite, say
with generating function $g: N$ to $N$. The author
shows the existence of a further function $am: N$ to
$N$ measuring the extent to which $\mbox{Mod(T)}$ fails
to satisfy the amalgamation property. The main result
is as follows: There exist explicitly described uniform
decision and quantifier elimination procedures for
$T'$, whose asymptotic complexity can be bounded from
above by an elementary recursive function in $g$ and
am, without any further reference to $T$ or $T'$. A
corresponding result (with $g$ replaced by $d$) holds,
if $T$ is not finitely axiomatized, provided there is a
function $d: N$ to $N$ bounding the size of suitable
descriptions of $n$-generated $T$-models.",
acknowledgement = ack-nhfb,
affiliation = "Lehrstuhl fur Math., Passau Univ., West Germany",
classification = "C1140E (Game theory); C4210 (Formal logic)",
keywords = "Asymptotic complexity; Decision procedures;
First-order language; Generating function; Locally
finite theories; Quantifier elimination procedures",
thesaurus = "Decision theory; Formal logic",
}
@InProceedings{White:1989:CF,
author = "N. L. White and T. McMillan",
title = "{Cayley} factorization",
crossref = "Gianni:1989:SAC",
pages = "521--533",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "An important problem in computer-aided geometric
reasoning is to automatically find geometric
interpretations for algebraic expressions. For
projective geometry this question can be reduced to the
Cayley factorization problem. A Cayley factorization of
a homogeneous bracket polynomial $P$ is a Cayley
algebra expression (using only the join and meet
operations) which evaluates to P. The authors give an
introduction to both Cayley algebra and bracket
algebra. The main result of the paper is an algorithm
which solves the Cayley factorization problem in the
important special case that $P$ is multilinear.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Florida Univ., Gainesville, FL, USA",
classification = "C4210 (Formal logic); C7310 (Mathematics)",
keywords = "Algebraic expressions; Bracket algebra; Cayley
factorization; Computer-aided geometric reasoning;
Homogeneous bracket polynomial; Projective geometry",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Winkler:1989:GDA,
author = "F. Winkler",
title = "A geometrical decision algorithm based on the
{Gr{\"o}bner} bases algorithm",
crossref = "Gianni:1989:SAC",
pages = "356--363",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Gr{\"o}bner bases have been used in various ways for
dealing with the problem of geometry theorem proving as
posed by Wu (1978). Kutzler and Stifter (1986) have
proposed a procedure centered around the computation of
a basis for the module of syzygies of the geometrical
hypotheses. The author elaborates this approach and
extends it to a complete decision procedure. Also, in
geometry theorem proving the problem of constructing
subsidiary (or degeneracy) conditions arises. Such
subsidiary conditions usually are not uniquely
determined and obviously one wants to keep them as
simple as possible. This problem, however, has not
received enough attention in the geometry theorem
proving literature. The author's algorithm is able to
construct the simplest subsidiary conditions with
respect to certain predefined criteria, such as lowest
degree or dependence on a given set of variables.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C4190 (Other numerical methods); C4210 (Formal
logic)",
keywords = "Geometrical decision algorithm; Gr{\"o}bner bases
algorithm; Geometry theorem proving; Complete decision
procedure; Subsidiary conditions",
thesaurus = "Computational geometry; Theorem proving",
}
@InProceedings{Winkler:1989:KPB,
author = "F. Winkler",
title = "{Knuth--Bendix} procedure and {Buchberger} algorithm
--- a synthesis",
crossref = "Gonnet:1989:PAI",
pages = "55--67",
year = "1989",
bibdate = "Thu Mar 12 08:33:50 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p55-winkler/",
abstract = "The Knuth--Bendix procedure for the completion of a
rewrite rule system and the Buchberger algorithm for
computing a Gr{\"o}bner basis of a polynomial ideal are
very similar in two respects: they both start with an
arbitrary specification of an algebraic structure
(axioms for an equational theory and a basis for a
polynomial ideal, respectively) which is transformed to
a very special specification of this algebraic
structure (a complete rewrite rule system and a
Gr{\"o}bner basis of the polynomial ideal,
respectively). This special specification allows many
problems concerning the given algebraic structure to be
decided. Moreover, both algorithms achieve their goals
by employing the same basic concepts: formation of
critical pairs and completion. Although the two methods
are obviously related, the exact nature of this
relation remains to be clarified. The author shows how
the Knuth--Bendix procedure and the Buchberger
algorithm can be seen as special cases of a more
general completion procedure.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4210 (Formal logic); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; theory; Decidability; Programming theory;
Knuth--Bendix procedure; Rewrite rule system;
Buchberger algorithm; Gr{\"o}bner basis; Polynomial;
Algebraic structure; Equational theory",
subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Grammars and Other Rewriting
Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving.",
thesaurus = "Decidability; Polynomials; Programming theory;
Rewriting systems; Set theory",
}
@InProceedings{Wissmann:1989:ART,
author = "D. Wissmann",
title = "Applying rewriting techniques to groups with
power-commutation-presentations",
crossref = "Gianni:1989:SAC",
pages = "378--389",
year = "1989",
bibdate = "Thu Sep 26 06:21:35 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The author applies rewriting techniques to certain
types of string-rewriting systems related to
power-commutation-presentations for finitely generated
(f.g.) abelian groups, f.g. nilpotent groups, f.g.
supersolvable groups and f.g. polycyclic groups. The
author develops a modified version of the Knuth--Bendix
completion procedure which transforms such a
string-rewriting system into an equivalent canonical
system of the same type. This completion procedure
terminates on all admissible inputs and works with a
fixed reduction ordering on strings. Since canonical
string-rewriting systems have decidable word problem
this procedure shows that the systems above have
uniformly decidable word problem. In addition, this
result yields a new purely combinatorial proof for the
well-known uniform decidability of the work problem for
the corresponding groups.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Kaiserslautern Univ., West
Germany",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic)",
keywords = "Abelian groups; Combinatorial proof; Decidable word
problem; Knuth--Bendix completion; Nilpotent groups;
Polycyclic groups; Power-commutation-presentations;
Rewriting techniques; String-rewriting systems;
Supersolvable groups; Uniform decidability",
thesaurus = "Decidability; Group theory; Rewriting systems",
}
@InProceedings{Aberer:1990:NFF,
author = "K. Aberer",
title = "Normal forms in function fields",
crossref = "Watanabe:1990:IPI",
pages = "1--7",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p1-aberer/",
abstract = "Considers function fields of functions of one variable
augmented by the binary operation of composition of
functions. It is shown that the straightforward
axiomatization of this concept allows the introduction
of a normal form for expressions denoting elements in
such fields. While the description of this normal form
seems relatively intuitive, it is surprisingly
difficult to prove this fact. The author presents an
algorithm for the normalization of expressions,
formulated in the symbolic computer algebra language
Mathematica. This allows us to effectively decide
compositional identities in such fields. Examples are
given.",
acknowledgement = ack-nhfb,
affiliation = "ETH, Zurich, Switzerland",
classification = "C1100 (Mathematical techniques); C4240 (Programming
and algorithm theory); C7310 (Mathematics)",
keywords = "algorithms; Axiomatization; Binary operation;
Compositional identities; Function fields; languages;
Mathematica; Symbolic computer algebra language",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Functions; Symbol manipulation",
}
@InProceedings{Adamchik:1990:ACI,
author = "V. S. Adamchik and O. I. Marichev",
title = "The algorithm for calculating integrals of
hypergeometric type functions and its realization in
{REDUCE} system",
crossref = "Watanabe:1990:IPI",
pages = "212--224",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p212-adamchik/",
abstract = "The most effective and the simplest algorithm for
analytical integration was made by O. I. Marichev
(1983). This algorithm allows one to calculate definite
and indefinite integrals of the products of elementary
and special functions of hypergeometric type. It
embraces about 70 per cent of integrals which are
included in the world reference-literature. It allows
one to calculate many other integrals too. The article
contains a short description of this algorithm and its
realization in the REDUCE system during the process of
creation of the INTEGRATOR system.",
acknowledgement = ack-nhfb,
affiliation = "Byelorussian Univ., Minsk, Byelorussian SSR, USSR",
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Analytical integration; Convergence;
Hypergeometric type functions; INTEGRATOR system;
languages; Pascal; REDUCE system; Residue number
theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Pascal.",
thesaurus = "Convergence of numerical methods; Integration",
}
@InProceedings{Baaz:1990:SPR,
author = "M. Baaz and A. Leitsch",
title = "A strong problem reduction method based on function
introduction",
crossref = "Watanabe:1990:IPI",
pages = "30--37",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p30-baaz/",
abstract = "Although problem reduction is a very important tool in
mathematical practice, relatively little attention has
been paid to problem reduction in automated theorem
proving. The authors propose problem reduction based on
a splitting rule of the form $C$ implies $C'$, where
$C\approx{}C_1vC_2,C'\approx{}C_1vC_2',C_2'\approx{}C_2$
$(x\mbox{from}f(y_1,\ldots{},y_n)),(x,y_1,\ldots{},y_n)$
is the set of variables both in $C_1$ and $C_2$ and $f$
is a new function symbol up to this point not occurring
in any clause. Finally the authors construct a sequence
of clause sets $C_n$ having resolution proofs
exponential in $n$ only, but application of the new
reduction rule reduces the problem to two problems
linear in $n$. Thus it turns out that the introduction
of (elementary) quantificational rules into clause
logic can strongly influence the structure of proofs
and the performance of theorem provers",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algebra und Diskrete Math., Tech. Univ.
Wien, Austria",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Automated theorem proving; Clause logic;
Problem reduction; Quantificational rules; Theorem
provers; theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic. {\bf I.2.3}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Deduction and Theorem Proving. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Functions; Theorem proving",
xxauthor = "M. Baaz and A. Leitsh",
}
@InProceedings{Belmesk:1990:EME,
author = "M. Belmesk",
title = "An execution model for exploiting and-or parallelism
in logic programs (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "288--288",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p288-belmesk/",
abstract = "Several models have been developed for parallel
execution of logic programming languages. Most of them
involve variations of two basic mechanisms: and
parallelism and or parallelism. The model developed
exploits both the and -and or- parallelism using a
compile-time program-level and clause-level data
dependence analysis to generate an execution graph that
embodies the possible parallel executions. The
execution graph is a directed acyclic graph, containing
one node per atom of the clause body and two nodes for
the head clause. Simple tests on the terms provided at
run-time determine which of the different possible
executions graph is to be used.",
acknowledgement = ack-nhfb,
affiliation = "Lifia-Inst. IMAG, Grenoble, France",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; And-or parallelism; Execution graph;
Execution model; Logic programming languages; Parallel
execution",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf F.1.2} Theory
of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes
of Computation, Parallelism and concurrency.",
thesaurus = "Logic programming; Parallel programming",
}
@InProceedings{Bini:1990:PPC,
author = "D. Bini and V. Pan",
title = "Parallel polynomial computations by recursive
processes",
crossref = "Watanabe:1990:IPI",
pages = "294--294",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p294-bini/",
abstract = "Let $\lg$ stand for $\log_2$, $\lg^{(0)}n=n$,
$\lg^{(h)}n=\lg\lg^{(h-1)}n,h=1,\ldots{},\lg*n,\lg*n=\min(h,\lg^{(h)}n<=1)$.
Given natural $N$, $h$, $1<=h<=\lg*N$, and polynomial
$p(x), p(0) \ne 0$, the authors compute
$r(x)=p(x)^{-1}\bmod{}x^N$ for the cost
$O_A(t,P),t=h\lg{}N, P=(N/h)\lg^{(h)}N$, under the PRAM
arithmetic model, that is, the authors need $O(t)$
steps and $O(P)$ processors (with $t$ and $P$ as
above), provided $DFT(m)$ costs $O_A(\lg{}m,m)$. For
$h=\lg*N$, the cost bounds turn into
$O_A(\lg{}N\lg*N,N/\lg*N)$. The results apply to
various related computations.",
acknowledgement = ack-nhfb,
affiliation = "Pisa Univ., Italy",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; Computational complexity; Parallel
computations; Polynomial computations; PRAM arithmetic
model; Recursive processes",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Parallel algorithms.",
thesaurus = "Computational complexity; Parallel algorithms;
Polynomials; Recursive functions",
}
@InProceedings{Bradford:1990:PBA,
author = "R. Bradford",
title = "A parallelization of the {Buchberger} algorithm",
crossref = "Watanabe:1990:IPI",
pages = "296--296",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p296-bradford/",
abstract = "Describes experiments with a little elementary
parallelism applied to Buchberger's algorithm. This is
in contrast to Ponder (1988) and Vidal (1990) as gains
can be achieved by using the method even on a single
processor.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory)",
keywords = "algorithms; Buchberger's algorithm; experimentation;
languages; Parallelism",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Parallel algorithms; Polynomials; Symbol
manipulation",
}
@InProceedings{Cantone:1990:DFE,
author = "D. Cantone and V. Cutello",
title = "A decidable fragment of the elementary theory of
relations and some applications",
crossref = "Watanabe:1990:IPI",
pages = "24--29",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p24-cantone/",
abstract = "The class of purely universal formulae of the
elementary theory of relations with equality is shown
to have an NP-complete satisfiability problem, under
the assumption that there is an a priori bound on the
length of quantifier prefixes and the arities of
relation variables. In the second part of the paper the
authors discuss possible applications in the field of
theorem proving in set and graph theory and of
consistency checking for queries in relational
databases.",
acknowledgement = ack-nhfb,
affiliation = "Archimedes SRL, Catania, Italy",
classification = "C4210 (Formal logic); C4250 (Database theory)",
keywords = "algorithms; Consistency checking; Decidable;
Elementary theory of relations; Graph theory;
Relational databases; Satisfiability; Theorem proving;
theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computability
theory. {\bf G.2.2} Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Database theory; Decidability; Relational databases;
Theorem proving",
}
@InProceedings{Char:1990:PRS,
author = "B. W. Char",
title = "Progress report on a system for general-purpose
parallel symbolic algebraic computation",
crossref = "Watanabe:1990:IPI",
pages = "96--103",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p96-char/",
abstract = "Discusses on-going work on large-grained parallel
symbolic computation using a system based on Maple and
Linda. The prototype runs on a Sequent Balance. The
approach can be used with most existing algebra/symbol
manipulation systems and provides the potential to
deliver of parallel symbolic computation on a variety
of architectures (e.g. shared memory, hypercubes,
networked workstations). Parallel speedup was achieved
on a variety of algebraic problems, although many
significant improvements in efficiency remain to be
achieved.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Algebraic computation; design; languages;
Large-grained; Linda; Maple; Parallel symbolic
computation; performance; Sequent Balance; Symbol
manipulation systems",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, Linda. {\bf D.1.3} Software,
PROGRAMMING TECHNIQUES, Concurrent Programming.",
thesaurus = "Parallel processing; Symbol manipulation",
}
@InProceedings{Chen:1990:ACF,
author = "Guoting Chen",
title = "An algorithm for computing the formal solutions of
differential systems in the neighborhood of an
irregular singular point",
crossref = "Watanabe:1990:IPI",
pages = "231--235",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p231-chen/",
abstract = "Discusses an algorithm for the computation of the
formal solutions of differential systems in the
neighborhood of an irregular singular point. In the
reduction of the differential systems, the author uses
its Arnold--Wasow's canonical form. He discusses also
an algorithm for the reduction of the differential
system to its Arnold--Wasow's canonical form. Then he
discusses the results of a shearing transformation on
this canonical form and gets the convergence of the
algorithm. This paper consists of a complete study of
the problem of computations of the formal solutions of
differential systems in the neighborhood of a singular
point (regular or irregular).",
acknowledgement = ack-nhfb,
affiliation = "LMC, IMAG INPC CNRS, Grenoble, France",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; Computation; Convergence; Differential
systems; Formal solutions; Irregular singular point;
languages; Shearing transformation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
thesaurus = "Convergence of numerical methods; Differential
equations; Symbol manipulation",
}
@InProceedings{Chen:1990:IAM,
author = "G. Chen and I. Gil",
title = "The implementation of an algorithm in {Macsyma}:
computing the formal solutions of differential systems
in the neighborhood of regular singular point",
crossref = "Watanabe:1990:IPI",
pages = "307--307",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p307-chen/",
abstract = "Discusses the problems arising in the implementation
in Macsyma of a direct algorithm for computing the
formal solutions of differential systems in the
neighborhood of regular singular point. The
differential system to be considered is of the form
$x^h dy/dx=A(x)y$ with $A(x)=A_0+A_1x+\ldots{}$ is an
$n$ by $n$ matrices of formal series.",
acknowledgement = ack-nhfb,
affiliation = "Equipe de Calcul Parallele et Calcul Formel, Grenoble,
France",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Differential systems; Formal solutions;
Macsyma; Regular singular point",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Cherief:1990:AMP,
author = "F. Cherief",
title = "An algebraic model for the parallel interpretation of
equationally defined functions (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "285--285",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p285-cherief/",
abstract = "Summary form only given. Algebraic Languages are well
suited for rapid prototyping. Their operational
semantics is given by means of term rewriting systems.
Here, the author proposes a new approach for the
parallel interpretation of term rewriting systems by
mapping every defined function into parallel processes.
The target language is HAL, a new process algebra where
parallel computations are described as a set of
interconnected processes which communicate through the
explicit sending and receiving of messages. HAL is
derived from LOTOS, FP2 and CCS. In HAL an event is a
set of simultaneous communications. Each communication
within an event transports one term along one
connector. When two connectors are linked, the
corresponding communication unifies the two terms. This
essential feature makes it possible to perform all
computations via communications
(computation=communication). In the case considered
here unification reduces to matching.",
acknowledgement = ack-nhfb,
affiliation = "LIFIA-IMAG, Grenoble, France",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "Algebraic model; algorithms; HAL; Interconnected
processes; languages; Operational semantics; Parallel
interpretation; Prototyping; Simultaneous
communications; Target language; Term rewriting
systems",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Grammars and Other Rewriting Systems.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.3.2} Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
of Programming Languages, Algebraic approaches to
semantics.",
thesaurus = "Formal languages; Parallel languages; Rewriting
systems",
}
@InProceedings{Chou:1990:ARG,
author = "Shang-Ching Chou",
title = "Automated reasoning in geometries using the
characteristic set method and {Gr{\"o}bner} basis
method",
crossref = "Watanabe:1990:IPI",
pages = "255--260",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p255-chou/",
abstract = "Presents an overview of the applications of the
characteristic set method and the Gr{\"o}bner basis
method to automated reasoning in elementary geometries,
differential geometries, and mechanics.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA",
classification = "C4190 (Other numerical methods); C4290 (Other
computer theory); C7310 (Mathematics)",
keywords = "Characteristic set method; Gr{\"o}bner basis method;
Automated reasoning; Elementary geometries;
Differential geometries; algorithms; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems. {\bf
F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND
FORMAL LANGUAGES, Mathematical Logic, Mechanical
theorem proving.",
thesaurus = "Computational geometry; Inference mechanisms; Symbol
manipulation",
}
@InProceedings{Chou:1990:MMG,
author = "Shang-Ching Chou and Xiao-Shan Gao",
title = "Methods for mechanical geometry formula deriving",
crossref = "Watanabe:1990:IPI",
pages = "265--270",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p265-chou/",
abstract = "A precise formulation for the relations among certain
variables under a set of polynomial equations and a set
of polynomial inequations (to exclude certain special
cases which cannot be excluded by the selection of
parameters alone) is given. Several methods are
presented to find such relations. The methods have been
implemented and used to find geometry formulas, to
discover geometry theorems, and to find geometry locus
equations. About 120 non-trivial problems have been
solved using the methods.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA",
classification = "C1120 (Analysis); C7310 (Mathematics)",
keywords = "algorithms; Geometry formulas; Geometry locus
equations; Geometry theorems; Mechanical geometry;
Polynomial equations; Polynomial inequations",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Computational geometry; Polynomials; Symbol
manipulation",
}
@InProceedings{Codognet:1990:EDU,
author = "P. Codognet",
title = "Equations, disequations and unsolvable subsets
(abstract)",
crossref = "Watanabe:1990:IPI",
pages = "289--289",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p289-codognet/",
abstract = "Presents a framework for solving a system of equations
and disequations that allow to determine, upon
unsolvability, the `cause' of the failure, i.e. the
minimal unsolvable subsets of equations and
disequations responsible of it.",
acknowledgement = ack-nhfb,
affiliation = "INRIA, Le Chesnay, France",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Disequations; Equations; Failure;
Unsolvability; Unsolvable subsets",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computational
logic. {\bf I.1.0} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory
of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic, Computability theory.
{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Cooperman:1990:RBC,
author = "G. Cooperman and L. Finkelstein and N. Sarawagi",
title = "A random base change algorithm for permutation
groups",
crossref = "Watanabe:1990:IPI",
pages = "161--168",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p161-cooperman/",
abstract = "A new random base change algorithm is presented for a
permutation group $G$ acting on $n$ points whose worst
case asymptotic running time is better for groups with
a small to moderate size base than any known
deterministic algorithm. To achieve this time bound,
the algorithm requires a \mbox{Rand}om generator
$\mbox{Rand}(G)$ producing a Random element of $G$ with
the uniform distribution and so that each call to
$\mbox{Rand}(G)$ takes time
$O(\log(\bmod{}G\bmod{})n)$. The random base change
algorithm has probability $1-1/\bmod{}G\bmod{}^2$ of
completing in time $ O(\log^2(\bmod{}G\bmod{})n)$ and
outputting a data structure for representing the point
stabilizer sequence relative to the new ordering which
requires $O(\log(\bmod{}g\bmod{})n)$ space and which
can be used to test group membership in time
$O(\log(\bmod{}G\bmod{})n)$. The time to build a data
structure for computing a $\mbox{Rand}(G)$ with the
above properties from a strong generating set for $G$
is dominated by the time to construct the strong
generating set of from the original set of
generators.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; Asymptotic running time; Data structure;
Deterministic algorithm; Permutation groups; Point
stabilizer sequence; Random base change algorithm;
Random generator; Space complexity; Time complexity",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Computations on
discrete structures.",
thesaurus = "Algorithm theory; Computational complexity; Data
structures; Group theory; Random functions",
}
@InProceedings{Doleh:1990:SSI,
author = "Y. Doleh and P. S. Wang",
title = "{SUI}: a system independent user interface for an
integrated scientific computing environment",
crossref = "Watanabe:1990:IPI",
pages = "88--95",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p88-doleh/",
abstract = "The design and implementation of a Scientific User
Interface is presented. Written in the C language, SUI
is a window-menu-mouse oriented graphical user
interface that is designed to provide a modern and
integrated computing environment for scientific work.
SUI can serve multiple client systems in parallel
including symbolic, numeric, graphics and document
formatting systems. SUI achieves hardware and operating
system independence as well as network transparency by
employing the X11 protocols and achieves client system
independence by defining a client-SUI protocol that is
simple and effective. Features of SUI includes input
editing, history, 2-D mathematical expression display,
interactive selection of subexpressions, interactive
display and manipulation of 2-D and 3-D plots of
mathematical functions, cut and paste with syntax
translation, command templates, incremental 2-D display
of mathematical input, and interactive configuration.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C6180 (User interfaces)",
keywords = "2-D display; 3-D plots; C language; Command templates;
Cut and paste; Document formatting; Graphical user
interface; Graphics; History; Input editing; Integrated
computing environment; Integrated scientific computing
environment; Interactive display; languages;
Mathematical expression display; Mathematical
functions; Network transparency; Numeric; Scientific
User Interface; SUI; Symbolic; Syntax translation;
Window-menu-mouse oriented",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C. {\bf I.3.6} Computing
Methodologies, COMPUTER GRAPHICS, Methodology and
Techniques, Interaction techniques. {\bf I.3.1}
Computing Methodologies, COMPUTER GRAPHICS, Hardware
Architecture, Input devices. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Graphical user interfaces; Symbol manipulation",
}
@InProceedings{Fateman:1990:ATD,
author = "R. J. Fateman",
title = "Advances and trends in the design and construction of
algebraic manipulation systems",
crossref = "Watanabe:1990:IPI",
pages = "60--67",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p60-fateman/",
abstract = "Compares and contrast several techniques for the
implementation of components of an algebraic
manipulation system. On one hand is the mathematical
algebraic approach which characterizes (for example)
IBM's Scratchpad II. On the other hand is the more ad
hoc approach which characterizes many other popular
systems (for example, Macsyma, Reduce, Maple, and
Mathematica). While the algebraic approach has
generally positive results, careful examination
suggests that there are significant remaining problems,
especially in the representation and manipulation of
analytical, as opposed to algebraic mathematics. The
author describes some of these problems, and some
general approaches for solutions.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Algebraic manipulation systems; Algebraic mathematics;
design; languages; Macsyma; Maple; Mathematica;
Mathematical algebraic; Reduce; Scratchpad II",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Faure:1990:MS,
author = "C. Faure",
title = "A {Meta} simplifier",
crossref = "Watanabe:1990:IPI",
pages = "290--290",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p290-faure/",
abstract = "The simplification process is a key point in computer
algebra systems. The author presents a model of a
simplifier based on two ideas: homogenizing the
computation over numerical and formal expressions, and
building a simplifier completely reachable by the user.
In order to evaluate numerical expressions, the
simplifier calls functions which compute the result or
raise a runtime type error. Formal expressions are
transformed modulo the properties of the operators. For
homogenizing those two processes, three basic
mechanisms come out: simplification by properties, type
checking, evaluation. Moreover a fourth mechanism using
rewriting rules is necessary to compute nonstandard
transformations needed by the user.",
acknowledgement = ack-nhfb,
affiliation = "INRIA, Centre de Sophia-Antipolis, Valbonne, France",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Computer algebra systems; design; Evaluation;
Homogenization; Meta amplifier; Nonstandard
transformations; Rewriting rules; Run-time error;
Runtime type error; Simplification; Type checking",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions.",
thesaurus = "Algebra; Rewriting systems; Symbol manipulation",
}
@InProceedings{Fee:1990:CCC,
author = "G. J. Fee",
title = "Computation of {Catalan}'s constant using
{Ramanujan}'s formula",
crossref = "Watanabe:1990:IPI",
pages = "157--160",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p157-fee/",
abstract = "The author uses some formulas due to Ramanujan for the
multiple precision computation of Catalan's constant
$C=0.915\ldots{}$. The algorithm has been implemented
in Maple and $C$ has been computed to 20000 decimal
places. The resulting program is very simple yet
efficient. It computes $N$ digits of $C$ in $O(N^2)$
time and $O(N)$ space.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada",
classification = "B0290D (Functional analysis); C4120 (Functional
analysis); C4240 (Programming and algorithm theory)",
keywords = "algorithms; C; Catalan constant; Function evaluation;
languages; Maple; Ramanujan formula",
subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications, C.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Computational complexity; Function evaluation",
}
@InProceedings{Fitch:1990:DSR,
author = "J. Fitch",
title = "A delivery system for {REDUCE}",
crossref = "Watanabe:1990:IPI",
pages = "76--81",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p76-fitch/",
abstract = "A nonLISP delivery system for REDUCE is described and
compared with other implementations of REDUCE for speed
and size, as well as ease of porting. The mechanism for
this delivery system is direct compilation of the
REDUCE sources into ANSI C, which is then compiled and
linked together with some support code for arithmetic
and space administration. The resulting system is
compared with a number of other implementations of true
REDUCE, and is shown to be similar in size, but faster.
The time to port the system is measured in hours. Also
considered are the difficulties in this method of
delivering LISP code, and an assessment of the loss of
flexibility.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C7310 (Mathematics)",
keywords = "algorithms; Delivery system; languages; LISP code;
REDUCE",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications, LISP.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Compilers.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Franova:1990:PIC,
author = "M. Franov{\'a}",
title = "{PRECOMAS}. {An} implementation of constructive
matching methodology",
crossref = "Watanabe:1990:IPI",
pages = "16--23",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p16-franova/",
abstract = "The system PRECOMAS (PRoofs Educed by COnstructive
MATching of Synthesis) implements the Constructive
Matching methodology for automatic constructions of
programs from formal specifications. The author
describes briefly the goal of PRECOMAS, its logical
background and the CM method applied to proving atomic
formulae. She shows how the user of the system is
involved in solving a program synthesis problem. She
shows that this interaction does not concern the
problem of guiding the program synthesis process, this
being solved by CM. The experimental version serves to
confirm that the system is worth being developed.",
acknowledgement = ack-nhfb,
affiliation = "CNRS, Univ. Paris Sud, Orsay, France",
classification = "C4240 (Programming and algorithm theory); C6115
(Programming support)",
keywords = "algorithms; Atomic formulae; Constructive Matching;
design; Formal specifications; PRECOMAS; Program
synthesis; theory",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf D.1.2}
Software, PROGRAMMING TECHNIQUES, Automatic
Programming.",
thesaurus = "Formal logic; Programming environments",
}
@InProceedings{Ganzha:1990:ARS,
author = "V. G. Ganzha and S. V. Meleshko and V. P. Shelest",
title = "Application of {REDUCE} system for analyzing
consistency of systems of {PDE}'s",
crossref = "Watanabe:1990:IPI",
pages = "301--301",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p301-ganzha/",
abstract = "Summary form only given. A consistency analysis of
differential equation systems involves a sequence of
differential-algebraic operations. At present there are
known two methods: the Cartan's and the
Riquier--Janet--Kuranishi (RJK) method which are
equivalent. The implementation of the both of the
methods with the purpose of their practical application
leads to large symbolic computations which often cannot
be performed without a computer.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR",
classification = "C4170 (Differential equations); C4240 (Programming
and algorithm theory); C7310 (Mathematics)",
keywords = "algorithms; Consistency; Consistency analysis;
Differential equation systems; Partial differential
equations; Riquier--Janet--Kuranishi method; RJK
method",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Computational complexity; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Ganzha:1990:LAS,
author = "V. G. Ganzha and M. Yu. Shashkov",
title = "Local approximation study of difference operators by
means of {REDUCE} system",
crossref = "Watanabe:1990:IPI",
pages = "185--192",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p185-ganzha/",
abstract = "Describes new algorithms and programs in the REDUCE
system for the automated study of a local order of the
approximation of difference operator written on
non-orthogonal meshes. The performance of the program
is demonstrated by local approximation of several
difference operators in one and two-dimensional
cases.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C4170
(Differential equations)",
keywords = "algorithms; Approximation; Difference operators;
languages; Local order; Nonorthogonal meshes; Numerical
methods; performance; REDUCE system",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Difference equations; Function approximation",
}
@InProceedings{Gatemann:1990:SSP,
author = "K. Gatemann",
title = "Symbolic solution polynomial equation systems with
symmetry",
crossref = "Watanabe:1990:IPI",
pages = "112--119",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p112-gatemann/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Gatermann:1990:SSP,
author = "K. Gatermann",
title = "Symbolic solution of polynomial equation systems with
symmetry",
crossref = "Watanabe:1990:IPI",
pages = "112--119",
year = "1990",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Systems of polynomial equations often have symmetry.
The Buchberger algorithm which may be used for the
solution ignores this symmetry. It is restricted to
moderate problems unless factorizing polynomials are
found leading to several smaller systems. Therefore two
methods are presented which use the symmetry to find
factorizing polynomials, decompose the ideal and thus
decrease the complexity of the system a lot. In a first
approach projections determine factorizing polynomials
as input for the solution process, if the group
contains reflections with respect to a hyperplane. Two
different ways are described for the symmetric group
$S_m$ and the dihedral group $D_m$. While for $S_m$
subsystems are ignored if they have the same zeros
modulo $G$ as another subsystem, for the dihedral group
$D_m$ polynomials with more than two factors are
generated with the help of the theory of linear
representations and restrictions are used as well.
These decomposition algorithms are independent of the
finally used solution technique. The author uses the
REDUCE package Gr{\"o}bner to solve examples which
illustrate the efficiency of the REDUCE program. A
short introduction to the theory of linear
representations is given. In a second approach problems
of another class are transformed such that more factors
are found during the computation; these transformations
are based on the theory of linear representations.
Examples illustrate these approaches. The range of
solvable problems is enlarged significantly.",
acknowledgement = ack-nhfb,
affiliation = "Konrad Zuse Zentrum fur Inf. Berlin, Germany",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "Symbolic solution; Polynomial equation systems;
Buchberger algorithm; Factorizing polynomials;
Symmetry; Complexity; Symmetric group; Dihedral group;
Linear representations; REDUCE package; Gr{\"o}bner;
Solvable problems",
thesaurus = "Computational complexity; Polynomials; Symbol
manipulation",
}
@InProceedings{Gerdt:1990:CGN,
author = "V. P. Gerdt and A. Yu. Zharkov",
title = "Computer generation of necessary integrability
conditions for polynomial nonlinear evolution systems",
crossref = "Watanabe:1990:IPI",
pages = "250--254",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p250-gerdt/",
abstract = "Uses the symmetry approach to establish an efficient
program in REDUCE for verifying necessary integrability
conditions for polynomial-nonlinear evolution equations
and systems in one-spatial and one-temporal dimensions.
These conditions follow from the existence of higher
infinitesimal symmetries and conservation law
densities. The authors briefly consider the
mathematical background of the symmetry approach to the
problem of integrability. In the description of the
algorithms and their implementation in REDUCE they
present in particular the basic algorithm for reversing
the operator of the total derivative with respect to
the spatial variable. One of the most interesting
applications of the present program is the problem of
classification when the complete list of integrable
equations from a given multiparametric family is
needed. In this case the program generates necessary
integrability conditions in form of a system of
nonlinear algebraic equations in the parameters present
in the initial equations. In spite of their often
complicated structure, there are systems for which the
solution can be found in exact form by applying the
technique of Gr{\"o}bner basis. The authors present
three examples of evolution equations for which this
system can in fact be solved.",
acknowledgement = ack-nhfb,
affiliation = "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Integrability; Polynomial nonlinear evolution systems;
REDUCE; Symmetry approach; Spatial variable; Nonlinear
algebraic equations; Gr{\"o}bner basis; algorithms;
languages; verification",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Gerdt:1990:SAS,
author = "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov",
title = "Solving algebraic systems which arise as necessary
integrability conditions for polynomial-nonlinear
evolution equations",
crossref = "Watanabe:1990:IPI",
pages = "299--299",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p299-gerdt/",
abstract = "The investigation of the problem of integrability of
polynomial-nonlinear evolution equations in particular,
verifying the existence of the higher symmetries and
conservation laws can often be reduced to the problem
of finding the exact solution of a complicated system
of nonlinear algebraic equations. It is remarkable that
these algebraic equations can be not only obtained
completely automatically by computer but also often not
only completely solved by computer, in spite of their
complicated structure and often infinitely many
solutions. The authors demonstrate this fact using the
Gr{\"o}bner basis method and obtain all (infinitely
many) solutions of the systems of algebraic equations
which are equivalent to integrability of three
different multiparametric families of NLEEs: the
seventh order scalar KdV-like equations, the seventh
order MKdV-like equations, and the third order coupled
KdV-like systems.",
acknowledgement = ack-nhfb,
affiliation = "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR",
classification = "C4170 (Differential equations); C4240 (Programming
and algorithm theory); C7310 (Mathematics)",
keywords = "Algebraic systems; Integrability; Polynomial-nonlinear
evolution equations; Nonlinear algebraic equations;
Gr{\"o}bner basis; Algebraic equations; NLEEs;
verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf K.8} Computing
Milieux, PERSONAL COMPUTING, IBM PC.",
thesaurus = "Differential equations; Nonlinear equations;
Polynomials; Symbol manipulation",
}
@InProceedings{Glueck:1990:AMT,
author = "R. Glueck and V. F. Turchin",
title = "Application of metasystem transition to function
inversion and transformation",
crossref = "Watanabe:1990:IPI",
pages = "286--287",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p286-glueck/",
abstract = "The authors prove by construction an application
considered theoretically by Turchin (1972) that
self-application of metacomputation will allow the
automatic construction of inverse algorithms, in
particular the algorithm of binary subtraction from the
algorithm of binary addition. Further, they present
results concerning the algorithmic construction of an
efficient pattern matcher, which leads to the Knuth,
Morris and Pratt algorithm. These results were achieved
with the first working model of a self-applicable
supercompiler system, implementing the concept of
metacomputation.",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Technol. Vienna, Austria",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Algorithmic construction; algorithms; Function
inversion; Inverse algorithms; Metacomputation;
Metasystem transition; Pattern matcher; theory;
Transformation; verification",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors. {\bf F.2.2} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Pattern matching.",
thesaurus = "Algorithm theory; Computation theory; Symbol
manipulation",
}
@InProceedings{Grigoriev:1990:CIT,
author = "D. Yu. Grigoriev",
title = "Complexity of irreducibility testing for a system of
linear ordinary differential equations",
crossref = "Watanabe:1990:IPI",
pages = "225--230",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p225-grigoriev/",
abstract = "Let a system of linear ordinary differential equations
of the first order $Y'=AY$ be given, where $A$ is $n*n$
matrix over a field $F(X)$, assume that the degree
$deg_X(A)<d$ and the size of any coefficient occurring
in $A$ is at most $M$. The system $Y'=AY$ is called
reducible if it is equivalent (over the field $F(X)$)
to a system $Y'_1=A_1Y_1$. An algorithm is described
for testing irreducibility of the system, with an
expression for the time complexity.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci.,
Leningrad, USSR",
classification = "C4170 (Differential equations); C4240 (Programming
and algorithm theory)",
keywords = "algorithms; Irreducibility; Irreducibility testing;
Linear ordinary differential equations; Time
complexity",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Differential equations",
}
@InProceedings{Grigoriev:1990:HTS,
author = "D. Yu. Grigoriev",
title = "How to test in subexponential time whether two points
can be connected by a curve in a semialgebraic set",
crossref = "Watanabe:1990:IPI",
pages = "104--105",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p104-grigoriev/",
abstract = "A subexponential-time algorithm is designed which
finds the number of connected components of a
semialgebraic set given by a quantifier-free formula of
the first-order theory of real closed fields. Moreover,
the algorithm allows for any two points from the
semialgebraic set to test, whether they belong to the
same connected component. Decidability of the mentioned
problems follows from the quantifier elimination method
in the first-order theory of real closed fields.
However, complexity bound of this method is
nonelementary, in particular, one cannot estimate it by
any finite iteration of the exponential function. G.
Collins (1975) has proposed a construction of
cylindrical algebraic decomposition which allows to
solve these problems in exponential time.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. V.A Steklov, Inst. of Acad. of Sci.,
Leningrad, USSR",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "algorithms; Complexity; Connected components;
Cylindrical algebraic decomposition; Decidability; Real
closed fields; Semialgebraic set; Subexponential time;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Computational complexity; Computational geometry;
Decidability; Symbol manipulation",
}
@InProceedings{Hong:1990:IPO,
author = "Hooh Hong",
title = "An improvement of the projection operator in
cylindrical algebraic decomposition",
crossref = "Watanabe:1990:IPI",
pages = "261--264",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p261-hong/",
abstract = "The Cylindrical Algebraic Decomposition (CAD) method
of Collins (1975) decomposes $r$-dimensional Euclidean
space into regions over which a given set of
polynomials have constant signs. An important component
of the CAD method is the projection operation: given a
set A of $r$-variate polynomials, the projection
operation produces a set $P$ of $(r-1)$-variate
polynomials such that a CAD of $r$-dimensional space
for $A$ can be constructed from a CAD of
$(r-1)$-dimensional space for $P$. The author presents
an improvement to the projection operation. By
generalizing a lemma on which the proof of the original
projection operation is based, he is able to find
another projection operation which produces a smaller
number of polynomials.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Ohio State Univ., Columbus, OH,
USA",
classification = "C4190 (Other numerical methods); C4290 (Other
computer theory); C7310 (Mathematics)",
keywords = "algorithms; CAD; Cylindrical Algebraic Decomposition;
Euclidean space; Polynomials; Projection operator",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Computational geometry; Polynomials; Symbol
manipulation",
}
@InProceedings{Kalkbrener:1990:SSB,
author = "M. Kalkbrener",
title = "Solving systems of bivariate algebraic equations by
using primitive polynomial remainder sequences",
crossref = "Watanabe:1990:IPI",
pages = "295--295",
year = "1990",
bibdate = "Sat Apr 25 12:58:10 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p295-kalkbrener/",
abstract = "Let $K$ be a field, $K$ the algebraic closure of $K$
and $f=q_m(x)y^m+ \cdots{} +q_o(x)$ a polynomial in
$K(x,y)$ with $q_m \ne 0$. The polynomial $q_m$ is
called the leading coefficient of $f$, abbreviated
$lc(f)$. The degree of $f$ in $y$ is denoted by
$\deg(f)$. Let $f_1, f_2,\ldots{}, f_k$ be the
primitive polynomial remainder sequence of the
primitive polynomials $f_1$ and $f_2$ in $K(x,y)$,
abbreviated $pprs(f_1,f_2)$. For every $i$ in
$(2,\ldots{},k-1)$ let $c_i$ be the content of the
pseudoremainder of $f_{i-}1$ and
$f_i,l_i:=lc(f_i)^{deg(fi-1)-deg(fi)+1},M_i:=(p\in{}K(x)-K\bmod{}p)$
is irreducible, monic and there exists a $j$ in $N$
such that $p^j$ divides $c_2\ldots{}c_i$ but not
$l_2\ldots{}l_i$,
$(\pi,1,\ldots{},\pi,s_i):=(p\in{}Mi\bmod{}p\in{}M_r
{\rm for } r=2,\ldots{},i-1)$ and
$e_i:=\pi,1\ldots{}pis_i.e_2,\ldots{},e_k-1$ is called
the elimination sequence of $f_1$ and $f_2$,
abbreviated $\mbox{elimseq}(f_1, f_2)$. Theorem 1 Let
$a=(a_1,a_2)$ be an element of $K^2$. $f_1(a)=f_2(a)=0$
iff $f_k(a)=0$ or there exists an $i$ in
$(2,\ldots{},k-1)$ with $(f_i/f_k)(a)=e_i(a)=0$. The
correctness of bsolve is based on this result. By using
this algorithm arbitrary systems of bivariate algebraic
equations can be solved.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "Algebraic closure; Algorithm correctness; algorithms;
Bivariate algebraic equations; Bsolve; Primitive
polynomial remainder sequences",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Algebra; Program verification; Symbol manipulation",
}
@InProceedings{Kaltofen:1990:MRS,
author = "E. Kaltofen and {Lakshman Y. N.} and J.-M. Wiley",
title = "Modular rational sparse multivariate polynomial
interpolation",
crossref = "Watanabe:1990:IPI",
pages = "135--139",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p135-kaltofen/",
abstract = "The problem of interpolating multivariate polynomials
whose coefficient domain is the rational numbers is
considered. The effect of intermediate number growth on
a speeded Ben-Or and Tiwari algorithm (1988) is
studied. Then the newly developed modular algorithm is
presented. The computing times for the speeded Ben-Or
and Tiwari and the modular algorithm are compared, and
it is shown that the modular algorithm is markedly
superior.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Computing times; Modular algorithm;
Multivariate polynomials; Polynomial interpolation;
Rational numbers; Rational sparse polynomials; Symbolic
expressions; Time complexity",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Interpolation; Polynomials",
}
@InProceedings{Kapur:1990:RPG,
author = "D. Kapur and H. K. Wan",
title = "Refutational proofs of geometry theorems via
characteristic set computation",
crossref = "Watanabe:1990:IPI",
pages = "277--284",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p277-kapur/",
abstract = "A refutational approach to geometry theorem proving
using Ritt--Wu's algorithm for computing a
characteristic set is discussed. A geometry problem is
specified as a quantifier-free formula consisting of a
finite set of hypotheses implying a conclusion, where
each hypothesis is either a geometry relation or a
subsidiary condition ruling out degenerate cases, and
the conclusion is another geometry relation. The
conclusion is negated, and each of the hypotheses
(including the subsidiary conditions) and the negated
conclusion is converted to a polynomial equation.
Characteristic set computation is used for checking the
inconsistency of a finite set of polynomial equations
over an algebraic closed field. The method is
contrasted with a related refutational method that used
Buchberger's Gr{\"o}bner basis algorithm for the
inconsistency check.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C1110 (Algebra); C4210 (Formal logic); C7310
(Mathematics)",
keywords = "Algebraic closed field; algorithms; Characteristic set
computation; Geometry theorem proving; Polynomial
equations; Refutational approach; Ritt--Wu's algorithm;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf I.1.4} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Applications.",
thesaurus = "Computational geometry; Polynomials; Theorem proving",
}
@InProceedings{Kohno:1990:RPT,
author = "M. Kohno",
title = "Reduction problems in the theory of differential
equations",
crossref = "Watanabe:1990:IPI",
pages = "244--249",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p244-kohno/",
abstract = "In studying the theory of differential equations, it
seems to be better to treat systems of differential
equations rather than single differential equations,
since the latter are included in a class of the former
and the theory can be made clear through full use of
matrix calculus. Even some specialists of numerical
analysis of differential equations recommend to deal
with systems rather than single equations in practical
calculation of approximate solutions. The objective of
this report is to show an attempt to solve the
reduction problems, illustrating some algorithms to be
applied by algebraic manipulation system.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kumamoto Univ., Japan",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Algebraic manipulation system; algorithms;
Differential equations; Matrix calculus; Reduction
problems; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Kolyada:1990:SSC,
author = "S. V. Kolyada",
title = "Systems for symbolic computations in {Boolean}
algebra",
crossref = "Watanabe:1990:IPI",
pages = "291--291",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p291-kolyada/",
abstract = "Boolean algebra as scientific discipline has a few
features. It is a pure mathematical theory and, on the
other hand, an applied mathematical theory too. Boolean
algebra is applied, for instance, to improve
intelligence of software, to automate integrated
circuit design and theorem proving as it can be used to
model situation analysis and decision making. Computer
algebra system for boolean algebra (APAL-PC) allows one
to write and process logical formulae in usual manner.
The system APAL-PC is developed for IBM PC personal
computers on the basis of the programming language C
and universal formula processing tools implemented at
Glushkov Institute of Cybernetics. The experience of
development of a similar system APAL-ES (implemented in
OS/360 environment) is taken into consideration in
designing of the APAL-PC.",
acknowledgement = ack-nhfb,
affiliation = "Glushkov Inst. of Cybernetics, Kiev, USSR",
classification = "C4210 (Formal logic); C7310 (Mathematics)",
keywords = "APAL-PC; Boolean algebra; design; IBM PC; languages;
Symbolic computations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic.",
thesaurus = "Boolean algebra; IBM computers; Symbol manipulation",
}
@InProceedings{Kuhn:1990:TLC,
author = "N. Kuhn and K. Madlener and F. Otto",
title = "A test for $\lambda$-confluence for certain prefix
rewriting systems with applications to the generalized
word problem",
crossref = "Watanabe:1990:IPI",
pages = "8--15",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p8-kuhn/",
abstract = "Applies rewriting techniques to the generalized word
problem for groups. Let $R$ be a finite
string-rewriting system on an alphabet $\Sigma$ such
that the monoid $M_R$ presented by $(\Sigma:R)$ is a
group, and let $U$ contained in $\Sigma ^+$ be a finite
set. The generalized word problem GWP is defined by
$GWP(w,U)$ iff $w \in (U)$, where $(U)$ is the subgroup
of $M_R$ generated by $U$. With $U$ we associate a
prefix rewriting relation $\mbox{implies}_P$ on
$\Sigma*$ such that $w$ implies/implied by $-{}_P$
$\lambda$ iff $GWP(w,U)$ holds. If $\mbox{implies} _P$
is $\lambda$-confluent then $w\mbox{implies}_P\lambda$
iff $w \in (U)$. Then $\mbox{implies} _P$ yields a
decision procedure for GWP. For groups given through
confluent string-rewriting systems $R$ the authors
develop a necessary and sufficient condition for
$\mbox{implies}_P$ being $\lambda$-confluent and show
that this condition becomes decidable in case of $R$
being length-reducing, in addition.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., Germany",
classification = "C4210 (Formal logic)",
keywords = "$\Lambda$-confluence; algorithms; Decidable;
Generalized word problem; languages; Length-reducing;
Prefix rewriting systems; Rewriting; String-rewriting
system; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems.",
thesaurus = "Decidability; Rewriting systems",
}
@InProceedings{Letichevsky:1990:APA,
author = "A. A. Letichevsky and J. V. Kapitonova",
title = "Algebraic programming in the {APS} system",
crossref = "Watanabe:1990:IPI",
pages = "68--75",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p68-letichevsky/",
abstract = "System APS (algebraic programming system) which was
developed in the Glushkov Institute of Cybernetics of
the Ukrainian Acadamy of Sciences is an instrumental
tool for designing applied systems by means of
algebraic programming. Systems of rewriting rules may
be interpreted in APS by means of different
computational strategies. This approach allows the use
of not only canonical (confluent and noetherian) but
any other systems of equalities, and algebraic programs
may be designed by combining rewriting rules with
different strategies of their applications. Another
peculiarity of APS is the possibility to combine
procedural and algebraic methods of programming.",
acknowledgement = ack-nhfb,
affiliation = "Glushkov Inst. of Cybernetics, Acad. of Sci., Kiev,
Ukrainian SSR, USSR",
classification = "C6115 (Programming support)",
keywords = "Algebraic programming; algorithms; APS system;
Computational strategies; languages; Rewriting rules",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf F.3.2}
Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Semantics of Programming Languages, Algebraic
approaches to semantics.",
thesaurus = "Programming environments; Symbol manipulation",
}
@InProceedings{Liska:1990:FRP,
author = "R. Liska and L. Drska",
title = "{FIDE}: a {REDUCE} package for automation of {FInite}
difference method for solving {pDE}",
crossref = "Watanabe:1990:IPI",
pages = "169--176",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p169-liska/",
abstract = "Discusses the automation of the process of numerical
solving of partial differential equations systems
(PDES) by means of computer algebra. For solving PDES
the finite difference method is applied. The computer
algebra system REDUCE and the numerical programming
language FORTRAN are used in the methodology presented,
its main aim being to speed up the process of preparing
numerical programs for solving PDES. Quite often,
especially for complicated systems, this process is a
tedious and time consuming task. In the process several
stages can be found in which computer algebra can be
used for performing routine analytical calculations,
namely: transformation of differential equations into
different coordinate systems, discretization of
differential equations, analysis of difference schemes,
and generation of numerical programs. The FIDE package
is applied to two physical problems. The first one is
the nonlinear Schr{\"o}dinger equation. The second one
is the Fokker--Planck equation. The numerical programs
have been tested and compared with similar published
calculations.",
acknowledgement = ack-nhfb,
affiliation = "Fac. of Nucl. Sci. and Phys. Eng., Tech. Univ. of
Prague, Czechoslovakia",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; Computer algebra; Coordinate systems;
Discretization; FIDE; FInite difference method;
Fokker--Planck equation; FORTRAN;
Integro-interpolation; languages; Nonlinear
Schr{\"o}dinger equation; Numerical solving; Partial
differential equations; PDE; REDUCE package",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Finite
difference methods. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
Language Classifications, FORTRAN.",
thesaurus = "Difference equations; Partial differential equations;
Software packages; Symbol manipulation",
xxauthor = "R. Liska and L. Drsda",
}
@InProceedings{Liu:1990:AFA,
author = "Zhuo-jun Liu",
title = "An algorithm for finding all isolated zeros of
polynomial systems",
crossref = "Watanabe:1990:IPI",
pages = "300--300",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p300-liu/",
abstract = "Solving algebraic equations is desired for many
problems appearing in applied science. Sometimes,
finding all isolated solutions is enough. Suppose a set
of polynomials (abbr. polset), denoted by PS, to be
given. As a usual convention, by Zero(PS) and
ISZero(PS), we respectively denote the zeros and
isolated zeros defined by PS. Recently, the homotopy
continuation method was widely used to find all
isolated zeros of polset. However, that method is not
good enough to find the isolated zeros of any polset.
Here, based on Wu's method, the author introduces a new
algorithm to solve this problem.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Algorithm; algorithms; Isolated zeros; Polset;
Polynomial systems; Polynomials; Wu's method",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Poles and zeros; Polynomials; Symbol manipulation",
}
@InProceedings{Llovet:1990:MAC,
author = "J. Llovet and J. R. Sendra",
title = "A modular approach to the computation of the number of
real roots",
crossref = "Watanabe:1990:IPI",
pages = "298--298",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p298-llovet/",
abstract = "The problem of computing the number of distinct real
roots of a real polynomial can be solved analyzing the
sign variations of the sequence of principal minors of
the Hankel matrix associated with the given polynomial.
In this paper, the authors present a modular algorithm
to achieve this goal. In this approach, the principal
minors sequence of the associated Hankel matrix is
computed using modular methods. The computing time
analysis shows that the maximum computing time function
of the modular algorithm is $O(n^5l^2)$, where $n$ is
the degree of the polynomial and $l$ its length.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Alcala Univ., Madrid, Spain",
classification = "C1110 (Algebra); C4240 (Programming and algorithm
theory); C7310 (Mathematics)",
keywords = "algorithms; Associated Hankel matrix; Computing time;
Distinct real roots; Hankel matrix; Modular algorithm;
Principal minors; Real polynomial",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Computational complexity; Polynomials; Symbol
manipulation",
}
@InProceedings{Manocha:1990:RCP,
author = "D. Manocha",
title = "Regular curves and proper parametrizations",
crossref = "Watanabe:1990:IPI",
pages = "271--276",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p271-manocha/",
abstract = "Presents an algorithm for determining whether a given
rational parametric curve, defined as vector valued
function over a finite domain, has a regular
parametrization. A curve has a regular parametrization
if it has no cusps in its defining interval. It has
been known that the vanishing of the derivative vector
is a necessary condition for the existence of cusps.
The author shows that if a curve is properly
parametrized, then the vanishing of the derivative
vector is a necessary and sufficient condition for the
existence of cusps. If a curve has no cusps in its
defining interval, its proper parametrization is a
regular parametrization. He presents a simple algorithm
to compute the proper parametrization of a polynomial
parametric curve which is used to analyze for cusps and
later on reduce the problem of detecting cusps in a
rational curve to that of a polynomial curve.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "algorithms; Cusps; Polynomial curve; Polynomial
parametric curve; Proper parametrization; Rational
parametric curve; Vector valued function",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.3.5} Computing
Methodologies, COMPUTER GRAPHICS, Computational
Geometry and Object Modeling, Geometric algorithms,
languages, and systems.",
thesaurus = "Computational geometry; Symbol manipulation",
}
@InProceedings{Mazurik:1990:SCS,
author = "S. I. Mazurik and E. V. Vorozhtsov",
title = "Symbolic-numerical computations in the stability
analyses of difference schemes",
crossref = "Watanabe:1990:IPI",
pages = "177--184",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p177-mazurik/",
abstract = "The authors propose a number of symbolic-numeric
approaches to the computer-aided construction of the
stability domains of difference schemes approximating
the partial differential equations with constant
coefficients. They use the Fourier method, the
algebraic methods of the Routh--Hurwitz and Schur--Cohn
theories for the localization of the polynomial zeros,
the methods of optimization theory as well as the means
of computer algebra, digital image processing and
computer graphics. The efficiency of the approaches is
demonstrated at the practical examples of difference
schemes for fluid dynamics problems.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, USSR",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algebraic methods; algorithms; Computer algebra;
Computer graphics; Difference schemes; Digital image
processing; Fluid dynamics problems; Fourier method;
Optimization theory; Partial differential equations;
Polynomial zeros; Routh--Hurwitz; Schur--Cohn theories;
Stability analyses; Symbolic-numeric approaches;
theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.8}
Mathematics of Computing, NUMERICAL ANALYSIS, Partial
Differential Equations, Finite difference methods. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Convergence of numerical methods; Difference
equations; Mathematics computing; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Mishra:1990:ARA,
author = "B. Mishra and P. Pedersen",
title = "Arithmetic with real algebraic numbers is in {NC}",
crossref = "Watanabe:1990:IPI",
pages = "120--126",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p120-mishra/",
abstract = "The authors describe NC algorithms for doing exact
arithmetic with real algebraic numbers in the
sign-coded representation introduced by Coste and Roy
(1988). They present polynomial sized circuits of depth
$O(\log^3N)$ for the monadic operations
$-\alpha,1/\alpha$, as well as $\alpha +r$,
$\alpha\cdot{}r$, and $\mbox{sgn} (\alpha -r)$, where
$r$ is rational and $\alpha$ is real algebraic. They
also present polynomial sized circuits of depth
$O(\log^7N)$ for the dyadic operations $\alpha+\beta$,
$\alpha\cdot\beta$, and $\mbox{sgn}(\alpha-\beta)$,
where $\alpha$ and $\beta$ are both real algebraic. The
algorithms employ a strengthened form of the NC
polynomial-consistency algorithm of Ben-Or, Kozen, and
Reif (1986).",
acknowledgement = ack-nhfb,
affiliation = "New York Univ., NY, USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "algorithms; Dyadic operations; Exact arithmetic; Fast
parallel algorithms; Monadic operations; NC algorithms;
NC polynomial-consistency algorithm; Polynomial sized
circuits; Real algebraic numbers; Sign-coded
representation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General.",
thesaurus = "Parallel algorithms; Polynomials",
}
@InProceedings{Murray:1990:RIT,
author = "N. V. Murray and E. Rosenthal",
title = "Reexamining intractability of tableau methods",
crossref = "Watanabe:1990:IPI",
pages = "52--59",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p52-murray/",
abstract = "Considers the class of formulas on which the method of
analytic tableaux was first shown to be intractable,
and shows that the applications of the ordinary
distributive law tableau methods admit linear time
proofs for this class. The authors introduce a new
class of formulas that are intractable for tableaux
(even with the distributive law), and demonstrate that
path dissolution admits linear proofs of these
formulas. Modifications of the tableau method are
described that would render this class tractable. Since
dissolution is linear on this class, these results
demonstrate that dissolution cannot be $p$-simulated by
the method of analytic tableau.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., State Univ. of New York,
Albany, NY, USA",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Analytic tableaux; Dissolution; Linear
proofs; Linear time proofs; Path dissolution; Tableau
methods; theory; verification",
subject = "{\bf G.2.2} Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory, Graph algorithms. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.2.3} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Deduction and Theorem Proving,
Deduction.",
thesaurus = "Formal logic",
}
@InProceedings{Noda:1990:SHI,
author = "Matu-Tarow T. Noda and E. Miyahiro",
title = "On the symbolic\slash numeric hybrid integration",
crossref = "Watanabe:1990:IPI",
pages = "304--304",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p304-noda/",
abstract = "Integrating a given function is one of the most
important areas in the mathematical computing. Both
numerical and symbolic integration methods have been
developed and widely used. Numerical methods, however,
have some defects such as (1) formal integrals are not
obtained, (2) wrong answers are given for pathological
integrand and (3) error estimates depend on types of
integrands. Symbolic methods have also difficulties on
(1) restrictions on an integrand and (2) uses of
wasteful big-number computation. To avoid difficulties,
some attempts in which both methods are combined have
been proposed, called hybrid methods. The authors
propose new hybrid integration method for a rational
function, (say $q/r$, $q$ and $r$ are polynomials) with
floating point but real coefficients.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Ehime Univ., Matsuyama, Japan",
classification = "C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Floating point; Hybrid integration;
Numerical; Numerical integration; Rational function;
Symbolic integration",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Nonalgebraic algorithms. {\bf G.1.4}
Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation.",
thesaurus = "Integration; Numerical methods; Symbol manipulation",
}
@InProceedings{Norman:1990:CBI,
author = "A. C. Norman",
title = "A critical-pair\slash completion based integration
algorithm",
crossref = "Watanabe:1990:IPI",
pages = "201--205",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p201-norman/",
abstract = "The presentation re-expresses the 1976 Risch method in
terms of rewrite rules, and thus exposes the major
problem it suffers from as a manifestation of the fact
that in certain circumstances the set of rewrites
generated is not confluent. This difficulty is then
attacked using a critical-pair/completion (CPC)
approach. For very many integrands it is then easy to
see that the initial set of rewrites used in the early
implementations do not need any extension, and this
fact explains the high level of competence of the
programs involved despite their shaky theoretical
foundations. For a further large collection of problems
even a simple CPC scheme converges rapidly; when the
techniques are applied to the REDUCE integration test
suite in all applicable cases a short computation
succeeds in completing the set of rewrites and hence
gives a secure basis for testing for integrability.
This paper describes the implementation of the CPC
process and discusses current limitations to and
possible future extended applications of it.",
acknowledgement = ack-nhfb,
affiliation = "Trinity Coll., Cambridge, UK",
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Convergence; CPC scheme;
Critical-pair/completion based integration algorithm;
experimentation; Integrability; REDUCE integration test
suite; Rewrite rules; Transcendental functions",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE. {\bf F.2.2} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Nonnumerical Algorithms and Problems, Computations on
discrete structures.",
thesaurus = "Convergence of numerical methods; Integration;
Rewriting systems",
}
@InProceedings{Okubo:1990:GTO,
author = "K. Okubo",
title = "Global theory of ordinary differential equations and
formula manipulation",
crossref = "Watanabe:1990:IPI",
pages = "193--200",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p193-okubo/",
abstract = "The author discusses the fundamental domain of the
monodromy group for hypergeometric equations. One can
classify these triangles formed by circular arcs with
the sum of inner angles greater, equal or less than
$\pi$. The domains have been classified into three
classes, those on the unit sphere, those on the open
complex plane and those on the unit disk. Any
algebraically integrable solution of a hypergeometric
equation is expressed by invariants of the groups of
five platonic solids or dipyramids. One can express the
key in terms of non-Euclidean expression by the sum of
inner angles of triangles. The authors rephrases this
into quadratic invariant of definite, degenerate or
indefinite sign. The quadratic invariants may be of
help as the key to the classification in higher
dimensions.",
acknowledgement = ack-nhfb,
affiliation = "Univ. of Electro-Commun., Chofu, Tokyo, Japan",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
keywords = "Algebraically integrable solution; Circular arcs;
Dipyramids; Five platonic solids; Formula manipulation;
Gauss equation; Hypergeometric equations; Inner angles;
Monodromy group; Open complex plane; Ordinary
differential equations; Quadratic invariant; Unit disk;
Unit sphere",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Padget:1990:UPS,
author = "J. Padget and A. Barnes",
title = "Univariate power series expansions in {Reduce}",
crossref = "Watanabe:1990:IPI",
pages = "82--87",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p82-padget/",
abstract = "Describes the development of a formal power series
expansion package for Reduce which takes advantage of
Reduce's domain mechanism to make for a seamless
integration of series values with the rest of the
Reduce system. Consequently, series values may be
manipulated with the same algebraic operators as other
algebraic objects. To create the illusion of infinite
power series a simulated lazy-evaluation mechanism has
been used. The paper reports experience of using the
Reduce domain mechanism and documents the algorithms
and data structures that can be used to implement and
to represent power series.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C7310 (Mathematics)",
keywords = "Algebraic operators; Algorithms; algorithms; Data
structures; Domain mechanism; languages;
Lazy-evaluation mechanism; Power series expansions;
Reduce; Series values",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
thesaurus = "Series [mathematics]; Symbol manipulation",
}
@InProceedings{Scott:1990:SAM,
author = "T. C. Scott and G. J. Fee",
title = "Some applications of {Maple} symbolic computation to
scientific and engineering problems",
crossref = "Watanabe:1990:IPI",
pages = "302--303",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p302-scott/",
abstract = "Presents a survey of use of the Maple symbolic
computation system at the University of Waterloo. This
represents only a sample of what has and can be done
with symbolic computation. However, these examples have
been chosen from a broad spectrum of areas which
includes: Quantum theory, general and special
relativity, audio engineering and asbestos fiber
analysis (an application of fluid and
magneto-dynamics). They represent new avenues of
research and illustrate the large untapped potential of
symbolic computation.",
acknowledgement = ack-nhfb,
affiliation = "Maple Symbolic Comput. Group, Waterloo Univ., Ont.,
Canada",
classification = "C7300 (Natural sciences); C7400 (Engineering)",
keywords = "Asbestos fiber analysis; Audio engineering; design;
General relativity; Maple; Quantum theory; Special
relativity; Symbolic computation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple.",
thesaurus = "Engineering computing; Natural sciences computing;
Symbol manipulation",
}
@InProceedings{Shirayanagi:1990:IPF,
author = "K. Shirayanagi",
title = "On the isomorphism problem for finite-dimensional
binomial algebras",
crossref = "Watanabe:1990:IPI",
pages = "106--111",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p106-shirayanagi/",
abstract = "Binomial algebras are finitely presented algebras
defined by monomials or binomials. Given two binomial
algebras, one important problem is to decide whether or
not they are isomorphic as algebras. The author studies
an algorithm for solving this problem, when both
algebras are finite-dimensional over a field. In
particular, when they are monomial algebras (i.e
binomial algebras defined by monomials only), the
problem has already been completely solved by the
presentation uniqueness. The author provides some
necessary conditions in terms of partially ordered sets
for two certain binomial algebras to be isomorphic. In
other words, invariants of the binomial algebras are
presented. These conditions together serve as an
effective procedure for solving the isomorphism
problem.",
acknowledgement = ack-nhfb,
affiliation = "NTT Software Lab., Tokyo, Japan",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "algorithms; Binomial algebras; Binomials; Finitely
presented algebras; Monomials; Partially ordered sets;
Presentation uniqueness; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Algebra; Set theory; Symbol manipulation",
}
@InProceedings{Smedley:1990:DAD,
author = "T. J. Smedley",
title = "Detecting algebraic dependencies between unnested
radicals (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "292--293",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p292-smedley/",
abstract = "There are a number of known methods for checking for
dependencies between unnested radicals. However, these
methods usually have one or both of the following
disadvantages: 1. They rely on integer factorisation,
or 2. They generate an algebraic extension field of
degree higher than is necessary to express the input.
The first disadvantage is not generally too important,
as the integers involved are usually quite small and
can be easily factored. However, the second
disadvantage can cause real problems. Since the degree
of the algebraic extension has a large influence on the
cost of algorithms involving algebraic numbers, the
author wants a method which detects dependencies but
keeps the degree of the extension field as low as
possible.",
acknowledgement = ack-nhfb,
affiliation = "Delaware Univ., Newark, DE, USA",
classification = "C4240 (Programming and algorithm theory)",
keywords = "Algebraic dependencies; Algebraic extension; Algebraic
numbers; Unnested radicals; verification",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Representations (general and
polynomial). {\bf I.1.1} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Symbol manipulation",
}
@InProceedings{Stachniak:1990:RPS,
author = "Z. Stachniak",
title = "Resolution proof systems with weak transformation
rules",
crossref = "Watanabe:1990:IPI",
pages = "38--43",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p38-stachniak/",
abstract = "In previous papers the author defined and explored a
formal methodological framework on the basis of which
resolution proof systems for strongly-finite logics can
be introduced and studied. In the present paper he
extends this approach to a wider class of so-called
resolution logics.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., York Univ., North York, Ont.,
Canada",
classification = "C4210 (Formal logic)",
keywords = "algorithms; Formal methodological framework;
Resolution logics; Resolution proof systems;
Strongly-finite logics; theory; verification; Weak
transformation rules",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Computational
logic. {\bf I.2.3} Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Deduction and Theorem Proving, Deduction.
{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic.",
thesaurus = "Formal logic",
}
@InProceedings{Takayama:1990:ACI,
author = "N. Takayama",
title = "An algorithm of constructing the integral of a module
--- an infinite dimensional analog of {Gr{\"o}bner}
basis",
crossref = "Watanabe:1990:IPI",
pages = "206--211",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p206-takayama/",
abstract = "Let $U$ be a left ideal of Weyl algebra:
$A_n=K(x_1,\ldots{},x_n,\delta_1,\ldots{},\delta_n)$.
Put $M=A_n/U$. M is a left $A_n$ module. The paper
presents an explicit construction of the left $A_{n-1}$
module by introducing an analog of Gr{\"o}bner basis of
a submodule of a kind of infinite dimensional free
module. The author gives a complete algorithm. The
algorithm is an answer to the research problem of the
paper (AZ).",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kobe Univ., Japan",
classification = "B0290R (Integral equations); C4180 (Integral
equations)",
keywords = "algorithms; Integral; Gr{\"o}bner basis; Left ideal;
Weyl algebra",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Integral equations; Symbol manipulation",
}
@InProceedings{Takayama:1990:GBI,
author = "N. Takayama",
title = "{Gr{\"o}bner} basis, integration and transcendental
functions",
crossref = "Watanabe:1990:IPI",
pages = "152--156",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p152-takayama/",
abstract = "It is well known that Gr{\"o}bner basis is a
fundamental and powerful tool to solve problems of
polynomials. One can use the Gr{\"o}bner basis of Weyl
algebra to solve the problems of integration and
formula verification of transcendental functions. The
paper surveys the theory of the Gr{\"o}bner basis of
the ring of differential operators and its applications
to the following problems: computation of differential
equations for a definite integral with parameters; zero
recognition of an expression that contains special
functions or binomial coefficients etc., i.e. formula
verification by a computer; derivations of some of
special function identities; solving a definite
integral or obtaining an asymptotic expansion of a
definite integral with parameters.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kobe Univ., Japan",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "Transcendental functions; Gr{\"o}bner basis;
Polynomials; Weyl algebra; Integration; Formula
verification; Differential operators; Differential
equations; Definite integral; Zero recognition;
Binomial coefficients; Special function identities;
Asymptotic expansion; algorithms; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Differential equations; Function approximation;
Integration; Polynomials; Symbol manipulation",
}
@InProceedings{Tan:1990:OTS,
author = "H. Q. Tan and X. Dong",
title = "Optimization techniques for symbolic equation solver
in engineering applications",
crossref = "Watanabe:1990:IPI",
pages = "305--305",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p305-tan/",
abstract = "In MACSYMA, there are procedures for solving systems
of equations, such as solve and linsolve. Because the
systems of equations we are dealing with are mostly
sparse, the application of Gaussian elimination which
is used in linsolve produces results that are usually
lengthy and inefficient. The authors have implemented a
new derivation procedure to solve the problem of
expression growth and increase the computational
efficiency. The underlying concept is the
identification of the smallest full subsystems
contained within the original and then subsequent
remaining systems, labeling common terms by
intermediate variables. Gaussian elimination is
employed to solve these subsystems independently and
sequentially instead of the complete system.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Akron Univ., OH, USA",
classification = "C7310 (Mathematics)",
keywords = "algorithms; Derivation procedure; Gaussian
elimination; Symbolic equation solver",
subject = "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Tao:1990:SAM,
author = "Qingsheng Tao",
title = "Symbolic and algebraic manipulation for formulae of
interpolation and quadrature",
crossref = "Watanabe:1990:IPI",
pages = "306--306",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p306-tao/",
abstract = "Computer algebra has been used for construction and
analysis of algorithms of numerical computation. In the
paper, an attempt has been made to derive the formulae
of interpolation and quadrature with Computer Algebra.
In REDUCE language, the formula manipulation system for
interpolation INTEP and for quadrature QUADRAT are
developed. The two formula manipulators can be used to
derive Lagrange, Hermite and Birkhoff interpolation
formulae with any degree of polynomials and to derive
Newton--Cotes quadrature formulae and the quadrature
formulae involving the derivatives of the integrand.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech., Zhejiang Univ., Hangzhou, China",
classification = "C4130 (Interpolation and function approximation);
C4160 (Numerical integration and differentiation)",
keywords = "Algebraic manipulation; algorithms; Birkhoff; Computer
Algebra; Formula manipulators; Hermite; INTEP;
Interpolation; Interpolation formulae; Lagrange;
languages; Newton--Cotes quadrature formulae; QUADRAT;
Quadrature; Symbolic manipulation",
subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL
ANALYSIS, Quadrature and Numerical Differentiation.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
thesaurus = "Integration; Interpolation; Symbol manipulation",
}
@InProceedings{Ulmer:1990:LSH,
author = "F. Ulmer and J. Calmet",
title = "On {Liouvillian} solutions of homogeneous linear
differential equations",
crossref = "Watanabe:1990:IPI",
pages = "236--243",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p236-ulmer/",
abstract = "Deals with the problem of finding Liouvillian
solutions of an $n$-th order homogeneous linear
differential equation $L(y)=0$ with coefficients in a
differential field $k$ whose field of constants is $C$.
For second order linear differential equations such an
algorithm has been given by J. Kovacic (1986) and
implemented. A general decision procedure for finding
Liouvillian solutions of $n$-th order equations has
been given by M. F. Singer (1981), but the resulting
algorithm, although constructive, is not in
implementable form even for second order equations. The
algorithm uses the fact that, if $L(y)=0$ has a
Liouvillian solution, then, $L(y)=0$ has a solution $z$
such that $u=z'/z$ is algebraic over $k$, which means
that $L(y)$ has a solution $z$ of the form
$e^{\int{}u}$, where $u$ is algebraic over $k$. Since
the logarithmic derivative $u=z'/z$ of a solution $z$
is a solution of the Riccati equation $R(y)=0$
associated to $L(y)=0$, the problem thus reduces to
find an algebraic solution $u$ of $R(y)=0$. This task
is now split into two parts: (i) to find the set DEG(n)
of possible degrees $N$ for the minimal polynomial
$P(x)=0$ of $u$ over $k$, (ii) to compute, for each
possible degree of $P(x)$, the possible coefficients of
$P(x)$. If we donate $c(ii)$ the complexity of the
second step and Hash DEG($n$) the size of the set
DEG($n$), one sees that the complexity of the whole
procedure is of the form $c(ii)^{Hash DEG(n)}$ and thus
exponential in Hash DEG($n$). This shows that the only
way to make the procedure effective is to get sharp
bounds on the size of the set DEG($n$), which is the
scope of this paper.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algebraic solution; algorithms; Complexity;
Homogeneous; Linear differential equations; Liouvillian
solutions; Sharp bounds",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Computational complexity; Differential equations;
Symbol manipulation",
}
@InProceedings{vonzurGathen:1990:PFF,
author = "J. {von zur Gathen}",
title = "Polynomials over finite fields with large images",
crossref = "Watanabe:1990:IPI",
pages = "140--144",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p140-von_zur_gathen/",
abstract = "A polynomial $f$ in $F_q(x)$, over a finite field
$F_q$ with $q$ elements, is $\rho$-large if its image
in $F_q$ contains at least $q-\rho$ elements. The
article presents an efficient probabilistic test for
this property, using expected time polynomial in
$\deg{}f$, $\log{}q$, and $\rho$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Toronto Univ., Ont., Canada",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Expected time polynomial; Finite fields;
Large images; Polynomial; Probabilistic test; Time
complexity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.1.2} Theory of Computation, COMPUTATION BY
ABSTRACT DEVICES, Modes of Computation, Probabilistic
computation.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Wang:1990:PUP,
author = "P. S. Wang",
title = "Parallel univariate polynomial factorization on
shared-memory multiprocessors",
crossref = "Watanabe:1990:IPI",
pages = "145--151",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p145-wang/",
abstract = "Using parallelism afforded by shared-memory
multiprocessors to speed up systems for polynomial
factorization is discussed. The approach is to take the
fastest known factoring algorithm for practical
purposes and parallelize key parts of it. The
univariate factoring algorithm consists of two major
tasks (a) factoring modulo small integer primes and (b)
EEZ lifting and recovery of true factors. A C coded
system PFACTOR that implements (a) in parallel is
described in detail. PFACTOR is a stand-alone parallel
factorizer that can take input from a file, a pipe or a
socket connection over a network. It can also be used
interactively as a UNIX command. PFACTOR consists of
parallel selection of primes, automatic balancing of
work, parallel Berlekamp algorithm, and parallel
reconciliation of degrees of factors modulo different
primes. Actual timings on the Encore Multimax show the
effectiveness of the approach.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; C coded system; EEZ lifting; Encore
Multimax; Modulo small integer primes; Parallel
Berlekamp algorithm; Parallel reconciliation;
Parallelism; performance; PFACTOR; Polynomial
factorization; Shared-memory multiprocessors; Time
complexity; Univariate factoring algorithm; UNIX
command",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Modes of Computation, Parallelism and
concurrency.",
thesaurus = "Computational complexity; Parallel algorithms;
Polynomials",
}
@InProceedings{Yamasaki:1990:DLP,
author = "S. Yamasaki",
title = "Dataflow for logic program as substitution
manipulator",
crossref = "Watanabe:1990:IPI",
pages = "44--51",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p44-yamasaki/",
abstract = "Shows a method of constructing a dataflow, which
denotes the deductions of a logic program, by means of
a sequence domain based on equivalence classes of
substitutions. The dataflow involves fair merge
functions to represent unions of atom subsets over a
sequence domain, as well as functions as manipulations
of unifiers for the deductions of clauses. A continuous
functional is associated with the dataflow on condition
that the dataflow completely and soundly denotes the
atom generation in terms of equivalent substitutions
sets. Its least fixpoint is interpreted as denoting the
whole atom generation based on manipulations of
equivalent substitutions sets.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Inf. Technol., Okayama Univ., Japan",
classification = "C4240 (Programming and algorithm theory)",
keywords = "algorithms; Continuous functional; Dataflow;
Equivalence classes; Fair merge functions; Logic
program; Sequence domain; Substitution manipulator;
theory",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic, Logic and
constraint programming. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Computational logic.",
thesaurus = "Logic programming; Programming theory",
}
@InProceedings{Yokoyama:1990:DSP,
author = "K. Yokoyama and M. Noro and T. Takeshima",
title = "On determining the solvability of polynomials",
crossref = "Watanabe:1990:IPI",
pages = "127--134",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p127-yokoyama/",
abstract = "Landau and Miller (1985) presented a method for
determining the solvability of a monic irreducible
polynomial over integers in polynomial time. In their
method, a series of polynomials is constructed so that
the original problem is reduced to determining the
solvability of new polynomials. The authors present an
improved method for finding such a series of
polynomials efficiently. More precisely, they introduce
a new notion on a series of blocks in the set of all
roots of the original polynomial under the action of
its Galois group, and then present an efficient method
for finding such a series of blocks by modifying Landau
and Miller's method for finding minimal imprimitive
blocks.",
acknowledgement = ack-nhfb,
affiliation = "IIAS-SIS, Fujitsu Ltd., Numazu, Japan",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Galois group; Minimal imprimitive blocks;
Monic irreducible polynomial; Polynomials; Problem
complexity; Solvability; Time complexity",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS,
Graph Theory, Graph algorithms.",
thesaurus = "Computability; Computational complexity; Polynomials",
}
@InProceedings{Yokoyama:1990:FMP,
author = "Kazuhiro Yokoyama and Masayuki Noro and Taku
Takeshima",
title = "On factoring multi-variate polynomials over
algebraically closed fields (abstract)",
crossref = "Watanabe:1990:IPI",
pages = "297--297",
year = "1990",
bibdate = "Thu Mar 12 08:36:58 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p297-yokoyama/",
abstract = "For a problem how to find an extension field over
which we can obtain an absolutely irreducible factor,
Kaltofen gave an answer in 1983 and explicitly in 1985
by employing analytic argument for showing his answer,
and Chistov and Grigor'ev also gave the same answer in
1983 by algebraic arguments. Here the authors give an
alternative proof for Kaltofen's answer in algebraic
way, independently to Chistov and Grigor'ev, and by the
benefit of new way, they also give several extensions
of his answer and properties of absolutely irreducible
factors. They also discuss usage of their results for
actual computation of absolutely irreducible factors.
They restrict themselves to bi-variate polynomials with
integer (or rational) coefficients.",
acknowledgement = ack-nhfb,
affiliation = "IIAS-SIS, Fujitsu Ltd., Japan",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Actual computation; Algebraic arguments; Algebraically
closed fields; Bi-variate polynomials; Irreducible
factor; Multi-variate polynomials; theory;
verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Abramov:1991:FAS,
author = "S. A. Abramov and K. Yu. Kvashenko",
title = "Fast algorithms to search for the rational solutions
of linear differential equations with polynomial
coefficients",
crossref = "Watt:1991:IPI",
pages = "267--270",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p267-abramov/",
abstract = "The paper is concerned with some ways for an
improvement with regard to solving the linear ordinary
differential equations of the form
$\sum_0^na_i(x)y^{(i)}(x)=b(x)$ where
$a_0(x),\ldots{},a_n(x),b(x)$ in $K(x)$ ($K$ is the
constant field), $a_n(x) \neq 0$. The authors consider
one after another of the problems of finding all the
polynomial and rational solutions of equation. They
consider the simplest approach and then its
improvement.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, USSR",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Linear differential equations; Polynomial
coefficients; Rational solutions; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Linear differential equations; Symbol manipulation",
}
@InProceedings{Amirkhanov:1991:BOV,
author = "I. V. Amirkhanov and E. P. Zhidkov and I. E.
Zhidkova",
title = "The betatron oscillations in the vicinity of nonlinear
resonance in cyclic accelerator investigation",
crossref = "Watt:1991:IPI",
pages = "452--453",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p452-amirkhanov/",
abstract = "Motion of charged particle in given fields in a cyclic
accelerator has been investigated. The nonlinear
problem of finding stable trajectories in the vicinity
of a resonance has been solved. The equations of motion
for charged particle deviation from ideal orbit or the
betatron oscillations equations (which are lateral to
the closed orbit oscillations with the frequencies
$\nu_x, \nu_z$) are studied using REDUCE-3.2. The study
of the equations formed by computer is applied to two
types of accelerators: (1) the averaged equations in
the vicinity of 19 resonances for a weakly focusing
accelerator (WFA) and (2) those in the vicinity of 24
resonances-for a strong focusing accelerator (SFA).",
acknowledgement = ack-nhfb,
affiliation = "JINR, Moscow, USSR",
classification = "A2920F (Betatrons); B7410 (Accelerators); C7320
(Physics and Chemistry)",
keywords = "algorithms; Betatron oscillations; Charged particle
deviation; Cyclic accelerator; Nonlinear resonance;
REDUCE-3.2; Strong focusing accelerator; Weakly
focusing accelerator",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics.",
thesaurus = "Betatrons; Physics computing",
}
@InProceedings{Apel:1991:FAA,
author = "Joachim Apel and Uwe Klaus",
title = "{FELIX}: an assistant for algebraists",
crossref = "Watt:1991:IPI",
pages = "382--389",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p382-apel/",
abstract = "FELIX is a special computer algebra system designed
for calculations with elements of algebraic structures
as well as with substructures and homomorphisms. It
covers both commutative polynomial rings and modules
and non-commutative structures. Buchberger's algorithm
for the computation of Gr{\"o}bner bases is fundamental
for many of the included operations. The articles
contains a short description of the system FELIX and
illustrates the sensitivity of Buchberger's algorithm
against changes of selection strategies.",
acknowledgement = ack-nhfb,
affiliation = "Leipzig Univ., Germany",
classification = "C7310 (Mathematics)",
keywords = "algorithms; design; FELIX; Computer algebra system;
Algebraic structures; Substructures; Homomorphisms;
Commutative polynomial rings; Modules; Non-commutative
structures; Buchberger's algorithm; Gr{\"o}bner bases",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Astrelin:1991:BDI,
author = "A. V. Astrelin",
title = "A bound of degree of irreducible eigenpolynomial of
some differential operator",
crossref = "Watt:1991:IPI",
pages = "265--266",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p265-astrelin/",
abstract = "Consider the following problem: for the differential
operator $D=P \delta / \delta x+Q \delta / \delta y$
find an integer $K$, such that any irreducible
polynomial $f$ dividing $Df$ has degree $\deg{}f<=K$.
This problem arises when one wants to find the symbolic
solution of a differential equation $dy/dx=R(x,y)$
where $R$ is a rational function. A solution when $P$
and $Q$ are homogeneous polynomials of equal degrees
i.e. $P(x,y)=x^mp(x/y),Q(x,y)=x^mq(x,y)$ for some $m$
is proposed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. and Math., Moscow State Univ., USSR",
classification = "C1110 (Algebra); C1120 (Analysis); C4170
(Differential equations)",
keywords = "algorithms; Differential equation; Differential
operator; Homogeneous polynomials; Irreducible
eigenpolynomial; Irreducible polynomial; Rational
function; Symbolic solution",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Differential equations; Polynomials",
}
@InProceedings{Babai:1991:NLT,
author = "L{\'a}szl{\'o} Babai and Gene Cooperman and Larry
Finkelstein and {\'A}kos Seress",
title = "Nearly linear time algorithms for permutation groups
with a small base",
crossref = "Watt:1991:IPI",
pages = "200--209",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p200-babai/",
abstract = "A base of a permutation group $G$ is a subset $B$ of
the permutation domain such that only the identity of
$G$ fixes $B$ pointwise. The permutation
representations of important classes of groups,
including all finite simple groups other than the
alternating groups, admit $O(\log{}n)$ size bases,
where $n$ is the size of the permutation domain. Groups
with very small bases dominate the work on permutation
groups in much of computational group theory. A series
of new combinatorial results allows us to present Monte
Carlo algorithms achieving $O(n \log^cn)$ ($c$ a
constant) time and space performance for such groups
with respect to the fundamental operations of finding
order and testing membership. (The input is a list of
generators of the group). Previous methods have
achieved similar space performance only at the expense
of increased time performance. Adaptations of a
`cube-doubling' technique (L. Babai, E. Szemeredi,
1984) and a local expansion property of groups (L.
Babai, 1991) are the key to theoretically reducing the
time complexity to $O(n \log^c n)$. The shared
principal novelty of the new ideas is in their ability
to build and manipulate certain chains of subsets of a
group, which are not themselves subgroups, in order to
build the point stabilizer subgroup chain. Further
combinatorial ideas are used to lower the constant $c$.
Comparative timing estimates, based on asymptotic
worst-case analysis, lead us to expect a new
implementation to be faster than previous
implementations for groups of high degree.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comp. Sci. Chicago Univ., IL, USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Alternating groups; Asymptotic worst-case
analysis; Computational group theory; Cube-doubling;
Finite simple groups; Fundamental operations; Group
order determination; Local expansion property;
Membership testing; Monte Carlo algorithms; Permutation
domain; Permutation group; Point stabilizer subgroup
chain; Shared principal novelty; theory; Time
complexity",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.3} Mathematics
of Computing, PROBABILITY AND STATISTICS, Probabilistic
algorithms (including Monte Carlo). {\bf G.2.1}
Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Combinatorial algorithms.",
thesaurus = "Computational complexity; Group theory",
}
@InProceedings{Backelin:1991:HWP,
author = "J{\"o}rgen Backelin and Ralf Fr{\"o}berg",
title = "How we proved that there are exactly 924 cyclic
7-roots",
crossref = "Watt:1991:IPI",
pages = "103--111",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p103-backelin/",
abstract = "The following problem has become some sort of test
problem for Gr{\"o}bner bases techniques: find all
solutions to $Sn=z_1+z_2+\ldots{}+z_{n-1}+z_n=0$,
$z_1z_2+z_2z_3+\ldots{}+z_{n-1}z_n+z_nz_1=0$, \ldots{}
$z_1z_2\ldots{}z_{n-1}+z_2z_3\ldots{}z_n+\ldots{}+z_{n-1}z_n\ldots{}z_{n-3}+z_nz_1\ldots{}z_{n-2}=0$,
$z_1z_2\ldots{}z_n=1$. The solutions are called cyclic
$n$-roots. In order to solve the problem one of the
authors constructed a new characteristic 0 Gr{\"o}bner
basis programme, Bergman. The authors describe some
features of Bergman, in particular its graph component
algorithm. They make some theoretical analysis and
practical tests of the differences in performance
between Bergman and some other Buchberger based
algorithms, mainly the Gebauer--Moller algorithm. With
the help of Bergman and some commutative algebra they
succeeded to prove: there are exactly 924 cyclic
7-roots. Each of them has multiplicity 1.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Stockholm Univ., Sweden",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; verification; Exact proof; Cyclic 7-roots;
Cyclic $n$-roots; Characteristic 0 Gr{\"o}bner basis
programme; Bergman; Graph component algorithm;
Gebauer--Moller algorithm; Multiplicity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials",
}
@InProceedings{Becker:1991:CRP,
author = "Thomas Becker and Volker Weispfenning",
title = "The {Chinese} remainder problem, multivariate
interpolation, and {Gr{\"o}bner} bases",
crossref = "Watt:1991:IPI",
pages = "64--69",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p64-becker/",
abstract = "Let $K(X)$ be a multivariate polynomial ring over a
field $K, I_1, \ldots{}, I_m$ ideals in $K(X)$, $U$
contained in $X$. Using a single Gr{\"o}bner basis in
an extension ring of $K(X)$, the authors solve the
following problems effectively. Given
$f_1,\ldots{},f_m$ in $K(X)$, put
$A_f=\cap_{k=1}^m(I_k+f_k)$. (1) Decide whether
$A_f\cap{}K(U)\ne0$ and if so, construct some element
of $A_f\cap{}K(U)$. (2) For given $g$ in $K(U)$, decide
whether $g\in{}A_f$. (3) Construct all elements of
$A_f\cap{}K(U)$. Taking for $I^k$ a suitable vanishing
ideal of some parametrized hypersurface in
$K^n(1<=k<=m)$, this solves a generalized Hermite and
spline interpolation problem.",
acknowledgement = ack-nhfb,
affiliation = "Fakultat fur Math. und Inf., Passau Univ., Germany",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; theory; Hermite problem; Chinese remainder
problem; Multivariate interpolation; Gr{\"o}bner bases;
Multivariate polynomial ring; Extension ring; Vanishing
ideal; Parametrized hypersurface; Spline
interpolation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf G.2.m} Mathematics of Computing, DISCRETE
MATHEMATICS, Miscellaneous. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations.",
thesaurus = "Interpolation; Polynomials; Splines [mathematics]",
}
@InProceedings{Belkov:1991:RUC,
author = "Alexander A. Bel'kov and Alexander V. Lanyov",
title = "{REDUCE} usage for calculation of low-energy process
amplitudes in chiral {QCD} model",
crossref = "Watt:1991:IPI",
pages = "454--455",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p454-bel_kov/",
abstract = "Describes the extension of REDUCE capabilities for the
calculations of strong and weak meson processes within
the chiral Lagrangians with higher derivatives. The
main non-trivial difficulty is to obtain the process
amplitude from the Lagrangian, describing these
interactions. Another one is to overcome some REDUCE
deficiencies such as the lack of arguments in the
matrix data type as well as of some physical operations
with the particle operators. This package of procedures
allows one to calculate the amplitudes of the strong
and weak processes by simple specifying the particles
involved and their momenta.",
acknowledgement = ack-nhfb,
affiliation = "Particle Phys. Lab., JINR, Moscow, USSR",
classification = "A0270 (Computational techniques); A1110 (Field
theory); A1130R (Chiral symmetries); A1235C (General
properties of quantum chromodynamics (dynamics,
confinement, etc.)); C7320 (Physics and Chemistry)",
keywords = "algorithms; Chiral Lagrangians; Meson processes;
REDUCE capabilities",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General. {\bf I.1.0} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Chiral symmetries; Colour model; Meson field theory;
Physics computing; Symbol manipulation",
}
@InProceedings{Berndt:1991:ACA,
author = "R. Berndt and A. Lock and G. Witte and C. h.
W{\"o}ll",
title = "Application of computer algebra to surface lattice
dynamics",
crossref = "Watt:1991:IPI",
pages = "433--438",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p433-berndt/",
abstract = "Lattice dynamical calculations for surfaces and in
particular for stepped and absorbed covered surfaces
are commonly hampered by the complexity of the
dynamical matrix for these systems. The authors propose
the use of computer algebra programs to set up the
dynamical matrix. In the present implementation the
dynamical matrix is calculated fully analytically
within the framework of a force constant-mode and
partially analytically for other interaction models
such as the shell model or the bond charge model.",
acknowledgement = ack-nhfb,
affiliation = "Max-Planck Inst. fur Stromungsforschung, Gottingen,
Germany",
classification = "A6830 (Dynamics of solid surfaces and interface
vibrations); A6845 (Solid-fluid interface processes);
C4140 (Linear algebra); C7320 (Physics and Chemistry)",
keywords = "Absorbed covered surfaces; algorithms; Bond charge
model; Computer algebra; Dynamical matrix; Force
constant-mode; Interaction models; languages; Shell
model; Surface lattice dynamics",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.2.m} Mathematics of
Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN.",
thesaurus = "Adsorbed layers; Crystal surface and interface
vibrations; Matrix algebra; Phonon dispersion
relations; Physics computing; Symbol manipulation",
}
@InProceedings{Beth:1991:FGN,
author = "T. Beth and W. Geiselmann and F. Meyer",
title = "Finding (good) normal bases in finite fields",
crossref = "Watt:1991:IPI",
pages = "173--178",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p173-beth/",
abstract = "An algorithm to generate low complexity normal bases
in finite fields is presented. This algorithm
generalizes the method of Ash et al. to fields of
arbitrary characteristic. It can be applied to most
finite fields and produces (under certain conditions)
the multiplication matrix for the normal basis
multiplication of $\mbox{GF}(q^n):\mbox{GF}(q)$ in
$O(n^2 \log^2 n \log{}q)$ bit-operations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C4240
(Programming and algorithm theory)",
keywords = "algorithms; Finite fields; Low complexity normal
bases; Multiplication matrix; Normal basis
multiplication",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations in finite fields. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Number theory",
}
@InProceedings{Bosma:1991:CFG,
author = "Wieb Bosma and Michael Pohst",
title = "Computations with finitely generated modules over
{Dedekind} rings",
crossref = "Watt:1991:IPI",
pages = "151--156",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p151-bosma/",
abstract = "In computer algebra the use of normal forms for
matrices is of eminent importance. Especially, Hermite
and Smith normal form techniques are frequently used
for various computational problems over Euclidean
rings. The paper discusses a generalization of these
concepts to Dedekind rings. It considers the problem of
normal forms for matrices in the context of basis
transformations for finitely generated modules.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Pure Math., Sydney Univ., NSW, Australia",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "algorithms; Basis transformations; Computer algebra;
Dedekind rings; Euclidean rings; Finitely generated
modules; Hermite normal form; Matrices; Smith normal
form; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Matrix algebra; Number theory",
}
@InProceedings{Bronstein:1991:RDE,
author = "Manuel Bronstein",
title = "The {Risch} differential equation on an algebraic
curve",
crossref = "Watt:1991:IPI",
pages = "241--246",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p241-bronstein/",
abstract = "The author presents a new rational algorithm for
solving Risch differential equations over algebraic
curves. This algorithm can also be used to solve
$n^{\mbox{th}}$-order linear ordinary differential
equations with coefficients in an algebraic extension
of the rational functions. In the general (`mixed
function') case, this algorithm finds the denominator
of any solution of the equation. The algorithm has been
implemented in the Maple and Scratchpad computer
algebra systems.",
acknowledgement = ack-nhfb,
affiliation = "Inf. ETH-Zentrum, Zurich, Switzerland",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "$N^{th}$-order linear ordinary differential equations;
Algebraic curve; algorithms; Computer algebra systems;
Maple; Rational algorithm; Rational functions; Risch
differential equation; Scratchpad",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
systems (direct and iterative methods). {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, SCRATCHPAD. {\bf
G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
Ordinary Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Buchmann:1991:CNP,
author = "Johannes Buchmann and Volker M{\"u}ller",
title = "Computing the number of points of elliptic curves over
finite fields",
crossref = "Watt:1991:IPI",
pages = "179--182",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p179-buchmann/",
abstract = "The authors study the problem of counting the points
on an elliptic curve over a prime field. Although
Schoof (1985) proves that the cardinality of an
elliptic curve group over a finite field can be
computed in polynomial time, his algorithm is extremely
inefficient in practice. On the other hand, the
application of Shanks' babystep giantstep idea (1970)
to the problem yields an algorithm which is efficient
for medium size prime numbers but of exponential
complexity. So far no experimental results concerning
those algorithms have been published. The authors
present a practical improvement of the algorithm of
Shanks which is based on the ideas of Schoof. It turns
out to be very efficient.",
acknowledgement = ack-nhfb,
affiliation = "FB 14 Inf., Saarlandes Univ., Saarbrucken, Germany",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Cardinality; Elliptic curves; Finite
fields; Medium size prime numbers; Prime field",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Number theory",
}
@InProceedings{Bundgen:1991:CIP,
author = "Reinhard B{\"u}ndgen",
title = "Completion of integral polynomials by {AC-term}
completion",
crossref = "Watt:1991:IPI",
pages = "70--78",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p70-bundgen/",
abstract = "The article presents a canonical term rewriting system
RX whose ground normal forms can directly be mapped to
integral polynomials in distributive normal form.
Completing RX and a set of ground equations simulates
the Gr{\"o}bner base computation for the ideal
presented by the ground equations. With this approach,
it clearly shows the correspondence of the key features
of algebraic completion procedures for integral
polynomial ideals and their simulation in a term
rewriting environment.",
acknowledgement = ack-nhfb,
affiliation = "Wilhelm-Schickard-Inst., Tubingen Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C4210 (Formal logic)",
keywords = "algorithms; AC-term completion; Canonical term
rewriting system; Ground normal forms; Distributive
normal form; Ground equations; Gr{\"o}bner base
computation; Algebraic completion procedures; Integral
polynomial ideals",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials; Rewriting systems",
}
@InProceedings{Burge:1991:SRI,
author = "William H. Burge",
title = "{Scratchpad} and the {Rogers--Ramanujan} identities",
crossref = "Watt:1991:IPI",
pages = "189--190",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p189-burge/",
abstract = "This note sketches the part played by Scratchpad in
obtaining new proofs of Euler's theorem and the
Rogers--Ramanujan Identities.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "algorithms; Euler theorem; Infinite series; Restricted
partition pairs; Rogers--Ramanujan identities;
Scratchpad",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, SCRATCHPAD.",
thesaurus = "Mathematics computing; Number theory; Symbol
manipulation",
}
@InProceedings{Butler:1991:DDG,
author = "Greg Butler and Sridhar S. Iyer and Susan H. Ley",
title = "A deductive database of the groups of order dividing
128",
crossref = "Watt:1991:IPI",
pages = "210--218",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p210-butler/",
abstract = "The paper describes the design and implementation of a
deductive database for the 2668 groups of order $2^n$,
($n<=7$). The system was implemented in NU-Prolog, a
Prolog system with built-in functions for creating and
using deductive databases. In addition to the database,
a simple query language was written. This enables
database users to assess the data using a simpler and
more familiar set-theoretic syntax than that provided
by the Prolog interpreter.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Sydney Univ., NSW, Australia",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C6160Z (Other DBMS); C6170 (Expert systems); C7310
(Mathematics)",
keywords = "Built-in functions; Deductive database; design;
languages; NU-Prolog; Query language; Set-theoretic
syntax",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Special-purpose algebraic
systems. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
Language Classifications, Prolog.",
thesaurus = "Deductive databases; Group theory; Knowledge based
systems; Mathematics computing; Set theory",
}
@InProceedings{Canny:1991:OCD,
author = "John Canny and J. Maurice Rojas",
title = "An optimal condition for determining the exact number
of roots of a polynomial system",
crossref = "Watt:1991:IPI",
pages = "96--102",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p96-canny/",
abstract = "It was shown by Bernshtein (1975) that the number of
roots in $(C*)^n$ of a polynomial system depends only
on the Newton polytopes of the system, for almost all
specializations of the coefficients. This result,
referred to as the BKK bound, gives an upper bound on
the number of roots of a polynomial system. The BKK
bound is often much better than the Bezout bound for
the same system, but the original theorem gives an
exact bound only if all the coefficients corresponding
to Newton polytope boundaries are generically chosen.
The current paper shows that the BKK bound is exact
under much weaker assumptions: only coefficients
corresponding to certain vertices of the Newton
polytopes need be generic. This result allows
application of the BKK bound to many practical
problems.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; BKK bound; Newton polytopes; Optimal
condition; Polynomial system; Roots; theory; Upper
bound; verification; Vertices",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Chen:1991:NNF,
author = "Guoting Chen and Jean Della Dora and Laurent
Stolovitch",
title = "Nilpotent normal form via {Carleman} linearization
(for systems of ordinary differential equations)",
crossref = "Watt:1991:IPI",
pages = "281--288",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p281-chen/",
abstract = "Considers in this paper the normal formal problem for
systems of nonlinear ordinary differential equations
with singularity at the origin. The problem has its
origin in the classical work of Poincare. The authors
define a normal form for differential systems whose
linear part is nilpotent which is called nilpotent
normal form. They give an algorithm for the computation
of the normal form and the transformation that leads a
system to its normal form. The elementary notations and
methods used in the paper are the Carleman
linearizations of differential systems and formal
diffeomorphisms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Math., Univ. Louis Pasteur, Strasbourg,
France",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Carleman linearizations; Formal
diffeomorphisms; Nilpotent normal form; Nonlinear
ordinary differential equations; Normal form;
Singularity; Transformation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Nonlinear differential equations",
}
@InProceedings{Cohen:1991:OES,
author = "Ian Cohen and Karl-Erik E. Thylwe",
title = "Obtaining exact steady-state responses in driven
undamped oscillators",
crossref = "Watt:1991:IPI",
pages = "319--320",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p319-cohen/",
abstract = "Exact solutions are very scarce in non-linear applied
mathematics. However, exact solutions can be an
invaluable aid to understanding how well an approximate
method is working. It can also be used as a `stepping
off' solution into parameter regions where no exact
solutions exist. Most importantly however, each exact
solution is a potential candidate for a new area of
research as it can contain new insights into the
physics of the equation under investigation or may be
used to replace numerical methods in an investigation.
Another important motivation is the synthesis in this
project of Gr{\"o}bner bases with dynamical systems
research, two areas at the forefront of modern
research.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech., R. Inst. of Technol., Stockholm,
Sweden",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Steady-state responses; Undamped
oscillators; Gr{\"o}bner bases; Dynamical systems",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Differential equations; Nonlinear systems",
}
@InProceedings{Crouch:1991:CID,
author = "Peter Crouch and Robert Grossman and Richard Larson",
title = "Computations involving differential operators and
their actions on functions",
crossref = "Watt:1991:IPI",
pages = "301--307",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p301-crouch/",
abstract = "Further develops the authors algorithms for rewriting
expressions involving differential operators. The
differential operators considered arise in the local
analysis of nonlinear dynamical systems. The authors
extend these algorithms in two different directions:
they generalize the algorithms so that they apply to
differential operators on groups and develop the data
structures and algorithms to compute symbolically the
action of differential operators on functions. Both of
these generalizations are needed for applications. The
paper is preliminary: a final paper containing proofs
and a further analysis of the algorithm will appear
elsewhere.",
acknowledgement = ack-nhfb,
affiliation = "Arizona State Univ., Tempe, AZ, USA",
classification = "C6120 (File organisation); C7310 (Mathematics)",
keywords = "algorithms; Data structures; Differential operators;
Nonlinear dynamical systems; Rewriting expressions;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures.",
thesaurus = "Rewriting systems; Symbol manipulation",
}
@InProceedings{Czapor:1991:HSS,
author = "S. R. Czapor",
title = "A heuristic selection strategy for lexicographic
{Gr{\"o}bner} bases?",
crossref = "Watt:1991:IPI",
pages = "39--48",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p39-czapor/",
abstract = "It is well known that the computation of lexicographic
Gr{\"o}bner bases using the Buchberger's algorithm is
more difficult than the computation of Gr{\"o}bner
bases with respect to total degree orderings. The
lexicographic algorithm is particularly susceptible to
the problem of intermediate expression swell; that is,
intermediate polynomials may be far larger than those
which make up the final basis. To some extent, this is
a function of `selection strategy', i.e. the order in
which S-polynomials are used to extend a partial basis.
The paper argues and provides empirical evidence that
for the lexicographic ordering (in direct contrast to
the case of degree orderings), a simple heuristic
strategy will in practice control intermediate growth
more effectively than the normal strategy based on the
lexicographic term ordering alone. The results is
usually a much more efficient computation, even for
nonzero dimension ideals.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Stat. and Comput. Sci., Dalhousie
Univ., Halifax, NS, Canada",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; Heuristic selection strategy;
Lexicographic Gr{\"o}bner bases; Buchberger's
algorithm; Intermediate expression swell; Intermediate
polynomials; S-polynomials; Partial basis;
Lexicographic ordering; Intermediate growth; Nonzero
dimension ideals",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.0} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, General.",
thesaurus = "Polynomials",
}
@InProceedings{Davenport:1991:SVA,
author = "J. H. Davenport and P. Gianni and B. M. Trager",
title = "{Scratchpad}'s view of algebra. {II}. {A} categorical
view of factorization",
crossref = "Watt:1991:IPI",
pages = "32--38",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p32-davenport/",
abstract = "For pt.I see Proc. DISCO 1990 (p.40-54). The paper
explains how Scratchpad solves the problem of
presenting a categorical view of factorization in
unique factorization domains, i.e. a view which can be
propagated by functors such as
SparseUnivariatePolynomial or Fraction. This is not
easy, as the constructive version of the classical
concept of UniqueFactorizationdomain cannot be so
propagated. The solution adopted is based largely on
the Seidenberg conditions ($F$) and ($P$), but there
are several additional points that have to be borne in
mind to produce reasonably efficient algorithms in the
required generality. The consequence of the algorithms
and interfaces presented is that Scratchpad can
factorize in any extension of the integers or finite
fields by any combination of polynomial, fraction and
algebraic extensions: a capability far more general
than any other computer algebra system possesses.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Bath Univ., Claverton Down, UK",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic extensions; algorithms; Categorical view;
Computer algebra system; Factorization; Finite fields;
Fraction; Integers; Polynomial; Scratchpad; Seidenberg
conditions",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations in finite fields.",
thesaurus = "Mathematics computing; Polynomials; Symbol
manipulation",
}
@InProceedings{deJager:1991:SCZ,
author = "Bram de Jager",
title = "Symbolic calculation of zero dynamics for nonlinear
control systems",
crossref = "Watt:1991:IPI",
pages = "321--322",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p321-de_jager/",
abstract = "The calculation of the zero dynamics of a nonlinear
system is of advantage in the design of controllers for
this system. Because the calculation is difficult to do
by hand, symbolic algebra programs are used. To access
the usefulness of these programs and to solve some
design problems, a MAPLE procedure, ZERODYN, is written
to calculate the zero dynamics symbolically. The
procedure can, however, not solve all problems, mainly
because general symbolic algebra programs have
insufficient capabilities to solve sets of nonlinear
equations and partial differential equations. A
realistic analysis problem shows this.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. Eng., Eindhoven Univ. of Technol.,
Netherlands",
classification = "C1340K (Nonlinear systems); C7310 (Mathematics)",
keywords = "algorithms; experimentation; MAPLE procedure;
Nonlinear control systems; Nonlinear system; Partial
differential equations; Symbolic algebra; Zero
dynamics; ZERODYN",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Nonlinear control systems; Symbol manipulation",
}
@InProceedings{Diaz:1991:DSD,
author = "A. Diaz and E. Kaltofen and K. Schmitz and T. Valente
and M. Hitz and A. Lobo and P. Smyth",
title = "{DSC}: a system for distributed symbolic computation",
crossref = "Watt:1991:IPI",
pages = "323--332",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p323-diaz/",
abstract = "DSC is a general purpose tool that allows the
distribution of a computation over a network of Unix
workstations. Its control mechanisms automatically
start up daemon processes on the participating
workstations in order to communicate data by the
standard IP/TCP/UDP protocols. The user's program
distributes either remote procedure calls or source
code of programs and their corresponding input data
files by calling a DSC library function. The authors
have tested DSC with a primarily test for large
integers and with a factorization algorithm for
polynomials over large finite fields and observed
significant speed-ups over executing the best-known
methods on a single workstation computation. These
experiments have been carried out not only on our local
area network but also on off-site workstations at the
University of Delaware.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst.,
Troy, NY, USA",
classification = "C7310 (Mathematics)",
keywords = "algorithms; Distributed symbolic computation; DSC;
experimentation; Factorization algorithm; Large
integers; Polynomials; Primarily test; Unix
workstations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf D.2.2} Software, SOFTWARE
ENGINEERING, Design Tools and Techniques, User
interfaces.",
thesaurus = "Distributed processing; Software packages; Symbol
manipulation",
}
@InProceedings{Faradzev:1991:CCC,
author = "I. A. Faradzev and M. H. Klin",
title = "For computations with coherent configurations",
crossref = "Watt:1991:IPI",
pages = "219--223",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p219-faradzev/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory. {\bf G.2.1} Mathematics of Computing, DISCRETE
MATHEMATICS, Combinatorics, Permutations and
combinations.",
}
@InProceedings{Faradzev:1991:CPC,
author = "I. A. Faradzev and M. H. Klin",
title = "Computer package for computations with coherent
configurations",
crossref = "Watt:1991:IPI",
pages = "219--223",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "A collection of computer programs based on the Galois
correspondence between coherent configurations and
permutation groups is described. A number of examples
of application of this package for construction of
combinatorial objects with interesting properties and
for solving some group theoretical problems (extension
of a permutation group and intersection of subgroups)
are presented.",
acknowledgement = ack-nhfb,
affiliation = "inst. for Syst. Studies, Acad. of Sci., Moscow, USSR",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "Coherent configurations; Combinatorial objects;
Computer programs; Galois correspondence; Group
theoretical problems; Permutation groups",
thesaurus = "Group theory; Mathematics computing; Software
packages; Symbol manipulation",
}
@InProceedings{Fateman:1991:CRL,
author = "Richard J. Fateman",
title = "Canonical representations in {Lisp} and applications
to computer algebra systems",
crossref = "Watt:1991:IPI",
pages = "360--369",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p360-fateman/",
abstract = "Lisp, as well as many other programming languages,
provides for the creation of compound data-structures
or objects. What if one follows a discipline in which
any time one constructs an object which happens to be
isomorphic to one previously stored, the constructor
function simply returns the same location in memory as
the first? The author discusses some of the advantages
and show how an implementation fits neatly into Common
Lisp. Some of the results are especially relevant for
the design and implementation of efficient `general
representation' computer algebra systems. The author
gives some experimental results showing speedups of a
factor of ten or more in basic operations such as
simplification of sums.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electron. Eng. and Comput. Sci., California
Univ., Berkeley, CA, USA",
classification = "C6120 (File organisation); C6140D (High level
languages); C7310 (Mathematics)",
keywords = "algorithms; Canonical representation; Computer algebra
systems; experimentation; languages; Lisp",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Common Lisp. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Data structures; LISP; Symbol manipulation",
}
@InProceedings{Gaal:1991:RIF,
author = "I. Ga{\'a}l and A. Peth{\"o} and M. Pohst",
title = "On the resolution of index form equations",
crossref = "Watt:1991:IPI",
pages = "185--186",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p185-gaal/",
abstract = "For practical applications it is very important to
know a power integral basis of the algebraic number
field $K$. The solutions of the index form equation,
$I(x_2,\ldots{},x_n)=\pm 1$ in $x_2,\ldots{},x_n$ in
$Z$ enable one to determine all power integral bases of
$K$. If there are no power integral bases, then the
best is to determine all integral elements of $K$,
having the least possible index, i.e. to determine the
least positive $m$ in $Z$ for which
$I(x_2,\ldots{},x_n)=\pm m$ in $x_2,\ldots{},x_n$ in
$Z$ is soluble and to compute all solutions of this
equation to find all integral elements with least
index. The authors discuss their attempts at
constructing algorithms to solve the equations and
results obtained.",
acknowledgement = ack-nhfb,
affiliation = "Kossuth Lajos Univ., Debrecen, Hungary",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "algorithms; Index form equations; Power integral
basis",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
thesaurus = "Algebra; Number theory",
}
@InProceedings{Ganzha:1991:SAD,
author = "V. G. Ganzha and B. Yu. Scobelev and E. V.
Vorozhtsov",
title = "Stability analysis of difference schemes by the
catastrophe theory methods and by means of computer
algebra",
crossref = "Watt:1991:IPI",
pages = "427--428",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p427-ganzha/",
abstract = "A new method for determining the stability domains of
difference schemes(d.s.) is based on the Fourier method
and the methods of catastrophe theory. In the paper the
authors propose a symbolic-numerical approach to a
realization of the method of the work.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, USSR",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Catastrophe theory; Computer algebra;
Difference schemes; Stability analysis; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Catastrophe theory; Convergence of numerical methods;
Difference equations; Symbol manipulation",
}
@InProceedings{Gao:1991:CPE,
author = "Xiao-Shan Gao and Shang-Ching Chou",
title = "Computations with parametric equations",
crossref = "Watt:1991:IPI",
pages = "122--127",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p122-gao/",
abstract = "The authors present a complete method of
implicitization for general rational parametric
equations. They also present a method to decide whether
the parameters of a set of parametric equations (PEs)
are independent, and if not, to reparameterize the PEs
so that the new PEs have independent parameters. They
give a method to compute the inversion maps of the PEs
with independent parameters, and as a consequence, they
can decide whether the PEs are proper. A new method to
find a proper reparameterization for a set of improper
PEs of algebraic curves is presented.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Algebraic curves; algorithms; Implicitization;
Independent parameters; Inversion maps; Rational
parametric equations; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials",
}
@InProceedings{Gatermann:1991:MSS,
author = "Karin Gatermann",
title = "Mixed symbolic-numeric solution of symmetrical
nonlinear systems",
crossref = "Watt:1991:IPI",
pages = "431--432",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p431-gatermann/",
abstract = "The mixed symbolic-numeric algorithm SYMCON for the
fully automatic treatment of equivariant systems is
presented. The global aspects of the theory of
Vanderbauwhede (1982) for these systems are viewed with
regard to the full bifurcation scenario containing
solution paths with different isotropy groups and
symmetry preserving and symmetry breaking bifurcation
points. The advanced exploitation of symmetry in the
numerical computations causes a comprehensive symmetry
analysis and complicated organization of numerical work
which is done by the symbolic part of the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Konrad-Zuse-Zentrum Berlin, Germany",
classification = "C1340K (Nonlinear systems); C4150 (Nonlinear and
functional equations)",
keywords = "algorithms; Bifurcation points; Equivariant systems;
Symbolic-numeric algorithm; SYMCON; Symmetrical
nonlinear systems; Symmetry analysis; theory",
subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Nonlinear systems; Symbol manipulation",
}
@InProceedings{Gebauer:1991:CCA,
author = "R. Gebauer and M. Kalkbrener and B. Wall and F.
Winkler",
title = "{CASA}: a computer algebra package for constructive
algebraic geometry",
crossref = "Watt:1991:IPI",
pages = "403--410",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p403-gebauer/",
abstract = "The program package CASA is designed to enhance the
power of a traditional computer algebra system by
adding programs for constructive algebraic geometry.
The objects that CASA works with are algebraic sets in
affine or projective spaces over a field. The geometric
objects may be given in various different
representations. CASA is able to analyse properties of
algebraic sets, such as to compute their dimensions,
compute their irreducible components, determine
singular points, determine intersection properties and
the like. The user can also create 2- and 3-dimensional
pictures of curves and surfaces.",
acknowledgement = ack-nhfb,
affiliation = "Johannes Kepler Univ., Linz, Austria",
classification = "C4190 (Other numerical methods)",
keywords = "Algebraic geometry; Algebraic sets; algorithms; CASA;
Computer algebra; Computer algebra package;
Constructive algebraic geometry; Intersection
properties; Irreducible components; Singular points",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Computational geometry; Symbol manipulation",
}
@InProceedings{Gerdt:1991:LSC,
author = "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov",
title = "{Lie--B{\"a}cklund} symmetries of coupled nonlinear
{Schr{\"o}dinger} equations",
crossref = "Watt:1991:IPI",
pages = "313--314",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p313-gerdt/",
abstract = "Applies computer-aided symmetry approach to an
investigation of an eight-parametric system of two
coupled nonlinear Schr{\"o}dinger equations. Symmetry
approach allows one not only to verify the necessary
integrability conditions which follow from the
existence of a higher infinitesimal or
Lie--B{\"a}cklund symmetry but often to find an
explicit form of the latter. The corresponding
necessary conditions in the form of existence of the
series of the local conservation laws lead to the
system of nonlinear algebraic equations in numeric
parameters. As a result of the first two necessary
integrability conditions the REDUCE program provided
with some new additional facilities, generates the
three set of algebraic equations.",
acknowledgement = ack-nhfb,
affiliation = "JINR, Moscow, USSR",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Lie--B{\"a}cklund symmetry; Nonlinear
Schr{\"o}dinger equations",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE.",
thesaurus = "Schr{\"o}dinger equation; Symbol manipulation",
}
@InProceedings{Giovini:1991:OSC,
author = "Alessandro Giovini and Teo Mora and Gianfranco Niesi
and Lorenzo Robbiano and Carlo Traverso",
title = "`One sugar cube, please' or selection strategies in
the {Buchberger} algorithm",
crossref = "Watt:1991:IPI",
pages = "49--54",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p49-giovini/",
abstract = "The paper describes some experimental findings on
selection strategies for Gr{\"o}bner basis computation
with the Buchberger algorithm. In particular, the
results suggest that the sugar flavor of the normal
selection is the best choice for a selection strategy.
It has to be combined with the straightforward
simplification strategy and with a special form of the
Gebauer--Moller criteria to obtain the best results.
The idea of the sugar flavor is the following: the
Buchberger algorithm for homogeneous ideals, with
degree-compatible term ordering and normal selection
strategy, usually works fine. Homogenizing the basis of
the ideal is good for the strategy, but bad for the
basis to be computed. The sugar flavor computes, for
every polynomial in the course of the algorithm, `the
degree that it would have if computed with the
homogeneous algorithm', and uses this phantom degree
(the sugar) only for the selection strategy.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Genova Univ., Italy",
classification = "C4130 (Interpolation and function approximation)",
keywords = "algorithms; experimentation; Selection strategies;
Buchberger algorithm; Gr{\"o}bner basis computation;
Sugar flavor; Normal selection; Straightforward
simplification strategy; Gebauer--Moller criteria;
Homogeneous ideals; Degree-compatible term ordering;
Polynomial; Homogeneous algorithm; Phantom degree",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Polynomials",
}
@InProceedings{Gonzalez-Vega:1991:STM,
author = "Laureano Gonz{\'a}lez-Vega",
title = "A subresultant theory for multivariate polynomials",
crossref = "Watt:1991:IPI",
pages = "79--85",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p79-gonzalez-vega/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Gonzalez-Vega:1991:WRA,
author = "Laureano Gonz{\'a}lez-Vega",
title = "Working with real algebraic plane curves in {REDUCE}
the {GCUR} package",
crossref = "Watt:1991:IPI",
pages = "397--402",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p397-gonzalez-vega/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Graph algorithms.",
}
@InProceedings{GonzalezVega:1991:STM,
author = "L. {Gonzalez Vega}",
title = "A subresultant theory for multivariate polynomials",
crossref = "Watt:1991:IPI",
pages = "79--85",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "In computer algebra, subresultant theory provides a
powerful method to construct algorithms solving
problems for polynomials in one variable in an optimal
way. The paper extends the subresultant theory to the
multivariate case. In order to achieve this, first of
all, it introduces the definition of a subresultant
sequence associated to two polynomials in one variable
with coefficients in an integral domain, describing the
properties of this sequence that one would like to
extend to the multivariate case. In the second section
it generalizes the definition of a subresultant
polynomial to the multivariate case, showing that many
of the properties obtained in the one variable case
work also in the multivariate case. In this way it
shows how these subresultants can be used to get a
greatest common divisor of $n$ polynomials in
$D(x_1,\ldots{},x_{n-1})$ where $D$ is an integral
domain. The paper then applies this subresultant theory
to get a determinantal formula for the solution set of
almost all $0$-dimensional ideals defined by $n$
polynomials in $D(x_1, \ldots{}, x_n)$, with $D$ an
integral domain. Finally, some open problems related
with this construction are shown.",
acknowledgement = ack-nhfb,
affiliation = "Dept. de Matematicas, Cantabria Univ., Santander,
Spain",
classification = "C4130 (Interpolation and function approximation)",
keywords = "0-Dimensional ideals; Computer algebra; Determinantal
formula; Greatest common divisor; Integral domain;
Multivariate polynomials; Solution set; Subresultant
polynomial; Subresultant sequence; Subresultant
theory",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{GonzalezVega:1991:WRA,
author = "L. {Gonzalez Vega}",
title = "Working with real algebraic plane curves in {REDUCE}:
the {GCUR} package",
crossref = "Watt:1991:IPI",
pages = "397--402",
year = "1991",
bibdate = "Sat Apr 25 12:53:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents an implementation in Reduce of a package to
get topological and geometric information about real
algebraic plane curves defined as the real zeros of
polynomials in $Z(x, y)$. More precisely, if $P$ in
$Z(x,y)$ the output using the package GCUR will be a
plane graph homeomorphic to the set:
$C(P)=((\alpha,\beta) {\rm in }
R^2/P(\alpha,\beta)=0)$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. Mat., Cantabria Univ., Santander, Spain",
classification = "C4190 (Other numerical methods)",
keywords = "Algebraic plane curves; GCUR; Geometric information;
Plane graph; REDUCE; Topological information",
thesaurus = "Computational geometry; Poles and zeros; Polynomials;
Symbol manipulation; Topology",
}
@InProceedings{Grigoriev:1991:ASR,
author = "Dima Yu. u. Grigoriev and Marek Karpinski",
title = "Algorithms for sparse rational interpolation",
crossref = "Watt:1991:IPI",
pages = "7--13",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p7-grigoriev/",
abstract = "Presents two algorithms for interpolating sparse
rational functions. The first is the interpolation
algorithm in a sense of sparse partial fraction
representation of rational functions. The second is the
algorithm for computing the entier and the remainder of
a rational function. The first algorithm works without
a priori known bound on the degree of a rational
function, the second one is in the parallel class NC
provided that the degree is known.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Bonn Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Entier; Interpolation algorithm; NC;
Parallel class; Remainder; Sparse partial fraction
representation; Sparse rational functions",
subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL
ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices.",
thesaurus = "Computational complexity; Interpolation; Parallel
algorithms",
}
@InProceedings{Grudtsin:1991:ISI,
author = "S. N. Grudtsin and V. N. Larin",
title = "Integrated system {INTERCOMP} and computer language
for physicists",
crossref = "Watt:1991:IPI",
pages = "377--381",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p377-grudtsin/",
abstract = "Contains a description of a general approach to
physics related integrated software elaborations. A
development history and modern stage of the INTERCOMP
system, containing a large set of language and program
means for a description and computer analysis of
physical models are also described. The system has a
high level interpreted language and includes a powerful
symbolic algebraic computation subsystem, a numeric
algorithms library, a relational DBMS, a graphic
package, editor and text processor.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for High Energy Phys., Protvino, USSR",
classification = "C6140D (High level languages); C7320 (Physics and
Chemistry)",
keywords = "Algebraic; Computer analysis; Computer language;
Graphic package; Integrated software elaborations;
INTERCOMP; languages; Numeric algorithms; Physical
models; Relational DBMS; Symbolic computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, FORTRAN. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "High level languages; Physics computing; Symbol
manipulation",
}
@InProceedings{Havas:1991:CES,
author = "George Havas",
title = "Coset enumeration strategies",
crossref = "Watt:1991:IPI",
pages = "191--199",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p191-havas/",
abstract = "A primary reference on computer implementation of
coset enumeration procedures is a 1973 paper of Cannon,
Dimino, Havas and Watson. Programs and techniques
described there are updated in this paper. Improved
coset definition strategies, space saving techniques
and advice for obtaining improved performance are
included. New coset definition strategies for
Felsch-type methods give substantial reductions in
total cosets defined for some pathological
enumerations. Significant time savings are achieved for
coset enumeration procedures in general. Statistics on
performance are presented, both in terms of time and in
terms of maximum and total cosets defined for selected
enumerations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Queensland Univ., St. Lucia,
Qld., Australia",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "Coset definition strategies; Coset enumeration
procedures; Felsch-type methods; Pathological
enumerations; performance; Subgroups",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, CAYLEY.",
thesaurus = "Mathematics computing; Set theory",
}
@InProceedings{Hietarinta:1991:SIP,
author = "Jarmo Hietarinta",
title = "Searching for integrable {PDE}'s by testing {Hirota}'s
three-soliton condition",
crossref = "Watt:1991:IPI",
pages = "295--300",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p295-hietarinta/",
abstract = "The search for integrable PDE's has been an active
research subject with computer algebra as a necessary
tool. The author describes a search method based on the
requirement that standard type three- and four-soliton
solution exist in the bilinear formalism of Hirota. The
existence of $N$-soliton solutions can be formulated as
a requirement that a certain high degree polynomial in
$N*M$ variables vanishes on an affine manifold defined
by $N$ polynomials of $M$ variables each. An exhaustive
search has been carried out for certain classes of
typical equations and several new equations have been
found.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Phys., Turku Univ., Finland",
classification = "A0230 (Function theory, analysis); A0340K (Waves and
wave propagation: general mathematical aspects)",
keywords = "algorithms; Bilinear formalism; Computer algebra;
Integrable PDE's; Search method; theory; Three-soliton
condition",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
thesaurus = "Partial differential equations; Search problems;
Solitons; Symbol manipulation",
}
@InProceedings{Ilyin:1991:PIF,
author = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodionov and
A. Yu. Taranov",
title = "{PC} implementation of fast {Dirac} matrix trace
calculations",
crossref = "Watt:1991:IPI",
pages = "456--457",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p456-ilyin/",
abstract = "Presents an implementation of a fast algorithm for
Dirac matrix trace calculations. This implementation is
made for IBM compatible PC and works under REDUCE
3.3.1. Name of package is CVIT. The algorithm is based
on intense use of Fierz identities in N-dimensional
space ($N$ is arbitrary natural number or symbol) and
may be considered as an extension of well known Kahane
algorithm on higher space dimensions.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Phys., Moscow State Univ., USSR",
classification = "C7320 (Physics and Chemistry)",
keywords = "algorithms; CVIT; Dirac matrix trace calculations;
Fierz identities; IBM compatible PC; Kahane algorithm;
N-dimensional space; REDUCE 3.3.1",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics.",
thesaurus = "IBM computers; Matrix algebra; Physics computing;
Symbol manipulation",
}
@InProceedings{Ilyin:1991:SST,
author = "V. A. Ilyin and A. P. Kryukov",
title = "Symbolic simplification of tensor expressions using
symmetries, dummy indices and identities",
crossref = "Watt:1991:IPI",
pages = "224--228",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p224-ilyin/",
abstract = "The algorithm based on simple geometrical ideas is
suggested for simplification of tensor expressions
which takes into account symmetries, dummy indices, and
linear identities with many terms. The results of the
realization in REDUCE system are adduced. The Riemann
tensor is used as an example.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Phys., Moscow State Univ., USSR",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "algorithms; Dummy indices; Geometrical ideas; Linear
identities; REDUCE; Simplification; Symbolic
simplification; Symmetries; Tensor expressions",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Kleczka:1991:SCA,
author = "W. Kleczka and E. Kreuzer",
title = "Systematic computer-aided analysis of dynamic
systems",
crossref = "Watt:1991:IPI",
pages = "429--430",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p429-kleczka/",
abstract = "An automated numerical-symbolical analysis concept for
dynamic systems in engineering mechanics is outlined.
Besides the computerized generation of symbolic
equations of motion, the subsequent analysis is also
performed by means of computer algebra in combination
with well-established numerical methods.",
acknowledgement = ack-nhfb,
affiliation = "Meerestech. II, Tech. Univ., Hamburg-Harburg,
Germany",
classification = "C1210 (General system theory); C7440 (Civil and
mechanical engineering)",
keywords = "algorithms; Computer-aided analysis; Dynamic systems;
Engineering mechanics; Numerical-symbolical analysis;
Symbolic equations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Engineering. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues and eigenvectors (direct and iterative
methods).",
thesaurus = "Computer aided analysis; Convergence of numerical
methods; Mechanical engineering computing; Symbol
manipulation",
}
@InProceedings{Kornyak:1991:PSA,
author = "V. V. Kornyak and W. I. Fushchich",
title = "A program for symmetry analysis of differential
equations",
crossref = "Watt:1991:IPI",
pages = "315--316",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p315-kornyak/",
abstract = "Proposes in this work a program for determining
Lie--B{\"a}cklund (LB) symmetries of (partial or
ordinary) differential equations and for classification
of equations containing arbitrary functions and
parameters with respect to symmetries of this kind. The
program was implemented in Turbo C language and
designed in such a way to be more effective for systems
of equations with multidimensional spaces of
independent and dependent variables. The internal data
structures for representation of expressions are
right-threaded binary trees. The program reduces input
system of equations to the passive form, computes the
differential consequences of equations up to the needed
order, constructs the invariance conditions for a given
order LB symmetries, eliminates the dependencies
between the invariance conditions using differential
manifold, separates the determining equations and tries
to integrate them.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Res., Acad. of Sci., Kiev, Ukrainian
SSR, USSR",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "algorithms; Differential equations; languages;
Lie--B{\"a}cklund symmetries; Symmetry analysis",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, Turbo C.",
thesaurus = "Differential equations",
}
@InProceedings{Kuchlin:1991:MCI,
author = "Wolfgang K{\"u}chlin",
title = "On the multi-threaded computation of integral
polynomial greatest common divisors",
crossref = "Watt:1991:IPI",
pages = "333--342",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p333-kuchlin/",
abstract = "Reports experiences and practical results from
parallelizing the Brown--Collins polynomial g.c.d.
algorithm, starting from Collins' SAC-2 implementation
IPGCDC. The parallelization environment is PARSAC-2, a
multi-threaded version of SAC-2 programmed in C with
the parallelization constructs of the C Threads
library. IPGCDC computes the g.c.d. and its co-factors
of two polynomials in $Z(x_1,\ldots{},x_r)$, by first
reducing the problem to multiple calculations of
modular polynomial g.c.d.'s in $Z_p(x_1,\ldots{},x_r)$,
and then recovering the result by Chinese remaindering.
After studying timings of the SAC-2 algorithm, the
author first parallelizes the Chinese remainder
algorithm, and then parallelizes the main loop of
IPGCDC by executing the modular g.c.d. computations
concurrently. Finally, he determines speed-up's and
speed-up efficiencies of our parallel algorithms over a
wide range of polynomials. The experiments were
conducted on a 12 processor Encore Multimax under
Mach.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ.,
Columbus, OH, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "algorithms; Brown--Collins polynomial g.c.d.
algorithm; Chinese remaindering; Encore Multimax;
Multi-threaded computation; PARSAC-2; Polynomial
greatest common divisors",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf I.1.3} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Mathematics computing; Parallel algorithms; Symbol
manipulation",
}
@InProceedings{Langemyr:1991:ASA,
author = "Lars Langemyr",
title = "An analysis of the subresultant algorithm over an
algebraic number field",
crossref = "Watt:1991:IPI",
pages = "167--172",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p167-langemyr/",
abstract = "The author shows that one can compute the subresultant
polynomial remainder sequence over an algebraic number
field in $O((n^5m^3+n^4m^5) \log^2(nDE^m))$ binary
operations, where the generator of the field is given
by a monic irreducible polynomial of degree $m$ with
integer coefficients bounded by $E$ in absolute value,
and where the two input polynomials are of degree at
most $n$ and with integer coefficients bounded by $D$
in absolute value.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Anal. and Comput. Sci., R. Inst. of
Technol., Stockholm, Sweden",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C4240
(Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Algebraic number field; algorithms; Greatest common
division; Integer coefficients; Monic irreducible
polynomial; Subresultant polynomial remainder
sequence",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Number-theoretic computations.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Algebra; Computational complexity; Mathematics
computing; Number theory; Polynomials",
}
@InProceedings{Letichevsky:1991:APO,
author = "A. A. Letichevsky and J. V. Kapitonova and S. V.
Konozenko",
title = "Algebraic programs optimization",
crossref = "Watt:1991:IPI",
pages = "370--376",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p370-letichevsky/",
abstract = "Algebraic program is a system of relations (equalities
of data algebra) with a given strategy for applying
these relations as rewriting rules. An algebraic
program may be optimized by transforming a system of
relations or by transforming a strategy. Only second
case of optimization is considered in the paper. The
problem of algebraic program optimization is
investigated in the context of programming in the APS-1
system.",
acknowledgement = ack-nhfb,
affiliation = "Glushkov Inst. of Cybern., Acad. of Sci., Kiev,
Ukrainian SSR, USSR",
classification = "C6110 (Systems analysis and programming); C7310
(Mathematics)",
keywords = "Algebraic program optimization; algorithms; APS-1;
Data algebra; languages; Programming; Rewriting rules;
System of relations",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf G.1.6} Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures.",
thesaurus = "Optimisation; Programming; Symbol manipulation",
}
@InProceedings{Liska:1991:ADS,
author = "Richard Liska and Michail Yu. u. Shashkov",
title = "Algorithms for difference schemes construction on
non-orthogonal logically rectangular meshes",
crossref = "Watt:1991:IPI",
pages = "419--426",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p419-liska/",
abstract = "Deals with the formalization of the basic operator
method for construction of difference schemes for the
numerical solving of partial differential equations.
The strength of the basic operator method lies in the
fact that it produces fully conservative difference
schemes. The difference mesh can be non-orthogonal but
has to be logically orthogonal. Algorithms for working
with grid functions and grid operators in symbolic form
which are necessary in the basic operator method are
described. The algorithms have been implemented in the
computer algebra system REDUCE.",
acknowledgement = ack-nhfb,
affiliation = "Fac. of Nucl. Sci. and Phys. Eng., Czech Tech. Univ.,
Prague, Czechoslovakia",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Basic operator method; Computer algebra;
Difference mesh; Difference schemes; Grid functions;
Grid operators; Logically orthogonal; Numerical
solving; Partial differential equations; Rectangular
meshes; REDUCE",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Numerical methods; Partial differential equations;
Symbol manipulation",
}
@InProceedings{Manocha:1991:ETM,
author = "Dinesh Manocha and John Canny",
title = "Efficient techniques for multipolynomial resultant
algorithms",
crossref = "Watt:1991:IPI",
pages = "86--95",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p86-manocha/",
abstract = "The paper presents efficient techniques for applying
multipolynomial resultant algorithms and shows their
effectiveness for manipulating systems of polynomial
equations. In particular, it presents efficient
algorithms for computing the resultant of a system of
polynomial equations (whose coefficients may be
symbolic variables). These algorithms can be used for
interpolating polynomials from their values and
expanding symbolic determinants. Moreover, it uses
multipolynomial resultants for computing the real or
complex solutions of nonlinear polynomial equations. It
also discusses the implementation of these algorithms
in the context of certain applications.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Complex solutions; Efficient algorithms;
Multipolynomial resultant algorithms; Nonlinear
polynomial equations; Polynomial interpolation; Real
solutions; Symbolic determinants; Symbolic variables",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Algorithm theory; Interpolation; Polynomials",
}
@InProceedings{Marinari:1991:GBI,
author = "M. G. Marinari and H. M. M{\"o}ller and T. Mora",
title = "{Gr{\"o}bner} bases of ideals given by dual bases",
crossref = "Watt:1991:IPI",
pages = "55--63",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p55-marinari/",
abstract = "In 1982, Buchberger and Moller proposed an algorithm
which, given a finite number of rational points in the
affine $n$-dimensional space, computes a Gr{\"o}bner
basis for the ideal I of the polynomials vanishing at
the points. In 1988, Faugere, Gianni, Lazard and Mora
supplied an algorithm, which, given the reduced
Gr{\"o}bner basis w.r.t. some term-ordering $<_1$ of a
0-dim. ideal I, returns its reduced Gr{\"o}bner basis
w.r.t. some other term-ordering $<_2$. The paper
systematizes and generalizes the common properties of
the Buchberger--M{\"o}ller and the FGLM algorithms to
the frame of ideals defined by functionals. It gives
two algorithms to compute the Gr{\"o}bner basis of an
ideal defined by functionals, together with a set of
biorthogonal polynomials: the first one is a direct
generalization of the B-M and the FGLM algorithms; the
second one iteratively for each $i$ solves the question
for the ideals defined by $L_1,\ldots{}, L_i$. It then
measures the complexity of the algorithms in terms of
the number of additions+multiplications in $K$ which
they require and proves that both have a complexity of
$1/2 s^3+s^2 b+f s (s+b)<=O (n s^3+f n s^2)$.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Genova Univ., Italy",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Gr{\"o}bner bases; Ideals; Dual bases;
Rational points; Affine $n$-dimensional space;
Term-ordering; Functionals; Biorthogonal polynomials;
Complexity",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Marzinkewitsch:1991:OCA,
author = "Reiner Marzinkewitsch",
title = "Operating computer algebra systems by handprinted
input",
crossref = "Watt:1991:IPI",
pages = "411--413",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p411-marzinkewitsch/",
abstract = "Nearly twenty years have passed since the first
computer algebra systems (CAS) came up in the beginning
of the seventies. Since then CAS have gained a lot of
computational power. In contrast to this fact CAS have
not experienced the deserved widespread use by
potential users. The main reason for this discrepancy
is the unnatural operation of CAS by artificial
linearized notations, which tend to give little
comprehensive survey of the problem under work.
Calculation with pencil and paper not only offers many
efficient techniques but also appeals to the user's
ease. Especially occasional users need a familiar i.e.
paperlike interface to CAS. In this paper an integrated
system is presented, which offers the demanded
facilities: Calculating by hand in a traditional, `two
dimensional' fashion with the computational support of
a CAS.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich 14, Saarlandes Univ., Saarbrucken,
Germany",
classification = "C5260B (Computer vision and picture processing);
C5530 (Pattern recognition and computer vision
equipment); C5540 (Terminals and graphic displays);
C7310 (Mathematics)",
keywords = "algorithms; CAS; Computer algebra systems; design;
Handprinted input",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
H.5.2} Information Systems, INFORMATION INTERFACES AND
PRESENTATION, User Interfaces, Interaction styles.",
thesaurus = "Character recognition; Neural nets; Symbol
manipulation; Workstations",
}
@InProceedings{Molenkamp:1991:IAA,
author = "J. H. J. Molenkamp and V. V. Goldman and J. A. {van
Hulzen}",
title = "An improved approach to automatic error cumulation
control",
crossref = "Watt:1991:IPI",
pages = "414--418",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p414-molenkamp/",
abstract = "For evaluation of arithmetical expressions using
multiple precision floating-point arithmetic, a method
is given to automatically perform error cumulation
control prior to the actual computations. Individual
errors and their effects are identified, and it is
shown how to compute these effects efficiently via
automatic differentiation. In the presented approach
these effects are used to determine which precisions
have to be chosen during the real computations, in
order to limit error cumulation to admissible, user
chosen error bounds.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Twente Univ., Enschede,
Netherlands",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
keywords = "algorithms; Arithmetical expressions; Computations;
Error bounds; Error cumulation control; Multiple
precision floating-point arithmetic",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Digital arithmetic; Error analysis",
}
@InProceedings{Oevel:1991:YES,
author = "Walter Oevel and Klaus Strack",
title = "The {Yang--Baxter} equation and a systematic search
for {Poisson} brackets on associative algebras",
crossref = "Watt:1991:IPI",
pages = "229--236",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p229-oevel/",
abstract = "Starting with an associative algebra equipped with a
linear map solving the Yang--Baxter equation three
Poisson brackets may be constructed admitting a common
hierarchy of functions in involution. Realizations of
the algebra lead to various integrable hierarchies
known to admit an infinite number of invariant Poisson
brackets. In all cases three of these brackets are
known to originate from the three abstract brackets
defined on the algebra. A systematic search for
abstract versions of the higher Poisson brackets is
performed using computer algebra. It is shown that
apart from the three known brackets no further relevant
abstract brackets of a certain `local' form may be
constructed from solutions of the Yang--Baxter
equations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. Sci., Univ. of Technol., Loubhborough,
UK",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Abstract brackets; algorithms; Associative algebras;
Computer algebra; Integrable hierarchies; Poisson
brackets; Yang--Baxter equation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Algebra; Mathematics computing",
}
@InProceedings{Pecelli:1991:FMD,
author = "Giampiero Pecelli",
title = "Formal methods in delay-differential equations",
crossref = "Watt:1991:IPI",
pages = "317--318",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p317-pecelli/",
abstract = "Studies formal methods in the solution of
delay-differential equations (DDEs). The motivation for
such study comes from the introduction of Hopf
bifurcation techniques and the method of averaging to
the study of stable oscillations in such systems. The
author concentrates on the formal aspects associated
with the construction of solutions required for an
application of the methods. These classes of solutions
are quite simple, being solutions to linear systems.
The paper concentrates on completing the formalization
and showing that an automated system is possible.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Lowell Univ., MA, USA",
classification = "C4170 (Differential equations)",
keywords = "algorithms; DDEs; Delay-differential equations; Formal
methods; Hopf bifurcation; Stable oscillations",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Differential equations",
}
@InProceedings{Petho:1991:AGB,
author = "Attila Peth{\"o}",
title = "Application of {Gr{\"o}bner} bases to the resolution
of systems of norm equations",
crossref = "Watt:1991:IPI",
pages = "144--150",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p144-petho/",
abstract = "Let $K$ be a cubic extension of the rational number
field $Q$. Denote by $Z_K$ the ring of integers of $K$
and by $N_KQ/(\gamma )$ the norm of $\gamma$ in $K$.
Let $P(x)=x^2+cx+d$ in $Z(x)$ and $a,b,n_1,n_2,n_3$, in
$Z$. The paper gives necessary and sufficient
conditions for the existence of cubic number fields $K$
and elements $\eta$ in $Z_K$ such that
$N_KQ/(\eta)=n_1,N_KQ/(\eta-a)=n_2,N_KQ/(\eta-b)=n_3$;
or $N_KQ/(\eta)=n_1,N_KQ/(P(\eta))=n_2$.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Kossuth Lajos Univ., Debrecen,
Hungary",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "algorithms; theory; Gr{\"o}bner bases; Norm equations;
Cubic extension; Rational number field; Integers;
Necessary and sufficient conditions; Cubic number
fields",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Number theory; Polynomials",
}
@InProceedings{Reid:1991:RSD,
author = "G. J. Reid and A. Boulton",
title = "Reduction of systems of differential equations to
standard form and their integration using directed
graphs",
crossref = "Watt:1991:IPI",
pages = "308--312",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p308-reid/",
abstract = "Discusses an algorithm developed in earlier work which
has been implemented in MACSYMA that reduces systems of
partial differential equations to a simplified standard
form by eliminating redundances and including all
integrability conditions. Once a system has been put in
standard form the authors show how directed graphs
representing the dependencies amongst the system's
variables can be used to simplify the problem of
explicitly or numerically integrating the system.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., British Columbia Univ., Vancouver, BC,
Canada",
classification = "C1160 (Combinatorial mathematics); C4160 (Numerical
integration and differentiation); C4170 (Differential
equations)",
keywords = "algorithms; Directed graphs; Integration; MACSYMA;
Partial differential equations; Standard form",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, MACSYMA.",
thesaurus = "Directed graphs; Integration; Partial differential
equations",
}
@InProceedings{Renner:1991:NEE,
author = "Friedrich Renner",
title = "Nonlinear evolution equations and the {Painleve}
analysis: a constructive approach with {REDUCE}",
crossref = "Watt:1991:IPI",
pages = "289--294",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p289-renner/",
abstract = "A number of necessary conditions for a class of
nonlinear partial differential equations to pass the
Painleve test with the Kruskal ansatz is given. Using
these one can (theoretically) construct all evolution
equations of certain form and this property with a
computer algebra package based on REDUCE.",
acknowledgement = ack-nhfb,
affiliation = "Kassel Univ., Germany",
classification = "C4170 (Differential equations)",
keywords = "algorithms; Computer algebra package; Evolution
equations; Kruskal ansatz; Nonlinear partial
differential equations; Painleve test; REDUCE; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Nonlinear differential equations; Partial differential
equations; Symbol manipulation",
}
@InProceedings{Richardson:1991:TCN,
author = "Daniel Richardson",
title = "Towards computing nonalgebraic cylindrical
decompositions",
crossref = "Watt:1991:IPI",
pages = "247--255",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p247-richardson/",
abstract = "Non algebraic cylindrical decompositions are
discussed. False derivatives and local Sturm sequences
are defined as tools for computing them. The crucial
fact in the algebraic case is that one can characterize
the number of distinct real roots of a polynomial
$p(y)$ by a condition on the coefficients. An attempt
is made to obtain an analogous characterization for
nonalgebraic functions such as polynomials in monomials
which are defined by algebraic differential equations.
An example would be an exponential polynomial
$p(y,e^y)$. The difficulties of applying this
characterization are described, using the example of
exponential polynomials in two variables,
$p(x,e^y,y,e^y)$. The characterization obtained does
not lead to quantifier elimination.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Bath Univ., UK",
classification = "C1110 (Algebra); C1120 (Analysis); C7310
(Mathematics)",
keywords = "Algebraic differential equations; algorithms;
Cylindrical decompositions; Differential geometry;
Distinct real roots; Exponential polynomials; Local
Sturm sequences; Monomials; Nonalgebraic functions;
theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Nonalgebraic algorithms.",
thesaurus = "Algebra; Differential equations; Polynomials",
}
@InProceedings{Roch-Siebert:1991:PFE,
author = "Fran{\c{c}}oise Roch-Siebert and Gilles Villard",
title = "{PAC}: first experiments on a 128 transputers
m{\'e}ganode",
crossref = "Watt:1991:IPI",
pages = "343--351",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p343-roch-siebert/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Parallel algorithms. {\bf G.1.3} Mathematics
of Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods).
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf C.1.2}
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Multiple-instruction-stream, multiple-data-stream
processors (MIMD).",
}
@InProceedings{RochSiebert:1991:PFE,
author = "F. Roch-Siebert and G. Villard",
title = "{PAC}: first experiments on a 128 transputers
meganode",
crossref = "Watt:1991:IPI",
pages = "343--351",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "From its beginning three years ago, the PAC project:
parallel algebraic computing, has been exploiting a 16
processors hypercube to validate some algebraic
computation algorithms, and to justify the use of
parallelism. Going further, the authors begin to
generalize the previous results and study new problems.
Experiments are now held on a more massively parallel
computer: a 128 Transputers network. The authors
present the first results have obtained: as an example,
they have been interested in applying the Chinese
remainder theorem in linear algebra. For a fixed number
of processors, they show how the behaviour of an
algorithm is influenced by the chosen network topology.
They point out the communication costs and the
constraints due to the storage requirements.",
acknowledgement = ack-nhfb,
affiliation = "Equipe Calcul Parallele et Calcul Formel, CNRS,
Grenoble, France",
classification = "C4140 (Linear algebra); C7310 (Mathematics)",
keywords = "Algebraic computation; Chinese remainder theorem;
Linear algebra; Network topology; PAC project; Parallel
algebraic computing; Parallelism",
thesaurus = "Linear algebra; Parallel algorithms; Symbol
manipulation",
}
@InProceedings{Roelofs:1991:IMO,
author = "Marcel Roelofs and Peter K. H. Gragert",
title = "Implementation of multilinear operators in {REDUCE}
and applications in mathematics",
crossref = "Watt:1991:IPI",
pages = "390--396",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p390-roelofs/",
abstract = "Introduces and implement a concept for dealing with
mathematical bases of linear spaces and mappings
(multi)linear with respect to such bases, in REDUCE
(cf. (1)). Using this concept the authors give some
examples how to implement some well known (multi)linear
mappings in mathematics with very little effort.
Moreover they implement a procedure operatorcoeff
similar to the standard REDUCE procedure coeff, but now
for linear spaces instead of polynomial rings.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Twente Univ., Enschede,
Netherlands",
classification = "C4140 (Linear algebra); C7310 (Mathematics)",
keywords = "algorithms; Linear spaces; Mappings; Multilinear
operators; REDUCE",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
thesaurus = "Linear algebra; Symbol manipulation",
}
@InProceedings{Roque:1991:QRD,
author = "W. L. Roque and R. P. {dos Santos}",
title = "Qualitative reasoning, dimensional analysis and
computer algebra",
crossref = "Watt:1991:IPI",
pages = "460--461",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p460-roque/",
abstract = "In this short application report the authors discuss
qualitative reasoning about physical processes under
the framework of dimensional analysis. The symbolic
system QDR-Qualitative Dimensional Reasoner-has been
developed to automate the whole qualitative reasoning
analysis.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence)",
keywords = "algorithms; Computer algebra; Dimensional analysis;
languages; Physical processes; Qualitative reasoning;
Reasoning; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics. {\bf I.1.4} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Special-purpose
algebraic systems.",
thesaurus = "Inference mechanisms; Symbol manipulation",
}
@InProceedings{Rudenko:1991:ACA,
author = "V. M. Rudenko and V. V. Leonov and A. F. Bragazin and
I. P. Shmyglevsky",
title = "Application of computer algebra to the investigation
of the orbital satellite motion",
crossref = "Watt:1991:IPI",
pages = "450--451",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p450-rudenko/",
abstract = "Presents the features of a program package
`Polymech-symbol' helping to solve some laborious
mechanical problems. The package was written by means
of the REDUCE system and contains several algorithms in
a form of REDUCE procedures. The authors consider the
problems of navigation and center of mass motion on
board a satellite.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Problems of Mech., Acad. of Sci., Moscow,
USSR",
classification = "C7460 (Aerospace engineering)",
keywords = "algorithms; Center of mass motion; Computer algebra;
Navigation; Orbital satellite motion; Polymech-symbol;
REDUCE system",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Aerospace.",
thesaurus = "Aerospace computing; Artificial satellites; Symbol
manipulation",
}
@InProceedings{Rybowicz:1991:ACI,
author = "Marc Rybowicz",
title = "An algorithm for computing integral bases of an
algebraic function field",
crossref = "Watt:1991:IPI",
pages = "157--166",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p157-rybowicz/",
abstract = "The author presents a new algorithm for function
fields which borrows techniques from previous methods
and works in any characteristic. Theorem 5 allows one
to reduce the problem to the factorization of rational
primes via some standard linear algebra techniques. He,
in turn, reduces this factorization problem to study
how two branches of the underlying curve intersect.
This latter task is achieved with the help of the
`Hamburger--Noether Development', a special type of
local parametrization. He expects the algorithm to be
more efficient than Zassenhaus' global approach and to
highlight the classical local approach. Moreover, the
techniques presented allow one to build a function with
specified zeros in any characteristic and could be
applied to other problems. Although the algorithm is
complete, some steps clearly need to be improved and
studied more carefully before attempting any
implementation. In particular, he assumes that the
constant field is algebraically closed, but a
`rational' extension of the algorithm would be
welcome.",
acknowledgement = ack-nhfb,
affiliation = "Symbolic Comput. Group, Waterloo Univ., Ont., Canada",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "Algebraic function field; algorithms; Factorization;
Hamburger--Noether Development; Integral bases; Linear
algebra; Local parametrization; Rational primes",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Group theory; Mathematics computing; Number theory;
Symbol manipulation",
}
@InProceedings{Schlegel:1991:DRS,
author = "H. Schlegel",
title = "Determination of the root system of semisimple {Lie}
algebras from the {Dynkin} diagram",
crossref = "Watt:1991:IPI",
pages = "239--240",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p239-schlegel/",
abstract = "One way to represent the properties of the Lie algebra
for calculations is by means of the commutation
relations, i.e. the structure constants. The paper
shows a way of the calculation of the Cartan--Weyl
basis for all simple Lie algebras starting from the
Dynkin diagram. The package DYNKIN written in REDUCE
implements the described relations and can as an
application be used to perform the calculations for a
specified Lie algebra.",
acknowledgement = ack-nhfb,
affiliation = "Zentralinstitut fur Elektronenphys., Berlin, Germany",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "algorithms; Cartan--Weyl basis; Commutation relations;
Dynkin diagram; Root system; Semisimple Lie algebras;
Simple Lie algebras; Structure constants",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Diagrams; Mathematics computing",
}
@InProceedings{Schmitt:1991:EAA,
author = "Joacheim Schmitt",
title = "An embedding algorithm for algebraic congruence
function fields",
crossref = "Watt:1991:IPI",
pages = "187--188",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p187-schmitt/",
abstract = "Provides an analogue of the Round 4 algorithm of
Ford/Zassenhaus (1978) for algebraic congruence
function fields. The reduction steps can also be used
in other embedding algorithms. The algorithm is
implemented within the computer algebra system SIMATH.
The corresponding programs are written in C. The
results can be used in integration and cryptography.",
acknowledgement = ack-nhfb,
affiliation = "Saarlandes Univ., Saarbrucken, Germany",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)",
keywords = "Algebraic congruence function fields; algorithms;
Computer algebra system; Cryptography; Embedding
algorithms; Integration; Round 4 algorithm; SIMATH",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Number theory",
}
@InProceedings{Schonhage:1991:FRC,
author = "Arnold Sch{\"o}nhage",
title = "Fast reduction and composition of binary quadratic
forms",
crossref = "Watt:1991:IPI",
pages = "128--133",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p128-schonhage/",
abstract = "Similar to the fast computation of integer gcd's,
reduction of binary quadratic forms $ax^2+bxy+cy^2$
with integral coefficients $a, b, c$ bounded by $2^n$
is possible in time $O (\mu (n) \log{}n)$, where
$\mu(n)$ is a time bound for $n$-bit integer
multiplication. This result is obtained by a
corresponding algorithm for the monotone reduction of
positive forms. The same time bound holds for the
composition of forms. Moreover, finding a reduced form
is shown to be at least as difficult as extended gcd
computation, up to terms of order $\mu (n)$.",
acknowledgement = ack-nhfb,
affiliation = "Bonn Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C4240
(Programming and algorithm theory)",
keywords = "algorithms; Binary quadratic forms; Integer
multiplication; Integral coefficients; Monotone
reduction; Positive forms; Time bound",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation.",
thesaurus = "Computational complexity; Number theory",
}
@InProceedings{Schulze-Pillot:1991:ACG,
author = "Rainer Schulze-Pillot",
title = "An algorithm for computing genera of ternary and
quaternary quadratic forms",
crossref = "Watt:1991:IPI",
pages = "134--143",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p134-schulze-pillot/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms.",
}
@InProceedings{SchulzePillot:1991:ACG,
author = "R. Schulze-Pillot",
title = "An algorithm for computing genera of ternary and
quaternary quadratic forms",
crossref = "Watt:1991:IPI",
pages = "134--143",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The paper reports on an algorithm for computing genera
of ternary and quaternary positive definite quadratic
forms over Z. It is well known that due to the simple
shape of the reduction conditions in these dimensions
it is in principle no problem to compute
representatives of all classes of such quadratic forms
whose discriminant is below a given bound. It is,
however, sometimes desirable to be able to quickly
determine representatives of all classes in some fixed
genus of quadratic forms of possibly high discriminant
without having to generate along the way all forms of
smaller discriminant. An obvious attempt in such a case
is to use Kneser's method of neighbouring or adjacent
lattices. The paper draws attention to the fact that it
is indeed not difficult to use this method in
dimensions 3 and 4 as the basis of an algorithm that
serves the purpose. With almost no extra work one
obtains at the same time the adjacency graph of the
classes determined; this has interesting arithmetic and
graph theoretic applications. It is intended to use the
algorithm for the experimental investigation of the
Fourier and Fourier--Jacobi coefficients of certain
linear combinations of Siegel $\theta$ series of
quaternary quadratic forms.",
acknowledgement = ack-nhfb,
affiliation = "Fakultat fur Math., Bielefeld Univ., Germany",
classification = "C1160 (Combinatorial mathematics)",
keywords = "Adjacency graph; Adjacent lattices; Discriminant;
Fourier--Jacobi coefficients; Genera; Linear
combinations; Neighbouring lattices; Quaternary
positive definite quadratic forms; Reduction
conditions; Siegel $\theta$ series; Ternary positive
definite quadratic forms",
thesaurus = "Number theory",
}
@InProceedings{Schwarz:1991:ETP,
author = "Fritz Schwarz",
title = "Existence theorems for polynomial first integrals",
crossref = "Watt:1991:IPI",
pages = "256--264",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p256-schwarz/",
abstract = "In various areas of applied mathematics there occur
autonomous systems of ordinary differential equations
of the form $x_i= \omega _i(x,c), i=1,\ldots{}n$ where
the right hand sides are polynomial in all arguments
$x=(x_1,\ldots{}x_n)$ and $c=(c_1,c_2,\ldots{})$; the
latter variables are parameters which are a priori
unspecified. There arises the following question: Do
first integrals of a certain type, e.g. polynomial
first integrals? The computer algebra package DYNSYS
allows one to find all polynomial first integrals up to
a given highest degree $D$ but does not provide any
information beyond $D$. To obtain a complete answer
these packages should be complemented by rigorous
results concerning the possible existence of first
integrals of any degree. Theorems of this kind are
obtained. The basic principle for obtaining them is to
identify subsystems of the determining system which
have a certain structure independent of $D$. This
method is applied to several two- and three-dimensional
systems. It is shown for example that the famous Lorenz
system in general does not allow any polynomial first
integrals. Furthermore some ideas are presented on how
these methods may be converted into algorithms such
that a machine may perform the necessary analysis.",
acknowledgement = ack-nhfb,
affiliation = "GMD, Inst. F1, St. Augustin, Germany",
classification = "C1120 (Analysis); C4170 (Differential equations);
C4180 (Integral equations)",
keywords = "algorithms; Applied mathematics; Autonomous systems;
Computer algebra package; DYNSYS; Lorenz system;
Ordinary differential equations; Polynomial first
integrals; theory; Three-dimensional systems",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Special-purpose algebraic
systems.",
thesaurus = "Differential equations; Integral equations;
Polynomials",
}
@InProceedings{Shoup:1991:FDA,
author = "Victor Shoup",
title = "A fast deterministic algorithm for factoring
polynomials over finite fields of small
characteristic",
crossref = "Watt:1991:IPI",
pages = "14--21",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p14-shoup/",
abstract = "Presents a new algorithm for factoring polynomials
over finite fields. The algorithm is deterministic, and
its running time is `almost' quadratic when the
characteristic is a small fixed prime. As such, the
algorithm is asymptotically faster than previously
known deterministic algorithms for factoring
polynomials over finite fields of small
characteristic.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Toronto Univ., Toronto, Ont.,
Canada",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Deterministic algorithm; Finite fields;
Polynomial factorisation; Small characteristic; Small
fixed prime; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Sit:1991:TPL,
author = "William Y. Sit",
title = "A theory for parametric linear systems",
crossref = "Watt:1991:IPI",
pages = "112--121",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p112-sit/",
abstract = "Presents a theoretical foundation for studying
parametric systems of linear equations and proves an
efficient algorithm for identifying all parametric
values (including degenerate cases) for which the
system is consistent. The algorithm gives a small set
of regimes where for each regime, the solutions of the
specialized systems may be given uniformly. For
homogeneous systems, or for systems where the right
hand side is arbitrary, this small set is irredundant.
A complexity analysis of the Gaussian elimination
method is given and compared with the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., City Coll. of New York, NY, USA",
classification = "C4140 (Linear algebra); C4240 (Programming and
algorithm theory)",
keywords = "algorithms; Complexity analysis; Degenerate cases;
Gaussian elimination; Homogeneous systems; Linear
equations; Parametric systems; Parametric values;
Regimes; Right hand side; Specialized systems; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
systems (direct and iterative methods).",
thesaurus = "Computational complexity; Linear algebra",
}
@InProceedings{Stein:1991:ADR,
author = "Andreas Stein and Horst G{\"u}nter Zimmer",
title = "An algorithm for determining the regulator and the
fundamental unit of a hyperelliptic congruence function
field",
crossref = "Watt:1991:IPI",
pages = "183--184",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p183-stein/",
abstract = "A continued fraction algorithm (baby steps) is
described by B. Weis, H. G. Zimmer (Mitt. Math. Ges:
Hamburg, 1991) for determining the regulator and the
fundamental unit of the congruence function field $K/k$
with respect to the indeterminate $X$. The algorithm is
based on work of Artin (Math Z vol. 19, p. 153--246,
1924) and was implemented within the computer algebra
system SIMATH. The authors show how the algorithm can
be substantially improved by applying to the function
field case D. Shanks' (1972) idea of the infrastructure
of a real quadratic number field. The improved version
of this algorithm has been implemented within the
computer algebra system SIMATH, too.",
acknowledgement = ack-nhfb,
affiliation = "Saarlandes Univ., Saarbrucken, Germany",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C7310 (Mathematics)",
keywords = "algorithms; Baby steps; Computer algebra system;
Congruence function field; Continued fraction
algorithm; Function field; Fundamental unit;
Hyperelliptic congruence function field; Indeterminate;
Real quadratic number field; Regulator; SIMATH",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations in finite fields. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Algebra; Number theory; Symbol manipulation",
}
@InProceedings{Surguladze:1991:APC,
author = "Levan R. Surguladze and Mark A. Samuel",
title = "Algebraic perturbative calculations in high energy
physics. {Methods}, algorithms, computer programs and
physical applications",
crossref = "Watt:1991:IPI",
pages = "439--447",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p439-surguladze/",
abstract = "The methods and algorithms for high order algebraic
perturbative calculations in theoretical high energy
physics are briefly reviewed. The SCHOONSCHIP program
MINCER and the REDUCE program LOOPS for analytical
computation of arbitrary massless, one-, two- and
three-loop Feynman diagrams of the propagator type are
described. The version of the program LOOPS for
personal computers and the extended version of the
program MINCER for four-loop renormalization group
calculations are presented. The new program for
algebraic perturbative calculations is also discussed.
This program is written on the new algebraic
programming system FORM. Some recent results of
application to the high energy physics are given.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Res., Acad. of Sci., Moscow, USSR",
classification = "A0270 (Computational techniques); A1110G
(Renormalization); C7320 (Physics and Chemistry)",
keywords = "Algebraic perturbative calculations; algorithms;
Feynman diagrams; High energy physics; LOOPS; MINCER;
REDUCE; SCHOONSCHIP program",
subject = "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE.",
thesaurus = "Feynman diagrams; Physics computing; Renormalisation;
Symbol manipulation",
}
@InProceedings{Trenkov:1991:ARS,
author = "I. Trenkov and M. Spiridonova and M. Daskalova",
title = "An application of the {REDUCE} system for solving a
mathematical geodesy problem",
crossref = "Watt:1991:IPI",
pages = "448--449",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p448-trenkov/",
abstract = "A REDUCE program package for solving some mathematical
geodesy problems now under development includes
capabilities for solving the problem: the geographical
coordinates (the geographical density $B_p$ and the
geographical longitude $L_p$) of a point $P$ on the
earthly ellipsoid are to be calculated when $n$
different points $C_i(i=1, 2, \ldots{}, n)$ with their
geographical coordinates $B_i$ and $L_i$ are given and
the azimuths $A_{ip}$ in all points $C_i$ to the point
$P$ are measured.",
acknowledgement = ack-nhfb,
affiliation = "Central Lab. for Geodesy, Bulgarian Acad. of Sci.,
Sofia, Bulgaria",
classification = "A9110B (Mathematical geodesy: general theory); C7310
(Mathematics); C7340 (Geophysics)",
keywords = "algorithms; Geographical coordinates; Mathematical
geodesy; Program package; REDUCE system",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics. {\bf J.2}
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Earth and atmospheric sciences.",
thesaurus = "Computational geometry; Geodesy; Geophysics computing;
Symbol manipulation",
}
@InProceedings{Trevisan:1991:PFU,
author = "Vilmar Trevisan and Paul Wang",
title = "Practical factorization of univariate polynomials over
finite fields",
crossref = "Watt:1991:IPI",
pages = "22--31",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p22-trevisan/",
abstract = "The research presented is part of an effort to
establish state-of-the-art factoring routines for
polynomials. The foundation of such algorithms lies in
the efficient factorization over a finite field
$\mbox{GF}(p^k)$. The Cantor--Zassenhaus algorithm
together with innovative ideas suggested by others is
compared with the Berlekamp algorithm. The studies led
to the design of a hybrid algorithm that combines the
strengths of the different approaches. The algorithms
are also implemented and machine timings are obtained
to measure the performance of these algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C4130 (Interpolation and function approximation);
C4240 (Programming and algorithm theory)",
keywords = "algorithms; Berlekamp algorithm; Cantor--Zassenhaus
algorithm; Factoring routines; Factorization; Finite
fields; Hybrid algorithm; performance; Univariate
polynomials",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations in finite fields.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms.",
thesaurus = "Computational complexity; Polynomials",
}
@InProceedings{Vinette:1991:FSC,
author = "F. Vinette",
title = "Features of symbolic computation exploited in the
calculation of lower energy bounds of cyclic polyene
models",
crossref = "Watt:1991:IPI",
pages = "458--459",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p458-vinette/",
abstract = "Symbolic computation has been applied in many
scientific disciplines and has proved to be a very
valuable research tool. In earlier studies, features of
symbolic computation including algebraic manipulations
and high decimal precision, were shown to be very
useful to solve nonrelativistic quantum mechanical
problems. The author illustrates the valuable
assistance of symbolic computation in solving quantum
chemical problems. The symbolic computational language
MAPLE is used throughout this study. The computational
aspects of the application of Lowdin's Optimized Inner
Projection (OIP) to determine lower bounds to the
ground state energy of the Pariser--Parr--Pople (PPP)
model of cyclic polyenes, is briefly presented. A
diagrammatic approach for evaluating the required
matrix elements is needed: this method is often used in
quantum chemistry. The evaluation of Brandow diagrams,
which is very tedious and almost impossible to do by
hand, is easily obtained using MAPLE.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Stat., York Univ., North York,
Ont., Canada",
classification = "A3115 (General mathematical and computational
developments); A3120 (Specific calculations and
results); C7320 (Physics and Chemistry)",
keywords = "algorithms; Brandow diagrams; Cyclic polyene models;
Ground state energy; languages; Lower energy bounds;
MAPLE; Optimized Inner Projection;
Pariser--Parr--Pople; Quantum chemical problems;
Symbolic computation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Chemistry. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN.",
thesaurus = "Chemistry computing; Molecular energy level
calculations; Organic compounds; Quantum chemistry;
Symbol manipulation",
}
@InProceedings{Wang:1991:TMI,
author = "Dongming Wang",
title = "A toolkit for manipulating indefinite summations with
application to neural networks",
crossref = "Watt:1991:IPI",
pages = "462--463",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p462-wang/",
abstract = "Presents the design of some rules and the
implementation of an application-oriented toolkit in
Macsyma by amending some of its incorrect computations
for the manipulation of indefinite summations. The
application of this toolkit to the analysis and
derivation of neural networks is briefly discussed.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C6115 (Programming support); C6170 (Expert
systems)",
keywords = "algorithms; Application-oriented toolkit; design;
Indefinite summations; Macsyma; Neural networks",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.4}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Applications. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA. {\bf I.2.6} Computing
Methodologies, ARTIFICIAL INTELLIGENCE, Learning,
Connectionism and neural nets.",
thesaurus = "Neural nets; Software tools; Symbol manipulation",
}
@InProceedings{Weibel:1991:AP,
author = "Trudy Weibel and Gaston H. Gonnet",
title = "An algebra of properties",
crossref = "Watt:1991:IPI",
pages = "352--359",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p352-weibel/",
abstract = "The purpose of the paper is to build a framework and
give algorithms to solve queries of the form obj in
Prop where the object obj is expressible in terms of
other given objects. The authors develop an algebra of
properties, PROP, in which we carry out computations.
They present a set of rules (axioms Ax1-Ax7) for the
behaviour of the basic functions on properties. In
addition, they represent the algorithmic components
such as if and while by the algebra operations meet and
join. They conclude by proposing an implementation of
the algebra PROP.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Theor. Comput. Sci., Zurich, Switzerland",
classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
keywords = "Algebra; Algebra of properties; Algorithmic
components; algorithms; PROP",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous.",
thesaurus = "Symbol manipulation",
}
@InProceedings{Yakubovich:1991:EIS,
author = "S. B. Yakubovich and Yu. F. Luchko",
title = "The evaluation of integrals and series with respect to
indices (parameters) of hypergeometric functions",
crossref = "Watt:1991:IPI",
pages = "271--280",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p271-yakubovich/",
abstract = "A general method for the evaluation of some integrals
of hypergeometric functions, and programming package,
which works on the basis of this method, were described
in Adamchik, Luchko, Marichev (1990). But many
integrals which have appeared in practice don't belong
to the class of convolution type integrals and,
consequently, one can't use the previous method for the
evaluation of such integrals. In particular, one needs
original methods for the evaluation of integrals and
series with respect to indices of special functions.",
acknowledgement = ack-nhfb,
affiliation = "Byelorussian State Univ., Minsk, Byelorussian SSR,
USSR",
classification = "C4160 (Numerical integration and differentiation)",
keywords = "algorithms; Evaluation of integrals; Hypergeometric
functions; Indices; Integrals; Special functions;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations.",
thesaurus = "Integration; Series [mathematics]",
}
@InProceedings{Ziel:1991:RFD,
author = "Richard Ziel",
title = "Rational function decomposition",
crossref = "Watt:1991:IPI",
pages = "1--6",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p1-zippel/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Rational
approximation. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Zippel:1991:RFD,
author = "R. Zippel",
title = "Rational function decomposition",
crossref = "Watt:1991:IPI",
pages = "1--6",
year = "1991",
bibdate = "Thu Sep 26 06:00:06 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Presents a polynomial time algorithm for determining
whether a given univariate rational function over an
arbitrary field is the composition of two rational
functions over that field, and finds them if so.",
acknowledgement = ack-nhfb,
affiliation = "Cornell Univ., Ithaca, NY, USA",
classification = "C4130 (Interpolation and function approximation)",
keywords = "Arbitrary field; Polynomial time algorithm; Univariate
rational function",
thesaurus = "Polynomials",
}
@InProceedings{Zolotykh:1991:PCS,
author = "A. A. Zolotykh",
title = "A package for computations in simple {Lie} algebra
representations",
crossref = "Watt:1991:IPI",
pages = "237--238",
year = "1991",
bibdate = "Thu Mar 12 08:38:03 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p237-zolotykh/",
abstract = "The author present a software package for calculations
of some numerical characteristics of simple Lie
algebras of rank not more than 12 and their irreducible
finite-dimensional representations over algebraically
closed fields of characteristic zero (for example, over
the field of complex numbers). Times of some
computations on an IBM PC/AT (processor 286) are given:
the times of character computations and times of tensor
square computations for the fundamental (basic)
representation of exceptional Lie algebras and of
12-rank Lie algebras. The table contains also the
dimensions of corresponding fundamental
representations.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Mech. and Math., Moscow State Univ., USSR",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Algebraically closed fields; algorithms; IBM PC/AT;
Irreducible finite-dimensional representations;
Numerical characteristics; Simple Lie algebra
representations; Tensor square computations; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Special-purpose
algebraic systems.",
thesaurus = "Algebra; Mathematics computing; Microcomputer
applications",
xxtitle = "A package for computation in simple {Lie} algebra
representations",
}
@InProceedings{Bischof:1992:AAD,
author = "Christian Bischof and Alan Carle and George Corliss
and Andreas Griewank",
title = "{ADIFOR}: {Automatic} differentiation in a source
translator environment",
crossref = "Wang:1992:PII",
pages = "294--302",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p294-bischof/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; experimentation; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.6}
Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Gradient methods. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems.",
}
@InProceedings{Bronstein:1992:LOD,
author = "Manuel Bronstein",
title = "Linear ordinary differential equations: breaking
through the order 2 barrier",
crossref = "Wang:1992:PII",
pages = "42--48",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p42-bronstein/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Burnel:1992:CCY,
author = "A. Burnel and H. Caprasse",
title = "The computation of $1$-loop contributions in {Y.M.}
theories with class {III} nonrelativistic gauges and
{REDUCE}",
crossref = "Wang:1992:PII",
pages = "103--107",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p103-burnel/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; Yang--Mills",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms.",
}
@InProceedings{Butler:1992:ECA,
author = "Greg Butler",
title = "Experimental comparison of algorithms for {Sylow}
subgroups",
crossref = "Wang:1992:PII",
pages = "251--262",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p251-butler/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous.",
}
@InProceedings{Cetinkaya:1992:SAL,
author = "Cetin Cetinkaya",
title = "On stability analysis of linear stochastic and
time-varying deterministic systems",
crossref = "Wang:1992:PII",
pages = "278--283",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p278-cetinkaya/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Eigenvalues and eigenvectors (direct
and iterative methods). {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative methods).
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
}
@InProceedings{Codutti:1992:NNL,
author = "M. Codutti",
title = "{NODES}: non linear ordinary differential equations
solver",
crossref = "Wang:1992:PII",
pages = "69--79",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p69-codutti/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
}
@InProceedings{Collins:1992:EAI,
author = "George E. Collins and Werner Krandick",
title = "An efficient algorithm for infallible polynomial
complex root isolation",
crossref = "Wang:1992:PII",
pages = "189--194",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p189-collins/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Cook:1992:CGA,
author = "Grant O. {Cook, Jr.}",
title = "Code generation in {ALPAL} using symbolic techniques",
crossref = "Wang:1992:PII",
pages = "27--35",
year = "1992",
DOI = "https://doi.org/10.1145/143242.143260",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p27-cook/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
FORTRAN. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
Language Classifications, C. {\bf G.1.6} Mathematics of
Computing, NUMERICAL ANALYSIS, Optimization. {\bf
D.3.4} Software, PROGRAMMING LANGUAGES, Processors,
Code generation.",
}
@InProceedings{Cooperman:1992:FCB,
author = "Gene Cooperman and Larry Finkelstein",
title = "A fast cyclic base change for permutation groups",
crossref = "Wang:1992:PII",
pages = "224--232",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p224-cooperman/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Trees. {\bf G.3} Mathematics of Computing,
PROBABILITY AND STATISTICS, Probabilistic algorithms
(including Monte Carlo).",
}
@InProceedings{Crouch:1992:ECI,
author = "P. E. Crouch and R. L. Grossman",
title = "The explicit computation of integration algorithms and
first integrals for ordinary differential equations
with polynomial coefficients using trees",
crossref = "Wang:1992:PII",
pages = "89--94",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p89-crouch/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.2}
Mathematics of Computing, DISCRETE MATHEMATICS, Graph
Theory, Trees. {\bf G.1.7} Mathematics of Computing,
NUMERICAL ANALYSIS, Ordinary Differential Equations.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms.",
}
@InProceedings{Dalmas:1992:PFL,
author = "St{\'e}phane Dalmas",
title = "A polymorphic functional language applied to symbolic
computation",
crossref = "Wang:1992:PII",
pages = "369--375",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p369-dalmas/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf F.3.3} Theory
of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Studies of Program Constructs, Type structure. {\bf
F.3.3} Theory of Computation, LOGICS AND MEANINGS OF
PROGRAMS, Studies of Program Constructs, Functional
constructs. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, SCRATCHPAD.",
}
@InProceedings{Davenport:1992:PTR,
author = "J. H. Davenport",
title = "Primality testing revisited",
crossref = "Wang:1992:PII",
pages = "123--129",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p123-davenport/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations.",
}
@InProceedings{Dewar:1992:UCA,
author = "Michael C. Dewar",
title = "Using computer algebra to select numerical
algorithms",
crossref = "Wang:1992:PII",
pages = "1--8",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p1-dewar/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
}
@InProceedings{Fateman:1992:HPG,
author = "Richard Fateman",
title = "Honest plotting, global extrema, and interval
arithmetic",
crossref = "Wang:1992:PII",
pages = "216--223",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p216-fateman/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.",
}
@InProceedings{Ganzha:1992:NSA,
author = "V. G. Ganzha and E. V. Vorozhtsov and J. A. {van
Hulzen}",
title = "A new symbolic-numeric approach to stability analysis
of difference schemes",
crossref = "Wang:1992:PII",
pages = "9--15",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p9-ganzha/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.4}
Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation, Finite
difference methods. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, FORTRAN. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, REDUCE.",
}
@InProceedings{Gao:1992:SPA,
author = "Xiao-Shan Gao and Shang-Ching Chou",
title = "Solving parametric algebraic systems",
crossref = "Wang:1992:PII",
pages = "335--341",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p335-gao/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Geddes:1992:HSI,
author = "K. O. Geddes and G. J. Fee",
title = "Hybrid symbolic-numeric integration in {MAPLE}",
crossref = "Wang:1992:PII",
pages = "36--41",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p36-geddes/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@InProceedings{Gil:1992:CJC,
author = "Isabelle Gil",
title = "Computation of the {Jordan} canonical form of a square
matrix (using the {Axiom} programming language)",
crossref = "Wang:1992:PII",
pages = "138--145",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p138-gil/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices. {\bf G.1.3}
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Eigenvalues and eigenvectors (direct
and iterative methods). {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Grigoriev:1992:ESP,
author = "Dima Y. u. Grigoriev and Marek Karpinski and Andrew M.
Odlyzko",
title = "Existence of short proofs for nondivisibility of
sparse polynomials under the extended {Riemann}
hypothesis",
crossref = "Wang:1992:PII",
pages = "117--122",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p117-grigoriev/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Analysis of algorithms. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial).",
}
@InProceedings{Gutierrez:1992:PIT,
author = "Jaime Gutierrez and Tomas Recio",
title = "A practical implementation of two rational function
decomposition algorithms",
crossref = "Wang:1992:PII",
pages = "152--157",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p152-gutierrez/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
}
@InProceedings{Hietarinta:1992:SCQ,
author = "Jarmo Hietarinta",
title = "Solving the constant quantum {Yang--Baxter} equation
in $2$ dimensions with massive use of factorizing
{Gr{\"o}bner} basis computations",
crossref = "Wang:1992:PII",
pages = "350--357",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p350-hietarinta/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices.",
}
@InProceedings{Hong:1992:SSF,
author = "Hoon Hong",
title = "Simple solution formula construction in cylindrical
algebraic decomposition based quantifier elimination",
crossref = "Wang:1992:PII",
pages = "177--188",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p177-hong/",
acknowledgement = ack-nhfb,
keywords = "algorithms; experimentation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications.",
}
@InProceedings{Johnson:1992:RAN,
author = "J. R. Johnson",
title = "Real algebraic number computation using interval
arithmetic",
crossref = "Wang:1992:PII",
pages = "195--205",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p195-johnson/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Kajler:1992:CPE,
author = "Norbert Kajler",
title = "{CAS\slash PI}: a portable and extensible interface
for computer algebra systems",
crossref = "Wang:1992:PII",
pages = "376--386",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p376-kajler/",
acknowledgement = ack-nhfb,
keywords = "algorithms; design; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
H.5.2} Information Systems, INFORMATION INTERFACES AND
PRESENTATION, User Interfaces. {\bf D.2.2} Software,
SOFTWARE ENGINEERING, Design Tools and Techniques, User
interfaces. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}
@InProceedings{Kaltofen:1992:CDM,
author = "Erich Kaltofen",
title = "On computing determinants of matrices without
divisions",
crossref = "Wang:1992:PII",
pages = "342--349",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p342-kaltofen/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
}
@InProceedings{Kirrinnis:1992:FCN,
author = "Peter Kirrinnis",
title = "Fast computation of numerical partial fraction
decompositions and contour integrals of rational
functions",
crossref = "Wang:1992:PII",
pages = "16--26",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p16-kirrinnis/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
}
@InProceedings{Kuhn:1992:CPS,
author = "Norbert Kuhn and Klaus Madlener and Friedrich Otto",
title = "Computing presentations for subgroups of context-free
groups",
crossref = "Wang:1992:PII",
pages = "240--250",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p240-kuhn/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems, Decision
problems. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes.",
}
@InProceedings{Lamagna:1992:DUI,
author = "Edmund A. Lamagna and Michael B. Hayden and Catherine
W. Johnson",
title = "The design of a user interface to a computer algebra
system for introductory calculus",
crossref = "Wang:1992:PII",
pages = "358--368",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p358-lamagna/",
acknowledgement = ack-nhfb,
keywords = "algorithms; human factors",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf H.5.2} Information
Systems, INFORMATION INTERFACES AND PRESENTATION, User
Interfaces, Interaction styles. {\bf H.5.2} Information
Systems, INFORMATION INTERFACES AND PRESENTATION, User
Interfaces, Input devices and strategies.",
}
@InProceedings{Lempken:1992:SPS,
author = "W. Lempken and R. Staszewski",
title = "The structure of the {PIMs} of {SL(3,4)} in
characteristic 2",
crossref = "Wang:1992:PII",
pages = "233--239",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p233-lempken/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Representations
(general and polynomial).",
}
@InProceedings{Manocha:1992:MRL,
author = "Dinesh Manocha and John F. Canny",
title = "Multipolynomial resultants and linear algebra",
crossref = "Wang:1992:PII",
pages = "158--167",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p158-manocha/",
acknowledgement = ack-nhfb,
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Sparse, structured, and very
large systems (direct and iterative methods). {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
}
@InProceedings{Marinuzzi:1992:LNS,
author = "Francesco Marinuzzi and Stefano Soliani",
title = "{LISA}: {A} new symbolic package for the definition,
analysis and resolution of {Markovian} processes:
symbolic and inductive techniques",
crossref = "Wang:1992:PII",
pages = "303--311",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p303-marinuzzi/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic.",
}
@InProceedings{Moller:1992:GBC,
author = "H. Michael M{\"o}ller and Teo Mora and Carlo
Traverso",
title = "Gr{\"o}bner bases computation using syzygies",
crossref = "Wang:1992:PII",
pages = "320--328",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p320-moller/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Morain:1992:ENE,
author = "F. Morain",
title = "Easy numbers for the elliptic curve primality proving
algorithm",
crossref = "Wang:1992:PII",
pages = "263--268",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p263-morain/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations. {\bf
I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.2.m} Mathematics of
Computing, DISCRETE MATHEMATICS, Miscellaneous.",
}
@InProceedings{Mutrie:1992:AFE,
author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
Char",
title = "An approach for floating-point error analysis using
computer algebra",
crossref = "Wang:1992:PII",
pages = "284--293",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf G.2.2} Mathematics
of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
algorithms.",
}
@InProceedings{Noro:1992:RCA,
author = "Masayuki Noro and Taku Takeshima",
title = "{Risa\slash Asir} --- a computer algebra system",
crossref = "Wang:1992:PII",
pages = "387--396",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p387-noro/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf D.2.5} Software,
SOFTWARE ENGINEERING, Testing and Debugging, Debugging
aids.",
}
@InProceedings{Painter:1992:MES,
author = "Jeffrey F. Painter",
title = "The matrix editor for symbolic {Jacobians} in
{ALPAL}",
crossref = "Wang:1992:PII",
pages = "312--319",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p312-painter/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, MACSYMA.",
}
@InProceedings{Reid:1992:ADC,
author = "G. J. Reid and I. G. Lisle and A. Boulton and A. D.
Wittkopf",
title = "Algorithmic determination of commutation relations for
{Lie} symmetry algebras of {PDEs}",
crossref = "Wang:1992:PII",
pages = "63--68",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p63-reid/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Richardson:1992:ECP,
author = "Daniel Richardson",
title = "The elementary constant problem",
crossref = "Wang:1992:PII",
pages = "108--116",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p108-richardson/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Rioboo:1992:RAC,
author = "Renaud Rioboo",
title = "Real algebraic closure of an ordered field:
implementation in {Axiom}",
crossref = "Wang:1992:PII",
pages = "206--215",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p206-rioboo/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Expressions and Their Representation,
Representations (general and polynomial).",
}
@InProceedings{Russo:1992:CSA,
author = "Mark F. Russo",
title = "A combined symbolic\slash numeric approach for the
integration of stiff nonlinear systems of {ODE}'s",
crossref = "Wang:1992:PII",
pages = "80--88",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p80-russo/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.1.2} Mathematics of
Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear
approximation.",
}
@InProceedings{Salvy:1992:AEF,
author = "Bruno Salvy and John Shackell",
title = "Asymptotic expansions of functional inverses",
crossref = "Wang:1992:PII",
pages = "130--137",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p130-salvy/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Analysis of algorithms.",
}
@InProceedings{Schwarz:1992:RCA,
author = "Fritz Schwarz",
title = "Reduction and completion algorithms for partial
differential equations",
crossref = "Wang:1992:PII",
pages = "49--56",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p49-schwarz/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Singer:1992:LST,
author = "Michael F. Singer and Felix Ulmer",
title = "{Liouvillian} solutions of third order linear
differential equations: new bounds and necessary
conditions",
crossref = "Wang:1992:PII",
pages = "57--62",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
Theory/cathode.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p57-singer/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
}
@InProceedings{Viklund:1992:OLS,
author = "Lars Viklund and Peter Fritzson",
title = "An object-oriented language for symbolic computation
--- applied to machine element analysis",
crossref = "Wang:1992:PII",
pages = "397--405",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p397-viklund/",
acknowledgement = ack-nhfb,
keywords = "design; languages",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Object-oriented languages. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C++. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
}
@InProceedings{Villard:1992:PLB,
author = "Gilles Villard",
title = "Parallel lattice basis reduction",
crossref = "Wang:1992:PII",
pages = "269--277",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p269-villard/",
acknowledgement = ack-nhfb,
keywords = "algorithms; performance",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic. {\bf G.2.m} Mathematics
of Computing, DISCRETE MATHEMATICS, Miscellaneous.",
}
@InProceedings{Wang:1992:PUA,
author = "Paul S. Wang",
title = "Parallel univariate $p$-adic lifting on shared-memory
multiprocessors",
crossref = "Wang:1992:PII",
pages = "168--176",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p168-wang/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
}
@InProceedings{Weispfenning:1992:FGB,
author = "V. Weispfenning",
title = "Finite {Gr{\"o}bner} bases in {non-Noetherian} skew
polynomial rings",
crossref = "Wang:1992:PII",
pages = "329--334",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p329-weispfenning/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.",
}
@InProceedings{Weisss:1992:HDP,
author = "J{\"u}rgen Weis{\ss}",
title = "Homogeneous decomposition of polynomials",
crossref = "Wang:1992:PII",
pages = "146--151",
year = "1992",
bibdate = "Wed Feb 06 10:44:34 2002",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p146-weiszlig/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
}
@InProceedings{Ye:1992:SLI,
author = "Honglin Ye and Robert M. Corless",
title = "Solving linear integral equations in {Maple}",
crossref = "Wang:1992:PII",
pages = "95--102",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p95-ye/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations.",
}
@InProceedings{Abramov:1993:DS,
author = "S. A. Abramov",
title = "On {d'Alembert} substitution",
crossref = "Bronstein:1993:IPI",
pages = "20--26",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p20-abramov/",
abstract = "Let some homogeneous linear ordinary differential
equation with coefficients in a differential field $F$
be given. If we know a nonzero solution $\psi$, then
the order of the equation can be reduced by d'Alembert
substitution $y= \psi integral \nu dx$, where $\nu$ is
a new unknown function. In the situation when
$\psi\in{}F$, after d'Alembert substitution an equation
with coefficients in $F$ arises again. Let the obtained
equation have a nonzero solution $\psi \in F$, then it
is possible to reduce the order of the equation again
and so on, until an equation without nonzero solutions
in $F$ is obtained. If we can find solutions not only
in $F$ but in some larger set $L$ as well ($L$ can be a
field or a linear space), then we can build up a
certain subspace $M$ (d'Alembertian subspace) of the
space of all solutions of the original equation. Thus
if we have algorithms $A_F$ and $A_L$ to search for the
solutions in $F$ and $L$, then by incorporating
d'Alembert substitution we can design a more general
algorithm (in case $L=F$ we will obtain a more general
algorithm than $A_F$). We would like, certainly, to
know the kind of solutions that can be found by the new
algorithm. The construction of the subspace $M$ is
described.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "C1180 (Optimisation techniques); C4170 (Differential
equations); C6130 (Data handling techniques); C7310
(Mathematics computing)",
keywords = "Alembert substitution; algorithms; Computer algebra
algorithms; Differential field; General algorithm;
Homogeneous linear ordinary differential equation;
Linear space; Nonzero solution; Search problems;
Subspace; theory; verification",
subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Linear differential equations; Search problems; Symbol
manipulation",
}
@InProceedings{Abramov:1993:DSP,
author = "S. A. Abramov",
title = "On {d'Alembert} substitution",
crossref = "Bronstein:1993:IPI",
pages = "20--26",
year = "1993",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "ACM; algebraic computation; ISSAC; SIGSAM; symbolic
computation",
}
@InProceedings{Abramov:1993:GCD,
author = "S. A. Abramov and K. Y. u. Kvashenko",
title = "On the greatest common divisor of polynomials which
depend on a parameter",
crossref = "Bronstein:1993:IPI",
pages = "152--156",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p152-abramov/",
abstract = "The following computer algebra problem is considered:
how to compute the gcd of the polynomials $u(x,a)$ and
$v(x,a)$ for various values of the parameter $a$?. This
problem appears, for example, in solving systems of
algebraic equations by elimination methods, in
computing the logarithmic part of the integral of a
rational function, in solving difference and
differential equations, in summing rational functions,
etc. A fast algorithm to solve this problem is
described, and some applications of this algorithm are
discussed.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "B0210 (Algebra); B0290F (Interpolation and function
approximation); C1110 (Algebra); C4130 (Interpolation
and function approximation); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; Algebraic equations;
algorithms; Computer algebra problem; Differential
equations; Elimination methods; Fast algorithm, ISSAC;
Greatest common divisor; languages; Polynomials;
Rational function; Rational functions; SIGSAM; symbolic
computation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Babai:1993:DCA,
author = "L{\'a}szl{\'o} Babai and Katalin Friedl and Markus
Stricker",
title = "Decomposition of $0*$-closed algebras in polynomial
time",
crossref = "Bronstein:1993:IPI",
pages = "86--94",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p86-babai/",
abstract = "Let A be a matrix algebra over $C$, closed under
Hermitian adjoints, and given by a basis. The authors
consider the classical problem of splitting the space
into the sum of A-irreducible subspaces. This includes
the problem of finding irreducible constituents of a
given unitary representation of a finite group. The
authors describe an algorithm which accomplishes the
splitting in a polynomial number of arithmetic
operations. Their model of computation assumes exact
arithmetic with complex numbers. Floating point
arithmetic is a reasonable approximation to this model;
they prove that their procedures are stable under minor
perturbation. The basic idea of their algorithms is
averaging via generalized Casimir operators. The result
generalizes to Frobenius algebras (algebras with a
non-degenerate associative bilinear form). The
corresponding problem in the model of exact symbolic
arithmetic does not seem tractable since it appears to
require handling field extensions of exponentially
large degree.",
acknowledgement = ack-nhfb,
affiliation = "Chicago Univ., IL, USA",
classification = "C1110 (Algebra); C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
keywords = "A-irreducible subspaces; ACM; algebraic computation;
Algorithm; algorithms; Arithmetic operations; Asterisk
closed algebra; Complex numbers; Computation theory;
Decomposition; Floating point arithmetic; Frobenius
algebra; Generalized Casimir operator; Hermitian
adjoints; Irreducible constituents; ISSAC; Matrix
algebra; Model; Nondegenerate associative bilinear
form; Polynomial number; Polynomial time; SIGSAM; Space
splitting; Subspace; Symbolic arithmetic; symbolic
computation; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Error analysis. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Algorithm theory; Matrix algebra; Matrix
decomposition; Polynomial matrices",
xxtitle = "Decomposition of $*$-closed algebras in polynomial
time",
}
@InProceedings{Babai:1993:DFM,
author = "L{\'a}szl{\'o} Babai and Robert Beals and Daniel
Rockmore",
title = "Deciding finiteness of matrix groups in deterministic
polynomial time",
crossref = "Bronstein:1993:IPI",
pages = "117--126",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p117-babai/",
abstract = "Let $G$ be a group of matrices with entries over an
algebraic number field $F$ (given symbolically). The
group $G$ is given by a list of generators. The authors
give several algorithms, both deterministic and
randomized, which can decide in polynomial time whether
or not $G$ is finite. It is easy to reduce the problem
to the case $F=Q$. As a next step, they present a
polynomial time algorithm which transforms $G$ into a
group of integral matrices whenever possible. Having
done so, the main results of the paper are several
polynomial time algorithms to handle the case of
integral matrices. They give both randomized and
deterministic algorithms to decide finiteness for
finitely generated integral matrix groups. Although
they are able to prove much better upper bounds for the
complexity of the deterministic algorithms, in
practice, the randomized algorithms support a much more
efficient implementation. Thus, both kinds of
algorithms are presented but only the implementation of
the randomized algorithm is explored.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Chicago Univ., IL, USA",
classification = "C1110 (Algebra); C1160 (Combinatorial mathematics);
C4240 (Programming and algorithm theory)",
keywords = "ACM; algebraic computation; Algorithm theory;
algorithms; Complexity; Deciding finiteness;
Deterministic algorithm; Deterministic polynomial time;
Finitely generated integral matrix groups; Group
theory; Integral matrices; Las Vegas algorithm, ISSAC;
Matrix algebra; Matrix groups; Monte Carlo algorithms;
Polynomial time algorithm; Randomized algorithm;
SIGSAM; Size; symbolic computation; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes. {\bf G.3} Mathematics of Computing,
PROBABILITY AND STATISTICS, Random number generation.",
thesaurus = "Decidability; Deterministic algorithms; Group theory;
Matrix algebra; Polynomial matrices; Randomised
algorithms",
}
@InProceedings{Beals:1993:EAC,
author = "Robert Beals",
title = "An elementary algorithm for computing the composition
factors of a permutation group",
crossref = "Bronstein:1993:IPI",
pages = "127--134",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p127-beals/",
abstract = "A permutation group $G$ may be concisely described by
a set $S$ of generators ($mod S mod$ need not be larger
than $\log\bmod{}G mod$ ). From such a short
description, however, it is not immediately clear how
to efficiently obtain various kinds of information
about the group. Furst, Hopcroft, and Luks (1980)
showed that an algorithm of Sims (1971) for computing
the order of $G$ and performing membership tests runs
in polynomial time. Sims's algorithm relies on
combinatorial methods, and there is no deep group
theory involved in the analysis. Polynomial time
algorithms for determining various aspects of the
structure of $G$ are also known. However, it seems that
algorithms which give us more information about $G$
require increasing amounts of group theory for their
analyses. An example is Luks's algorithm (1987) to find
composition factors (the `building blocks' of $G$),
which requires the classification of finite simple
groups (CFSG) for its proof of correctness. Kantor's
algorithm (1985) for finding Sylow subgroups likewise
requires CFSG. As the proof of CFSG is 15,000
manuscript pages long, it is reasonable to ask whether
so much group theory is necessary to study the
computational complexity of permutation group problems.
We give a deterministic polynomial time algorithm to
compute the composition factors of a permutation group,
given by a set of generators. This is the first
polynomial time algorithm for the composition factor
problem with an analysis that does not depend on CFSG.
In addition, we give a Monte Carlo version of our
algorithm which runs in nearly linear ($0(n \log^c n)$)
time for the class of `small-base' permutation groups
introduced by (Babai et al., 1991).",
acknowledgement = ack-nhfb,
classification = "C1110 (Algebra); C1140G (Monte Carlo methods);
C4240C (Computational complexity)",
keywords = "ACM; algebraic computation; algorithms; CFSG;
Combinatorial methods; Composition factors;
Computational complexity; Deterministic polynomial time
algorithm; Elementary algorithm; Finite simple groups;
Group theory; Membership tests; Monte Carlo version,
ISSAC; Permutation group; Permutation group problems;
Polynomial time; Polynomial time algorithms; SIGSAM;
symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf G.2.1} Mathematics of Computing,
DISCRETE MATHEMATICS, Combinatorics, Permutations and
combinations. {\bf F.1.3} Theory of Computation,
COMPUTATION BY ABSTRACT DEVICES, Complexity Measures
and Classes.",
thesaurus = "Computational complexity; Group theory; Monte Carlo
methods",
}
@InProceedings{Bini:1993:PCT,
author = "Dario Bini and Victor Pan",
title = "Parallel computations with {Toeplitz-like} and
{Hankel-like} matrices",
crossref = "Bronstein:1993:IPI",
pages = "193--200",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p193-bini/",
abstract = "The known fast algorithms for computations with
general Toeplitz, Hankel, Toeplitz-like, and
Hankel-like matrices are inherently sequential. We
develop some new techniques in order to devise fast
parallel algorithms for computations with such
matrices, including the evaluation of their
characteristic polynomials, with further extensions to
computing the solution to a linear system of equations
with such a matrix and to several polynomial
computations (such as computing gcd, lcm, Pad{\'e}
approximation and extended Euclidean scheme for two
polynomials), as well as to computing the minimum span
of a linear recurrence sequence. The algorithms can be
applied over any field of constants, consist of simple
computational blocks (mostly reduced to fast Fourier
transforms, FFT's), and have potential practical value.
We also extend them to the case of matrices
representable as the sums of Toeplitz-like and
Hankel-like matrices.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Pisa Univ., Italy",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); B0290Z (Other numerical
methods); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4190 (Other
numerical methods); C4240P (Parallel programming and
algorithm theory)",
keywords = "ACM; algebraic computation; algorithms; Characteristic
polynomials; Computational blocks; Extended Euclidean
scheme; Fast Fourier transforms, ISSAC; Hankel-like
matrices; Pad{\'e} approximation; Parallel algorithms;
Parallel computations; Polynomials; SIGSAM; symbolic
computation; theory; Toeplitz-like matrices",
subject = "{\bf I.0} Computing Methodologies, GENERAL. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computation of transforms.",
thesaurus = "Fast Fourier transforms; Hankel matrices; Parallel
algorithms; Polynomials; Toeplitz matrices",
}
@InProceedings{Bronstein:1993:FPF,
author = "Manuel Bronstein and Bruno Salvy",
title = "Full Partial Fraction Decomposition of Rational
Functions",
crossref = "Bronstein:1993:IPI",
pages = "157--160",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p157-bronstein/",
abstract = "We describe a rational algorithm that computes the
full partial fraction expansion of a rational function
over the algebraic closure of its field of definition.
The algorithm uses only gcd operations over the initial
field but the resulting decomposition is expressed with
linear denominators. We give examples from its Axiom
and Maple implementations.",
acknowledgement = ack-nhfb,
affiliation = "Wissenschaftliches Rechnen, Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "B0290D (Functional analysis); B0290H (Linear
algebra); B0290M (Numerical integration and
differentiation); C4120 (Functional analysis); C4140
(Linear algebra); C4160 (Numerical integration and
differentiation); C7310 (Mathematics computing)",
keywords = "ACM; Algebraic closure; algebraic computation; Axiom;
Decomposition; Full partial fraction decomposition; Gcd
operations; Maple; Polynomial; Rational functions;
SIGSAM; symbolic computation; Symbolic integration,
ISSAC; theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
thesaurus = "Function evaluation; Integration; Matrix
decomposition; Polynomial matrices; Symbol
manipulation",
}
@InProceedings{Caboara:1993:DAG,
author = "Massimo Caboara",
title = "A Dynamic Algorithm for {Gr{\"o}bner} basis
computation",
crossref = "Bronstein:1993:IPI",
pages = "275--283",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p275-caboara/",
abstract = "We recall preliminaries on Gr{\"o}bner bases,
Gr{\"o}bner Fans and Hilbert functions. We give an
outline of the dynamic algorithm. We report statistics
on some experiments and a few conclusions are given.
Experiments performed (and reported in this paper) show
an actual improvement of the combinatorial complexity.
However this doesn't reflect on timings, since the
`arithmetical' complexity both of the basis (number of
monomials appearing in it) and of the algorithm (number
of monomial operations) is not reduced. In the
important case of binomial ideals (where the
arithmetical complexity of the basis is constant), the
dynamic algorithm gives superior timings than the
classical one.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Genoa Univ., Italy",
classification = "C4240C (Computational complexity); C6130 (Data
handling techniques); C7310 (Mathematics computing)",
keywords = "algorithms; theory; ISSAC; symbolic computation;
algebraic computation; ACM; SIGSAM; Dynamic algorithm;
Gr{\"o}bner basis computation; Gr{\"o}bner Fans;
Hilbert functions; Combinatorial complexity; Monomial
operations; Binomial ideals; Arithmetical complexity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Symbol manipulation",
}
@InProceedings{Cantone:1993:DPS,
author = "Domenico Cantone and Vincenzo Cutello",
title = "Decision procedures for stratified set-theoretic
syllogistics",
crossref = "Bronstein:1993:IPI",
pages = "105--110",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p105-cantone/",
abstract = "It is shown that a class of unquantified multi-sorted
set-theoretic formulae involving the notions of
powerset, general union, and singleton has a solvable
satisfiability problem. The authors show by means of a
model normalization procedure that any given
satisfiable formula in their theory has a finite model
whose size is bounded by a function of the number of
variables occurring in it.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Catania Univ., Italy",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic); C4210L (Formal languages and computational
linguistics)",
keywords = "ACM; algebraic computation; Computation theory;
Decidability; Decision procedure; Finite model; Formal
logic, ISSAC; General union; languages; Model
normalization procedure; Multisorted language;
Powerset; Set theory; SIGSAM; Singleton; Solvability;
Solvable satisfiability problem; Stratified
set-theoretic syllogistics; Syllogistic; symbolic
computation; theory; Unquantified multi-sorted
set-theoretic formulae",
subject = "{\bf F.4.3} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Formal Languages, Decision
problems. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Computability theory. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General.",
thesaurus = "Computability; Computation theory; Decidability;
Decision theory; Set theory",
}
@InProceedings{Chou:1993:AGT,
author = "Shang-Ching Chou and Xiao-Shan Gao and Jing-Zhong
Zhang",
title = "Automated geometry theorem proving by vector
calculation",
crossref = "Bronstein:1993:IPI",
pages = "284--291",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p284-chou/",
abstract = "Based on a vector approach, we present a theorem
proving method for a class of constructive geometric
statements which covers a large portion of the equality
type geometry theorems about lines and circles. The
method is to eliminate the constructed points from the
conclusions of geometry statements based on a few basic
equalities on the inner and vector products of vectors
in the Euclidean plane. The method has been implemented
and the program has proved 410 nontrivial theorems
entirely automatically. The proofs produced by our
program are significantly shorter than the proofs
provided by programs based on the coordinate approach.
In spite of fact that the complexity of our algorithm
is exponential in the number of points in the geometry
statements, our program is practically very fast: 75
(95) percent of the 410 theorems can be proved within
one (five) second (seconds).",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Wichita State Univ., KS, USA",
classification = "C1160 (Combinatorial mathematics); C4210 (Formal
logic); C4240C (Computational complexity); C4260
(Computational geometry)",
keywords = "algorithms; Automated geometry theorem proving;
Circles; Complexity; Equality type geometry theorems;
Euclidean plane; experimentation; Lines; theory; Vector
calculation; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving. {\bf I.1.4}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Applications.",
thesaurus = "Computational complexity; Computational geometry;
Theorem proving",
}
@InProceedings{Collins:1993:HMH,
author = "George E. Collins and Werner Krandick",
title = "A Hybrid Method for High Precision Calculation of
Polynomial Real Roots",
crossref = "Bronstein:1993:IPI",
pages = "47--52",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p47-collins/",
abstract = "A straightforward implementation of Newton's method
for polynomial real root calculation using exact
arithmetic is inefficient. In each step the length of
the iterate multiplies by the degree of the polynomial
while its accuracy merely doubles. We present an exact
algorithm which keeps the length of each iterate
proportional to its accuracy. The resulting speed up is
dramatic. The average computing time can be further
reduced by trying floating point computations. Several
floating point Newton steps are executed; interval
arithmetic is used to check whether the result is
sufficiently close to the root; if this condition
cannot be verified the exact algorithm is invoked.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Average
computing time; Exact algorithm; Floating point
computations; Floating point Newton steps; High
precision calculation; Hybrid method; Interval
arithmetic, ISSAC; Newton method; Polynomial real
roots; SIGSAM; symbolic computation; verification",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Floating point arithmetic; Mathematics computing;
Newton method; Polynomials",
}
@InProceedings{Edneral:1993:CGN,
author = "Victor F. Edneral",
title = "Computer Generation of Normalizing Transformation for
Systems of Nonlinear {ODE}",
crossref = "Bronstein:1993:IPI",
pages = "14--19",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p14-edneral/",
abstract = "The article describes the Standard LISP program for
building a normal form and a corresponding normalizing
transformation of a system of ordinary differential
equations (ODE) in A. D. Bruno's notation (1972) up to
the specified order. This program also includes a
complete set of procedures of arithmetic for the
truncated power series and input/output services. This
gives us an opportunity to continue a treatment of
obtained results autonomically or in a REDUCE
environment. The program can work in a rational
arithmetic or in an approximate rational arithmetic, or
in a floating point arithmetic. The program usage is
illustrated by treating systems of weakly nonlinear
ODEs in the language of the truncated series. The
approximate solution is produced from the normal form
calculated up to enough high order and from the
corresponding normalizing transformation. This method
demonstrates rather good agreement with numerical
solutions of some well known equations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Nucl. Phys., Moscow Univ., Russia",
classification = "C4170 (Differential equations); C6110 (Systems
analysis and programming); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; algorithms; Approximate
rational arithmetic; Computer generation; Floating
point arithmetic; Input/output services; languages;
Nonlinear ODE systems; Normal form; Normalizing
transformation; Ordinary differential equations; REDUCE
environment; SIGSAM; Standard LISP program; symbolic
computation; Truncated power series; Truncated series,
ISSAC; verification; Weakly nonlinear ODEs",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, LISP. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues and eigenvectors (direct and iterative
methods). {\bf I.1.2} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Difference equations; LISP; Programming; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Emiris:1993:PMS,
author = "Ioannis Emiris and John Canny",
title = "A Practical Method for the Sparse Resultant",
crossref = "Bronstein:1993:IPI",
pages = "183--192",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p183-emiris/",
abstract = "We propose an efficient method for computing the
resultant of a sparse polynomial system of $n+1$
equations in $n$ unknowns. Our approach constructs a
matrix whose determinant is a non-zero multiple of the
resultant and from which the latter is easily
extracted. For certain classes of systems, it attains
optimality by expressing the resultant as a single
determinant. An implementation of the algorithm is
described and empirical results presented and compared
with previous works. In addition, the important
subproblem of computing mixed volumes is examined and
an efficient algorithm is implemented.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
keywords = "ACM; algebraic computation; algorithms;
experimentation; Mixed volumes, ISSAC; SIGSAM; Sparse
polynomial system; Sparse resultant; symbolic
computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.2.9} Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Robotics. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Polynomials",
}
@InProceedings{Ganzha:1993:PSM,
author = "V. G. Ganzha and E. V. Vorozhtsov",
title = "A Probabilistic Symbolic-Numerical Method for the
Stability Analyses of Difference Schemes for {PDEs}",
crossref = "Bronstein:1993:IPI",
pages = "9--13",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p9-ganzha/",
abstract = "We present a new symbolic numerical method for an
automatic stability analysis of difference schemes
approximating scalar linear of nonlinear partial
differential equations (PDEs) of hyperbolic or
parabolic type. In this method the grid values of the
numerical solution for any fixed moment of time are
considered as random correlated variables obeying the
normal distribution law. Therefore, one can apply the
notion of the C. E. Shannon's (1948) entropy to
characterize the stability of a difference scheme. The
reduction of this entropy, or uncertainty, is taken as
a stability criterion. It is shown at a number of
examples that this criterion yields the same stability
regions in the cases of linear difference initial value
problems, as the Fourier method. In the case of two
spatial variables the present probabilistic method is
computationally faster than the Fourier method by two
orders of magnitude.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, Russia",
classification = "C1140Z (Other topics in statistics); C4170
(Differential equations); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; algorithms; Automatic
stability analysis; Difference schemes; Fixed moment;
Fourier method; Grid values; Linear difference initial
value problems; Nonlinear partial differential
equations; Normal distribution law; Parabolic type;
PDEs; Probabilistic symbolic-numerical method; Random
correlated variables; SIGSAM; Spatial variables, ISSAC;
Stability analyses; Stability criterion; symbolic
computation; Symbolic numerical method; theory",
subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation, Finite difference methods.",
thesaurus = "Difference equations; Nonlinear differential
equations; Normal distribution; Numerical stability;
Partial differential equations; Symbol manipulation",
}
@InProceedings{Godlevsky:1993:PPA,
author = "A. B. Godlevsky and A. E. Doroshenko",
title = "Parallelizing Programs with {APS}",
crossref = "Bronstein:1993:IPI",
pages = "55--62",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p55-godlevsky/",
abstract = "An approach to parallelizing sequential programs as
rewriting rules application by means of the algebraic
programming system APS is considered. It gives the
advantages of rapid prototyping and evolutionary
development of efficient parallelizers.",
acknowledgement = ack-nhfb,
affiliation = "V. M. Glushkov Inst. of Cybern., Acad. of Sci., Kiev,
Ukraine",
classification = "C4210L (Formal languages and computational
linguistics); C5440 (Multiprocessing systems); C6110P
(Parallel programming); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; Algebraic programming
system; algorithms; APS; Distributed memory parallel
computers; Efficient parallelizers; Evolutionary
development; ISSAC; languages; Massively parallel
computer systems; Rapid prototyping; Rewriting rules;
SIGSAM, Sequential program parallelization; symbolic
computation",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems. {\bf
D.1.3} Software, PROGRAMMING TECHNIQUES, Concurrent
Programming, Parallel programming.",
thesaurus = "Distributed memory systems; Parallel programming;
Rewriting systems; Software prototyping; Symbol
manipulation",
}
@InProceedings{Gruntz:1993:NAC,
author = "Dominik Gruntz",
title = "A New Algorithm for Computing Asymptotic Series",
crossref = "Bronstein:1993:IPI",
pages = "239--244",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p239-gruntz/",
abstract = "We describe a new algorithm for computing asymptotic
expansions for a large class of expressions, whereby
the asymptotic series are of a form more complicated
than mere Puiseux series. Today's computer algebra
systems still lack good algorithms for handling such
asymptotic expansions, although in theory some
algorithms have been presented. The algorithm we
present in this article is directly induced by the
limit computation algorithm presented in Gonnet and
Gruntz (1992) which is based on series computations in
terms of the most rapidly varying subexpression of a
given expression. Examples of the algorithm implemented
in Maple are shown.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Sci. Comput., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "C1100 (Mathematical techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Asymptotic
expansions; Computer algebra; ISSAC; Maple; SIGSAM,
Asymptotic series; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems.",
thesaurus = "Series [mathematics]; Symbol manipulation",
}
@InProceedings{Gutnik:1993:ACA,
author = "S. A. Gutnik",
title = "Application of Computer Algebra to Investigation of
the Relative Equilibria of a Satellite",
crossref = "Bronstein:1993:IPI",
pages = "63--64",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p63-gutnik/",
abstract = "A new approach for the symbolic analysis of the
satellites dynamical equations is presented. The
investigation is made by means of Gr{\"o}bner Basis
method. The presence of various perturbations is
supposed, such as gravitational and constant torques.
It is shown that a satellite moving in a circular orbit
with a prescribed constant torque and prescribed
central moments of inertia has at most 24 equilibrium
positions in an orbiting frame in the general case.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Comput. Aided Design, Acad. of Sci., Moscow,
Russia",
classification = "C7310 (Mathematics computing)",
keywords = "algorithms; Computer algebra; Relative equilibria;
Symbolic analysis; Satellites dynamical equations;
Gr{\"o}bner Basis; Perturbations; Gravitational
torques; Constant torques; Circular orbit, ISSAC;
symbolic computation; algebraic computation; ACM;
SIGSAM",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Aerospace. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Algebraic algorithms.",
thesaurus = "Angular velocity; Symbol manipulation",
}
@InProceedings{Halstead:1993:APS,
author = "R. H. Halstead and T. Chikayama and R. Gabriel and D.
Waltz",
title = "Applications for Parallel Symbolic Computation",
crossref = "Halstead:1993:PSC",
pages = "417--417",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hong:1993:QEF,
author = "Hoon Hong",
title = "Quantifier elimination for formulas constrained by
quadratic equations",
crossref = "Bronstein:1993:IPI",
pages = "264--274",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p264-hong/",
abstract = "An algorithm is given for constructing a quantifier
free formula (a boolean expression of polynomial
equations and inequalities) equivalent to a given
formula of the form: (There exists $x$ in
$R$)($a_2x^2+a_1x+a_0=O V-product F$), where $F$ is a
quantifier free formula in $x_1,\ldots{},x_r,x,$ and
$a_2, a_1, a_0$ are polynomials in $x_1,\ldots{},x_r$
with real coefficients such that the system
($a_2=0,a_1=0, a_0=0$) has no solution in $R^r$.
Formulas of this form frequently occur in the context
of constraint logic programming over the real numbers.
The output formulas are made of resultants and two
variants, which we call trace and slope resultants.
Both of these variant resultants can be expressed as
determinants of certain matrices.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence); C4130
(Interpolation and function approximation); C4210
(Formal logic); C6110L (Logic programming)",
keywords = "algorithms; Boolean expression; Constraint logic
programming; Determinants; Inequalities; Polynomial
equations; Polynomials; Quadratic equations; Quantifier
elimination; Quantifier free formula; theory;
verification",
subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Applications. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Analysis of algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Boolean algebra; Logic programming; Polynomials",
}
@InProceedings{Ito:1993:MPA,
author = "T. Ito and R. Nikhil and J. Padget and N. Suzuki",
title = "Massively Parallel Architectures and Symbolic
Computation",
crossref = "Halstead:1993:PSC",
pages = "408--416",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jebelean:1993:GBG,
author = "T. Jebelean",
title = "A Generalization of the Binary {GCD} Algorithm",
crossref = "Bronstein:1993:IPI",
pages = "111--116",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p111-jebelean/",
abstract = "A generalization of the binary algorithm for operation
at `word level' by using a new concept of `modular
conjugates' computes the GCD of multiprecision integers
two times faster than the Lehmer--Euclid method. Most
importantly, however, the new algorithm is suitable for
systolic parallelization, in `least-significant digits
first' pipelined manner and for aggregation with other
systolic algorithms for the arithmetic of
multiprecision rational numbers.",
acknowledgement = ack-nhfb,
affiliation = "RISC, Linz, Austria",
classification = "C4240P (Parallel programming and algorithm theory)",
keywords = "ACM; algebraic computation; algorithms; Arithmetic;
Binary algorithm; Binary GCD algorithm; Computation
speed; Computational efficiency; experimentation;
Least-significant digits first; Modular conjugates;
Multiprecision integer; Multiprecision rational
numbers; Parallel processing; Pipelined; SIGSAM;
symbolic computation; Systolic algorithm; Systolic
array, ISSAC; Systolic parallelization; Word level",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf F.1.2}
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Modes of Computation, Parallelism and concurrency. {\bf
I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms.",
thesaurus = "Algorithm theory; Parallel algorithms; Symbol
manipulation; Systolic arrays",
}
@InProceedings{Jeffrey:1993:IOE,
author = "D. J. Jeffrey",
title = "Integration to obtain expressions valid on domains of
maximum extent",
crossref = "Bronstein:1993:IPI",
pages = "34--41",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p34-jeffrey/",
abstract = "In certain circumstances, the integration routines
used by computer algebra systems return expressions
whose domains of validity are unnecessarily restricted
by the presence of discontinuities. It is argued that
this is undesirable and that integration routines
should meet an additional requirement: they should
return expressions that are valid on domains of maximum
extent. The contention is supported by general
mathematical arguments, by an examination of existing
practises and by a demonstration that two standard
algorithms can be modified to meet the requirement.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Univ. of Western Ontario,
London, Ont., Canada",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Computer
algebra systems; Discontinuities; General mathematical
arguments; Integration routines; languages; Maximum
extent; SIGSAM; Standard algorithms, ISSAC; symbolic
computation; Validity domains",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple.",
thesaurus = "Integration; Symbol manipulation",
}
@InProceedings{Jinzhao:1993:RPG,
author = "Wu-Jinzhao and Li-Lian",
title = "The regular problem and {Green} equivalences for
special monoids",
crossref = "Bronstein:1993:IPI",
pages = "78--85",
year = "1993",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "For the monoid presented by a finite special
Church--Rosser Thue system, whether it is a regular
semigroup is decidable in polynomial time. The number
of each kind of Green equivalence classes is either one
or infinite and it is computable in polynomial time.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C1160 (Combinatorial mathematics); C4210L (Formal
languages and computational linguistics)",
keywords = "ACM; algebraic computation; Computability; Computation
theory; Decidability; Decidable; Finite special
Church--Rosser Thue system; Green equivalences; ISSAC;
Polynomial time; Regular problem; Regular semigroup;
SIGSAM; Special monoid; String rewriting Green
equivalence class; symbolic computation",
thesaurus = "Computability; Decidability; Equivalence classes;
Group theory; Rewriting systems",
}
@InProceedings{Kalkbrener:1993:UBN,
author = "Michael Kalkbrener",
title = "An upper bound on the number of monomials in the
{Sylvester} resultant",
crossref = "Bronstein:1993:IPI",
pages = "161--163",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p161-kalkbrener/",
abstract = "The Sylvester resultant is not only a classical
concept in commutative algebra but also a useful tool
for actually computing solutions of systems of
algebraic equations. We derive an upper bound on the
number of monomials in the Sylvester resultant using a
result from the theory of partially ordered sets.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Eidgenossische Tech. Hochschule,
Zurich, Switzerland",
classification = "B0210 (Algebra); B0250 (Combinatorial mathematics);
B0290F (Interpolation and function approximation);
C1110 (Algebra); C1160 (Combinatorial mathematics);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
keywords = "ACM; algebraic computation; Algebraic equations;
algorithms; Commutative algebra $b$; Monomials;
Partially ordered sets, ISSAC; SIGSAM; Sylvester
resultant; symbolic computation; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.2.m}
Mathematics of Computing, DISCRETE MATHEMATICS,
Miscellaneous. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Polynomials; Set theory; Symbol manipulation",
}
@InProceedings{Keady:1993:AIS,
author = "G. Keady and M. G. Richardson",
title = "An application of {IRENA} to systems of nonlinear
equations arising in equilibrium flows in networks",
crossref = "Bronstein:1993:IPI",
pages = "311--320",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p311-keady/",
abstract = "IRENA --- an Interface from REDUCE to NAG --- runs
under the REDUCE Computer Algebra (CA) system and
provides an interactive front end to the NAG Fortran
Library. Here IRENA is tested on a problem closer to an
engineering problem than previously published
examples. We also illustrate the use of the codeonly
switch, which is relevant to larger scale problems. We
describe progress on an issue raised in the `Future
Developments' section in our SIGSAM Bulletin article by
K. A. Broughan et al. (1991): the progress improves the
practical effectiveness of IRENA.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Western Australia Univ., Nedlands, WA,
Australia",
classification = "C4150 (Nonlinear and functional equations); C6130
(Data handling techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Codeonly
switch; Equilibrium flows; Interactive front end;
Interface from REDUCE to NAG; ISSAC; languages; NAG
Fortran Library; REDUCE Computer Algebra; SIGSAM,
IRENA; symbolic computation; Systems of nonlinear
equations; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, REDUCE. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Network problems.
{\bf F.2.2} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures. {\bf I.1.4} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
thesaurus = "Mathematics computing; Nonlinear equations; Symbol
manipulation",
}
@InProceedings{Klimov:1993:SEN,
author = "D. M. Klimov and V. M. Rudenko and V. V. Leonov",
title = "Symbolic Evaluation in the Nonlinear Mechanical
Systems",
crossref = "Bronstein:1993:IPI",
pages = "53--54",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p53-klimov/",
abstract = "The paper presents the features of a program package,
Polymech-symbol, helping to solve some laborious
mechanical problems. The package was written by means
of the REDUCE system and contains several algorithms in
a form of REDUCE procedures. The computer algebra
methods may be successfully used for solving the
problems of navigation and defining the trajectory of
satellite mass centre motion. The preliminary
analytical research provides the effective algorithm
for on-board solving the problem of prediction. To
assure necessary accuracy, we need to construct several
higher approximations. Such sophisticated problems can
be solved only with the help of symbolic computations
that deal with the processing of cumbersome analytical
expressions. For effective analytical investigation of
such kinds of problems, the choice of parameters which
describe the perturbed orbital motion is critical. In
addition to the natural requirements of the calculation
process efficiency and the absence of singularities in
equations of motion, it is useful to have a unified
mathematical description for the angular motion and for
the motion of the mass centre.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Problems of Mech., Acad. of Sci., Moscow,
Russia",
classification = "C7310 (Mathematics computing); C7320 (Physics and
chemistry computing)",
keywords = "ACM; algebraic computation; algorithms; Analytical
expressions; Angular motion; Calculation process
efficiency; Computer algebra methods; Higher
approximations; languages; Mass centre motion, ISSAC;
Mechanical problems; Nonlinear mechanical systems;
Perturbed orbital motion; Polymech-symbol; Prediction;
Program package; REDUCE procedures; REDUCE system;
Satellite mass centre motion; SIGSAM; symbolic
computation; Symbolic computations; Symbolic
evaluation; Trajectory; Unified mathematical
description",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE.",
thesaurus = "Mechanics; Physics computing; Symbol manipulation",
}
@InProceedings{Lin:1993:SRT,
author = "Dongdai Lin and Zhuojun Liu",
title = "Some results on theorem proving in geometry over
finite fields",
crossref = "Bronstein:1993:IPI",
pages = "292--300",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p292-lin/",
abstract = "In this paper, we discuss Wu's well ordering principle
and theorem proving over finite fields, try to prove
some theorems in the geometry over finite fields.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C1230 (Artificial intelligence); C4210 (Formal
logic); C4240 (Programming and algorithm theory); C4260
(Computational geometry)",
keywords = "ACM; algebraic computation; algorithms; Finite fields;
ISSAC; SIGSAM; symbolic computation; Theorem proving;
theory; verification; Well ordering principle",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations in finite fields. {\bf F.4.1} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Mathematical Logic, Mechanical theorem proving. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Computational geometry; Theorem proving",
}
@InProceedings{Madlener:1993:CGB,
author = "Klaus Madlener and Birgit Reinert",
title = "Computing {Gr{\"o}bner} Bases in Monoid and Group
Rings",
crossref = "Bronstein:1993:IPI",
pages = "254--263",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p254-madlener/",
abstract = "Following Buchberger's approach to computing a
Gr{\"o}bner basis of a polynomial ideal in polynomial
rings, a completion procedure for finitely generated
right ideals in $Z(H)$ is given, where $H$ is an
ordered monoid presented by a finite, convergent
semi-Thue system $(\Sigma,T)$. Taking a finite set $F$
contained in $Z(H)$ we get a (possibly infinite) basis
of the right ideal generated by $F$, such that using
this basis we have unique normal forms for all $p$ in
$Z(H)$ (especially the normal form is zero in case $p$
is an element of the right ideal generated by $F$). As
the ordering and multiplication on H need not be
compatible, reduction has to be defined carefully in
order to make it Noetherian. Further we no longer have
$p.x$ to $-{}_p0$ for $p$ in $Z(H)$, $x$ in $H$.
Similar to Buchberger's $s$-polynomials, confluence
criteria are developed and a completion procedure is
given. In case $T= \phi$ or $(\Sigma,T)$ is a
convergent, 2-monadic presentation of a group with
inverses of length 1, termination can be shown. An
application to the subgroup problem is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Kaiserslautern Univ., Germany",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
keywords = "algorithms; theory; verification; ISSAC; symbolic
computation; algebraic computation; ACM; SIGSAM, Group
rings; Gr{\"o}bner bases; Polynomial rings; Semi-Thue
system; Monoid rings",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Group theory; Polynomials; Symbol manipulation",
}
@InProceedings{Monagan:1993:GAD,
author = "Michael B. Monagan and Walter M. Neuenschwander",
title = "{GRADIENT}: algorithmic differentiation in {Maple}",
crossref = "Bronstein:1993:IPI",
pages = "68--76",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p68-monagan/",
abstract = "Many scientific applications require computation of
the derivatives of a function $f:R^n$ to $R^m$ as well
as the function values of $f$ itself. All computer
algebra systems can differentiate functions represented
by formulae. But not all functions can be described by
formulae. And formulae are not always the most
effective means for representing functions and
derivatives. In this paper we describe the algorithms
used by the Maple (2) routine GRADIENT that accepts as
input a Maple procedure for the computation of $f$ and
outputs a new Maple procedure that computes the
gradient of $f$. The design of the GRADIENT routine is
such that it is also trivial to generate Maple
procedures for the computation of Jacobians and
Hessians.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
Tech. Hochschule, Zurich, Switzerland",
classification = "C4160 (Numerical integration and differentiation);
C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; Algorithmic
differentiation; algorithms; Computer algebra systems;
Function values; GRADIENT; Hessians, ISSAC; Jacobians;
languages; Maple; Scientific applications; SIGSAM;
symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf G.2.2} Mathematics of Computing,
DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Computations on discrete structures.",
thesaurus = "Differentiation; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Mourrain:1993:GPP,
author = "B. Mourrain",
title = "The 40 ``generic'' positions of a parallel robot",
crossref = "Bronstein:1993:IPI",
pages = "173--182",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p173-mourrain/",
abstract = "We consider the direct kinematic problem of a parallel
robot (called the Stewart platform or left hand). We
want to show how the use of formal tools help us to
guess the solution of this problem and then to
establish it. We do not try to give real-time and
numerical solutions to the problem of inverse images
but focus on tools of effective algebra, which can help
us to know a little more about the geometric aspects of
the question. We describe experiments done in order to
obtain the number of generic positions of this robot,
once the length of the arms are known. We also sketch
the proof that the degree of the corresponding map is
40. We use explicit elimination techniques in order to
remove the solution at infinity and we use Bezout's
theorem on surfaces with circularity as a conclusion.",
acknowledgement = ack-nhfb,
affiliation = "SAFIR, Valbonne, France",
classification = "C1110 (Algebra); C1310 (Control system analysis and
synthesis methods); C3390M (Manipulators); C4260
(Computational geometry); C7420D (Control system design
and analysis)",
keywords = "ACM; algebraic computation; Arms; Bezout's theorem;
Circularity, ISSAC; Direct kinematic problem; Effective
algebra; experimentation; Explicit elimination
techniques; Formal tools; Generic positions; Geometric
aspects; Left hand; Parallel robot; Proof; SIGSAM;
Stewart platform; Surfaces; symbolic computation;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf I.2.9}
Computing Methodologies, ARTIFICIAL INTELLIGENCE,
Robotics. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Computations on discrete
structures.",
thesaurus = "Algebra; Computational geometry; Control system
analysis computing; Manipulator kinematics; Theorem
proving",
}
@InProceedings{Petkovsek:1993:FAH,
author = "M. Petkovsek and B. Salvy",
title = "Finding All Hypergeometric Solutions of Linear
Differential Equations",
crossref = "Bronstein:1993:IPI",
pages = "27--33",
year = "1993",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Hypergeometric sequences are such that the quotient of
two successive terms is a fixed rational function of
the index. We give a generalization of M. Petkovsek's
algorithm (1992) to find all hypergeometric sequence
solutions of linear recurrences, and we describe a
program to find all hypergeometric functions that solve
a linear differential equation.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Ljubljana Univ., Slovenia",
classification = "C4170 (Differential equations); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "ACM; algebraic computation; Computer algebra, ISSAC;
Fixed rational function; Hypergeometric sequences;
Hypergeometric solutions; Linear differential
equations; Linear recurrences; Quotient; SIGSAM;
Successive terms; symbolic computation",
thesaurus = "Linear differential equations; Sequences; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Petkovsek:1993:FAHb,
author = "Marko Petkov{\v{s}}ek and Bruno Salvy",
title = "Finding all hypergeometric solutions of linear
differential equations",
crossref = "Bronstein:1993:IPI",
pages = "27--33",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p27-petkovscaronek/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
}
@InProceedings{Richardson:1993:ZST,
author = "Daniel Richardson",
title = "A Zero Structure Theorem for Exponential Polynomials",
crossref = "Bronstein:1993:IPI",
pages = "144--151",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p144-richardson/",
abstract = "An exponential system is a system of equations
$(S=O,E=O)$, where $S$ is a finite set of polynomials
in $Q(x_1,\ldots{},x_n,y_1,\ldots{},y_n)$, and $E$ is a
subset of $(y_1-e^{x1},\ldots{},y_n-e^{xn})$. Wu's
method (1984) is used effectively to decompose such
systems into finitely many subsystems which have
triangular algebraic part, and whose solution sets in
$C^{2n}$ are equidimensional and also, in a sense
explained, non singular. The problem of solving
exponential systems in bounded regions of $R^n$ is also
discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Bath Univ., UK",
classification = "B0210 (Algebra); B0290F (Interpolation and function
approximation); B0290H (Linear algebra); C1110
(Algebra); C4130 (Interpolation and function
approximation); C4140 (Linear algebra)",
keywords = "ACM; algebraic computation; algorithms; Bounded
regions; Exponential polynomials; Exponential system;
ISSAC; SIGSAM, Zero structure theorem; Solution sets;
symbolic computation; theory; Triangular algebraic
part",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.1.3} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
thesaurus = "Matrix decomposition; Polynomial matrices",
}
@InProceedings{Roy:1993:AGA,
author = "Marie-Fran{\c{c}}oise Roy and T. {Van Effelterre}",
title = "Aspect graphs of algebraic surfaces",
crossref = "Bronstein:1993:IPI",
pages = "135--143",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p135-roy/",
abstract = "An aspect graph is a representation of 3D objects that
is used in the field of computer vision for recognition
in 2D images. The viewspace around the object is
tesselated in a finite number of cells by the semi
algebraic visual events locus. The topology of the
image contour remains stable in each cell and may only
change on the visual events locus. An aspect graph
represents a 3D object whose surface boundary is
algebraic or semi algebraic by the finite number of
different topological aspects of its image contour and
by the visual events that make a stable aspect switch
to another one. We show that the number of different
topological aspects of an algebraic surface of degree
$d$ is upper bounded by a $O(d^{12})$ for orthographic
projection and $O(d^{18})$ for perspective projection.
This result is a generalisation of the upper bound of
$O(d^6)$ obtained by M.-F. Roy and T. Van Effelterre
(1992) for surfaces of revolution under perspective
projection and improves the most recent upper bounds of
$O(d^{20})$ for orthographic projection and $O(d^{30})$
for perspective projection. We also show how to compute
the equations of the visual events locus with
Gr{\"o}bner bases systems and Hermite's method.",
acknowledgement = ack-nhfb,
affiliation = "IRMAR, Rennes I Univ., France",
classification = "C1160 (Combinatorial mathematics); C4260
(Computational geometry); C5260B (Computer vision and
image processing techniques)",
keywords = "algorithms; design; Aspect graph; Algebraic surfaces;
3D objects; Computer vision; 2D image recognition;
Viewspace; Semi algebraic visual events locus; Image
contour; Visual events locus; Surface boundary;
Orthographic projection; Perspective projection;
Gr{\"o}bner bases systems; Hermite method, ISSAC;
symbolic computation; algebraic computation; ACM;
SIGSAM",
subject = "{\bf I.0} Computing Methodologies, GENERAL. {\bf
I.5.4} Computing Methodologies, PATTERN RECOGNITION,
Applications, Computer vision. {\bf J.6} Computer
Applications, COMPUTER-AIDED ENGINEERING,
Computer-aided design (CAD).",
thesaurus = "Computational geometry; Computer vision; Graph theory;
Object recognition",
}
@InProceedings{Santas:1993:TSC,
author = "Phillip S. Santas",
title = "A type system for computer algebra (abstract)",
crossref = "Bronstein:1993:IPI",
pages = "77--77",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p77-santas/",
abstract = "Summary form only given. Examines type systems for
support of subtypes and categories in computer algebra
systems. By modelling representation of instances in
terms of existential types instead of recursive types,
the author obtains not only a simplified model, but
also builds a basis for defining subtyping among
algebraic domains. The introduction of metaclasses
facilitates the task by allowing the inference of type
classes. By means of type classes and existential
subtypes, relations are constructed without involving
coercions.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Sci. Comput., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory)",
keywords = "ACM; algebraic computation; Algebraic domain;
Categories; Computer algebra; design; Existential
subtype; Existential type; ISSAC; Metaclass; Model;
Representation of instances; SIGSAM, Type system;
Subtype; Subtyping; symbolic computation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.3.3} Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Type structure.",
thesaurus = "Process algebra; Symbol manipulation; Type theory",
}
@InProceedings{Sendra:1993:EAH,
author = "Juan R. Sendra and Juan Llovet",
title = "Efficient algorithms for {Hankel} matrices over
${Z}(x_1,\ldots{},x_r)$",
crossref = "Bronstein:1993:IPI",
pages = "201--208",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p201-sendra/",
abstract = "In this paper, we investigate the problem of the rank
and the determinant of Hankel matrices over
$Z(x_1,\ldots{},x_r)$. A modular algorithm for
determining the rank of a Hankel matrix with entries
that are multivariate polynomials over the integers is
presented. The algorithm is based on modular
techniques, which consist in computing the rank of
Hankel matrices over finite fields by a special
algorithm that needs $O(n^2)$ arithmetic operations,
where $n$ is the order of the matrix. The general
solution is achieved by determining the maximum of the
ranks computed over the finite fields. Similarly, we
give a theorem that shows how to compute Hankel
determinants in $O(n^2)$ arithmetic operations. The
worst case complexity of the algorithm is
$O((n^{r+3}G^r+n^{r+2}G^{r+1}) \log{}n \log^2 L)$,
where $G$ and $L$ are some appropriate bounds for the
degree and the norm of the entries respectively.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Alcala Univ., Madrid, Spain",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity)",
keywords = "ACM; algebraic computation; algorithms; Determinant;
Hankel matrices; Modular algorithm; Multivariate
polynomials, ISSAC; Rank; SIGSAM; symbolic computation;
theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations in finite fields. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
thesaurus = "Computational complexity; Determinants; Hankel
matrices; Polynomials",
}
@InProceedings{Shackell:1993:NEH,
author = "John Shackell",
title = "Nested Expansions and {Hardy} Fields",
crossref = "Bronstein:1993:IPI",
pages = "234--238",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p234-shackell/",
abstract = "Let $X$ denote the ring of germs, at $+ \infty$, of
$C^\infty$ real-valued functions each defined on some
subinterval of $R$ of the form $(a, infinity )$. Using
a common abuse of terminology we shall often treat
elements of $X$ as functions rather than the germs of
functions. A Hardy field is a subfield of $X$ closed
under differentiation. The definition is simple and
natural, but the connection with asymptotics is perhaps
not apparent at first sight. Let $F$ be any Hardy
field. A non-zero element, $f$, of $F$ has to have an
inverse in $F$ and so cannot have arbitrarily large
zeros. Therefore $f$ is either ultimately positive or
ultimately negative. If $g$ is another element of $F$
we can define $f > g$ to mean that $f-g$ is ultimately
positive. This makes $F$ into a totally ordered field
with the order reflecting the asymptotic behaviour of
elements. Since $F$ is closed under differentiation,
its elements must either be ultimately increasing,
ultimately decreasing or ultimately constant. Hardy,
showed that the exp-log functions form a field with
these properties. One of the obvious difficulties with
nested expansions is the fact that they are complicated
to manipulate. However that need not be a barrier for
computer algebra systems. A complexity which is doubly
exponential in the number of terms could be more
serious though. Perhaps only experience will determine
whether this is a real obstacle in practice.",
acknowledgement = ack-nhfb,
classification = "C4170 (Differential equations); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Asymptotics;
Complexity; Computer algebra systems; Hardy field;
ISSAC; Nested expansions; SIGSAM, Hardy fields;
symbolic computation; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General.",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Shevchenko:1993:SRP,
author = "Ivan I. Shevchenko and Andrej G. Sokolsky",
title = "Studies of Regular Precessions of a Symmetric
Satellite by Means of Computer Algebra",
crossref = "Bronstein:1993:IPI",
pages = "65--67",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p65-shevchenko/",
abstract = "The perturbed motion in the neighbourhood of regular
precessions of a dynamically symmetric satellite on a
circular orbit is studied. The `Norma' specialized
program package (A. G. Sokolsky, I. I. Shevenko, 1990;
1991), intended for normalization of autonomous
Hamiltonian systems by means of computer algebra, is
used to obtain normal forms of the Hamiltonian. A full
catalogue of non resonant and resonant normal forms up
to the 6th order of normalization is constructed for
the case of hyperboloidal precession. The case of
cylindrical precession, more complicated in analytical
sense, is considered as well. Analytical expressions
for coefficients of terms of the normal forms are
derived as dependences on the frequencies and the
initial physical parameters of the system. Though the
intermediary expressions occupy megabytes of computer
memory, the final normal forms are compact.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. Astron., Acad. of Sci., St.
Petersburg, Russia",
classification = "C4140 (Linear algebra); C6130 (Data handling
techniques); C7310 (Mathematics computing); C7350
(Astronomy and astrophysics computing)",
keywords = "ACM; algebraic computation; algorithms; Analytical
expressions; Autonomous Hamiltonian systems; Circular
orbit; Computer algebra; Cylindrical precession;
design; Dynamically symmetric satellite; Hyperboloidal
precession; Initial physical parameters; Intermediary
expressions, ISSAC; Norma specialized program package;
Perturbed motion; Regular precessions; Resonant normal
forms; SIGSAM; symbolic computation; Symmetric
satellite",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf I.1.0} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
General. {\bf J.2} Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Aerospace.",
thesaurus = "Astronomy computing; Matrix algebra; Series
[mathematics]; Symbol manipulation",
}
@InProceedings{Siegl:1993:PAS,
author = "K. Siegl",
title = "Parallelizing algorithms for symbolic computation
using $\parallel${Maple}$\parallel$",
crossref = "ACM:1993:PFA",
pages = "179--186",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
standardno = "1",
}
@InProceedings{Stifter:1993:GTP,
author = "Sabine Stifter",
title = "Geometry Theorem Proving in Vector Spaces by Means of
{Gr{\"o}bner} Bases",
crossref = "Bronstein:1993:IPI",
pages = "301--310",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p301-stifter/",
abstract = "Within the last few years several approaches to
automated geometry theorem proving have been developed
and proposed that are based (1) on the formulation of a
geometric statement as the implication of a polynomial
equation (the `conclusion') from a set of polynomial
equations (the `hypotheses'), and (2) the proof of the
implication by algebraic methods, namely Gr{\"o}bner
bases and Ritt's bases. All these approaches require
the introduction of coordinates for the points
involved. Many geometric theorems, however, can be
formulated as relations between points directly,
without needing coordinates. In this paper we develop a
new method, based on Gr{\"o}bner bases in vector
spaces, that can prove geometric theorems that are
formulated as relations between points directly. Our
approach has the advantages that theorems can be
formulated more naturally and fewer variables are
needed for their formulations. This results in shorter
and faster proofs.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence); C4210 (Formal
logic); C4260 (Computational geometry)",
keywords = "theory; Geometry theorem proving; Vector spaces;
Gr{\"o}bner bases; Geometric statement; Coordinates;
Geometric theorems, ISSAC; symbolic computation;
algebraic computation; ACM; SIGSAM",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Computational geometry; Theorem proving",
}
@InProceedings{Vallier:1993:ACN,
author = "L. Vallier",
title = "An Algorithm for the Computation of Normal Forms and
Invariant Manifolds",
crossref = "Bronstein:1993:IPI",
pages = "225--233",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p225-vallier/",
abstract = "This paper deals with an algorithm to compute normal
forms and invariant manifolds of ordinary differential
equations. This algorithm based on transformation
theory, gives us a useful tool in the study of such
equations, in the neighborhood of singular points. This
tool involves a lot of computations on homogeneous
polynomials. Then in addition, a tree data structure is
described to represent homogeneous polynomials in an
efficient way, and we give the cost of the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "LMC, IMAG, Grenoble, France",
classification = "B0290F (Interpolation and function approximation);
B0290P (Differential equations); C4130 (Interpolation
and function approximation); C4170 (Differential
equations); C4240C (Computational complexity)",
keywords = "ACM; algebraic computation; Algorithm, ISSAC;
algorithms; Homogeneous polynomials; Invariant
manifolds; Normal forms; Ordinary differential
equations; SIGSAM; Singular points; symbolic
computation; theory; Transformation theory; Tree data
structure",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf E.1} Data, DATA
STRUCTURES, Trees. {\bf G.1.3} Mathematics of
Computing, NUMERICAL ANALYSIS, Numerical Linear
Algebra, Linear systems (direct and iterative
methods).",
thesaurus = "Computational complexity; Differential equations;
Polynomials; Tree data structures",
}
@InProceedings{vanderPut:1993:RRK,
author = "Marius {van der Put} and Peter A. Hendriks",
title = "A rationality result for {Kovacic}'s algorithm",
crossref = "Bronstein:1993:IPI",
pages = "4--8",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p4-van_der_put/",
abstract = "We want to prove the following rationality result (J.
J. Kovacic, 1986). Suppose that the Riccati equation
$u^1+u^2=r$ has a solution, which is algebraic over
$Q^{cl}(x)$. Then there exists an algebraic solution
$u$ of minimal degree $n$ of the Riccati equation such
that the coefficients of the minimum polynomial of $u$
over $Q^{cl}(x)$ lie in a field $K(x)$ with $(K:Q)<=2$.
Moreover, only in the cases: $n=1$ and $G$ is the
multiplicative group $G_m$ or a finite cyclic group of
order $>2$ or $n=4$ and $G$ the tetrahedral group, a
field extension $K$ of degree 2 of $Q$ can be needed.",
acknowledgement = ack-nhfb,
classification = "C1160 (Combinatorial mathematics); C4140 (Linear
algebra); C4170 (Differential equations)",
keywords = "ACM; algebraic computation; Algebraic solution;
algorithms; Field extension; Finite cyclic group;
ISSAC; Kovacic algorithm; Minimum polynomial;
Multiplicative group; Riccati equation; SIGSAM,
Rationality result; symbolic computation; Tetrahedral
group; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic.",
thesaurus = "Group theory; Linear differential equations; Riccati
equations",
}
@InProceedings{Villard:1993:CSN,
author = "Gilles Villard",
title = "Computation of the {Smith} normal form of polynomial
matrices",
crossref = "Bronstein:1993:IPI",
pages = "209--217",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p209-villard/",
abstract = "We describe a new algorithm for the computation of the
Smith normal form of polynomial matrices. This
algorithm computes the normal form and pre- and
post-multipliers in deterministic polynomial time.
Noticing that the computation reduces to a linear
algebra problem over the field of the coefficients, we
obtain a good worst-case complexity bound.",
acknowledgement = ack-nhfb,
affiliation = "Lab. LMC, IMAG, Grenoble, France",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity)",
keywords = "ACM; algebraic computation; algorithms; Deterministic
polynomial time; Linear algebra, ISSAC; Polynomial
matrices; SIGSAM; Smith normal form; symbolic
computation; theory; Worst-case complexity",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Linear algebra; Polynomial
matrices",
}
@InProceedings{Volcheck:1993:NSS,
author = "E. J. Volcheck",
title = "{Noether}'s {S-transformation} simplifies curve
singularities rationally: a local analysis",
crossref = "Bronstein:1993:IPI",
pages = "164--172",
year = "1993",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "The singularities of algebraic plane curves over $Q$
may be resolved into ordinary multiple points by the
classical method of standard quadratic transformations.
The author analyzes a birational plane transformation
described by Max Noether (1884) which improves upon the
classical method in two ways: first, it requires no
ground field extension; second, the degree of the curve
it produces is an exponential factor lower than that
produced by the standard method.",
acknowledgement = ack-nhfb,
classification = "B0210 (Algebra); B0230 (Integral transforms); C1110
(Algebra); C1130 (Integral transforms); C7310
(Mathematics computing)",
keywords = "ACM; algebraic computation; Algebraic plane curves;
Birational plane transformation; Curve singularities;
ISSAC; Local analysis; Quadratic transformations;
SIGSAM, Noether S-transformation; Singularities;
symbolic computation",
thesaurus = "Polynomials; Symbol manipulation; Transforms",
}
@InProceedings{Volcheck:1993:NTS,
author = "Emil J. Volcheck",
title = "{Noether}'s ${S}$-transformation simplifies curve
singularities rationally: a local analysis",
crossref = "Bronstein:1993:IPI",
pages = "164--172",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p164-volcheck/",
acknowledgement = ack-nhfb,
keywords = "algorithms; languages; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple.",
}
@InProceedings{Weispfenning:1993:DT,
author = "Volker Weispfenning",
title = "Differential term-orders",
crossref = "Bronstein:1993:IPI",
pages = "245--253",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p245-weispfenning/",
abstract = "In the theory of Gr{\"o}bner bases for multivariate
polynomials the concept of a term-order plays a central
role. Such term-orders can be characterized by linear
forms, whose coefficients are univariate real
polynomials. For multivariate partial differential
polynomials a corresponding concept is of great
importance for potential extensions of the
Riquier--Janet technique. So far, only the weaker
concepts of rankings and comparative rank have been
defined by Kolchin. This note presents an axiomatic
definition of differential term-orders on arbitrary
partial differential terms and proves that all these
orders are well-orders. Moreover, we give a
characterization of differential term-orders in terms
of systems of linear forms whose coefficients are
univariate real polynomials. This characterization
provides an explicit construction of an abundance of
differential term-orders. As an application, we obtain
a simple characterization of differential term-orders
on finite sets of differential terms and an algorithm
for computing all differential term-orders on such
sets. Finally, we characterize the term-orders, for
which differentiation preserves the ordering between
the highest terms of non-zero differential
polynomials.",
acknowledgement = ack-nhfb,
affiliation = "Passau Univ., Germany",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics computing)",
keywords = "algorithms; theory; verification; Gr{\"o}bner bases;
Multivariate polynomials; Multivariate partial
differential polynomials; Differential term-orders;
Term-order",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation. {\bf F.4.1}
Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Mathematical Logic.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Weispfenning:1993:DTP,
author = "V. Weispfenning",
title = "Differential Term-Orders",
crossref = "Bronstein:1993:IPI",
pages = "245--253",
year = "1993",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
keywords = "ACM; algebraic computation; ISSAC; SIGSAM; symbolic
computation",
}
@InProceedings{Willis:1993:CSP,
author = "T. J. Willis and E. A. Bogucz",
title = "Coupling Symbolic Processing with Parallel Numeric
Computation",
crossref = "Sincovec:1993:PSS",
pages = "788--792",
year = "1993",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wu:1993:ACU,
author = "Hongzhong Wu",
title = "On the assignment complexity of uniform trees",
crossref = "Bronstein:1993:IPI",
pages = "95--104",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p95-wu/",
abstract = "This paper discusses the assignment complexity of the
uniform tree, which is made up of identical cells
realizing a function $f$. The assignment complexity of
a tree is defined as the cardinal number of the minimum
complete assignment set of the tree. When a complete
assignment set is applied to the primary input lines of
the tree, every internal $f$ cell in the tree can be
excited by all possible input combinations. The
assignment problem is a basic problem in the VLSI
system design, test and optimization. The relation
between the property of $f$ and the assignment
complexity of the uniform tree is analyzed. It is shown
that, the assignment complexity of a balanced uniform
tree with $n$ primary input lines is either $O(1)$ or
$Omega ((\lg{}n)^{\alpha}) (\alpha in (0,1))$. In the
first case, the cardinal number of the minimum complete
assignment set for a tree is constant and independent
of the size and structure of the tree. In the second
case, the assignment complexity depends on the number
of the primary input lines of the tree. If a balanced
uniform tree is based on a commutative function, then
it is either $Theta (1)$ or $Theta (\lg{}n)$
assignable.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Inf., Saarlandes Univ., Saarbrucken,
Germany",
classification = "B0250 (Combinatorial mathematics); B1110 (Network
topology); B1130 (General circuit analysis and
synthesis methods); C1160 (Combinatorial mathematics);
C4240C (Computational complexity)",
keywords = "ACM; algebraic computation; algorithms; Assignable;
Assignment complexity; Cardinal number; Commutative
function; Computational complexity; Computer circuit
design; design; Identical cells; ISSAC; Minimum
complete assignment set; Optimization; SIGSAM; symbolic
computation; Test; theory; Tree; Uniform trees; VLSI
system design",
subject = "{\bf B.7.1} Hardware, INTEGRATED CIRCUITS, Types and
Design Styles, VLSI (very large scale integration).
{\bf G.2.2} Mathematics of Computing, DISCRETE
MATHEMATICS, Graph Theory, Trees. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Computational complexity; Network synthesis; Network
topology; Trees [mathematics]; VLSI",
}
@InProceedings{Wu:1993:RPG,
author = "Jinzhao Wu and Lian Li",
title = "The regular problem and green equivalences for special
monoids",
crossref = "Bronstein:1993:IPI",
pages = "78--85",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p78-wu/",
acknowledgement = ack-nhfb,
keywords = "algorithms; theory",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf F.1.3}
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Measures and Classes. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms.",
}
@InProceedings{Yokoyama:1993:HCE,
author = "Kazuhiro Yokoyama and Taku Takeshima",
title = "On {Hensel} Construction of Eigenvalues and
Eigenvectors of Matrices with Polynomial Entries",
crossref = "Bronstein:1993:IPI",
pages = "218--224",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p218-yokoyama/",
abstract = "Hensel's lemma is now widely used in algebraic
computation as a tool of lifting procedure in modular
methods, and this lifting procedure based on Hensel's
lemma is called a Hensel construction. Significant
examples are found in polynomial computation problems;
factorization, GCD computation and division.
Furthermore, several Hensel constructions are applied
to solve systems of polynomial equations or to compute
inverses of matrices with polynomial entries
(Krishnamurthy, 1985). For a natural application, we
propose a method for finding eigenvalues and
eigenvectors of matrices simultaneously. The authors
study the problem and show several Hensel constructions
for the problem. For simplicity, they only deal with
matrices with univariate polynomial entries over a
field and they consider linear lifting.",
acknowledgement = ack-nhfb,
affiliation = "IIAS-SIS, Fujitsu Labs. Ltd., Shizuoka, Japan",
classification = "C4140 (Linear algebra); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; Algebraic computation;
algorithms; Eigenvalues; Eigenvectors; Hensel
construction; Linear lifting; Matrices; Polynomial
computation, ISSAC; Polynomial entries; SIGSAM;
symbolic computation; theory; Univariate polynomial
entries; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.3} Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues and eigenvectors (direct and iterative
methods). {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices.",
thesaurus = "Eigenvalues and eigenfunctions; Polynomial matrices;
Symbol manipulation",
}
@InProceedings{Zharkov:1993:ASF,
author = "Alexey Y. Zharkov",
title = "On algebraic solutions of first order {Riccatti}
equation",
crossref = "Bronstein:1993:IPI",
pages = "1--3",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p1-zharkov/",
abstract = "In this paper we prove the following theorem. If the
Riccatti equation $w^1+w^2=R(x)$, $R$ in $Q(x)$, has
algebraic solutions then one can find a minimal
polynomial defining such solutions whose coefficients
are in a quadratic extension of the field $Q$.",
acknowledgement = ack-nhfb,
affiliation = "Saratov Univ., Russia",
classification = "C4140 (Linear algebra); C4170 (Differential
equations)",
keywords = "ACM; algebraic computation; Algebraic solutions;
algorithms; Coefficients; Differential equations,
ISSAC; First order Riccatti equation; Minimal
polynomial; Quadratic extension; SIGSAM; symbolic
computation; Theorem proving; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic. {\bf G.1.7} Mathematics of Computing, NUMERICAL
ANALYSIS, Ordinary Differential Equations.",
thesaurus = "Differential equations; Polynomials; Riccati
equations; Theorem proving",
}
@InProceedings{Zima:1993:NCO,
author = "E. V. Zima",
title = "Numeric Code Optimization in Computer Algebra Systems
and Recurrent Relations Technique",
crossref = "Bronstein:1993:IPI",
pages = "42--46",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p42-zima/",
abstract = "Computer algebra provides good tools for code
optimization. In particular it concerns
source-to-source optimization. But existing tools
(SCOPE, Gentran, etc.) provide code transmission from
computer algebra system to numeric system only. That's
why we have started developing in MSU a
source-to-source optimization library using Reduce as
an intellectual tool. This library contains algorithms
and special tools that provide reliable bilateral
connection between Reduce and systems for numeric
computations on MS DOS computers (Turbo-Pascal,
Turbo-C, MathCad, etc.).",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Math. and Cybern., Moscow State
Univ., Russia",
classification = "C6110 (Systems analysis and programming); C6130
(Data handling techniques); C6150C (Compilers,
interpreters and other processors); C7310 (Mathematics
computing)",
keywords = "ACM; algebraic computation; algorithms; Code
optimization; Code transmission; Computer algebra
systems; Gentran; Intellectual tool; languages; MS DOS
computers, ISSAC; Numeric code optimization;
performance; Recurrent relations technique; Reduce;
Reliable bilateral connection; SCOPE; SIGSAM;
Source-to-source optimization; Source-to-source
optimization library; symbolic computation",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Pascal.",
thesaurus = "Optimising compilers; Programming; Symbol
manipulation",
}
@InProceedings{Abramov:1994:DSL,
author = "Sergei A. Abramov and Marko Petkov{\v{s}}ek",
title = "{D'Alembertian} solutions of linear differential and
difference equations",
crossref = "ACM:1994:IPI",
pages = "169--174",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p169-abramov/",
abstract = "D'Alembertian solutions of differential (resp.
difference) equations are those expressible as nested
indefinite integrals (resp. sums) of hyperexponential
functions. They are a subclass of Liouvillian
solutions, and can be constructed by recursively
finding hyperexponential solutions and reducing the
order. Knowing d'Alembertian solutions of $Ly=0$, one
can write down the corresponding solutions of $Ly=f$
and of $L*y=0$.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Center, Acad. of Sci., Moscow, Russia",
classification = "C4170 (Differential equations)",
keywords = "algorithms; D'Alembertian solutions; Difference
equations; Hyperexponential functions; Hyperexponential
solutions; Linear differential equations; Liouvillian
solutions; Nested indefinite integrals; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms,
Nonalgebraic algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Difference equations; Linear differential equations",
}
@InProceedings{Andreoli:1994:CKB,
author = "J.-M. Andreoli and U. M. Borghoff and R. Pareschi",
title = "Constraint-Based Knowledge Brokers",
crossref = "Hong:1994:FIS",
pages = "1--11",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Attardi:1994:SPB,
author = "G. Attardi and C. Traverso",
title = "A strategy-accurate parallel {Buchberger} algorithm",
crossref = "Hong:1994:FIS",
pages = "12--21",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bachmann:1994:CRM,
author = "Olaf Bachmann and Paul S. Wang and Eugene V. Zima",
title = "Chains of recurrences --- a method to expedite the
evaluation of closed-form functions",
crossref = "ACM:1994:IPI",
pages = "242--249",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p242-bachmann/",
abstract = "Chains of Recurrences (CRs) are introduced as an
effective method to evaluate functions at regular
intervals. Algebraic properties of CRs are examined and
an algorithm that constructs a CR for a given function
is explained. Finally, an implementation of the method
in MAXIMA/Common Lisp is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
keywords = "Algebraic properties; algorithms; Chains of
recurrences; Closed-form functions; languages;
MAXIMA/Common Lisp; performance; theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, Common Lisp. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Function evaluation; Symbol manipulation",
}
@InProceedings{Baddoura:1994:CIF,
author = "Jamil Baddoura",
title = "A conjecture on integration in finite terms with
elementary functions and polylogarithms",
crossref = "ACM:1994:IPI",
pages = "158--162",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p158-baddoura/",
abstract = "In this abstract, we report on a conjecture that gives
the form of an integral if it can be expressed using
elementary functions and polylogarithms. The conjecture
is proved by the author in the cases of the dilogarithm
and the trilogarithm (1993) and consists of a
generalization of Liouville's theorem on integration in
finite terms with elementary functions. Those last
structure theorems, for the dilogarithm and the
trilogarithm, are the first case of structure theorems
where logarithms can appear with non-constant
coefficients. In order to prove the conjecture for
higher polylogarithms we need to find the functional
identities, for the polylogarithms that we are using,
that characterize all the possible algebraic relations
among the considered polylogarithms of functions that
are built up from the rational functions by taking the
considered polylogarithms, exponentials, logarithms and
algebraics. The task of finding those functional
identities seems to be a difficult one and is an
unsolved problem for the most part to this date.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., MIT, Cambridge, MA, USA",
classification = "C4160 (Numerical integration and differentiation);
C7310 (Mathematics computing)",
keywords = "algorithms; Elementary functions; Integration;
Polylogarithms; Structure theorems; theory;
Trilogarithm; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
algorithms. {\bf G.1.4} Mathematics of Computing,
NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation.",
thesaurus = "Integration; Symbol manipulation",
}
@InProceedings{Becker:1994:SSL,
author = "Eberhard Becker and Teo Mora and Maria Grazia Marinari
and Carlo Traverso",
title = "The shape of the {Shape Lemma}",
crossref = "ACM:1994:IPI",
pages = "129--133",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p129-becker/",
abstract = "The Shape Lemma was originally introduced in 1989 and
so christened by Lakshman (1990). It is an easy
generalization of the Primitive Element Theorem and it
states that a $O$-dimensional radical ideal in a
polynomial ring$ k(X_1,\ldots{},X_n)$, after most
changes of coordinates, has a basis
$(g_1(X_1),X_2-g_2(X_2),\ldots{},X_n-g_n(X_1))$.
Notwithstanding its triviality, it has proved
ubiquitous in recent papers on polynomial system
solving. The obvious example $(X^2, XY, Y^2)$ is
sufficient to show that some assumption is needed on a
$O$-dimensional ideal in order that it holds; the
obvious example $(X^2, Y)$ is sufficient to show that
radicality is too strong an assumption. Since most of
the results making use of the Shape Lemma are valid
whenever the Shape Lemma holds and are of interest also
for non radical ideals, it is worthwhile to exactly
characterize those $O$-dimensional ideals to which the
Shape Lemma applies. It turns out that this exact
characterization is as trivial as the original Shape
Lemma itself. In fact both this characterization and
the generalization of it we give are easy
specializations of a classical result in algebraic
geometry on the minimum dimension of a generic
biregular projection of a variety as a function of its
dimension and of the dimension of its tangent bundle.
We give a direct, elementary, self-contained proof of
this specialization.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math., Dortmund Univ., Germany",
classification = "C1160 (Combinatorial mathematics); C4260
(Computational geometry); C7310 (Mathematics
computing)",
keywords = "Algebraic geometry; algorithms; Polynomial ring;
Primitive Element Theorem; Shape lemma; theory;
verification",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms. {\bf
F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Geometrical problems and computations.",
thesaurus = "Computational geometry; Polynomials; Symbol
manipulation",
}
@InProceedings{Berman:1994:OCR,
author = "Benjamin P. Berman and Richard J. Fateman",
title = "Optical character recognition for typeset
mathematics",
crossref = "ACM:1994:IPI",
pages = "348--353",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p348-berman/",
abstract = "There is a wealth of mathematical knowledge that could
be potentially very useful in many computational
applications, but is not available in electronic form.
This knowledge comes in the form of mechanically
typeset books and journals going back more than a
hundred years. Besides these older sources, there are a
great many current publications, filled with useful
mathematical information, which are difficult if not
impossible to obtain in electronic form. What we would
like to do is extract character information from these
documents, which could then be passed to higher-level
parsing routines for further extraction of mathematical
content (or any other useful $2$-dimensional semantic
content). Unfortunately, current commercial OCR
(optical character recognition) software packages are
quite unable to handle mathematical formulas, since
their algorithms at all levels use heuristics developed
for other document styles. We are concerned with the
development of OCR methods that are able to handle this
specialized task of mathematical expression
recognition.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "C1250B (Character recognition); C5260B (Computer
vision and image processing techniques); C7310
(Mathematics computing)",
keywords = "algorithms; Character information; Higher-level
parsing routines; Journals; Mechanically typeset books;
Optical character recognition; Software packages;
Typeset mathematics",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf B.4.2}
Hardware, INPUT/OUTPUT AND DATA COMMUNICATIONS,
Input/Output Devices. {\bf I.5.4} Computing
Methodologies, PATTERN RECOGNITION, Applications, Text
processing.",
thesaurus = "Grammars; Optical character recognition; Symbol
manipulation",
}
@InProceedings{Bertrand:1994:INA,
author = "Laurent Bertrand",
title = "On the implementation of a new algorithm for the
computation of hyperelliptic integrals",
crossref = "ACM:1994:IPI",
pages = "211--215",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p211-bertrand/",
abstract = "We present an implementation in Maple of a new
algorithm for the algebraic function integration
problem in the particular case of hyperelliptic
integrals. This algorithm is based on the general
algorithm of Trager (1984) and on the arithmetic in the
Jacobian of hyperelliptic curves of Cantor (1987).",
acknowledgement = ack-nhfb,
affiliation = "Lab. d'Arithmetique, Calcul Formel et Optimisation,
Limoges Univ., France",
classification = "B0290M (Numerical integration and differentiation);
B0290R (Integral equations); C4160 (Numerical
integration and differentiation); C4180 (Integral
equations); C7310 (Mathematics computing)",
keywords = "Algebraic function integration problem; algorithms;
Hyperelliptic curves; Hyperelliptic integrals; Maple;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf F.2.1} Theory of Computation,
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
Numerical Algorithms and Problems, Computations on
polynomials.",
thesaurus = "Elliptic equations; Integral equations; Integration;
Symbol manipulation",
}
@InProceedings{Bonacina:1994:RPD,
author = "M. P. Bonacina",
title = "On the reconstruction of proofs in distributed theorem
proving with contraction: a modified {Clause-Diffusion}
method",
crossref = "Hong:1994:FIS",
pages = "22--33",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Borst:1994:GRP,
author = "W. N. Borst and V. V. Goldman and J. A. {Van Hulzen}",
title = "{GENTRAN} 90: a {REDUCE} package for the generation of
{Fortran} 90 code",
crossref = "ACM:1994:IPI",
pages = "45--51",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p45-borst/",
abstract = "GENTRAN is a code generator and translator running
under REDUCE and MACSYMA. It is a tool for generating
Fortran 77, RATFOR or C programs from program
specifications and symbolic expressions. Its facilities
include template processing, automatic segmentation of
large expressions and a file handling mechanism.
GENTRAN can be used in combination with SCOPE 1.5, a
source code optimization package for REDUCE. We present
an extension of the REDUCE version of GENTRAN, called
GENTRAN 90. It makes generation of Fortran 90 code
possible.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Twente Univ., Enschede,
Netherlands",
classification = "C6115 (Programming support); C6140D (High level
languages); C6150C (Compilers, interpreters and other
processors); C7310 (Mathematics computing)",
keywords = "algorithms; C; Code generation; Code generator; Code
translator; design; File handling; Fortran 77; Fortran
90 code; GENTRAN 90; languages; MACSYMA; Program
specifications; RATFOR; REDUCE; REDUCE package; SCOPE
1.5; Source code optimization package; Symbolic
expression; Template processing",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Code generation. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf D.3.2} Software,
PROGRAMMING LANGUAGES, Language Classifications,
Fortran 90. {\bf D.3.4} Software, PROGRAMMING
LANGUAGES, Processors, Translator writing systems and
compiler generators.",
thesaurus = "FORTRAN; Optimisation; Program interpreters; Software
packages; Software tools; Symbol manipulation",
}
@InProceedings{Bosma:1994:PAS,
author = "Wieb Bosma and John Cannon and Graham Matthews",
title = "Programming with algebraic structures: design of the
{Magma} language",
crossref = "ACM:1994:IPI",
pages = "52--57",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p52-bosma/",
abstract = "MAGMA is a new software system for computational
algebra, number theory and geometry whose design is
centred on the concept of algebraic structure (magma).
The use of algebraic structure as a design paradigm
provides a natural strong typing mechanism. Further,
structures and their morphisms appear in the language
as first class objects. Standard mathematical notions
are used for the basic data types. The result is a
powerful, clean language which deals with objects in a
mathematically rigorous manner. The conceptual and
implementation ideas behind MAGMA will be examined in
this paper. This conceptual base differs significantly
from those underlying other computer algebra systems.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Sydney Univ., NSW, Australia",
classification = "C1160 (Combinatorial mathematics); C6110 (Systems
analysis and programming); C6130 (Data handling
techniques); C7310 (Mathematics computing)",
keywords = "Algebraic structures; algorithms; Computational
algebra; Computer algebra systems; Data types; design;
Magma language; Mathematical notions; Number theory;
Software system; Strong typing mechanism",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf D.3.3}
Software, PROGRAMMING LANGUAGES, Language Constructs
and Features, Data types and structures. {\bf F.3.3}
Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Studies of Program Constructs, Type structure. {\bf
D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Number theory; Programming; Symbol manipulation",
}
@InProceedings{Bratvold:1994:PFP,
author = "T. A. Bratvold",
title = "Parallelising a Functional Program Using a
List-Homomorphism Skeleton",
crossref = "Hong:1994:FIS",
pages = "44--53",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Briek:1994:SCT,
author = "S. Briek and A. Rauzy",
title = "Synchronization of Constrained Transition Systems",
crossref = "Hong:1994:FIS",
pages = "54--62",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bronstein:1994:IAF,
author = "Manuel Bronstein",
title = "An improved algorithm for factoring linear ordinary
differential operators",
crossref = "ACM:1994:IPI",
pages = "336--340",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p336-bronstein/",
abstract = "We describe an efficient algorithm for computing the
associated equations appearing in the Beke--Schlesinger
factorisation method for linear ordinary differential
operators. This algorithm, which is based on elementary
operations with sets of integers, can be easily
implemented for operators of any order, produces
several possible associated equations, of which only
the simplest can be selected for solving, and often
avoids the degenerate case, where the order of the
associated equation is less than in the generic case.
We conclude with some fast heuristics that can produce
some factorisations while using only linear
computations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
Tech. Hochschule, Zurich, Switzerland",
classification = "B0290P (Differential equations); C4170 (Differential
equations); C4240 (Programming and algorithm theory)",
keywords = "algorithms; Beke--Schlesinger factorisation method;
Efficient algorithm; Elementary operations; Fast
heuristics; Improved algorithm; Integer sets; Linear
ordinary differential operator factoring; theory;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems.",
thesaurus = "Algorithm theory; Difference equations; Mathematical
operators",
}
@InProceedings{Buendgen:1994:MAT,
author = "R. Buendgen and M. Goebel and W. Kuechlin",
title = "Multi-Threaded {AC} Term Rewriting",
crossref = "Hong:1994:FIS",
pages = "84--93",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bueno:1994:CSM,
author = "F. Bueno and M. {Garcia de la Banda} and M.
Hermenegildo",
title = "A Comparative Study of Methods for Automatic
Compile-time Parallelization of Logic Programs",
crossref = "Hong:1994:FIS",
pages = "63--73",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bundgen:1994:FPC,
author = "Reinhard B{\"u}ndgen and Manfred G{\"o}bel and
Wolfgang K{\"u}chlin",
title = "A fine-grained parallel completion procedure",
crossref = "ACM:1994:IPI",
pages = "269--277",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p269-bundgen/",
abstract = "We present a parallel Knuth--Bendix completion
algorithm where the inner loop, deriving the
consequences of adding a new rule to the system, is
multithreaded. The selection of the best new rule in
the outer loop, and hence the completion strategy, is
exactly the same as for the sequential algorithm. Our
implementation, which is within the PARSAC-2 parallel
symbolic computation system, exhibits good parallel
speedups on a standard multiprocessor workstation.",
acknowledgement = ack-nhfb,
affiliation = "Wilhelm-Schickard-Inst. fur Inf., Tubingen Univ.,
Germany",
classification = "C4210L (Formal languages and computational
linguistics); C4240P (Parallel programming and
algorithm theory); C6130 (Data handling techniques);
C6150N (Distributed systems software); C7310
(Mathematics computing)",
keywords = "algorithms; Fine grained parallel completion
procedure; Fine-grained parallel completion procedure;
Multithreaded inner loop; Parallel Knuth--Bendix
completion algorithm; Parallel speedups; PARSAC-2
parallel symbolic computation system; Standard
multiprocessor workstation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.0} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf
I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems. {\bf F.4.2} Theory
of Computation, MATHEMATICAL LOGIC AND FORMAL
LANGUAGES, Grammars and Other Rewriting Systems,
Parallel rewriting systems. {\bf F.1.2} Theory of
Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of
Computation, Parallelism and concurrency.",
thesaurus = "Parallel algorithms; Parallel machines; Rewriting
systems; Symbol manipulation",
}
@InProceedings{Burke-Perline:1994:PCU,
author = "T. Burke-Perline",
title = "The Parallel Computation of $f(x)0(00-010)0/02 \bmod
h(x)$ using {Sugarbush 1.1}",
crossref = "Hong:1994:FIS",
pages = "74--83",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Char:1994:AIT,
author = "Bruce W. Char and Mark F. Russo",
title = "Automatic identification of time scales in enzyme
kinetics models",
crossref = "ACM:1994:IPI",
pages = "74--83",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p74-char/",
abstract = "Many chemical reaction systems studied in the
pharmaceutical industry have phenomena that occur on
two or more vastly different time scales. When modeling
the chemical reaction system as ordinary differential
equations, if a small parameter $E$ can be identified
then one can isolate the behavior of the system on long
and short time scales using singular perturbation
theory. In practice, the small parameter is discovered
using knowledge about the chemical reaction system that
is not necessarily contained in the mathematics of the
model. If a small parameter cannot be easily
identified, then the approach is typically abandoned.
The authors present a procedure that derives algebraic
expressions for dual time scales in mathematical models
of chemical reaction systems. Unlike conventional
practice, this derivation proceeds using only
information contained in the model, without knowledge
of a small parameter derived through external
considerations. The authors' procedure, Scales, is
based on rules that arise from the `art and practice'
of applying the quasi-steady-state assumption to derive
the Michaelis--Menton equations. The authors depart
from standard practice of singular perturbation theory,
using instead the viewpoint of Segel and Slemrod
(1989). They have implemented Scales in Maple. Scales
is closer to an `expert system' than a `scale oracle'
or decision procedure. Its shortcomings necessitate
subsequent verification of its results, typically
through numerical or laboratory experimentation. If
validated, additional computer algebra techniques can
be used to simplify the mathematical model and isolate
the long time scale behavior.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Drexel Univ.,
Philadelphia, PA, USA",
classification = "A8220W (Computational modelling of chemical
kinetics); A8230V (Homogeneous catalysis); A8240
(Chemical kinetics and reactions: special regimes);
A8715D (Physical chemistry of biomolecular solutions;
C1220 (Simulation, modelling and identification); C4170
(Differential equations); C6170 (Expert systems); C7320
(Physics and chemistry computing); C7450 (Chemical
engineering computing); condensed states)",
keywords = "Algebraic expression; algorithms; Automatic
identification; Biochemistry; Biology computing;
Catalysis; Chemical kinetics model; Chemical reaction;
Dual time scale; Enzyme; Maple; Mathematical model;
Metabolism; Michaelis--Menton equations; Ordinary
differential equations; Pharmaceutical; Reaction
kinetics; Scales; Singular perturbation theory; Time
scale; verification",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems, Maple.
{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Chemistry. {\bf G.1.7} Mathematics of
Computing, NUMERICAL ANALYSIS, Ordinary Differential
Equations. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation.",
thesaurus = "Chemical engineering computing; Differential
equations; Identification; Knowledge based systems;
Pharmaceutical industry; Proteins; Reaction kinetics
theory; Scaling phenomena; Symbol manipulation",
}
@InProceedings{Char:1994:SEP,
author = "B. Char and J. Johnson and D. Saunders and A. P.
Wack",
title = "Some Experiments with Parallel Bignum Arithmetic",
crossref = "Hong:1994:FIS",
pages = "94--103",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cooperman:1994:CPR,
author = "Gene Cooperman and Larry Finkelstein and Bryant York
and Michael Tselman",
title = "Constructing permutation representations for large
matrix groups",
crossref = "ACM:1994:IPI",
pages = "134--138",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p134-cooperman/",
abstract = "New techniques, both theoretical and practical, are
presented for constructing a permutation representation
for a matrix group. We assume that the resulting
permutation degree, $n,$ can be 10,000,000 and larger.
The key idea is to build the new permutation
representation using the conjugation action on a
conjugacy class of subgroups of prime order. A unique
signature for each group element corresponding to the
conjugacy class is used in order to avoid matrix
multiplication. The requirement of at least $n$ matrix
multiplications would otherwise have made the
computation hopelessly impractical. Additional software
optimizations are described, which reduce the CPU time
by at least an additional factor of 10. Further, a
special data structure is designed that serves both as
a search tree and as a hash array, while requiring
space of only $1.6 n log_2 n$ bits. The technique has
been implemented and tested on the sporadic simple
group Ly, discovered by Lyons (1972), in both a
sequential (SPARCserver 670 MP) and parallel SIMD
(MasPar MP-1) version. Starting with a generating set
for $Ly$ as a subgroup of $GL(111, 5)$, a set of
generating permutations for $Ly$ acting on 9, 606, 125
points is constructed as well as a base for this
permutation representation. The sequential version
required four days of CPU time to construct a data
structure which can be used to compute the permutation
image of an arbitrary matrix. The parallel version did
so in 12 hours. Work is in progress on a faster
parallel implementation.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA,
USA",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity); C7310 (Mathematics computing)",
keywords = "algorithms; Conjugacy class; Conjugation action; Data
structure; design; Hash array; Large matrix groups;
Parallel version; performance; Permutation
representation; Permutation representations; Search
tree",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on matrices. {\bf G.2.1}
Mathematics of Computing, DISCRETE MATHEMATICS,
Combinatorics, Permutations and combinations. {\bf E.1}
Data, DATA STRUCTURES, Arrays. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms.",
thesaurus = "Computational complexity; Matrix multiplication;
Symbol manipulation",
}
@InProceedings{Corless:1994:SAC,
author = "Robert M. Corless",
title = "Sufficiency analysis for the calculus of variations",
crossref = "ACM:1994:IPI",
pages = "197--204",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p197-corless/",
abstract = "Many of the computations in the calculus of variations
are algebraic in nature: computing the Euler--Lagrange
equations and solving them, for example. However,
deciding whether or not the computed extremals provide
minima or maxima is an analytic problem, and one that
has not been previously attempted in a computer algebra
package. I describe here a Maple implementation of some
techniques for making these decisions, and detail some
successes and failures. Some of the failures point to
areas where computer algebra systems could be
improved.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Appl. Math., Univ. of Western Ontario,
London, Ont., Canada",
classification = "C6130 (Data handling techniques); C7310 (Mathematics
computing)",
keywords = "algorithms; Calculus of variations; Computer algebra
package; Computer algebra systems; Euler--Lagrange
equations; Maple implementation; Sufficiency analysis;
theory",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Maple. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems, Special-purpose algebraic systems.",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Cremanns:1994:CCP,
author = "Robert Cremanns and Friedrich Otto",
title = "Constructing canonical presentations for subgroups of
context-free groups in polynomial time-extended
abstract",
crossref = "ACM:1994:IPI",
pages = "147--153",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p147-cremanns/",
abstract = "Canonical presentations of groups are of interest,
since they provide structurally simple algorithms for
computing normal forms. A class of groups that has
received much attention is the class of context-free
groups. This class of groups can be characterized
algebraically as well as through some language
theoretical properties as well as through certain
combinatorial properties of presentations. Here we use
the fact that a finitely generated group is
context-free if and only if it admits a finite
canonical presentation of a certain form that we call a
virtually free presentation. Since finitely generated
subgroups of context-free groups are again
context-free, they admit presentations of the same
form. We present a polynomial-time algorithm that,
given a finite virtually free presentation of a
context-free group $G$ and a finite subset $U$ of $G$
as input, computes a virtually free presentation for
the subgroup $<U>$ of $G$ that is generated by $U$.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math./Inf., Kassel Univ., Germany",
classification = "C1110 (Algebra); C4210L (Formal languages and
computational linguistics); C4240C (Computational
complexity)",
keywords = "algorithms; Canonical presentations; Context-free
groups; Language theoretical properties; languages;
Polynomial time; Subgroups; theory; verification;
Virtually free presentation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Analysis of
algorithms. {\bf F.4.2} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and
Other Rewriting Systems, Grammar types. {\bf I.1.0}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, General.",
thesaurus = "Computational complexity; Context-free languages;
Group theory",
}
@InProceedings{Dalmas:1994:DCA,
author = "S. Dalmas and M. Gaetano and A. Sausse",
title = "Distributed Computer Algebra: the Central Control
Approach",
crossref = "Hong:1994:FIS",
pages = "104--113",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{DeBosschere:1994:LCB,
author = "K. {De Bosschere} and J.-M. Jacquet",
title = "Local and Conditional Blackboard Operations in Log:
Semantics, Applicability, and Implementation",
crossref = "Hong:1994:FIS",
pages = "34--43",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{DelPozo-Prieto:1994:ISP,
author = "A. {Del Pozo-Prieto} and J. J. Moreno-Navarro",
title = "Independent Subexpressions Parallelism with Delayed
Synchronization for Functional Logic Languages",
crossref = "Hong:1994:FIS",
pages = "316--325",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Denzinger:1994:RAP,
author = "J. Denzinger and S. Schulz",
title = "Recording, Analyzing and Presenting Distributed
Deduction Processes",
crossref = "Hong:1994:FIS",
pages = "114--123",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dingle:1994:BCC,
author = "Adam Dingle and Richard J. Fateman",
title = "Branch cuts in computer algebra",
crossref = "ACM:1994:IPI",
pages = "250--257",
year = "1994",
DOI = "https://doi.org/10.1145/190347.190424",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p250-dingle/",
abstract = "Most computer algebra systems provide little
assistance in working with expressions involving
functions with complex branch cuts. Worse, by their
ignorance of the existence of branch cuts, algebra
systems sometimes simplify complex expressions
incorrectly. We propose a computer representation for
branch cuts; we show how a complex expression's branch
cuts may be mechanically computed, and how an
expression with branch cuts may sometimes be
algebraically simplified within each of its branches.",
acknowledgement = ack-nhfb,
affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
classification = "C1100 (Mathematical techniques); C6130 (Data
handling techniques); C7310 (Mathematics computing)",
keywords = "Algebraic simplification; algorithms; Complex branch
cuts; Complex expressions; Computer algebra systems;
Computer representation; languages",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf I.1.3} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and
Systems. {\bf I.1.1} Computing Methodologies, SYMBOLIC
AND ALGEBRAIC MANIPULATION, Expressions and Their
Representation, Simplification of expressions. {\bf
G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica.",
thesaurus = "Functions; Symbol manipulation",
}
@InProceedings{Du:1994:ISA,
author = "Hong Du",
title = "On the isomorphisms of smooth algebraic curves",
crossref = "ACM:1994:IPI",
pages = "15--19",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p15-du/",
abstract = "I consider some problems of algebraic curves in a
constructive way, especially, I provide an algorithm
for determining whether two given smooth plane curves
are isomorphic and find all isomorphic maps. I present
a survey of some miscellaneous results related to the
classification of curves. In the appendix, I give some
other results which implies a more efficient algorithm
for deciding whether two plane curves are isomorphic
and find all isomorphic maps. The method can be
generalized to smooth projective complete intersection
varieties.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China",
classification = "C4130 (Interpolation and function approximation);
C4260 (Computational geometry)",
keywords = "algorithms; Curve classification; Isomorphic maps;
Isomorphisms; Plane curves; Smooth algebraic curves;
Smooth plane curves; Smooth projective complete
intersection; theory; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations.",
thesaurus = "Computational geometry; Curve fitting",
xxabstract = "In this paper, I have considered some problems of
algebraic curves in some constructive way, especially,
I give an algorithm for determining whether two given
smooth plane curves are isomorphic and finding all
isomorphic maps. I also have given a survey of some
miscellaneous results related to the classification of
curves. In the appendix, I give some other results
which implies a more efficient algorithm for deciding
whether two plane curves are isomorphic and finding all
isomorphic maps. It is clear our method in this paper
can be generalized to smooth projective complete
intersection varieties.",
}
@InProceedings{Dyer:1994:ASC,
author = "Charles C. Dyer",
title = "An application of symbolic computation in the physical
sciences",
crossref = "ACM:1994:IPI",
pages = "181--186",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p181-dyer/",
abstract = "An example of a problem in the physical sciences is
discussed where application of various symbolic
computation facilities available in many algebraic
computing systems leads to a significant expansion of
the range of problems that can be solved. Since most
interesting problems in the physical sciences
eventually require the numerical solution of systems of
equations, of various types, we introduce an example
and describe an approach to a solution, beginning at
the development of relevant differential equations,
using, for example REDUCE, and leading eventually to
the generation of highly efficient and stable numerical
code for the solution, using, in our case, the C
language. The use of SCOPE and GENTRAN, as well as
series packages in REDUCE are discussed. In many areas
of interest, a considerable amount of work has to be
performed to arrive at the symbolic equations to solve,
and this is particularly true in General Relativity and
related gravitation theories. Some packages, such as
REDTEN, for calculation in this field are discussed.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Astron., Toronto Univ., Ont., Canada",
classification = "C4170 (Differential equations); C7310 (Mathematics
computing); C7320 (Physics and chemistry computing)",
keywords = "Algebraic computing systems; algorithms; C language;
Calculation; Differential equations; General
Relativity; GENTRAN; Gravitation theories; languages;
Numerical code; Numerical solution; Physical sciences;
REDTEN; REDUCE; reliability; SCOPE; Series packages;
Symbolic computation; Symbolic equations;
verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, REDUCE. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics. {\bf D.2.5} Software, SOFTWARE ENGINEERING,
Testing and Debugging, Debugging aids.",
thesaurus = "Differential equations; Gravitation; Mathematics
computing; Physics computing; Symbol manipulation",
}
@InProceedings{Emiris:1994:MBP,
author = "Ioannis Z. Emiris and Ashutosh Rege",
title = "Monomial bases and polynomial system solving (extended
abstract)",
crossref = "ACM:1994:IPI",
pages = "114--122",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p114-emiris/",
abstract = "This paper addresses the problem of efficient
construction of monomial bases for the coordinate rings
of zero-dimensional varieties. Existing approaches rely
on Gr{\"o}bner bases methods-in contrast, we make use
of recent developments in sparse elimination techniques
which allow us to strongly exploit the structural
sparseness of the problem at hand. This is done by
establishing certain properties of a matrix formula for
the sparse resultant of the given polynomial system. We
use this matrix construction to give a simpler proof of
the result of Pedersen and Sturmfels (1994) for
constructing monomial bases. The monomial bases so
obtained enable the efficient generation of
multiplication maps in coordinate rings and provide a
method for computing the common roots of a generic
system of polynomial equations with complexity singly
exponential in the number of variables and polynomial
in the number of roots. i.e. describe the
implementations based on our algorithms and provide
empirical results on the well-known problem of cyclic
$n$-roots; our implementation gives the first known
upper bounds in the case of $n=10$ and $n=11$. We also
present some preliminary results on root finding for
the Stewart platform and motion from point matches
problems in robotics and vision respectively.",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA,
USA",
classification = "C7310 (Mathematics computing)",
keywords = "algorithms; theory; verification; Polynomial system
solving; Monomial bases; Coordinate rings;
Zero-dimensional varieties; Gr{\"o}bner bases; Sparse
elimination techniques; Matrix formula; Multiplication
maps; Root finding",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Encarnacion:1994:MAC,
author = "Mark J. Encarnaci{\'o}n",
title = "On a modular algorithm for computing {GCDs} of
polynomials over algebraic number fields",
crossref = "ACM:1994:IPI",
pages = "58--65",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p58-encarnacion/",
abstract = "Modular methods for computing the gcd of two
univariate polynomials over an algebraic number field
require {\em a priori\/} knowledge about the
denominators of the rational numbers in the
representation of the gcd. We derive a multiplicative
bound for these denominators without assuming that the
number generating the field is an algebraic integer.
Consequently, the gcd algorithm of Langemyr and
McCallum [{\em J. Symbolic Computation\/}, 8:429-448,
1989] can now be applied directly to polynomials that
are not necessarily represented in terms of an
algebraic integer. Worst-case analyses and experiments
with an implementation show that by avoiding a
conversion of representation the reduction in the
computing time can be significant. We also suggest the
use of an algorithm for recovering a rational number
from its modular residue so that the denominator bound
need not be computed explicitly. Experiments and
analyses indicate that this is a good practical
alternative.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C6130
(Data handling techniques); C7310 (Mathematics
computing)",
keywords = "A priori knowledge; Algebraic number fields;
algorithms; Computing GCDs; Denominators;
experimentation; Modular algorithm; Multiplicative
bound; Polynomials; theory; verification; Worst-case
analysis",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on polynomials.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Number-theoretic computations.",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Faugere:1994:PGB,
author = "J. C. Faugere",
title = "Parallelization of {Gr{\"o}bner} Basis",
crossref = "Hong:1994:FIS",
pages = "124--132",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ganzha:1994:SSI,
author = "V. G. Ganzha and E. V. Vorozhtsov and J. Boers and J.
A. {van Hulzen}",
title = "Symbolic-numeric stability investigations of
{Jameson}'s schemes for the thin-layer {Navier--Stokes}
equations",
crossref = "ACM:1994:IPI",
pages = "234--241",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p234-ganzha/",
abstract = "The Navier--Stokes equations governing the
three-dimensional flows of a viscous, compressible,
heat-conducting gas and augmented by turbulence
modeling present the most realistic model for gas flows
around the elements of aircraft configurations. We
study the stability of one of the Jameson's schemes of
1981, which approximates the set of five Navier--Stokes
equations completed by the turbulence model of Baldwin
and Lomax (1978). The analysis procedure implements the
check-up of the necessary von Neumann stability
criterion. It is shown with the aid of the proposed
symbolic-numeric strategy that the physical viscosity
terms in the Navier--Stokes equations have a dominant
effect on the sizes of the stability region in
comparison with the heat conduction terms. It turns out
that the consideration of turbulence with the aid of
eddy viscosity model of Baldwin and Lomax has an
insignificant effect on the size of the necessary
stability region.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci.,
Novosibirsk, Russia",
classification = "A0260 (Numerical approximation and analysis); A4710
(General fluid dynamics theory, simulation and other
computational methods); A4725 (Turbulent flows,
convection, and heat transfer); C4170 (Differential
equations); C7320 (Physics and chemistry computing)",
keywords = "3D flows; Aircraft configurations; algorithms;
Compressible gas; Eddy viscosity model; Heat-conducting
gas; Jameson schemes; languages; Stability region;
Symbolic-numeric stability; Thin-layer Navier--Stokes
equations; Turbulence modeling; Viscosity terms;
Viscous gas; Von Neumann stability",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Aerospace. {\bf J.2} Computer Applications, PHYSICAL
SCIENCES AND ENGINEERING, Physics. {\bf F.2.1} Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices. {\bf G.1.4} Mathematics of
Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
Differentiation.",
thesaurus = "Navier--Stokes equations; Numerical stability; Physics
computing; Symbol manipulation; Turbulence; Viscosity",
}
@InProceedings{Gautier:1994:PSP,
author = "T. Gautier and J.-L. Roch",
title = "{PAC++} System and Parallel Algebraic Numbers
Computation",
crossref = "Hong:1994:FIS",
pages = "145--153",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giesbrecht:1994:FAR,
author = "Mark Giesbrecht",
title = "Fast algorithms for rational forms of integer
matrices",
crossref = "ACM:1994:IPI",
pages = "305--311",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p305-giesbrecht/",
abstract = "A Monte Carlo type probabilistic algorithm is
presented for finding the Frobenius rational form $F$
in $Z^{n*n}$ of any $A$ in $Z^{n*n}$ which requires an
expected number of $O(n^4(\log{}n+//A//)^2)$ bit
operations using standard integer and matrix arithmetic
(where $//A//$ is the largest absolute value of any
entry of $A$). This improves dramatically on the
fastest previously known algorithm, which requires
$O(n^6\log{}//A//)$ bit operations using fast integer
arithmetic. We also give a Las Vegas type probabilistic
algorithm which finds the Frobenius form $F$ and a
transition matrix $U$ in $Q^{n*n}$ such that
$U^{-1}/AU=F$ and requires an expected number of
$O(n^5(\log{}n+log //A//)^{52})$ bit operations.
Finally, a Las Vegas algorithm for computing the
rational Jordan form of an integer matrix is shown,
which requires about the same number of bit operations
as our algorithm to find the Frobenius form, plus the
time required to factor the characteristic polynomial
of that matrix.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
Canada",
classification = "C1140G (Monte Carlo methods); C4140 (Linear
algebra); C4240C (Computational complexity); C7310
(Mathematics computing)",
keywords = "algorithms; Bit operations; Characteristic polynomial;
Expected number; Fast algorithms; Fast integer
arithmetic; Frobenius rational form; Integer matrices;
Largest absolute value; Las Vegas type probabilistic
algorithm; Matrix arithmetic; Monte Carlo type
probabilistic algorithm; Rational Jordan form; Standard
integer arithmetic; Transition matrix; verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
Algorithms and Problems, Computations on matrices. {\bf
G.3} Mathematics of Computing, PROBABILITY AND
STATISTICS, Probabilistic algorithms (including Monte
Carlo). {\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems, Computations on polynomials.",
thesaurus = "Computational complexity; Matrix algebra; Monte Carlo
methods; Symbol manipulation",
}
@InProceedings{Gladitz:1994:PIG,
author = "K. Gladitz and H. Kuchen",
title = "Parallel Implementation of the Gamma-Operation on
Bags",
crossref = "Hong:1994:FIS",
pages = "154--163",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gonzalez:1994:MPE,
author = "A. Gonzalez and J. Tubella",
title = "The Multipath Parallel Execution Model for {Prolog}",
crossref = "Hong:1994:FIS",
pages = "164--173",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Goriely:1994:HCM,
author = "Alain Goriely and Michael Tabor",
title = "How to compute the {Melnikov} vector?",
crossref = "ACM:1994:IPI",
pages = "205--210",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p205-goriely/",
abstract = "It is shown that transverse homoclinic intersections
such as the ones described by the Melnikov theory can
be computed by a local analysis of the complex-time
singularities of the solutions. This provides a new
algorithmic procedure to compute homoclinic
intersections in $n$-dimensions once the homoclinic
manifold is known. It also gives new insights on the
singularity structure of integrable and nonintegrable
systems.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Libre de Bruxelles, Belgium",
classification = "C1110 (Algebra); C4170 (Differential equations);
C4240 (Programming and algorithm theory)",
keywords = "Algorithm; algorithms; Complex-time singularities;
Differential equations; Homoclinic intersection;
Homoclinic manifold; Local analysis; Melnikov theory;
Melnikov vector; N-dimensions; Singularity structure;
Symbolic computation; theory; Transverse homoclinic
intersections",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.7}
Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
Differential Equations. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Algorithm theory; Differential equations; Symbol
manipulation; Vectors",
}
@InProceedings{Graebe:1994:PGF,
author = "H.-G. Graebe and W. Lassner",
title = "A Parallel {Gr{\"o}bner} Factorizer",
crossref = "Hong:1994:FIS",
pages = "174--180",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gray:1994:MPE,
author = "Simon Gray and Norbert Kajler and Paul Wang",
title = "{MP}: a protocol for efficient exchange of
mathematical expressions",
crossref = "ACM:1994:IPI",
pages = "330--335",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p330-gray/",
abstract = "The Multi Protocol (MP) is designed for integrating
symbolic, numeric, graphics, document processing, and
other tools for scientific computation, into a single
distributed problem-solving environment. MP is layered,
reflecting the logically distinct aspects of tool
integration. Data representation issues are addressed
by specifying a set of basic data types and a mechanism
for constructing non-basic types. MP passes all data in
the form of annotated parse trees. The parse tree
provides a simple, flexible and tool-independent way to
represent and exchange data, and annotations provide a
powerful and generic expressive facility for
transmitting additional information. MP also provides
efficient encodings for numeric data and includes
different types of optimizations to reduce the cost of
exchanging data. The optimizations are important when
transmitting large expressions typically encountered in
symbolic and numeric computation. MP is extensible.
Users can define additional sets of operators and
annotations as well as tailor the generic optimization
mechanisms to efficiently encode their own data
structures. A clear distinction between MP-defined and
user-defined definitions is enforced.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH,
USA",
classification = "C1180 (Optimisation techniques); C4210L (Formal
languages and computational linguistics); C5640
(Protocols); C6115 (Programming support); C6120 (File
organisation); C6130B (Graphics techniques); C6130D
(Document processing techniques); C6150N (Distributed
systems software); C6170K (Knowledge engineering
techniques); C7310 (Mathematics computing)",
keywords = "algorithms; Annotated parse trees; Annotations; Basic
data types; Data exchange cost reduction; Data
representation issues; design; Distributed
problem-solving environment; Document processing;
Efficient encodings; Efficient mathematical expression
exchange; Generic optimization mechanisms; Graphics;
languages; Large expression transmission; Layered; MP
protocol; Multi Protocol; Nonbasic types; Numeric
processing; Operators; performance; Scientific
computation; Symbolic processing; Tool integration",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.3}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Languages and Systems, Maple. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C. {\bf D.2.2} Software, SOFTWARE
ENGINEERING, Design Tools and Techniques.",
thesaurus = "Computer graphics; Distributed processing; Document
handling; Grammars; Mathematics computing; Natural
sciences computing; Optimisation; Problem solving;
Protocols; Software tools; Symbol manipulation; Tree
data structures",
}
@InProceedings{Guergueb:1994:EAT,
author = "Ahmed Guergueb and Jean Mainguen{\'e} and
Marie-Fran{\c{c}}oise Roy",
title = "Examples of automatic theorem proving in real
geometry",
crossref = "ACM:1994:IPI",
pages = "20--24",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p20-guergueb/",
abstract = "We show that computer algebra methods in mechanical
geometry theorem proving can also be applied to obtain
new theorems involving inequalities. An interesting
feature is that in real geometry, several cases can
occur, none of them being more generic than the other.
The examples we give come from the geometry of the
triangle, more precisely comparing radii of circles
defined in the triangle.",
acknowledgement = ack-nhfb,
affiliation = "Rennes I Univ., France",
classification = "C4260 (Computational geometry); C7310 (Mathematics
computing)",
keywords = "algorithms; Automatic theorem proving; Computer
algebra methods; Inequalities; Mechanical geometry
theorem proving; Radii of circles; theory; Triangle;
verification",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS
OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
Algorithms and Problems, Geometrical problems and
computations. {\bf F.4.1} Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical
Logic, Mechanical theorem proving.",
thesaurus = "Computational geometry; Symbol manipulation; Theorem
proving",
xxtitle = "Examples of automatic theorem proving a real
geometry",
}
@InProceedings{Hammond:1994:PFP,
author = "K. Hammond",
title = "Parallel Functional Programming: An Introduction
(Invited Tutorial)",
crossref = "Hong:1994:FIS",
pages = "181--193",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Harris:1994:IRR,
author = "Jason F. Harris",
title = "Inheritance of rewrite rule structures applied to
symbolic computation",
crossref = "ACM:1994:IPI",
pages = "318--323",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p318-harris/",
abstract = "This paper defines and presents a method of
inheritance for structures that are defined by rewrite
rules. This method is natural in the sense that it can
be easily and cleanly implemented in rewrite rules
themselves. This framework of inheritance is not that
of classical Object-Oriented Programming. It is shown
that this inheritance has particular application to
structures implemented in rewrite rules and, more
generally, to symbolic computation. The treatment is
practical, and examples are presented in {\em
Mathematica\/} for concreteness.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Phys. and Astron., Canterbury Univ.,
Christchurch, New Zealand",
classification = "C4210L (Formal languages and computational
linguistics); C6110F (Formal methods); C6120 (File
organisation)",
keywords = "Abstract data type; Algebraic specification;
algorithms; Inheritance; Natural method; Rewrite rule
structures; Rewriting; Structure; Symbolic computation;
Symbolic specification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of
Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES,
Grammars and Other Rewriting Systems. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Mathematica. {\bf D.1.5} Software, PROGRAMMING
TECHNIQUES, Object-oriented Programming.",
thesaurus = "Algebraic specification; Inheritance; Rewriting
systems; Symbol manipulation",
}
@InProceedings{Hasegawa:1994:PMM,
author = "R. Hasegawa and M. Koshimura",
title = "An {AND} Parallelization Method for {MGTP} and Its
Evaluation",
crossref = "Hong:1994:FIS",
pages = "194--203",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hill:1994:VM,
author = "J. M. D. Hill and K. M. Clarke and R. Bornat",
title = "The Vectorisation Monad",
crossref = "Hong:1994:FIS",
pages = "204--213",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jacobs:1994:ANA,
author = "David P. Jacobs",
title = "The {Albert} nonassociative algebra system: a progress
report",
crossref = "ACM:1994:IPI",
pages = "41--44",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p41-jacobs/",
abstract = "After four years of experience with the nonassociative
algebra program Albert, we highlight its successes and
drawbacks. Among its successes are the discovery of
several new results in nonassociative algebra. Each of
these results has been independently verified-either
with a traditional mathematical proof or with an
independent computation.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Clemson Univ., SC, USA",
classification = "C7310 (Mathematics computing)",
keywords = "Albert; algorithms; Computation; Mathematical proof;
Nonassociative algebra system; theory",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf I.1.2}
Computing Methodologies, SYMBOLIC AND ALGEBRAIC
MANIPULATION, Algorithms. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials.",
thesaurus = "Algebra; Mathematics computing; Symbol manipulation;
Theorem proving",
}
@InProceedings{Jenks:1994:HMA,
author = "Richard D. Jenks and Barry M. Trager",
title = "How to make {AXIOM} into a {Scratchpad}",
crossref = "ACM:1994:IPI",
pages = "32--40",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p32-jenks/",
abstract = "Scratchpad (Griesmer and Jenks, 1971) was a computer
algebra system that had one principal representation
for mathematical formulae based on expression trees.
Its user interface design was based on a
pattern-matching paradigm with infinite rewrite rule
semantics, providing what we believe to be the most
natural paradigm for interactive symbolic problem
solving. Like M and M, however, user programs were
interpreted, often resulting in poor performance
relative to similar facilities coded in standard
programming languages such as FORTRAN and C. Scratchpad
development stopped in 1976 giving way to a new system
design that evolved into AXIOM. AXIOM has a
strongly-typed programming language for building a
library of parameterized types and algorithms, and a
type-inferencing interpreter that accesses the library
and can build any of an infinite number of types for
interactive use. We suggest that the addition of an
expression tree type to AXIOM can allow users to
operate with the same freedom and convenience of
untyped systems without giving up the expressive power
and run-time efficiency provided by the type system. We
also present a design that supports a multiplicity of
programming styles, from the Scratchpad
pattern-matching paradigm to functional programming to
more conventional procedural programming.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C6180 (User interfaces); C7310 (Mathematics
computing)",
keywords = "algorithms; AXIOM; C; Computer algebra system; design;
Expression trees; FORTRAN; Functional programming;
Infinite rewrite rule semantics; languages; Library;
Mathematical formulae; Pattern-matching; performance;
Procedural programming; Run-time efficiency;
Scratchpad; Strongly-typed programming language;
Symbolic problem solving; Type-inferencing interpreter;
Untyped systems; User interface design; User programs",
subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Languages and Systems,
Special-purpose algebraic systems. {\bf D.3.3}
Software, PROGRAMMING LANGUAGES, Language Constructs
and Features, Data types and structures. {\bf F.2.2}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Nonnumerical Algorithms and
Problems, Pattern matching. {\bf I.1.1} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Expressions and Their Representation, Simplification of
expressions.",
thesaurus = "Mathematics computing; Pattern matching; Program
interpreters; Programming; Symbol manipulation; User
interfaces",
}
@InProceedings{Kaib:1994:FVG,
author = "M. Kaib",
title = "A fast variant of the {Gaussian} reduction algorithm",
crossref = "Adleman:1994:ANT",
pages = "159",
year = "1994",
bibdate = "Thu Sep 26 05:50:11 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "Summary form only given. We propose a fast variant of
the Gaussian algorithm for the reduction of
two-dimensional lattices for the $\ell_1$-, $\ell_2$-
and $\ell_\infty-norm$. The algorithm uses at most
$O(M(B)(n+log B))$ bit operations for the
$\ell_2$-norm, $O(nM(B)\log{}B)$ bit operations for the
$\ell_\infty$-norm and in $O(n \log{}n M (B) \log{}B)$
bit operations for the $\ell_1$-norm on input vectors
$a$, $b$ in $Z^n$ with norm at most $2^B$ where $M(B)$
is a time bound for $B$-bit integer multiplication.
This generalizes Schonhages fast algorithm for monotone
reduction of binary quadratic forms (Proc. ISSAC 1991,
ACM 1991, p. 128--133) to the centered case and to
various norms. The basic idea is to perform most of the
arithmetic on the leading bits of the integers,
following the techniques of the fast gcd-algorithms due
to Lehmer and Schonhage. We extend the techniques to
the classical `centered' case. The Gaussian algorithm
performs reduction steps $(a, b)$ to
$H(\pm(b-\mu{}a),a)$ where the integer $\mu$ is chosen
to minimize $//b-\mu{}a//$. Our new consideration is,
that the core of the Gaussian algorithm operates stable
until the approximation error exceeds $^1/_12 //a//$,
what is valid for arbitrary norms. We use the
characterization of the transformation matrices which
Kaib and Schnorr gave in their sharp worst case
analysis for the number of reduction steps for
arbitrary norms.",
acknowledgement = ack-nhfb,
affiliation = "Fachbereich Math., Frankfurt Univ., Germany",
classification = "C1160 (Combinatorial mathematics)",
keywords = "Approximation error; Arbitrary norms; B-bit integer
multiplication; Binary quadratic forms; Fast
gcd-algorithms; Fast variant; Gaussian algorithm;
Gaussian reduction algorithm; Input vectors; Integers;
Monotone reduction; Transformation matrices;
Two-dimensional lattices",
thesaurus = "Arithmetic; Data reduction; Matrix algebra; Number
theory",
}
@InProceedings{Kakas:1994:PAL,
author = "A. C. Kakas and G. A. Papadopoulos",
title = "Parallel Abduction in Logic Programming",
crossref = "Hong:1994:FIS",
pages = "214--224",
year = "1994",
bibdate = "Thu Mar 12 11:28:58 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaltofen:1994:AFS,
author = "Erich Kaltofen",
title = "Asymptotically fast solution of {Toeplitz-like}
singular linear systems",
crossref = "ACM:1994:IPI",
pages = "297--304",
year = "1994",
bibdate = "Thu Mar 12 08:41:19 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p297-kaltofen/",
abstract = "The Toeplitz likeness of a matrix (T. Kailath et al.,
1979) is the generalization of the notion that a matrix
is Toeplitz. Block matrices with Toeplitz blocks, such
as the Sylvester matrix 
