%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "2.23", %%% date = "30 October 2017", %%% time = "06:25:46 MDT", %%% filename = "issac.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "18713 38214 189770 1948584", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, ISSAC, International %%% Symposium on Symbolic and Algebraic %%% Computation", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of papers presented %%% at the annual ISSAC (International Symposia %%% on Symbolic and Algebraic Computation) %%% conferences. These conferences have been %%% held most years since 1966, with the 23th on %%% August 13--15, 1998 at the University of %%% Rostock, Germany. %%% %%% It also includes papers from the PASCO %%% (Parallel Symbolic Computation) %%% conferences, the SYMSAC (Symbolic and %%% Algebraic Computation) conferences, and a %%% few papers on symbolic algebra from other %%% conferences not specifically devoted to %%% that subject. %%% %%% Companion bibliographies sigsam.bib and %%% jsymcomp.bib cover papers in the area of %%% symbolic and algebraic computation %%% published in SIGSAM Bulletin and the %%% Journal of Symbolic Computation. %%% %%% At version 2.23, the year coverage looked %%% like this: %%% %%% 1976 ( 1) 1989 ( 106) 2002 ( 36) %%% 1977 ( 0) 1990 ( 64) 2003 ( 40) %%% 1978 ( 0) 1991 ( 86) 2004 ( 47) %%% 1979 ( 1) 1992 ( 50) 2005 ( 52) %%% 1980 ( 0) 1993 ( 58) 2006 ( 55) %%% 1981 ( 2) 1994 ( 103) 2007 ( 54) %%% 1982 ( 1) 1995 ( 52) 2008 ( 47) %%% 1983 ( 0) 1996 ( 50) 2009 ( 54) %%% 1984 ( 0) 1997 ( 88) 2010 ( 52) %%% 1985 ( 0) 1998 ( 49) 2011 ( 50) %%% 1986 ( 50) 1999 ( 41) 2012 ( 53) %%% 1987 ( 0) 2000 ( 44) 2013 ( 55) %%% 1988 ( 0) 2001 ( 48) %%% %%% Article: 3 %%% Book: 1 %%% InProceedings: 1441 %%% Proceedings: 44 %%% %%% Total entries: 1489 %%% %%% Regrettably, bibliographic data for most of %%% these conferences prior to 1989 are %%% inaccessible electronically. With an %%% estimated 60 papers at each conference, a %%% complete bibliography would have about 1800 %%% entries, so the coverage is only about 25%. %%% %%% This bibliography has been collected from %%% bibliographies in the author's personal %%% files, from the OCLC and IEEE INSPEC %%% (1989--1995) databases, and from the %%% computer science bibliography collection on %%% ftp.ira.uka.de in /pub/bibliography to %%% which many people of have contributed. The %%% snapshot of this collection was taken on %%% 5-May-1994, and it consists of 441 BibTeX %%% files, 2,672,675 lines, 205,289 entries, %%% and 6,375 <at>String{} abbreviations, %%% occupying 94.8MB of disk space. %%% %%% Numerous errors have been corrected, and TeX %%% mathematics mode markup has been added %%% manually to more than 1000 text fragments in %%% the key values. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted %%% first by ascending year, and within each %%% year, alphabetically by author or editor, %%% and then, if necessary, by the 3-letter %%% abbreviation at the end of the BibTeX %%% citation tag, using the bibsort -byyear %%% utility. Year order has been chosen to %%% make it easier to identify the most recent %%% work. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Journal abbreviations:

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

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AW= "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr= "Reading, MA, USA"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-SIAM= "SIAM Press"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WORLD-SCI= "World Scientific Publishing Co."} @String{pub-WORLD-SCI:adr= "Singapore; Philadelphia, PA, USA; River Edge, NJ, USA"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LNCS= "Lecture Notes in Computer Science"}

%%% ==================================================================== %%% Bibliography entries:

@InProceedings{Fateman:1981:CAN, author = "Richard J. Fateman", title = "Computer Algebra and Numerical Integration", crossref = "Wang:1981:SPA", pages = "228--232", year = "1981", bibdate = "Mon Apr 25 07:01:52 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Algebraic manipulation systems such as MACSYMA include algorithms and heuristic procedures for indefinite and definite integration, yet these system facilities are not as generally useful as might be thought. Most isolated definite integration problems are more efficiently tackled with numerical programs. Unfortunately, the answers obtained are sometimes incorrect, in spite of assurances of accuracy; furthermore, large classes of problems can sometimes be solved more rapidly by preliminary algebraic transformations. In this paper we indicate various directions for improving the usefulness of integration programs given closed form integrands, via algebraic manipulation techniques. These include expansions in partial fractions or Taylor series, detection and removal of singularities and symmetries, and various approximation techniques for troublesome problems.", acknowledgement = ack-nhfb, } @Book{Buchberger:1982:CAS, author = "Bruno Buchberger and George Edward Collins and Rudiger Loos and R. Albrecht", title = "Computer algebra: symbolic and algebraic computation", volume = "4", publisher = pub-SV, address = pub-SV:adr, pages = "vi + 283", year = "1982", ISBN = "0-387-81684-4", ISBN-13 = "978-0-387-81684-5", LCCN = "QA155.7.E4 C65 1982", bibdate = "Thu Dec 28 13:48:31 1995", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", series = "Computing. Supplementum", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; theory", subject = "S1 Algebra --- Data processing; S2 Machine theory", } @InProceedings{Abbott:1986:BAN, author = "J. A. Abbott and R. J. Bradford and J. H. Davenport", title = "The {Bath} algebraic number package", crossref = "Char:1986:PSS", pages = "250--253", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p250-abbott/", acknowledgement = ack-nhfb, keywords = "design; measurement; performance", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", } @InProceedings{Abdali:1986:OOA, author = "S. K. Abdali and Guy W. Cherry and Neil Soiffer", title = "An object-oriented approach to algebra system design", crossref = "Char:1986:PSS", pages = "24--30", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p24-abdali/", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf D.3.3} Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Abstract data types. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Run-time environments. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Specialized application languages. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Very high-level languages.", } @InProceedings{Akritis:1986:TNU, author = "Alkiviadis G. Akritis", title = "There is no ``{Uspensky}'s method''", crossref = "Char:1986:PSS", pages = "88--90", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p88-akritis/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for. {\bf K.2} Computing Milieux, HISTORY OF COMPUTING, Systems. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Arnborg:1986:ADR, author = "S. Arnborg and H. Feng", title = "Algebraic decomposition of regular curves", crossref = "Char:1986:PSS", pages = "53--55", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p53-arnborg/", acknowledgement = ack-nhfb, keywords = "theory", subject = "{\bf I.1.m} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Miscellaneous.", } @InProceedings{Bachmair:1986:CPC, author = "Leo Bachmair and Nachum Dershowitz", title = "Critical-pair criteria for the {Knuth--Bendix} completion procedure", crossref = "Char:1986:PSS", pages = "215--217", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p215-bachmair/", acknowledgement = ack-nhfb, keywords = "languages; theory; verification", subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems, Parallel rewriting systems. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf F.2.3} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Tradeoffs between Complexity Measures. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Complexity of proof procedures.", } @InProceedings{Bajaj:1986:LAS, author = "Chanderjit Bajaj", title = "Limitations to algorithm solvability: {Galois} methods and models of computation", crossref = "Char:1986:PSS", pages = "71--76", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p71-bajaj/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis.", } @InProceedings{Bayer:1986:DMS, author = "D. Bayer and M. Stillman", title = "The design of {Macaulay}: a system for computing in algebraic geometry and commutative algebra", crossref = "Char:1986:PSS", pages = "157--162", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p157-bayer/", acknowledgement = ack-nhfb, keywords = "design; performance; theory", subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", } @InProceedings{Beck:1986:SAL, author = "Robert E. Beck and Bernard Kolman", title = "Symbolic algorithms for {Lie} algebra computation", crossref = "Char:1986:PSS", pages = "85--87", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p85-beck/", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.2.2} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA. {\bf K.2} Computing Milieux, HISTORY OF COMPUTING, Systems.", } @InProceedings{Bradford:1986:ERD, author = "R. J. Bradford and A. C. Hearn and J. A. Padget and E. Schr{\"u}fer", title = "Enlarging the {REDUCE} domain of computation", crossref = "Char:1986:PSS", pages = "100--106", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p100-bradford/", acknowledgement = ack-nhfb, keywords = "algorithms; languages; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", } @InProceedings{Bronstein:1986:GFA, author = "Manuel Bronstein", title = "Gsolve: a faster algorithm for solving systems of algebraic equations", crossref = "Char:1986:PSS", pages = "247--249", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p247-bronstein/", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @InProceedings{Butler:1986:DCC, author = "Greg Butler", title = "Divide-and-conquer in computational group theory", crossref = "Char:1986:PSS", pages = "59--64", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p59-butler/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.2.0} Mathematics of Computing, DISCRETE MATHEMATICS, General. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", } @InProceedings{Chaffy:1986:HCM, author = "C. Chaffy", title = "How to compute multivariate {Pad{\'e}} approximants", crossref = "Char:1986:PSS", pages = "56--58", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p56-chaffy/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @InProceedings{Char:1986:CAU, author = "B. W. Char and K. O. Geddes and G. H. Gonnet and B. J. Marshman and P. J. Ponzo", title = "Computer algebra in the undergraduate mathematics classroom", crossref = "Char:1986:PSS", pages = "135--140", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p135-char/", acknowledgement = ack-nhfb, keywords = "algorithms; design; documentation; experimentation; human factors; performance", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION, Computer Uses in Education, Computer-assisted instruction (CAI).", } @InProceedings{Cooperman:1986:SMC, author = "Gene Cooperman", title = "A semantic matcher for computer algebra", crossref = "Char:1986:PSS", pages = "132--134", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p132-cooperman/", acknowledgement = ack-nhfb, keywords = "experimentation; human factors; languages", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Evaluation strategies. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Pattern matching. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.", } @InProceedings{Czapor:1986:IBA, author = "S. R. Czapor and K. O. Geddes", title = "On implementing {Buchberger}'s algorithm for {Gr{\"o}bner} bases", crossref = "Char:1986:PSS", pages = "233--238", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p233-czapor/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Davenport:1986:PSM, author = "J. H. Davenport and C. E. Roth", title = "{PowerMath}: a system for the {Macintosh}", crossref = "Char:1986:PSS", pages = "13--15", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p13-davenport/", acknowledgement = ack-nhfb, keywords = "design; theory", subject = "{\bf K.8} Computing Milieux, PERSONAL COMPUTING, Apple. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems.", } @InProceedings{Dora:1986:FSL, author = "J. Della Dora and E. Tournier", title = "Formal solutions of linear difference equations: method of {Pincherle--Ramis}", crossref = "Char:1986:PSS", pages = "192--196", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p192-della_dora/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms.", } @InProceedings{Fitch:1986:AIA, author = "J. Fitch and A. Norman and M. A. Moore", title = "Alkahest {III}: automatic analysis of periodic weakly nonlinear {ODEs}", crossref = "Char:1986:PSS", pages = "34--38", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p34-fitch/", acknowledgement = ack-nhfb, keywords = "algorithms; design; human factors; theory", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and Techniques, User interfaces.", } @InProceedings{Freeman:1986:SMP, author = "T. Freeman and G. Imirzian and E. Kaltofen", title = "A system for manipulating polynomials given by straight-line programs", crossref = "Char:1986:PSS", pages = "169--175", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p169-freeman/", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for.", } @InProceedings{Furukawa:1986:GBM, author = "A. Furukawa and T. Sasaki and H. Kobayashi", title = "The {Gr{\"o}bner} basis of a module over {KUX1,\ldots{},Xne} and polynomial solutions of a system of linear equations", crossref = "Char:1986:PSS", pages = "222--224", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p222-furukawa/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @InProceedings{Gates:1986:NCG, author = "Barbara L. Gates", title = "A numerical code generation facility for {REDUCE}", crossref = "Char:1986:PSS", pages = "94--99", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p94-gates/", acknowledgement = ack-nhfb, keywords = "design; languages; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation.", } @InProceedings{Gebauer:1986:BAS, author = "R{\"u}diger Gebauer and H. Michael M{\"o}ller", title = "{Buchberger}'s algorithm and staggered linear bases", crossref = "Char:1986:PSS", pages = "218--221", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p218-gebauer/", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", } @InProceedings{Geddes:1986:NIS, author = "K. O. Geddes", title = "Numerical integration in a symbolic context", crossref = "Char:1986:PSS", pages = "185--191", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p185-geddes/", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", } @InProceedings{Golden:1986:OAM, author = "J. P. Golden", title = "An operator algebra for {Macsyma}", crossref = "Char:1986:PSS", pages = "244--246", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p244-golden/", acknowledgement = ack-nhfb, keywords = "design; theory; verification", subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, MACSYMA. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.", } @InProceedings{Gonnet:1986:IOS, author = "G. H. Gonnet", title = "An implementation of operators for symbolic algebra systems", crossref = "Char:1986:PSS", pages = "239--243", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p239-gonnet/", acknowledgement = ack-nhfb, keywords = "design; languages; theory", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", } @InProceedings{Gonnet:1986:NRR, author = "Gaston H. Gonnet", title = "New results for random determination of equivalence of expressions", crossref = "Char:1986:PSS", pages = "127--131", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p127-gonnet/", acknowledgement = ack-nhfb, keywords = "theory", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous.", } @InProceedings{Hadzikadic:1986:AKB, author = "M. Hadzikadic and F. Lichtenberger and D. Y. Y. Yun", title = "An application of knowledge-base technology in education: a geometry theorem prover", crossref = "Char:1986:PSS", pages = "141--147", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p141-hadzikadic/", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; human factors; languages; performance; verification", subject = "{\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION, Computer Uses in Education, Computer-assisted instruction (CAI). {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving. {\bf I.2.3} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and Theorem Proving.", } @InProceedings{Hayden:1986:SBC, author = "Michael B. Hayden and Edmund A. Lamagna", title = "Summation of binomial coefficients using hypergeometric functions", crossref = "Char:1986:PSS", pages = "77--81", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p77-hayden/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf I.2.2} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming, Automatic analysis of algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Iterative methods.", } @InProceedings{Hilali:1986:ACF, author = "A. Hilali and A. Wazner", title = "Algorithm for computing formal invariants of linear differential systems", crossref = "Char:1986:PSS", pages = "197--201", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p197-hilali/", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues and eigenvectors (direct and iterative methods). {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", } @InProceedings{Jurkovic:1986:EES, author = "N. Jurkovic", title = "Edusym --- educational symbolic manipulator on a microcomputer", crossref = "Char:1986:PSS", pages = "154--156", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p154-jurkovic/", acknowledgement = ack-nhfb, keywords = "human factors; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MuMATH. {\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION, Computer Uses in Education, Computer-assisted instruction (CAI).", } @InProceedings{Kaltofen:1986:FPA, author = "E. Kaltofen and M. Krishnamoorthy and B. D. Saunders", title = "Fast parallel algorithms for similarity of matrices", crossref = "Char:1986:PSS", pages = "65--70", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p65-kaltofen/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @InProceedings{Kapur:1986:GTP, author = "Deepak Kapur", title = "Geometry theorem proving using {Hilbert}'s {Nullstellensatz}", crossref = "Char:1986:PSS", pages = "202--208", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p202-kapur/", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Logic and constraint programming. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf I.2.3} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and Theorem Proving. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", } @InProceedings{Knowles:1986:ILF, author = "P. H. Knowles", title = "Integration of {Liouvillian} functions with special functions", crossref = "Char:1986:PSS", pages = "179--184", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p179-knowles/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous.", } @InProceedings{Kobayashi:1986:GBI, author = "H. Kobayashi and A. Furukawa and T. Sasaki", title = "Gr{\"o}bner bases of ideals of convergent power series", crossref = "Char:1986:PSS", pages = "225--227", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p225-kobayashi/", acknowledgement = ack-nhfb, keywords = "theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.m} Mathematics of Computing, MISCELLANEOUS.", } @InProceedings{Kryukov:1986:CRA, author = "A. P. Kryukov and Y. Rodionov and G. L. Litvinov", title = "Construction of rational approximations by means of {REDUCE}", crossref = "Char:1986:PSS", pages = "31--33", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p31-kryukov/", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", } @InProceedings{Kryukov:1986:DRE, author = "A. P. Kryukov", title = "Dialogue in {REDUCE}: experience and development", crossref = "Char:1986:PSS", pages = "107--109", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p107-kryukov/", acknowledgement = ack-nhfb, keywords = "design; human factors; performance; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and Techniques, User interfaces.", } @InProceedings{Kryukov:1986:URC, author = "A. P. Kryukov and A. Y. Rodionov", title = "Usage of {REDUCE} for computations of group-theoretical weight of {Feynman} diagrams in {non-Abelian} gauge theories", crossref = "Char:1986:PSS", pages = "91--93", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p91-kryukov/", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous.", } @InProceedings{Kutzler:1986:AGT, author = "B. Kutzler and S. Stifter", title = "Automated geometry theorem proving using {Buchberger}'s algorithm", crossref = "Char:1986:PSS", pages = "209--214", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p209-kutzler/", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Logic and constraint programming. {\bf I.2.3} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and Theorem Proving. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", } @InProceedings{Leff:1986:CSG, author = "L. Leff and D. Y. Y. Yun", title = "Constructive solid geometry: a symbolic computation approach", crossref = "Char:1986:PSS", pages = "121--126", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p121-leff/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED ENGINEERING. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf I.1.m} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Miscellaneous.", } @InProceedings{Leong:1986:IDU, author = "B. L. Leong", title = "{Iris}: design of an user interface program for symbolic algebra", crossref = "Char:1986:PSS", pages = "1--6", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p1-leong/", acknowledgement = ack-nhfb, keywords = "design; human factors; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and Techniques, User interfaces. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf H.1.2} Information Systems, MODELS AND PRINCIPLES, User/Machine Systems, Human factors.", } @InProceedings{Lucks:1986:FIP, author = "Michael Lucks", title = "A fast implementation of polynomial factorization", crossref = "Char:1986:PSS", pages = "228--232", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p228-lucks/", acknowledgement = ack-nhfb, keywords = "algorithms; design; experimentation; performance; theory", subject = "{\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations.", } @InProceedings{Mawata:1986:SDR, author = "C. P. Mawata", title = "A sparse distributed representation using prime numbers", crossref = "Char:1986:PSS", pages = "110--114", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p110-mawata/", acknowledgement = ack-nhfb, keywords = "experimentation; performance; theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms.", } @InProceedings{Purtilo:1986:ASI, author = "J. Purtilo", title = "Applications of a software interconnection system in mathematical problem solving environments", crossref = "Char:1986:PSS", pages = "16--23", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p16-purtilo/", acknowledgement = ack-nhfb, keywords = "design; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.m} Mathematics of Computing, MISCELLANEOUS. {\bf D.2.m} Software, SOFTWARE ENGINEERING, Miscellaneous.", } @InProceedings{Renbao:1986:CAS, author = "Z. Renbao and X. Ling and R. Zhaoyang", title = "The computer algebra system {CAS1} for the {IBM-PC}", crossref = "Char:1986:PSS", pages = "176--178", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p176-renbao/", acknowledgement = ack-nhfb, keywords = "design; theory", subject = "{\bf K.8} Computing Milieux, PERSONAL COMPUTING, IBM PC. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", } @InProceedings{Sasaki:1986:SAE, author = "Tateaki Sasaki", title = "Simplification of algebraic expression by multiterm rewriting rules", crossref = "Char:1986:PSS", pages = "115--120", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p115-sasaki/", acknowledgement = ack-nhfb, keywords = "algorithms; design; languages", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems, Parallel rewriting systems.", } @InProceedings{Seymour:1986:CCM, author = "Harlan R. Seymour", title = "Conform: a conformal mapping system", crossref = "Char:1986:PSS", pages = "163--168", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p163-seymour/", acknowledgement = ack-nhfb, keywords = "design; languages; performance; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, LISP. {\bf D.3.3} Software, PROGRAMMING LANGUAGES, Language Constructs and Features.", } @InProceedings{Shavlik:1986:CUG, author = "Jude W. Shavlik and Gerald F. DeJong", title = "Computer understanding and generalization of symbolic mathematical calculations: a case study in physics problem solving", crossref = "Char:1986:PSS", pages = "148--153", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p148-shavlik/", acknowledgement = ack-nhfb, keywords = "design; human factors; languages; performance; theory; verification", subject = "{\bf I.2.6} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Learning. {\bf K.3.1} Computing Milieux, COMPUTERS AND EDUCATION, Computer Uses in Education, Computer-assisted instruction (CAI). {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation. {\bf I.2.1} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Applications and Expert Systems. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Substitution mechanisms**. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Evaluation strategies. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", } @InProceedings{Smith:1986:MUI, author = "C. J. Smith and N. Soiffer", title = "{MathScribe}: a user interface for computer algebra systems", crossref = "Char:1986:PSS", pages = "7--12", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p7-smith/", acknowledgement = ack-nhfb, keywords = "design; human factors; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and Techniques, User interfaces.", } @InProceedings{Yun:1986:FCF, author = "D. Y. Y. Yun and C. N. Zhang", title = "A fast carry-free algorithm and hardware design for extended integer {GCD} computation", crossref = "Char:1986:PSS", pages = "82--84", year = "1986", bibdate = "Thu Mar 12 07:38:29 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/32439/p82-yun/", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis. {\bf B.7.1} Hardware, INTEGRATED CIRCUITS, Types and Design Styles, Algorithms implemented in hardware.", } @InProceedings{A:1989:SSG, author = "R. A. and J. r. Ravenscroft and E. A. Lamagna", title = "Symbolic summation with generating functions", crossref = "Gonnet:1989:PAI", pages = "228--233", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p228-ravenscroft/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Generating functions. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @InProceedings{Abbot:1989:RAN, author = "J. Abbot", title = "Recovery of algebraic numbers from their $p$-adic approximations", crossref = "Gonnet:1989:PAI", pages = "112--120", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author describes three ways to generalize Lenstra's algebraic integer recovery method. One direction adapts the algorithm so that rational numbers are automatically produced given only upper bounds on the sizes of the numerators and denominators. Another direction produces a variant which recovers algebraic numbers as elements of multiple generator algebraic number fields. The third direction explains how the method can work if a reducible minimal polynomial had been given for an algebraic generator. Any two or all three of the generalisations may be employed simultaneously.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "Algebraic generator; Algebraic integer recovery method; Algebraic numbers; Computer algebra; Denominators; Factorisation; Lenstra; Multiple generator algebraic number fields; Numerators; P-adic approximations; Rational numbers; Reducible minimal polynomial; Upper bounds", thesaurus = "Computation theory; Number theory; Polynomials; Symbol manipulation", } @InProceedings{Abbott:1989:RAN, author = "John Abbott", title = "Recovery of algebraic numbers from their $p$-adic approximations", crossref = "Gonnet:1989:PAI", pages = "112--120", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p112-abbott/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Abdali:1989:EQR, author = "S. K. Abdali and D. S. Wiset", title = "Experiments with quadtree representation of matrices", crossref = "Gianni:1989:SAC", pages = "96--108", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The quadtrees matrix representation has been recently proposed as an alternative to the conventional linear storage of matrices. If all elements of a matrix are zero, then the matrix is represented by an empty tree; otherwise it is represented by a tree consisting of four subtrees, each representing, recursively, a quadrant of the matrix. Using four-way block decomposition, algorithms on quadtrees accelerate on blocks entirely of zeros, and thereby offer improved performance on sparse matrices. The paper reports the results of experiments done with a quadtree matrix package implemented in REDUCE to compare the performance of quadtree representation with REDUCE's built-in sequential representation of matrices. Tests on addition, multiplication, and inversion of dense, triangular, tridiagonal, and diagonal matrices (both symbolic and numeric) of sizes up to 100*100 show that the quadtree algorithms perform well in a broad range of circumstances, sometimes running orders of magnitude faster than their sequential counterparts.", acknowledgement = ack-nhfb, affiliation = "Tektronix Labs., Beaverton, OR, USA", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4140 (Linear algebra); C6120 (File organisation); C7310 (Mathematics)", keywords = "Addition; Dense matrices; Diagonal matrices; Empty tree; Four-way block decomposition; Inversion; Multiplication; Performance comparison; Quadrant; Quadtree algorithms; Quadtree matrix package; Quadtrees matrix representation; REDUCE; Sparse matrices; Subtrees; Triangular matrices; Tridiagonal matrices; Zero elements", thesaurus = "Data structures; Mathematics computing; Matrix algebra; Trees [mathematics]", } @InProceedings{Abdulrab:1989:EW, author = "H. Abdulrab", title = "Equations in words", crossref = "Gianni:1989:SAC", pages = "508--520", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The study of equations in words was introduced by Lentin (1972). There is always a solution for any equation with no constant. Makanin (1977) showed that solving equations with constants is decidable. Pecuchet (1981) unified the two theories of equations with or without constants and gave a new description of Makanin's algorithm. This paper describes some new results in the field of solving equations in words.", acknowledgement = ack-nhfb, affiliation = "LITP, Fac. des Sci., Mont Saint Aignan, France", classification = "C4210 (Formal logic)", keywords = "Decidable; Equations in words", thesaurus = "Decidability", } @InProceedings{Abhyankar:1989:CAC, author = "S. S. Abhyankar and C. L. Bajaj", title = "Computations with algebraic curves", crossref = "Gianni:1989:SAC", pages = "274--284", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present a variety of computational techniques dealing with algebraic curves both in the plane and in space. The main results are polynomial time algorithms: (1) to compute the genus of plane algebraic curves; (2) to compute the rational parametric equations for implicitly defined rational plane algebraic curves of arbitrary degree; (3) to compute birational mappings between points on irreducible space curves and points on projected plane curves and thereby to compute the genus and rational parametric equations for implicitly defined rational space curves of arbitrary degree; and (4) to check for the faithfulness (one to one) of parameterizations.", acknowledgement = ack-nhfb, affiliation = "Purdue Univ., West Lafayette, IN, USA", classification = "C4130 (Interpolation and function approximation); C4190 (Other numerical methods)", keywords = "Algebraic curves; Birational mappings; Computational techniques; Irreducible space curves; Polynomial time algorithms; Rational parametric equations", thesaurus = "Computational geometry; Polynomials", } @InProceedings{Alonso:1989:CAS, author = "M. E. Alonso and T. Mora and M. Raimondo", title = "Computing with algebraic series", crossref = "Gonnet:1989:PAI", pages = "101--111", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p101-alonso/", abstract = "The authors develop a computational model for algebraic formal power series, based on a symbolic codification of the series by means of the implicit function theorem: i.e. they consider algebraic series as the unique solutions of suitable functional equations. They show that most of the usual local commutative algebra can be effectively performed on algebraic series, since they can reduce to the polynomial case, where the tangent cone algorithm can be used to effectively perform local algebra. The main result to the paper is an effective version of Weierstrass theorems, which allows effective elimination theory for algebraic series and an effective noether normalization lemma.", acknowledgement = ack-nhfb, affiliation = "Univ. Complutense, Madrid, Spain", classification = "C1110 (Algebra); C1120 (Analysis); C4150 (Nonlinear and functional equations); C4240 (Programming and algorithm theory)", keywords = "Algebraic formal power series; Algebraic series; algorithms; Computational model; Elimination theory; Functional equations; Implicit function theorem; Local commutative algebra; Noether normalization lemma; Polynomial; Symbolic codification; Tangent cone algorithm; theory; Weierstrass theorems", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic.", thesaurus = "Computability; Functional equations; Polynomials; Series [mathematics]; Symbol manipulation", } @InProceedings{Arnborg:1989:EPO, author = "S. Arnborg", title = "Experiments with a projection operator for algebraic decomposition", crossref = "Gianni:1989:SAC", pages = "177--182", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Reports an experiment with the projection phase of an algebraic decomposition problem. The decomposition asked for is a collection of rational sample points, at least one in each full-dimensional region of a decomposition, sign-invariant with respect to a set of polynomials and with a cylindrical structure. Such a decomposition is less general than a cylindrical algebraic decomposition, but still useful for purposes such as solving collision and motion planning problems in theoretical robotics. Specifically, there is no information about the structure of less than full-dimensional regions and intersections between projections of regions. This makes quantifier elimination with alternating quantifiers difficult or impossible.", acknowledgement = ack-nhfb, affiliation = "Dept. of Numer. Anal. and Comput. Sci., R. Inst. of Technol., Stockholm, Sweden", classification = "C1110 (Algebra)", keywords = "Algebraic decomposition; Cylindrical structure; Full-dimensional region; Polynomials; Projection operator; Projection phase; Rational sample points; Sign-invariant", thesaurus = "Algebra; Polynomials", } @InProceedings{Ausiello:1989:DMP, author = "G. Ausiello and A. Marchetti Spaccamela and U. Nanni", title = "Dynamic maintenance of paths and path expressions on graphs", crossref = "Gianni:1989:SAC", pages = "1--12", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "In several applications it is necessary to deal with data structures that may dynamically change during a sequence of operations. In these cases the classical worst case analysis of the cost of a single operation may not adequately describe the behaviour of the structure but it is rather more meaningful to analyze the cost of the whole sequence of operations. The paper first discusses some results on maintaining paths in dynamic graphs. Besides, it considers paths problems on dynamic labeled graphs and shows how to maintain path expressions in the acyclic case when insertions of new arcs are allowed.", acknowledgement = ack-nhfb, affiliation = "Dipartimento di Inf. e Sistemistica, Rome Univ., Italy", classification = "C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory); C6120 (File organisation)", keywords = "Acyclic case; Data structures; Dynamic graphs; Dynamic labeled graphs; Dynamic maintenance; Insertions; New arcs; Path expressions; Paths problems", thesaurus = "Computational complexity; Data structures; Graph theory", } @InProceedings{Avenhaus:1989:URT, author = "J. Avenhaus and D. Wi{\ss}mann", title = "Using rewriting techniques to solve the generalized word problem in polycyclic groups", crossref = "Gonnet:1989:PAI", pages = "322--337", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p322-avenhaus/", abstract = "The authors apply rewriting techniques to the generalized word problem GWP in polycyclic groups. They assume the group $G$ to be given by a canonical polycyclic string-rewriting system $R$ and consider GWP in $G$ which is defined by $GWP(w,U)$ iff $w$ in $<U>$ for $w$ in $G$, finite $U$ contained in $G$, where $<U>$ is the subgroup of $G$ generated by $U$. They describe $<U>$ also by a rewrite system $S$ and define a rewrite relation $\mbox{implies}_{S,R}$ in such a way that $w$ implied by * $\mbox{implies}_{S,R} \lambda$ iff $w$ in $<U>$ ($\lambda$ the empty word). For this rewrite relation the authors develop different critical pair criteria for $\mbox{implies}_{S,R}$ to be $\lambda$-confluent, i.e. confluent on the left-congruence class $(\lambda )$ of implied by * $\mbox{implies}_{S,R}$. Using any of these $\lambda$-confluence criteria they construct a completion procedure which stops for every input $S$ and computes a $\lambda$-confluent rewrite system equivalent to $S$. This leads to a decision procedure for GWP in G. Thus the authors give an explicit uniform algorithm for deciding GWP in polycyclic groups and a new proof based almost only on rewriting techniques for the decidability of this problem. Further, they define a rewrite relation $\mbox{implies}_{LM,U}$ which is stronger than $\mbox{implies}_{S,R}$. They show that if $G$ is given by a nilpotent string-rewriting system, then by a completion procedure the input $U$ can be transformed into $V$ such that $\mbox{implies}_{LM,V}$ is even confluent, not just $\lambda$-confluent.", acknowledgement = ack-nhfb, affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany", classification = "C1110 (Algebra); C4210 (Formal logic)", keywords = "$\Lambda$-confluent; algorithms; Canonical polycyclic string-rewriting system; Completion procedure; Critical pair criteria; Decidability; design; Explicit uniform algorithm; Generalized word problem; Group theory; Nilpotent string-rewriting system; Polycyclic groups; Rewrite relation; Rewriting techniques; theory", subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Decidability; Group theory; Rewriting systems; Symbol manipulation", } @InProceedings{Bajaj:1989:FRP, author = "C. Bajaj and J. Canny and T. Garrity and J. Warren", title = "Factoring rational polynomials over the complexes", crossref = "Gonnet:1989:PAI", pages = "81--90", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p81-bajaj/", abstract = "The authors give NC algorithms for determining the number and degrees of the absolute factors (factors irreducible over the complex numbers $C$) of a multivariate polynomial with rational coefficients. NC is the class of functions computable by logspace-uniform boolean circuits of polynomial size and polylogarithmic dept. The measures of size of the input polynomial are its degree $d$, coefficient length $c$, number of variables $n$, and for sparse polynomials, the number of nonzero coefficients $s$. For the general case, the authors give a random (Monte-Carlo) NC algorithm in these input measures. If $n$ is fixed, or if the polynomial is dense, they give a deterministic NC algorithm. The algorithm also works in random NC for polynomial represented by straight-line programs, provided the polynomial can be evaluated at integer points in NC. The authors discuss a method for obtaining an approximation to the coefficients of each factor whose running time is polynomial in the size of the original (dense) polynomial. These methods rely on the fact that the connected components of a complex hypersurface $P(z_1,\ldots{},z_n)=0$ minus its singular points correspond to the absolute factors of $P$.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Purdue Univ., Lafayette, IN, USA", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory)", keywords = "Absolute factors; algorithms; Complex numbers; Factorisation; Functions; Logspace-uniform boolean circuits; measurement; Monte-Carlo; Multivariate polynomial; NC algorithms; Rational coefficients; Rational polynomials; Set theory; theory; verification", subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving.", thesaurus = "Approximation theory; Computability; Computational complexity; Monte Carlo methods; Polynomials; Set theory; Symbol manipulation", xxauthor = "C. Bajaj and J. Canny and R. Garrity and J. Warren", } @InProceedings{Barkatou:1989:RLS, author = "M. A. Barkatou", title = "On the reduction of linear systems of difference equations", crossref = "Gonnet:1989:PAI", pages = "1--6", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p1-barkatou/", abstract = "The author deals with linear systems of difference equations whose coefficients admit generalized factorial series representations at $z=\infty$. He gives a criterion by which a given system is determined to have a regular singularity. He gives an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations on an irreducible form.", acknowledgement = ack-nhfb, affiliation = "Lab. TIM3-IMAG, Grenoble, France", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; Computer algebra system; Convergence; Generalized factorial series; Irreducible form; Linear difference equations; Regular singularity; theory", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", thesaurus = "Convergence; Difference equations; Linear differential equations; Mathematics computing; Matrix algebra; Series [mathematics]; Symbol manipulation", } @InProceedings{Barkatou:1989:RNA, author = "M. A. Barkatou", title = "Rational {Newton} algorithm for computing formal solutions of linear differential equations", crossref = "Gianni:1989:SAC", pages = "183--195", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents a new algorithm for solving linear differential equations in the neighbourhood of an irregular singular point. This algorithm is based upon the same principles as the Newton algorithm, however it has a lower cost and is more suitable for computing algebra.", acknowledgement = ack-nhfb, affiliation = "CNRS, INPG, IMAG, Grenoble, France", classification = "C1120 (Analysis); C4170 (Differential equations)", keywords = "Formal solutions; Irregular singular point; Linear differential equations; Neighbourhood; Rational Newton algorithm", thesaurus = "Linear differential equations", } @InProceedings{BoydelaTour:1989:FAS, author = "T. {Boy de la Tour} and R. Caferra", title = "A formal approach to some usually informal techniques used in mathematical reasoning", crossref = "Gianni:1989:SAC", pages = "402--406", year = "1989", bibdate = "Mon Dec 01 16:57:16 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "One of the striking characteristics of mathematical reasoning is the contrast between the formal aspects of mathematical truth and the informal character of the ways to that truth. Among the many important and usually informal mathematical activities the authors are interested in proof analogy (i.e. common pattern between proofs of different theorems) in the context of interactive theorem proving.", acknowledgement = ack-nhfb, affiliation = "LIFIA-INPG, Grenoble, France", classification = "C4210 (Formal logic)", keywords = "Formal approach; Informal character; Interactive theorem proving; Mathematical reasoning; Mathematical truth; Usually informal techniques", thesaurus = "Theorem proving", } @InProceedings{Bradford:1989:ETC, author = "R. J. Bradford and J. H. Davenport", title = "Effective tests for cyclotomic polynomials", crossref = "Gianni:1989:SAC", pages = "244--251", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present two efficient tests that determine if a given polynomial is cyclotomic, or is a product of cyclotomics. The first method uses the fact that all the roots of a cyclotomic polynomial are roots of unity, and the second the fact that the degree of a cyclotomic polynomial is a value of $\phi (n)$, for some $n$. The authors also find the cyclotomic factors of any polynomial.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C4130 (Interpolation and function approximation)", keywords = "Cyclotomic polynomials; Roots", thesaurus = "Polynomials", } @InProceedings{Bradford:1989:SRD, author = "R. Bradford", title = "Some results on the defect", crossref = "Gonnet:1989:PAI", pages = "129--135", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p129-bradford/", abstract = "The defect of an algebraic number field (or, more correctly, of a presentation of the field) is the largest rational integer that divides the denominator of any algebraic integer in the field when written using that presentation. Knowing the defect, or estimating it accurately is extremely valuable in many algorithms, the factorization of polynomials over algebraic number fields being a prime example. The author presents a few results that are a move in the right direction.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "Algebraic integer; Algebraic number field; algorithms; Defect; Factorization; Polynomials; Rational integer; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations.", thesaurus = "Computation theory; Number theory; Polynomials; Symbol manipulation", } @InProceedings{Bronstein:1989:FRR, author = "M. Bronstein", title = "Fast reduction of the {Risch} differential equation", crossref = "Gianni:1989:SAC", pages = "64--72", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents a weaker definition of weak-normality which: can always be obtained in a tower of transcendental elementary extensions, and gives an explicit formula for the denominator of $y$, so the equation $y'+fy=g$ can be reduced to a polynomial equation in one reduction step. As a consequence, a new algorithm is obtained for solving y'+fy=g. The algorithm is very similar to the one described by Rothstein (1976), except that the present one uses weak normality to prevent finite cancellation, rather than having to find integer roots of polynomials over the constant field of $K$ in order to detect it.", acknowledgement = ack-nhfb, affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1120 (Analysis); C4170 (Differential equations)", keywords = "Denominator; Explicit formula; Fast reduction; Polynomial equation; Reduction step; Risch differential equation; Transcendental elementary extensions; Weak-normality", thesaurus = "Differential equations", } @InProceedings{Bronstein:1989:SRE, author = "M. Bronstein", title = "Simplification of real elementary functions", crossref = "Gonnet:1989:PAI", pages = "207--211", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p207-bronstein/", abstract = "The author describes an algorithm, based on Risch's real structure theorem, that determines explicitly all the algebraic relations among a given set of real elementary functions. He provides examples from its implementation in the scratchpad computer algebra system that illustrate the advantages over the use of complex logarithms and exponentials.", acknowledgement = ack-nhfb, affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "algorithms; Computer algebra system; Real elementary functions; Real structure theorem; Scratchpad; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", thesaurus = "Functions; Mathematics computing; Symbol manipulation", } @InProceedings{Brown:1989:SPP, author = "C. Brown and G. Cooperman and L. Finkelstein", title = "Solving permutation problems using rewriting systems", crossref = "Gianni:1989:SAC", pages = "364--377", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "A new approach is described for finding short expressions for arbitrary elements of a permutation group in terms of the original generators which uses rewriting methods. This forms an important component in a long term plan to find short solutions for `large' permutation problems (such as Rubik's cube), which are difficult to solve by existing search techniques. In order for this methodology to be successful, it is important to start with a short presentation for a finite permutation group. A new method is described for giving a presentation for an arbitrary permutation group acting on $n$ letters. This can be used to show that any such permutation group has a presentation with at most $n-1$ generators and $(n-1)^2$ relations. As an application of this method, an $O(n^4)$ algorithm is described for determining if a set of generators for a permutation group of $n$ letters is a strong generating set (in the sense of Sims). The `back end' includes a novel implementation of the Knuth--Bendix technique on symmetrization classes for groups.", acknowledgement = ack-nhfb, affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA, USA", classification = "C4210 (Formal logic)", keywords = "Knuth--Bendix technique; Permutation problems; Rewriting systems", thesaurus = "Rewriting systems", } @InProceedings{Butler:1989:CVU, author = "G. Butler and J. Cannon", title = "{Cayley}, version 4: the user language", crossref = "Gianni:1989:SAC", pages = "456--466", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Cayley, version 4, is a proposed knowledge-based system for modern algebra. The proposal integrates the existing powerful algorithm base of Cayley with modest deductive facilities and large sophisticated databases of groups and related algebraic structures. The outcome will be a revolutionary computer algebra system. The user language of Cayley, version 4, is the first stage of the project to develop a computer algebra system which integrates algorithmic, deductive, and factual knowledge. The language plays an important role in shaping the users' communication of their knowledge to the system, and in presenting the results to the user. The very survival of a system depends upon its acceptance by the users, so the language must be natural, extensible, and powerful. The major changes in the language (over version 3) are the definitions of algebraic structures, set constructors and associated control structures, the definitions of maps and homomorphisms, the provision of packages for procedural abstraction and encapsulation, database facilities, and other input/output. The motivation for these changes has been the need to provide facilities for a knowledge-based system; to allow sets to be defined by properties; and to remove semantic ambiguities of structure definitions.", acknowledgement = ack-nhfb, affiliation = "Sydney Univ., NSW, Australia", classification = "C6170 (Expert systems); C7310 (Mathematics)", keywords = "Algebra; Algebraic structures; Associated control structures; Cayley; Computer algebra system; Deductive facilities; Encapsulation; Factual knowledge; Homomorphisms; Knowledge-based system; Procedural abstraction; Set constructors; Sophisticated databases; User language; Version 4", thesaurus = "Knowledge based systems; Symbol manipulation", } @InProceedings{Cabay:1989:FRA, author = "S. Cabay and G. Labahn", title = "A fast, reliable algorithm for calculating {Pad{\'e}--Hermite} forms", crossref = "Gonnet:1989:PAI", pages = "95--100", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p95-cabay/", abstract = "The authors present a new fast algorithm for the calculation of a Pad{\'e}--Hermite form for a vector of power series. When the vector of power series is normal, the algorithm is shown to calculate a Pad{\'e}--Hermite form of type $(n_0, \ldots{}, n_k)$ in $O(k.(n_0^2+\ldots{} +n_k^2))$ operations. This complexity is the same as that of other fast algorithms for computing Pad{\'e}--Hermite approximants. However, unlike other algorithms, the new algorithm also succeeds in the nonnormal case, usually with only a moderate increase in cost.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Alberta Univ., Edmonton, Alta., Canada", classification = "C1120 (Analysis); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Complexity; Iterative methods; Nonnormal case; Pad{\'e}--Hermite approximants; Pad{\'e}--Hermite forms; theory; Vector of power series", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations.", thesaurus = "Computational complexity; Iterative methods; Linear differential equations; Series [mathematics]; Vectors", } @InProceedings{Canny:1989:GCP, author = "J. Canny", title = "Generalized characteristic polynomials", crossref = "Gianni:1989:SAC", pages = "293--299", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author generalises the notion of characteristic polynomial for a system of linear equations to systems of multivariate polynomial equations. The generalization is natural in the sense that it reduces to the usual definition when all the polynomials are linear. Whereas the constant coefficient of the characteristic polynomial of a linear system is the determinant, the constant coefficient of the general characteristic polynomial is the resultant of the system. This construction is applied to solve a traditional problem with efficient methods for solving systems of polynomial equations: the presence of infinitely many solutions `at infinity'. The author gives a single-exponential time method for finding all the isolated solution points of a system of polynomials, even in the presence of infinitely many solutions at infinity or elsewhere.", acknowledgement = ack-nhfb, affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA, USA", classification = "C4130 (Interpolation and function approximation)", keywords = "Generalised characteristic polynomials; Multivariate polynomial equations; Single-exponential time method; System of linear equations", thesaurus = "Polynomials", } @InProceedings{Canny:1989:SSN, author = "J. F. Canny and E. Kaltofen and L. Yagati", title = "Solving systems of non-linear polynomial equations faster", crossref = "Gonnet:1989:PAI", pages = "121--128", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p121-canny/", abstract = "Finding the solution to a system of $n$ non-linear polynomial equations in $n$ unknowns over a given field, say the algebraic closure of the coefficient field, is a classical and fundamental problem in computational algebra. The authors give a method that allows the computation of resultants and $u$-resultants of polynomial systems in essentially linear space and quadratic time. The algorithm constitutes the first improvement over Gaussian elimination-based methods for computing these fundamental invariants.", acknowledgement = ack-nhfb, affiliation = "Div. of Comp. Sci., California Univ., Berkeley, CA, USA", classification = "C1110 (Algebra); C1120 (Analysis); C4130 (Interpolation and function approximation); C4150 (Nonlinear and functional equations); C4240 (Programming and algorithm theory)", keywords = "Algebraic closure; algorithms; Coefficient field; Computational algebra; Computational complexity; Linear space; Nonlinear polynomial equations; Quadratic time; Resultants; theory; U-resultants", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", thesaurus = "Computational complexity; Nonlinear equations; Polynomials; Symbol manipulation", } @InProceedings{Cantone:1989:DPE, author = "D. Cantone and V. Cutello and A. Ferro", title = "Decision procedures for elementary sublanguages of set theory. {XIV}. {Three} languages involving rank related constructs", crossref = "Gianni:1989:SAC", pages = "407--422", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present three decidability results for some quantifier-free and quantified theories of sets involving rank related constructs.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Courant Inst. of Math. Sci., New York Univ., NY, USA", classification = "C1160 (Combinatorial mathematics); C4210 (Formal logic)", keywords = "Decidability results; Decision procedures; Elementary sublanguages; Quantified theories; Quantifier-free; Rank related constructs; Set theory", thesaurus = "Decidability; Formal logic; Set theory", } @InProceedings{Caprasse:1989:CEB, author = "H. Caprasse and J. Demaret and E. Schrufer", title = "Can {EXCALC} be used to investigate high-dimensional cosmological models with nonlinear {Lagrangians}?", crossref = "Gianni:1989:SAC", pages = "116--124", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Recent work in cosmology is characterized by the extension of the traditional four-dimensional general relativity models in two directions: Kaluza--Klein type models which have more than four dimensions, and models with Lagrangians containing nonlinear terms in the Riemann curvature tensor and its contractions. The package EXCALC 2 seems particularly well suited to investigate these models further. The implementation of all operations of EXTERIOR CALCULUS opens the way to perform these calculations efficiently. The article presents the current stage of investigation in this direction.", acknowledgement = ack-nhfb, affiliation = "Inst. de Phys., Liege Univ., Belgium", classification = "A9575P (Mathematical and computer techniques); A9880D (Theoretical cosmology); C7350 (Astronomy and astrophysics)", keywords = "Contractions; Cosmology; EXCALC 2; Four-dimensional general relativity models; High-dimensional cosmological models; Kaluza--Klein type models; Nonlinear Lagrangians; Package; Riemann curvature tensor", thesaurus = "Astronomy computing; Astrophysics computing; Cosmology; Software packages", } @InProceedings{ChaffyCamus:1989:ARA, author = "C. Chaffy-Camus", title = "An application of {REDUCE} to the approximation of $f(x,y)$", crossref = "Gianni:1989:SAC", pages = "73--84", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Pad{\'e} approximants are an important tool in numerical analysis, to evaluate $f(x)$ from its power series even outside the disk of convergence, or to locate its singularities. The paper generalizes this process to the multivariate case and presents two applications of this method: the approximation of implicit curves and the approximation of double power series. Computations are carried out on a computer algebra system REDUCE.", acknowledgement = ack-nhfb, affiliation = "TIM3-INPG, Grenoble, France", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Approximation; Computer algebra system; Convergence; Double power series; Implicit curves; Multivariate case; Numerical analysis; Pad{\'e} approximants; Reduce; Singularities", thesaurus = "Approximation theory; Convergence of numerical methods; Mathematics computing; Software packages", } @InProceedings{Char:1989:ARA, author = "B. W. Char", title = "Automatic reasoning about numerical stability of rational expressions", crossref = "Gonnet:1989:PAI", pages = "234--241", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p234-char/", abstract = "While numerical (e.g. Fortran) code generation from computer algebra is nowadays relatively easy to do, the expressions as they are produced via computer algebra typically benefit from nontrivial reformulation for efficiency and numerical stability. To assist in automatic `expert reformulation', we desire good automated tools to assess the stability of a particular form of an expression. The author discusses an approach to proofs of numerical stability (with respect to roundoff error) of rational expressions. The proof technique is based upon the ability to propagate properties such as sign, exact representability, or a certain kind of numerical stability, to floating point results from properties of their antecedents. The qualitative approach to numerical stability lends itself to implementation as a backwards-chaining theorem prover. While it is not a replacement for alternative forms of stability analysis, it can sometimes discover stability and explain it straightforwardly.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN, USA", classification = "C4100 (Numerical analysis); C7310 (Mathematics)", keywords = "algorithms; Backwards-chaining theorem prover; Code generation; Computer algebra; Floating point; Numerical stability; Rational expressions; Roundoff error; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", thesaurus = "Automatic programming; Convergence of numerical methods; Mathematics computing; Symbol manipulation", } @InProceedings{Char:1989:DIC, author = "B. W. Char and A. R. Macnaughton and P. A. Strooper", title = "Discovering inequality conditions in the analytical solutions of optimization problems", crossref = "Gianni:1989:SAC", pages = "109--115", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The Kuhn--Tucker conditions can provide an analytic solution to the problem of maximizing or minimizing a function subject to inequality constraints, if the artificial variables known as Lagrange multipliers can be eliminated. The paper describes an automated reasoning program that assists in the solution process. The program may also be useful for other problems involving algebraic reasoning with inequalities.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN, USA", classification = "C1180 (Optimisation techniques); C1230 (Artificial intelligence); C7310 (Mathematics)", keywords = "Algebraic reasoning; Analytic solution; Artificial variables; Automated reasoning program; Function maximization; Function minimization; Inequality conditions; Inequality constraints; Kuhn--Tucker conditions; Lagrange multipliers; Optimization problems", thesaurus = "Inference mechanisms; Mathematics computing; Optimisation", } @InProceedings{Chen:1989:CNF, author = "Guoting Chen", title = "Computing the normal forms of matrices depending on parameters", crossref = "Gonnet:1989:PAI", pages = "242--249", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p242-chen/", abstract = "The author considers an algorithm for the exact computation of the Frobenius, Jordan and Arnold's form of matrices depending holomorphically on parameters. The problem originates from the problem of formal resolution of a first order system of differential equations depending on parameter. This algorithm has been implemented in Macsyma.", acknowledgement = ack-nhfb, affiliation = "Equipe de Calcul Formel et Algorithmique Parallele, Laboratoire TIM3-IMAG, Grenoble, France", classification = "C1110 (Algebra); C1120 (Analysis); C4140 (Linear algebra); C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; design; Differential equations; Formal resolution; Macsyma; Matrices; Normal forms; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", thesaurus = "Differential equations; Mathematics computing; Matrix algebra; Symbol manipulation", } @InProceedings{Collins:1989:PRP, author = "G. E. Collins and J. R. Johnson", title = "The probability of relative primality of {Gaussian} integers", crossref = "Gianni:1989:SAC", pages = "252--258", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors generalize, to an arbitrary number field, the theorem which gives the probability that two integers are relatively prime. The probability that two integers are relatively prime is $ 1/ \zeta (2)$, where $\zeta$ is the Riemann $\zeta$ function and $1/\zeta(2)=6/\pi^2$. The theorem for an arbitrary number field states that the probability that two ideals are relatively prime is the reciprocal of the $\zeta$ function of the number field evaluated at two. In particular, since the Gaussian integers are a unique factorization domain, the authors get the probability that two Gaussian integers are relatively prime is $1/\zeta_G(2)$ where $\zeta_G$ is the $\zeta$ function associated with the Gaussian integers. In order to calculate the Gaussian probability, they use a theorem that enables them to factor the $\zeta$ function into a product of the Riemann $\zeta$ function and a Dirichlet series called an L-series.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ., Columbus, OH, USA", classification = "C1140 (Probability and statistics); C1160 (Combinatorial mathematics)", keywords = "Arbitrary number field; Dirichlet series; Gaussian integers; L-series; Probability; Relative primality; Riemann $\zeta$ function", thesaurus = "Number theory; Probability", } @InProceedings{Collins:1989:QES, author = "G. E. Collins and J. R. Johnson", title = "Quantifier elimination and the sign variation method for real root isolation", crossref = "Gonnet:1989:PAI", pages = "264--271", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p264-collins/", abstract = "An important aspect of the construction of a cylindrical algebraic decomposition (CAD) is real root isolation. Root isolation involves finding disjoint intervals, each containing a single root, for all of the real roots of a given polynomial. Root isolation is used to construct a CAD of the real line, which serves as the base case in the construction of higher dimensional CAD's. It is also an essential part of the extension phase, which lifts an induced CAD to the next higher dimension. The authors reexamine the sign variation method of root isolation devised by Collins and Akritas (1976). A new proof of termination is given, which more accurately describes the behavior of the algorithm. This theorem is then sharpened for the special case of cubic polynomials. The result for cubic polynomials is obtained with the aid of Collins's CAD based quantifier elimination algorithm.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ., Columbus, OH, USA", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation)", keywords = "algorithms; Cubic polynomials; Cylindrical algebraic decomposition; design; Disjoint intervals; Polynomial; Quantifier elimination; Real root isolation; Sign variation method; Symbol manipulation; theory", subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED ENGINEERING. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Cooperman:1989:RGC, author = "G. Cooperman and L. Finkelstein and E. Luks", title = "Reduction of group constructions to point stabilizers", crossref = "Gonnet:1989:PAI", pages = "351--356", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p351-cooperman/", abstract = "The construction of point stabilizer subgroups is a problem which has been studied intensively. This work describes a general reduction of certain group constructions to the point stabilizer problem. Examples are given for the centralizer, the normal closure, and a restricted group intersection problem. For the normal closure problem, this work provides an alternative to current algorithms, which are limited by the need for repeated closures under conjugation. For the centralizer and restricted group intersection problems, one can use an existing point stabilizer sequence along with a recent base change algorithm to avoid generating a new point stabilizer sequence. This reduces the time complexity by at least an order of magnitude. Algorithms and theoretical time estimates for the special case of a small base are also summarized. An implementation is in progress.", acknowledgement = ack-nhfb, affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA, USA", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory)", keywords = "algorithms; Base change algorithm; Centralizer; Group constructions; Group intersection; Group theory; Normal closure; Point stabilizers; theory; Time complexity", subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Permutations and combinations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving.", thesaurus = "Computational complexity; Group theory; Symbol manipulation", } @InProceedings{Deprit:1989:MPS, author = "A. Deprit and E. Deprit", title = "Massively parallel symbolic computation", crossref = "Gonnet:1989:PAI", pages = "308--316", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p308-deprit/", abstract = "A massively parallel processor proves to be a powerful tool for manipulating the very large Poisson series encountered in nonlinear dynamics. Exploiting the algebraic structure of Poisson series leads quite naturally to parallel data structures and algorithms for symbolic manipulation. Exercising the parallel symbolic processor on the solution of Kepler's equation reveals the need to reexamine the serial computational methods traditionally applied to problems in dynamics.", acknowledgement = ack-nhfb, affiliation = "Nat. Inst. of Stand. and Technol., Gaithersburg, MD, USA", classification = "C1120 (Analysis); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Algebraic structure; algorithms; design; Massively parallel processor; Nonlinear dynamics; Parallel data structures; Symbolic manipulation; theory; Very large Poisson series", subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf E.1} Data, DATA STRUCTURES. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf C.1.3} Computer Systems Organization, PROCESSOR ARCHITECTURES, Other Architecture Styles, Stack-oriented processors**.", thesaurus = "Data structures; Mathematics computing; Nonlinear equations; Parallel algorithms; Series [mathematics]; Symbol manipulation", } @InProceedings{Devitt:1989:UCA, author = "J. S. Devitt", title = "Unleashing computer algebra on the mathematics curriculum", crossref = "Gonnet:1989:PAI", pages = "218--227", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author presents examples of the actual use of a computer algebra system in the mathematics classroom. These methods and observations are based on the daily use of symbolic algebra during lectures. The potential for focusing student energies on the concepts and ideas of mathematical instead of just mimicking routine computations is enormous. Considerable work remains to make such tools widely accessible but the observations presented will help to make others aware of the great potential which exists for these and similar methods.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Saskatchewan Univ., Saskatoon, Sask., Canada", classification = "C7310 (Mathematics); C7810C (Computer-aided instruction)", keywords = "Computer algebra; Educational computing; Mathematics curriculum; Symbolic algebra", thesaurus = "Educational computing; Mathematics computing; Symbol manipulation", } @InProceedings{Dewar:1989:IIS, author = "M. C. Dewar", title = "{IRENA}: an integrated symbolic and numerical computation environment", crossref = "Gonnet:1989:PAI", pages = "171--179", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Computer algebra systems provide an extremely user-friendly and natural problem-solving environment, but are comparatively slow and limited in the scope of problems they can treat. Programs which call routines from numerical software libraries are fast, but require longer development and testing time, as well as forcing potential users to describe their problems in what is, to them, an unnatural form. Both approaches have advantages and disadvantages, but until now it has been rather difficult to mix the two. The author describes IRENA, an interface between the computer algebra system REDUCE and the NAG numerical subroutine library, which provides the NAG user with the advantages of a computer algebra system and the REDUCE user with the facilities of an extensive library of numerical software. He discusses how the two methods could be used side-by-side to solve problems in definite integration.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C4160 (Numerical integration and differentiation); C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "Computer algebra system; Definite integration; IRENA; NAG; Numerical software; Numerical subroutine library; REDUCE", thesaurus = "Integration; Mathematics computing; Symbol manipulation; User interfaces", } @InProceedings{Dicrescenzo:1989:AEA, author = "C. Dicrescenzo and D. Duval", title = "Algebraic extensions and algebraic closure in {Scratchpad II}", crossref = "Gianni:1989:SAC", pages = "440--446", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Many problems in computer algebra, as well as in high-school exercises, are such that their statement only involves integers but their solution involves complex numbers. For example, the complex numbers $\sqrt{2}$ and $-\sqrt{2}$ appear in the solutions of elementary problems in various domains. The authors describe an implementation of an algebraic closure domain constructor in the language Scratchpad II. In the first part they analyze the problem, and in the second part they describe a solution based on the D5 system.", acknowledgement = ack-nhfb, affiliation = "TIM3, INPG, Grenoble, France", classification = "C7310 (Mathematics)", keywords = "Algebraic closure domain constructor; D5 system; Language Scratchpad II", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Edelsbrunner:1989:TPS, author = "H. Edelsbrunner and F. P. Preparata and D. B. West", title = "Tetrahedrizing point sets in three dimensions", crossref = "Gianni:1989:SAC", pages = "315--331", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of $n$ points in general position in three dimensions, i.e. such that no four points are coplanar. It also presents an algorithm that in $O(n\log{}n)$ time constructs a tetrahedrization of a set of $n$ points consisting of at most $3n-11$ tetrahedra.", acknowledgement = ack-nhfb, affiliation = "Illinois Univ., Urbana, IL, USA", classification = "C4190 (Other numerical methods)", keywords = "Combinatorial results; Extremum problems; Tetrahedra; Tetrahedrization", thesaurus = "Computational geometry", } @InProceedings{Einwohner:1989:MPG, author = "T. H. Einwohner and R. J. Fateman", title = "A {MACSYMA} package for the generation and manipulation of {Chebyshev} series", crossref = "Gonnet:1989:PAI", pages = "180--185", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p180-einwohner/", abstract = "Techniques for a MACSYMA package for expanding an arbitrary univariate expression as a truncated series in Chebyshev polynomials and manipulating such expansions are described. A data structure is introduced to represent a truncated expansion in a set of orthogonal polynomials which contains the independent variable, the name of the orthogonal polynomial set, the number of terms retained, and a list of the expansion coefficients. The package converts a given expression into the aforementioned data structure. Special cases are the conversion of sums, products, the ratio, or the composition of truncated Chebyshev expansions. Another special case is converting an expression free of truncated Chebyshev expansions. The package generates exact expansion coefficients whenever possible. In addition to well-known Chebyshev expansions, such as for polynomials, the authors provide new methods for getting exact Chebyshev expansions for reciprocals of polynomials of degree one or two, meromorphic functions, arbitrary powers of a first-degree polynomial, the error-function, and generalized hypergeometric functions.", acknowledgement = ack-nhfb, affiliation = "Lawrence Livermore Lab., California Univ., CA, USA", classification = "C4130 (Interpolation and function approximation); C6120 (File organisation); C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "algorithms; Chebyshev polynomials; Chebyshev series; Data structure; MACSYMA; Orthogonal polynomials; theory; Univariate expression", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf E.1} Data, DATA STRUCTURES. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Chebyshev approximation; Data structures; Mathematics computing; Polynomials; Series [mathematics]; Software packages; Symbol manipulation", } @InProceedings{Fateman:1989:LTR, author = "R. J. Fateman", title = "Lookup tables, recurrences and complexity", crossref = "Gonnet:1989:PAI", pages = "68--73", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p68-fateman/", abstract = "The use of lookup tables can reduce the complexity of calculation of functions defined typically by mathematical recurrence relations. Although this technique has been adopted by several algebraic manipulation systems, it has not been examined critically in the literature. While the use of tabulation or `memoization' seems to be particularly simple and worthwhile technique in some areas, there are some negative consequences. Furthermore, the expansion of this technique to other areas (other than recurrences) has not been subjected to analysis. The paper examines some of the assumptions.", acknowledgement = ack-nhfb, affiliation = "California Univ., Berkeley, CA, USA", classification = "C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "Algebraic manipulation; algorithms; Complexity; Functions; Lookup tables; Mathematical recurrence relations; theory", subject = "{\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Computational complexity; Number theory; Recursive functions; Symbol manipulation; Table lookup", } @InProceedings{Fateman:1989:SSA, author = "R. J. Fateman", title = "Series solutions of algebraic and differential equations: a comparison of linear and quadratic algebraic convergence", crossref = "Gonnet:1989:PAI", pages = "11--16", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p11-fateman/", abstract = "Speed of convergence of Newton-like iterations in an algebraic domain can be affected heavily by the increasing cost of each step, so much so that a quadratically convergent algorithm with complex steps may be comparable to a slower one with simple steps. The author gives two examples: solving algebraic and first-order ordinary differential equations using the MACSYMA algebraic manipulation system, demonstrating this phenomenon. The relevant programs are exhibited in the hope that they might give rise to more widespread application of these techniques.", acknowledgement = ack-nhfb, affiliation = "California Univ., Berkeley, CA, USA", classification = "C4130 (Interpolation and function approximation); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algebraic equations; Algebraic manipulation system; algorithms; Convergence; Differential equations; Linear algebraic convergence; MACSYMA; Newton-like iterations; Polynomials; Quadratic algebraic convergence; Series solutions; theory", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Iterative methods. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Convergence of numerical methods; Differential equations; Iterative methods; Mathematics computing; Polynomials; Series [mathematics]; Symbol manipulation", } @InProceedings{Fitch:1989:CRB, author = "J. Fitch", title = "Can {REDUCE} be run in parallel?", crossref = "Gonnet:1989:PAI", pages = "155--162", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p155-fitch/", abstract = "In order to make a substantial improvement in the performance of algebra systems it will eventually be necessary to use a parallel execution system. This paper considers one approach to detecting parallelism, an automatic method related to compilation, and applies it to REDUCE, and to the factoriser in particular.", acknowledgement = ack-nhfb, classification = "C6130 (Data handling techniques); C6150C (Compilers, interpreters and other processors); C7310 (Mathematics)", keywords = "Algebra systems; algorithms; Automatic method; Compilation; Factoriser; measurement; Parallel execution system; Parallelism; REDUCE", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf F.3.2} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics of Programming Languages.", thesaurus = "Mathematics computing; Parallel programming; Program compilers; Symbol manipulation", } @InProceedings{Freire:1989:ASC, author = "E. Freire and E. Gamero and E. Ponce and L. G. Franquelo", title = "An algorithm for symbolic computation of center manifolds", crossref = "Gianni:1989:SAC", pages = "218--230", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "A useful technique for the study of local bifurcations is part of the center manifold theory because a dimensional reduction is achieved. The computation of Taylor series approximations of center manifolds gives rise to several difficulties regarding the operational complexity and the computational effort. Previous works proceed in such a way that the computational effort is not optimized. In the paper an algorithm for center manifolds well suited to symbolic computation is presented. The algorithm is organized according to an iterative scheme making good use of the previous steps, thereby minimizing the number of operations. The results of two examples obtained through a REDUCE 3.2 implementation of the algorithm are included.", acknowledgement = ack-nhfb, affiliation = "Escuela Superior Ingenieros Ind., Sevilla, Spain", classification = "C1120 (Analysis); C4130 (Interpolation and function approximation); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algorithm; Center manifold theory; Computational effort; Dimensional reduction; Iterative scheme; Local bifurcations; Operational complexity; REDUCE 3.2; Symbolic computation; Taylor series approximations", thesaurus = "Approximation theory; Differential equations; Mathematics computing; Symbol manipulation", } @InProceedings{Galligo:1989:GEC, author = "Andr\'e Galligo and Lo{\"\i}c Pottier and Carlo Traverso", title = "Greater easy common divisor and standard basis completion algorithms", crossref = "Gianni:1989:SAC", pages = "162--176", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The paper considers arithmetic complexity problems; the main problem is how to limit the growth of the coefficients in the algorithms and the complexity of the field operations involved. The problem is important with every ground field, with the obvious exception of finite fields.", acknowledgement = ack-nhfb, affiliation = "Nice Univ., France", classification = "C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "Algorithms; Arithmetic complexity problems; Coefficients; Field operations; Greater easy common divisor; Standard basis completion algorithms", thesaurus = "Computational complexity; Rewriting systems", } @InProceedings{Gaonzalez:1989:SS, author = "L. Gaonzalez and H. Lombardi and T. Recio and M.-F. Roy", title = "{Sturm--Habicht} sequence", crossref = "Gonnet:1989:PAI", pages = "136--146", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p136-gaonzalez/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @InProceedings{Geddes:1989:HMO, author = "K. O. Geddes and G. H. Gonnet and T. J. Smedley", title = "Heuristic methods for operations with algebraic numbers", crossref = "Gianni:1989:SAC", pages = "475--480", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Algorithms for doing computations involving algebraic numbers have been known for quite some time and implementations now exist in many computer algebra systems. Many of these algorithms have been analysed and shown to run in polynomial time and space, but in spite of this many real problems take large amounts of time and space to solve. The authors describe a heuristic method which can be used for many operations involving algebraic numbers. They give specifics for doing algebraic number inverses, and algebraic number polynomial exact division and greatest common divisor calculation. The heuristic will not solve all instances of these problems, but it returns either the correct result or with failure very quickly, and succeeds for a very large number of problems.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Algebraic numbers; Heuristic methods; Polynomial", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Geddes:1989:NAC, author = "K. O. Geddes and G. H. Gonnet", title = "A new algorithm for computing symbolic limits using hierarchical series", crossref = "Gianni:1989:SAC", pages = "490--495", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors describe an algorithm for computing symbolic limits, i.e. limits of expressions in symbolic form, using hierarchical series. A hierarchical series consists of two levels: an inner level which uses a simple generalization of Laurent series with finite principal part and which captures the behaviour of subexpressions without essential singularities, and an outer level which captures the essential singularities. Once such a series has been computed for an expression at a given point, the limit of the expression at the point is determined by looking at the most significant term of the series. This algorithm solves the limit problem for a large class of expressions.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "Algorithm; Finite principal part; Hierarchical series; Laurent series; Limit problem; Singularities; Symbolic form; Symbolic limits", thesaurus = "Series [mathematics]; Symbol manipulation", } @InProceedings{Geddes:1989:RIM, author = "K. O. Geddes and L. Y. Stefanus", title = "On the {Risch--Norman} integration method and its implementation in {MAPLE}", crossref = "Gonnet:1989:PAI", pages = "212--217", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p212-geddes/", abstract = "Unlike the recursive Risch algorithm for the integration of transcendental elementary functions, the Risch--Norman method processes the tower of field extensions directly in one step. In addition to logarithmic and exponential field extensions, this method can handle extensions in terms of tangents. Consequently, it allows trigonometric functions to be treated without converting them to complex exponential form. The authors review this method and describe its implementation in MAPLE. A heuristic enhancement to this method is also presented.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "C1110 (Algebra); C1120 (Analysis); C4160 (Numerical integration and differentiation); C7310 (Mathematics)", keywords = "algorithms; Exponential field extensions; Logarithmic field extensions; MAPLE; Risch--Norman integration; Tangents; theory; Transcendental elementary functions; Trigonometric functions", subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", thesaurus = "Functions; Integration; Mathematics computing; Symbol manipulation", } @InProceedings{Gianni:1989:DA, author = "P. Gianni and V. Miller and B. Trager", title = "Decomposition of algebras", crossref = "Gianni:1989:SAC", pages = "300--308", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors deal with the problem of decomposing finite commutative Q-algebras as a direct product of local Q-algebras. They solve this problem by reducing it to the problem of finding a decomposition of finite algebras over finite field. They show that it is possible to define a lifting process that allows to reconstruct the answer over the rational numbers. This lifting appears to be very efficient since it is a quadratic lifting that doesn't require stepwise inversions. It is easy to see that the Berlekamp--Hensel algorithm for the factorization of polynomials is a special case of this argument.", acknowledgement = ack-nhfb, affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1110 (Algebra); C4190 (Other numerical methods)", keywords = "Berlekamp--Hensel algorithm; Decomposing finite commutative Q-algebras; Lifting process", thesaurus = "Algebra; Computational geometry", } @InProceedings{Giusti:1989:ATP, author = "M. Giusti and D. Lazard and A. Valibouze", title = "Algebraic transformations of polynomial equations, symmetric polynomials and elimination", crossref = "Gianni:1989:SAC", pages = "309--314", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors define a general transformation of polynomials and study the following concrete problem: how to perform such a transformation using a standard system of computer algebra, providing the usual algebraic tools.", acknowledgement = ack-nhfb, affiliation = "Centre de Math., Ecole Polytech., Palaiseau, France", classification = "C4130 (Interpolation and function approximation); C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "Algebraic tools; Algebraic transformations of polynomial equations; Computer algebra; Elimination; Symmetric polynomials", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Giusti:1989:CRC, author = "M. Giusti", title = "On the {Castelnuovo} regularity for curves", crossref = "Gonnet:1989:PAI", pages = "250--253", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p250-giusti/", abstract = "Let $k$ be a field of characteristic zero; let us consider an algebraic subvariety of the projective space $P_k^n$, defined by a homogeneous ideal I of the polynomial algebra $R=k(x_o,\ldots{},x_n)$. There exists different objects measuring the complexity of this subvariety. Some invariants are naturally intrinsic: the dimension and the degree of the subvariety, the Hilbert function and its regularity, and the Castelnuovo regularity. A natural question is to study the relationships between the integers, at least when the dimension is small (less or equal to one). The author gives a slightly different version of the Castelnuovo--Gruson--Lazarsfeld--Peskine theorem (1983), which relates the Castelnuovo regularity and the degree in the case of curves with more general hypotheses but unfortunately slightly weaker conclusion.", acknowledgement = ack-nhfb, affiliation = "Centre de Mathematiques, CNRS, Ecole Polytechnique, Palaiseau, France", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation)", keywords = "algorithms; Castelnuovo regularity; Complexity; Curves; design; Hilbert function; measurement; Polynomial algebra; Polynomials; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes.", thesaurus = "Computational complexity; Curve fitting; Polynomials", } @InProceedings{Gonzalez:1989:SS, author = "L. Gonzalez and H. Lombardi and T. Recio and M.-F. Roy", title = "{Sturm--Habicht} sequence", crossref = "Gonnet:1989:PAI", pages = "136--146", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Formal computations with inequalities is a subject of general interest in computer algebra. In particular it is fundamental in the parallelisation of basic algorithms and quantifier elimination for real closed fields. The authors give a generalisation of the Sturm theorem essentially due to Sylvester, which is the key for formal computations with inequalities. They study the subresultant sequence, precise some of the classical definitions in order to avoid problems and study specialisation properties. They introduce the Sturm--Habicht sequence, which generalizes Habicht's work (1948). This new sequence, obtained automatically from a subresultant sequence, has some remarkable properties: it gives the same information as the Sturm sequence, recovered by looking only at its principal coefficients; it can be computed by ring operations and exact divisions only, in polynomial time in case of integer coefficients, eventually by modular methods; it has good specialisation properties. Some information about applications and implementation of the Sturm--Habicht sequence is given.", acknowledgement = ack-nhfb, affiliation = "Dept. de Matematicas, Cantabria Univ., Spain", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "Computational complexity; Computer algebra; Inequalities; Integer coefficients; Modular methods; Parallelisation; Polynomial time; Quantifier elimination; Ring operations; Sturm theorem; Sturm--Habicht sequence", thesaurus = "Computational complexity; Parallel algorithms; Polynomials; Series [mathematics]; Symbol manipulation", } @InProceedings{Grigorev:1989:CCC, author = "D. Yu. Grigor'ev", title = "Complexity of computing the characters and the genre of a system of exterior differential equations", crossref = "Gianni:1989:SAC", pages = "534--543", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Let a system $(\sum_JA_{J,i}(dX_{j1},\ldots{},dX_{jm})=0)_{m,i}$ of exterior differential equations be given, where $A_{J,i}$ are polynomials in $n$ variables $X_1,\ldots{}, X_n$ of degrees less than $d$ and skew-symmetric relatively to multiindices $J=(j_1,\ldots{}, j_m)$, the square brackets denote the exterior product of the differentials $dX_{j1},\ldots{}, dX_{jm}$. E. Cartan (1945) introduced the characters and the genre $h$ of the system. Cauchy--Kovalevski theorem guarantees the existence of an integral manifold (and even of the general form) with the dimension less or equal to $h$ satisfying the given system. An algorithm for computing the characters and the genre is designed with the running time polynomial in $L$, $(dn)^n$, herein $L$ denotes the bit-size of the system. The algorithm involves the subexponential-time procedures for finding the irreducible components of an algebraic variety.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci., Leningrad, USSR", classification = "C4130 (Interpolation and function approximation); C4170 (Differential equations)", keywords = "Algebraic variety; Cauchy--Kovalevski theorem; Characters; Exterior differential equations; Integral manifold; Irreducible components; Polynomials", thesaurus = "Differential equations; Polynomials", } @InProceedings{Grossman:1989:LTE, author = "R. Grossman and R. G. Larson", title = "Labeled trees and the efficient computation of derivations", crossref = "Gonnet:1989:PAI", pages = "74--80", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p74-grossman/", abstract = "The paper is concerned with the effective parallel symbolic computation of operators under composition. Examples include differential operators under composition and vector fields under the Lie bracket. In general, such operators do not commute. An important problem is to find efficient algorithms to write expressions involving noncommuting operators in terms of operators which do commute. If the original expression enjoys a certain symmetry, then naive rewriting requires the computation of terms which in the end cancel. Previously, the authors gave an algorithm which in some cases is exponentially faster than the naive expansion of the noncommutating operators (1989). In this paper they show how that algorithm can be naturally parallelized.", acknowledgement = ack-nhfb, affiliation = "Illinois Univ., Chicago, IL, USA", classification = "C1120 (Analysis); C1160 (Combinatorial mathematics); C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "algorithms; Computational complexity; Data structures; Derivations; Differential operators; Labeled trees; Lie bracket; Noncommuting operators; Operators; Parallel algorithms; Parallel symbolic computation; theory; Vector fields", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency.", thesaurus = "Computational complexity; Data structures; Differentiation; Parallel algorithms; Symbol manipulation; Trees [mathematics]", } @InProceedings{Hentzel:1989:VNA, author = "I. R. Hentzel and D. J. Pokrass", title = "Verification of non-identities in algebras", crossref = "Gianni:1989:SAC", pages = "496--507", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present a computer assisted algorithm which establishes whether or not a proposed identity is a consequence of the defining identities of a variety of nonassociative algebras. When the nonassociative polynomial is not an identity, the algorithm produces a proof called a characteristic function. Like an ordinary counterexample, the characteristic function can be used to convince a verifier that the polynomial is not identically zero. However the characteristic function appears to be computationally easier to verify. Also, it reduces or eliminates problems with characteristic. The authors used this method to obtain and verify a new result in the theory of nonassociative algebras. Namely, in a free right alternative algebra $(a,a,b)^3 \ne 0$.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Iowa State Univ., Ames, IA, USA", classification = "C7310 (Mathematics)", keywords = "Algebras; Characteristic function; Computer assisted algorithm; Nonassociative polynomial; Nonidentities verification", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Juozapavicius:1989:SCW, author = "A. Juozapavicius", title = "Symbolic computation for {Witt} rings", crossref = "Gianni:1989:SAC", pages = "271--273", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author considers bilinear and quadratic forms over polynomial rings, such that they can carry linear discrete orderings. The author defines the notion of reduced form and presents theorems concerning equivalence of forms to their reduced presentation. The proofs of these statements are based on the Buchberger's algorithms and their modifications to Gr{\"o}bner bases.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Vilnius State Univ., Lithuanian SSR, USSR", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Bilinear forms; Symbolic computation; Witt rings; Quadratic forms; Polynomial rings; Linear discrete orderings; Reduced form; Gr{\"o}bner bases", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Kaltofen:1989:ISM, author = "E. Kaltofen and L. Yagati", title = "Improved sparse multivariate polynomial interpolation algorithms", crossref = "Gianni:1989:SAC", pages = "467--474", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors consider the problem of interpolating sparse multivariate polynomials from their values. They discuss two algorithms for sparse interpolation, one due to Ben-Or and Tiwari (1988) and the other due to Zippel (1988). They present efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of equations, the use of which greatly improves the time complexities of the two interpolation algorithms.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C4130 (Interpolation and function approximation)", keywords = "Sparse multivariate polynomial interpolation algorithms; Time complexities; Toeplitz systems; Transposed Vandermonde systems of equations", thesaurus = "Interpolation; Polynomials", } @InProceedings{Kaltofen:1989:IVP, author = "E. Kaltofen and T. Valente and N. Yui", title = "An improved {Las Vegas} primality test", crossref = "Gonnet:1989:PAI", pages = "26--33", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p26-kaltofen/", abstract = "The authors present a modification of the Goldwasser--Kilian--Atkin primality test, which, when given an input $n$, outputs either prime or composite, along with a certificate of correctness which may be verified in polynomial time. Atkin's method computes the order of an elliptic curve whose endomorphism ring is isomorphic to the ring of integers of a given imaginary quadratic field $Q(\sqrt{-D})$. Once an appropriate order is found, the parameters of the curve are computed as a function of a root modulo $n$ of the Hilbert class equation for the Hilbert class field of $Q(\sqrt{-D})$. The modification proposed determines instead a root of the Watson class equation for $Q(\sqrt{-D})$ and applies a transformation to get a root of the corresponding Hilbert equation. This is a substantial improvement, in that the Watson equations have much smaller coefficients than do the Hilbert equations.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Certificate of correctness; Elliptic curve; Endomorphism ring; Goldwasser--Kilian--Atkin primality test; Hilbert equation; Imaginary quadratic field; Las Vegas primality test; Number theory; Polynomial time; Prime number; Programming theory; theory; Watson class equation", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Hyperbolic equations. {\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", thesaurus = "Computational complexity; Mathematics computing; Number theory; Program verification; Programming theory", } @InProceedings{Kirchner:1989:CER, author = "C. Kirchner and H. Kirchner", title = "Constrained equational reasoning", crossref = "Gonnet:1989:PAI", pages = "382--389", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p382-kirchner/", abstract = "The theory of constrained equational reasoning is outlined. Many questions and prolongations of this work arise.", acknowledgement = ack-nhfb, classification = "C4210 (Formal logic)", keywords = "algorithms; Constrained equational reasoning; Formal logic; Theorem proving; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Logic and constraint programming. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic.", thesaurus = "Formal logic; Theorem proving", } @InProceedings{Kobayashi:1989:SSA, author = "H. Kobayashi and S. Moritsugu and R. W. Hogan", title = "Solving systems of algebraic equations", crossref = "Gianni:1989:SAC", pages = "139--149", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Shows an algorithm for computing all the solutions with their multiplicities of a system of algebraic equations. The algorithm previously proposed by the authors for the case where the ideal is zero-dimensional and radical seems to have practical efficiency. The authors present a new method for solving systems which are not necessarily radical. The set of all solutions is partitioned into subsets each of which consists of mutually conjugate solutions having the same multiplicity.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Coll. of Sci. and Technol., Nihon Univ., Tokyo, Japan", classification = "C1110 (Algebra); C4210 (Formal logic)", keywords = "Algebraic equations; Algorithm; Ideal; Multiplicities; Mutually conjugate solutions; Radical; Subsets; Zero-dimensional", thesaurus = "Algebra; Problem solving; Theorem proving", } @InProceedings{Kredel:1989:SDC, author = "H. Kredel", title = "Software development for computer algebra or from {ALDES\slash SAC-2} to {WEB\slash Modula-2}", crossref = "Gianni:1989:SAC", pages = "447--455", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author defines a new concept for developing computer algebra software. The development system will integrate a documentation system, a programming language, algorithm libraries, and an interactive calculation facility. The author exemplifies the workability of this concept by applying it to the well known ALDES/SAC-2 system. The ALDES Translator is modified to help in converting ALDES/SAC-2 Code to Modula-2. The implementation and module setup of the SAC-2 basic system, list processing system and arithmetic system in Modula-2 are discussed. An example gives a first idea of the performance of the system. The WEB System of Structured Documentation is used to generate documentation with {\TeX}.", acknowledgement = ack-nhfb, affiliation = "Passau Univ., West Germany", classification = "C6110B (Software engineering techniques); C7310 (Mathematics)", keywords = "ALDES/SAC-2 system; Algorithm libraries; Computer algebra software; Documentation system; Interactive calculation facility; Performance; Programming language; WEB/Modula-2", thesaurus = "Mathematics computing; Software engineering; Symbol manipulation", } @InProceedings{Kuhn:1989:MEC, author = "N. Kuhn and K. Madlener", title = "A method for enumerating cosets of a group presented by a canonical system", crossref = "Gonnet:1989:PAI", pages = "338--350", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p338-kuhn/", abstract = "The application of rewriting techniques to enumerate cosets of subgroups in groups is investigated. Given a class of groups $G$ having canonical string rewriting presentations the authors consider the GWP for this class which is defined by $GWP(w,U)$ iff $w$ in $<U>$ for $w$ in finite $U$ contained in $G$, $G \in G$, where $<U>$ is the subgroup of $G$ generated by $U$. They show how to associate to $U$ two rewriting relations to $-{}_U$ and implies $-{}_U$ on strings such that $w$ in $<U>$ iff $w$ from $*$ to $-{}_U\lambda$ iff $w$ implied by $*\mbox{implies}-_U\lambda$ ($\lambda$ the empty word), both representing the left congruence generated by $<U>$. They derive general critical pair criteria for confluence and $\lambda$-confluence for these relations. Using these criteria completion procedures can be constructed which enumerate cosets like the Todd--Coxeter algorithm without explicit definition of all cosets. The procedures are shown to be terminating if the index of the subgroup is finite or for groups with finite canonical monadic group presentations. If the completion procedure terminates it returns a prefix rewriting system which is confluent on $\Sigma *$, thus deciding the GWP and the index problem for this class of groups. The normal forms of the rewriting relations form a minimal Schreier-representative system of $<U>$ in $G$.", acknowledgement = ack-nhfb, affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany", classification = "C1110 (Algebra); C4210 (Formal logic)", keywords = "$\Lambda$-confluence; algorithms; Canonical string rewriting presentations; Completion procedures; Confluence; Cosets; Critical pair criteria; Decidability; Finite canonical monadic group presentations; Generalized word problem; Group theory; Minimal Schreier-representative system; Rewriting relations; Rewriting techniques; Subgroups; theory; Todd--Coxeter algorithm", subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems, Decision problems. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Decidability; Group theory; Rewriting systems; Symbol manipulation", } @InProceedings{Kutzler:1989:CAT, author = "B. Kutzler", title = "Careful algebraic translations of geometry theorems", crossref = "Gonnet:1989:PAI", pages = "254--263", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p254-kutzler/", abstract = "Modern application areas like computer-aided design and robotics have revived interest in geometry. The algorithmic techniques of computer algebra are important tools for solving large classes of nonlinear geometric problems. However, their application requires a translation of geometric problems into algebraic form. So far, this algebraization process has not gained special attention, since it was considered `obvious'. In the context of automated geometry theorem proving, the use of algebraic deduction techniques led to very promising results, but it seemed to change the nature of proof problems from deciding the validity of a theorem to finding nondegeneracy conditions under which the theorem holds. A careful analysis shows, that this is mainly due to the `careless' translation method. A careful translation technique is presented that resolves this defect. The usefulness of the new algebraization method is demonstrated on concrete examples. A practical comparison with the former `careless' translation is done.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C1160 (Combinatorial mathematics); C4190 (Other numerical methods); C4210 (Formal logic); C4290 (Other computer theory); C7310 (Mathematics)", keywords = "Algebraic deduction; algorithms; Automated geometry theorem proving; Computer algebra; experimentation; Geometry theorems; Nonlinear geometric problems; theory", subject = "{\bf I.2.0} Computing Methodologies, ARTIFICIAL INTELLIGENCE, General. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics.", thesaurus = "Computational geometry; Symbol manipulation; Theorem proving", } @InProceedings{MacCallum:1989:ODE, author = "M. A. H. MacCallum", title = "An ordinary differential equation solver for {REDUCE}", crossref = "Gianni:1989:SAC", pages = "196--205", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Progress and plans for the implementation of an ordinary differential equation solver in REDUCE 3.3 are reported; the aim is to incorporate the best available methods for obtaining closed-form solutions, and to aim at the `best possible' alternative when this fails. It is hoped that this will become a part of the standard REDUCE program library. Elementary capabilities have already been implemented, i.e. methods for first order differential equations of simple types and linear equations of any order with constant coefficients. The further methods to be used include: for first-order equations, an adaptation of Shtokhamer's MACSYMA program; for higher-order linear equations, factorisation of the operator where possible; and for nonlinear equations, the exploitation of Lie symmetries.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Queen Mary Coll., London, UK", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Closed-form solutions; Factorisation; First-order equations; Lie symmetries; MACSYMA program; Nonlinear equations; Ordinary differential equation solver; REDUCE 3.3; REDUCE program library", thesaurus = "Differential equations; Mathematics computing; Software packages; Subroutines", } @InProceedings{Menezes:1989:SCA, author = "A. J. Menezes and P. C. {van Oorschot} and S. A. Vanstone", title = "Some computational aspects of root finding in ${GF}(q^m)$", crossref = "Gianni:1989:SAC", pages = "259--270", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "This paper is an implementation report comparing several variations of a deterministic algorithm for finding roots of polynomials in finite extension fields. Running times for problem instances in fields $\mbox{GF}(2^m)$, including $m>1000$, are given. Comparisons are made between the variations, and improvements achieved in running times are discussed.", acknowledgement = ack-nhfb, affiliation = "Waterloo Univ., Ont., Canada", classification = "C4130 (Interpolation and function approximation)", keywords = "Computational aspects; Root finding; Roots of polynomials", thesaurus = "Polynomials", } @InProceedings{Miller:1989:PGE, author = "B. R. Miller", title = "A program generator for efficient evaluation of {Fourier} series", crossref = "Gonnet:1989:PAI", pages = "199--206", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p199-miller/", abstract = "Many fields require the evaluation of large multi-variate Fourier series, but the naive method of calling sine and cosine for each term can be prohibitive where computing resources are constrained or the series are extremely large (30000 terms). Although the number of such calls can be reduced by using trigonometric identities, such a reduction is usually not possible by hand. Indeed, even when it is carried out by computer, care must be taken to generate compact programs and avoid generating large numbers of intermediate terms. The author describes an algorithm for automatically generating very efficient Fortran programs directly from the mathematical description of the series to be evaluated. The resulting Fortran programs are 5-7 times faster than the naive version and sometimes significantly more compact.", acknowledgement = ack-nhfb, affiliation = "Nat. Inst. of Stand. and Technol., Gaithersbury, MD, USA", classification = "C6115 (Programming support); C7310 (Mathematics)", keywords = "algorithms; design; Fortran programs; Fourier series; languages; Program generator", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computability theory. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf D.3.3} Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Procedures, functions, and subroutines.", thesaurus = "Automatic programming; Mathematics computing; Series [mathematics]; Symbol manipulation", } @InProceedings{Mora:1989:GBN, author = "T. Mora", title = "{Gr{\"o}bner} bases in noncommutative algebras", crossref = "Gianni:1989:SAC", pages = "150--161", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author has studied, in 1988, the concept of standard and Gr{\"o}bner bases and algorithms for their computation in a very wide algebraic context (graded structures). It is easy to show that if $R=k<X_1,\ldots{}, X_n>/H$, where $H$ is the ideal generated by $(X_jX_j-c_{ij}X_iX_j-p_{ij})$ and $\deg(p_{ij})<\deg(X_iX_j)$ for each $i,j$, then $R$ is such a graded structure; so his previous techniques can be applied to it in order to define a concept of Gr{\"o}bner basis and to produce an algorithm for their computation, provided that if $J$ is the ideal generated by $(X_jX_i-c_{ij}X_iX_j:i<j)$, it holds that: (1) Each ideal in $k<X_1, \ldots{}, X_n>$, homogeneous for the graduation defined above and containing J, is finitely generated; (2) For each homogeneous ideal $(h_1, \ldots{}, h_s)$ in $k<X_1,\ldots{},X_n>/J$, it is possible to compute a finite set of syzygies, which together with the trivial ones, generate the module of syzygies; and (3) For each homogeneous ideal $(h_1, \ldots{}, h_s)$ and each homogeneous element $h$ in $k<X_1,\ldots{}, X_n>/J$, it is possible to decide whether $h$ in $(h_1,\ldots{},h_s)$, in which case it is possible to compute a representation of $h$ in terms of $(h_1,\ldots{},h_s)$. It turns out that the above conditions hold whenever for no $i<j<k,c_{ij}=c_{jk}=0$. The author shows how to solve problems (2) and (3) in case for no $i<j<k,C_{ij}=c_{jk}=0$.", acknowledgement = ack-nhfb, affiliation = "Genova Univ., Italy", classification = "C4210 (Formal logic)", keywords = "Gr{\"o}bner bases; Noncommutative algebras; Graded structures; Ideal; Homogeneous; Set of syzygies; Decide", thesaurus = "Algebra; Decidability; Theorem proving", } @InProceedings{Murray:1989:EPD, author = "N. V. Murray and E. Rosenthal", title = "Employing path dissolution to shorten tableaux proofs", crossref = "Gonnet:1989:PAI", pages = "373--381", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p373-murray/", abstract = "Path dissolution is an inferencing mechanism that generalizes the method of analytic tableaux. The main result presented is that every nontrivial step in any tableau proof can be speeded up with the application of dissolution techniques.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., State Univ. of New York, Albany, NY, USA", classification = "C1160 (Combinatorial mathematics); C1230 (Artificial intelligence); C4210 (Formal logic)", keywords = "algorithms; Analytic tableaux; Formal logic; Graph theory; Inferencing mechanism; Path dissolution; Rewrite operations; Tableau proof; Tableaux proofs; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic.", thesaurus = "Graph theory; Inference mechanisms; Rewriting systems; Theorem proving", } @InProceedings{Musser:1989:GP, author = "D. R. Musser and A. A. Stepanov", title = "Generic programming", crossref = "Gianni:1989:SAC", pages = "13--25", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Generic programming centers around the idea of abstracting from concrete, efficient algorithms to obtain generic algorithms that can be combined with different data representations to produce a wide variety of useful software. Four kinds of abstraction-data, algorithmic, structural, and representational-are discussed, with examples of their use in building an Ada library of software components. The main topic discussed is generic algorithms and an approach to their formal specification and verification, with illustration in terms of a partitioning algorithm such as is used in the quicksort algorithm. It is argued that generically programmed software component libraries offer important advantages for achieving software productivity and reliability.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C6110 (Systems analysis and programming); C6120 (File organisation)", keywords = "Abstracting; Ada library; Algorithmic abstraction; Data abstraction; Data representations; Formal specification; Formal verification; Generic algorithms; Generic programming; Generically programmed software component libraries; Partitioning algorithm; Quicksort algorithm; Representational abstraction; Software productivity; Software reliability; Structural abstraction", thesaurus = "Data structures; Programming", } @InProceedings{OHearn:1989:NTP, author = "P. O'Hearn and Z. Stachniak", title = "Note on theorem proving strategies for resolution counterparts of nonclassical logics", crossref = "Gonnet:1989:PAI", pages = "364--372", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p364-o_hearn/", abstract = "The paper shows that two of the more powerful speed-up techniques available for the classical first-order logic, namely the set of support and the polarity strategies, can be formulated and applied to resolution proof systems for nonclassical logics. The authors review background information on propositional logics and propositional resolution proof systems. They introduce the set of support and polarity strategies. They show that resolution counterparts of most structural propositional logics admit both strategies preserving their refutational completeness.", acknowledgement = ack-nhfb, affiliation = "Queen's Univ., Kingston, Ont., Canada", classification = "C1160 (Combinatorial mathematics); C1230 (Artificial intelligence); C4210 (Formal logic)", keywords = "algorithms; Deductive systems; First-order logic; Inference rules; Nonclassical logics; Polarity; Propositional logics; Propositional resolution proof systems; Resolution counterparts; Resolution proof systems; Speed-up techniques; Support; Theorem proving; theory; Trees", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory.", thesaurus = "Formal logic; Inference mechanisms; Theorem proving; Trees [mathematics]", } @InProceedings{Okada:1989:SNC, author = "M. Okada", title = "Strong normalizability for the combined system of the typed $\lambda$ calculus and an arbitrary convergent term rewrite system", crossref = "Gonnet:1989:PAI", pages = "357--363", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p357-okada/", abstract = "The author gives a proof of strong normalizability of the typed $\lambda$-calculus extended by an arbitrary convergent term rewriting system, which provides the affirmative answer to the open problem proposed in Breazu-Tannen (1988). Klop (1980) showed that a combined system of the untyped $\lambda$-calculus and convergent term rewriting system is not Church--Rosser in general, though both are Church--Rosser. It is well-known that the typed $\lambda$-calculus is convergent (Church--Rosser and terminating). Breazu-Tannen showed that a combined system of the typed $\lambda$-calculus and an arbitrary Church--Rosser term rewriting system is again Church--Rosser. The strong normalization result in this paper shows that the combined system of the typed $\lambda$-calculus and an arbitrary convergent term rewriting system is again convergent. The strong normalizability proof is easily extended to the case of the second order (polymorphically) typed $\lambda$ calculus and the case in which $\mu$-reduction rule is added.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Concordia Univ., Montreal, Que., Canada", classification = "C4210 (Formal logic)", keywords = "algorithms; Church--Rosser; Convergent term rewrite system; design; Polymorphically; Rewriting system; Strong normalizability; theory; Typed $\lambda$ calculus; Typed $\lambda$-calculus", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Lambda calculus and related systems. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic.", thesaurus = "Convergence; Rewriting systems; Symbol manipulation", } @InProceedings{Ollivier:1989:IRM, author = "F. Ollivier", title = "Inversibility of rational mappings and structural identifiability in automatics", crossref = "Gonnet:1989:PAI", pages = "43--54", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p43-ollivier/", abstract = "The author investigates different methods for testing whether a rational mapping $f$ from $k^n$ to $k^m$ admits a rational inverse, or whether a polynomial mapping admits a polynomial one. He gives a new solution, which seems much more efficient in practice than previously known ones using `tag' variables and standard basis, and a majoration for the degree of the standard basis calculations which is valid for both methods in the case of a polynomial map which is birational. He shows that a better bound can be given for the method, under some assumption on the form of $f$. The method can also extend to check whether a given polynomial belongs to the subfield generated by a finite set of fractions. The author illustrates the algorithm with an application to structural identifiability. The implementation has been done in the IBM computer algebra system Scratchpad II.", acknowledgement = ack-nhfb, affiliation = "Lab. d'Inf. de l'X, Ecole Polytech., Palaiseau, France", classification = "C1110 (Algebra); C1120 (Analysis); C7310 (Mathematics)", keywords = "algorithms; Computer algebra system; experimentation; Fractions; IBM; Inversibility; Polynomial inverse; Polynomial mapping; Rational inverse; Rational mappings; Scratchpad II; Structural identifiability; theory", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Inverse problems; Mathematics computing; Polynomials; Set theory; Symbol manipulation", } @InProceedings{Pan:1989:SCD, author = "Victor Pan", title = "On some computations with dense structured matrices", crossref = "Gonnet:1989:PAI", pages = "34--42", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p34-pan/", abstract = "The author reduces several computations with Hilbert and Vandermonde type matrices to matrix computations of the Hankel--Toeplitz type (and vice versa). This unifies various known algorithms for computations with dense structured matrices and allows the extension of any progress in computations with matrices of one class to the computations with other classes. This allows the computation of the inverses and the determinants of $n*n$ matrices of Vandermonde and Hilbert types for the cost of $O(n \log^2n)$ arithmetic operations. Previously, such results were only known for the more narrow class of Vandermonde and generalized Hilbert matrices.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., City Univ. of New York, Bronx, NY, USA", classification = "C1110 (Algebra); C4140 (Linear algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Computational complexity; Dense structured matrices; Determinants; Hankel--Toeplitz type; Hilbert; Inverses; theory; Vandermonde", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Computational complexity; Determinants; Inverse problems; Mathematics computing; Matrix algebra", } @InProceedings{Porter:1989:DRA, author = "S. C. Porter", title = "Dense representation of affine coordinate rings of curves with one point at infinity", crossref = "Gonnet:1989:PAI", pages = "287--297", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p287-porter/", abstract = "Traditional methods of representing rational functions on curves are unwieldy and unsuitable for solution of many problems. This paper describes a simple and elegant representation of elements of the affine coordinate ring of an algebraic curve and describes efficient, easy to implement algorithms to perform addition, subtraction, multiplication and polynomial evaluation. This data structure overcomes many of the disadvantages of more unwieldy traditional representations. Elements are represented as vectors of elements of the ground field in a manner similar to the representation of polynomials of one variable as an array of coefficients. This data structure is a fundamental ingredient in the author's decoding method for algebraic geometry codes. The rational function approximation techniques used for decoding could not have been described with multivariate polynomials or truncated infinite series.", acknowledgement = ack-nhfb, affiliation = "Baise State Univ., ID, USA", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Affine coordinate rings; Algebraic curve; Algebraic geometry codes; algorithms; Curves; Data structure; Decoding; Polynomial; Rational function approximation; Rational functions; theory; Vectors", subject = "{\bf E.1} Data, DATA STRUCTURES. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf E.4} Data, CODING AND INFORMATION THEORY.", thesaurus = "Computational geometry; Data structures; Functions; Mathematics computing; Polynomials; Programming theory; Symbol manipulation; Vectors", xxpages = "288--297", } @InProceedings{Purtilo:1989:MEO, author = "J. M. Purtilo", title = "Minion: an environment to organize mathematical problem solving", crossref = "Gonnet:1989:PAI", pages = "147--154", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p147-purtilo/", abstract = "Maryland University are constructing a management assistant that works in conjunction with existing symbolic computation systems. Called Minion, it allows users to express simple plans for solving large problems in the interactive environment, and then guides the user's interaction according to that plan. Key features are that plans are easy to construct; the assistant helps a user visualize progress towards solving the global problem; and individual steps within a plan can be executed by arbitrary software tools, whether symbolic-, numeric- or logic-based in their implementation. The author briefly portrays the organizational problem that must be treated, and motivates the need for structure management tools in mathematical problem solving environments. He details features of the Minion prototype. After a brief update on the status of the existing Polylith system, he describes how Minion is implemented using an interconnection resource.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park, MD, USA", classification = "C6130 (Data handling techniques); C6180 (User interfaces); C7310 (Mathematics)", keywords = "algorithms; Interactive environment; Interconnection resource; Management assistant; Maryland University; Mathematical problem solving; Minion; Polylith; Structure management tools; Symbolic computation systems; theory; User interfaces", subject = "{\bf I.3.1} Computing Methodologies, COMPUTER GRAPHICS, Hardware Architecture. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.", thesaurus = "Interactive systems; Mathematics computing; Symbol manipulation; User interfaces", } @InProceedings{Rabinowitz:1989:CSS, author = "S. Rabinowitz", title = "On the computer solution of symmetric homogeneous triangle inequalities", crossref = "Gonnet:1989:PAI", pages = "272--286", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p272-rabinowitz/", abstract = "The article presents an effective systematic algorithm that one can use to prove inequalities. A computer algorithm that can prove many inequalities is presented.", acknowledgement = ack-nhfb, affiliation = "Alliant Comput. Syst. Corp., Littleton, MA, USA", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Computer algorithm; Symmetric homogeneous triangle inequalities; theory", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Equations; Mathematics computing; Programming theory; Symbol manipulation", } @InProceedings{Ravenscroft:1989:SSG, author = "R. A. {Ravenscroft, Jr.} and E. A. Lamagna", title = "Symbolic summation with generating functions", crossref = "Gonnet:1989:PAI", pages = "228--233", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The generating function technique presented is an important addition to the area of summation algorithms. With it, many summations that cannot be evaluated by existing algorithms can be solved. Among these are hybrid sums and sums involving special classes of functions including binomial coefficients, Fibonacci numbers, and harmonic numbers. However, the method is not viable for hand calculation since the algebraic manipulation gets very complex. Fortunately, the steps used in the procedure are consistent regardless of the particular generating functions that are involved.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Brown Univ., Providence, RI, USA", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Generating functions; Hybrid sums; Summation algorithms; Symbolic summation", thesaurus = "Computation theory; Functions; Series [mathematics]; Symbol manipulation", } @InProceedings{Roch:1989:CAM, author = "J.-L. Roch and P. Senechaud and F. Siebert-Roch and G. Villard", title = "Computer algebra on {MIMD} machine", crossref = "Gianni:1989:SAC", pages = "423--439", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "PAC is a computer algebra system, based on MIMD type parallelism. It uses parallelism as a tool for processing problems which are too complex for a sequential treatment. Basic fundamentals of the system are firstly discussed. Then, different problems are studied, particularly the implementation of infinite-precision arithmetic, the solution of linear systems and of Diophantine equations, the parallelization of Buchberger's algorithm for Gr{\"o}bner bases. A prototype of PAC is implemented on the Floating Point System hypercube Tesseract 20 (16 nodes), and different timing results obtained on this machine are given.", acknowledgement = ack-nhfb, affiliation = "TIM3, INPG, Grenoble, France", classification = "C7310 (Mathematics)", keywords = "MIMD machine; PAC; Computer algebra system; Infinite-precision arithmetic; Solution of linear systems; Diophantine equations; Parallelization; Gr{\"o}bner bases; Floating Point System hypercube Tesseract 20; Timing results", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Rolletschek:1989:SDC, author = "H. Rolletschek", title = "Shortest division chains in imaginary quadratic number fields", crossref = "Gianni:1989:SAC", pages = "231--243", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Let $O_d$ be the set of algebraic integers in an imaginary quadratic number field $Q(\sqrt{d})$, $d<0$, where $d$ is the discriminant of $O_d$. Consider the Euclidean Algorithm (EA), applied to algebraic integers $\xi$, $\eta$ in $O_d$. It consists in computing a sequence of remainders $\rho_0=\xi,\rho_1=\eta,\rho_2,\ldots{},\rho_{n+1}=0$, where $\rho_{i+1}=\rho_{i-1}-\gamma_i\rho_i$ for algebraic integers $\gamma _i \in K, i=1, \ldots{}, n$. It is shown that except for $d=-11$ the number of divisions to be carried out is always minimized by choosing each $\gamma_i$ such that $N(\rho_{i-1}-\gamma_i\rho_i)$, the norm of $\rho_{i-1}-\gamma_i\rho_i$, is minimal. This result has been proven previously in special cases. It also applies to those imaginary quadratic number rings which are not Euclidean; in this case the division chains may be infinite. For $d=-7,-8$ the methods applied so far must be modified somewhat, and for $d=-11$ a counterexample is provided and a theorem which partially answers the question, how shortest division chains can be obtained.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Kent State Univ., OH, USA", classification = "C1160 (Combinatorial mathematics)", keywords = "Algebraic integers; Discriminant; Divisions; EA; Euclidean Algorithm; Imaginary quadratic number fields; Norm; Remainders; Set; Shortest division chains", thesaurus = "Number theory", } @InProceedings{Saunders:1989:PIC, author = "B. D. Saunders and H. R. Lee and S. K. Abdali", title = "A parallel implementation of the cylindrical algebraic decomposition algorithm", crossref = "Gonnet:1989:PAI", pages = "298--307", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p298-saunders/", abstract = "The authors describe a parallelization scheme for Collins's cylindrical algebraic decomposition algorithm for quantifier elimination in the theory of real closed fields. They discuss a parallel implementation of the computer algebra system SAC2 in which a complete sequential implementation of Collins's algorithm already exists. They report some initial results on the speedup obtained, drawing on a suite of examples previously given by Arnon.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. and Inf. Sci., Delaware Univ., Newark, DE, USA", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Computer algebra system; Cylindrical algebraic decomposition algorithm; Parallel implementation; Parallelization; Polynomials; Quantifier elimination; Real closed fields; SAC2; theory", subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Mathematics computing; Parallel algorithms; Polynomials; Programming theory; Symbol manipulation", } @InProceedings{Schwarz:1989:FAL, author = "F. Schwarz", title = "A factorization algorithm for linear ordinary differential equations", crossref = "Gonnet:1989:PAI", pages = "17--25", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p17-schwarz/", abstract = "The reducibility and factorization of linear homogeneous differential equations are of great theoretical and practical importance in mathematics. Although it has been known for a long time that factorization is in principle a decision procedure, its use in an automatic differential equation solver requires a more detailed analysis of the various steps involved. Especially important are certain auxiliary equations, the so-called associated equations. An upper bound for the degree of its coefficients is derived. Another important ingredient is the computation of optimal estimates for the size of polynomial and rational solutions of certain differential equations with rotational coefficients. Applying these results, the design of the factorization algorithm LODEF and its implementation in the Scratchpad II Computer Algebra System is described.", acknowledgement = ack-nhfb, affiliation = "GMD, Inst. F1, St. Augustin, West Germany", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; Associated equations; Automatic differential equation solver; Factorization algorithm; Linear ordinary differential equations; LODEF; Optimal estimates; Polynomial solutions; Rational solutions; Rotational coefficients; Scratchpad II Computer Algebra System; theory; Upper bound", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", thesaurus = "Linear differential equations; Mathematics computing; Polynomials; Symbol manipulation", } @InProceedings{Sergeraert:1989:NRN, author = "F. Sergeraert", title = "From a noncomputability result to new interesting definitions and computability results", crossref = "Gianni:1989:SAC", pages = "26--32", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Examines the strange situation encountered in algebraic topology: on one hand no general algorithm is able to decide whether some topological space is simply connected; this is an easy consequence of the undecidability of the word problem. On the other hand most of the important results in algebraic topology assume that the spaces under consideration are simply connected. So that one can ask for algorithms that use some method or other, and always compute something, in such a way that if the space given is simply connected, then the result obtained is the good one. The problem is to explain what is something in general. The paper explains that a solution can be found for the computing problems of the homotopy groups. Then something is a K-theory group. It obtains in this way a new understanding of the algebraic K-theory groups and positive results about their computability.", acknowledgement = ack-nhfb, affiliation = "Inst. Fourier, St. Martin d'Heres, France", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)", keywords = "Algebraic K-theory groups; Algebraic topology; Computability; Homotopy groups; Simply connected; Topological space; Undecidability; Word problem", thesaurus = "Group theory; Topology", } @InProceedings{Shackell:1989:AEO, author = "J. Shackell", title = "Asymptotic estimation of oscillating functions using an interval calculus", crossref = "Gianni:1989:SAC", pages = "481--489", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author considers the problem of estimating the asymptotic growth of functions defined by expressions involving exponentials, logarithms, algebraic operations and also sine functions. Modulo the assumption that zero-equivalence can be decided on the set of constant terms, an algorithm exists for the case when there are no trigonometric functions in the expression.", acknowledgement = ack-nhfb, affiliation = "Inst. of Math., Kent Univ., Canterbury, UK", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Algebraic operations; Asymptotic estimation; Asymptotic growth; Exponentials; Interval calculus; Logarithms; Oscillating functions; Sine functions; Zero-equivalence", thesaurus = "Approximation theory; Estimation theory; Symbol manipulation", } @InProceedings{Shackell:1989:DAF, author = "J. Shackell", title = "A differential-equations approach to functional equivalence", crossref = "Gonnet:1989:PAI", pages = "7--10", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "To seek algebraic dependencies between functions is to ask whether there exists a polynomial in them which is functionally equivalent to zero. The methods outlined work directly with the given expression, which is regarded as a polynomial in a top-level basic function with coefficients in a function field containing the other basic functions. The top-level function is defined by a differential equation over the coefficient field. The techniques are entirely elementary and involve differentiation, substitution and calculation of GCDs. The methods decide zero-equivalence in fields built using arithmetic operations and functional composition with functions defined as solutions of algebraic differential equations. The paper treats only first-order, first-degree equations.", acknowledgement = ack-nhfb, affiliation = "Kent Univ., Canterbury, UK", classification = "C1110 (Algebra); C1120 (Analysis); C4130 (Interpolation and function approximation); C4170 (Differential equations)", keywords = "Algebraic dependencies; Differential-equations; Differentiation; Functional equivalence; Functions; Polynomial; Substitution; Zero-equivalence", thesaurus = "Differential equations; Functions; Polynomials", } @InProceedings{Shackle:1989:DAF, author = "J. Shackle", title = "A differential-equations approach to functional equivalence", crossref = "Gonnet:1989:PAI", pages = "7--10", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p7-shackle/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @InProceedings{Sharma:1989:SDA, author = "N. Sharma and P. S. Wang", title = "Symbolic derivation and automatic generation of parallel routines for finite element analysis", crossref = "Gianni:1989:SAC", pages = "33--56", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Describes some initial results of a joint research project involving engineering and computer science. Based on earlier work on the automatic derivation and generation of numeric code for finite element analysis, the authors are conducting research into the mapping of finite element computations on parallel architectures. Software is being developed to automatically derive and generate parallel code that can be used with existing sequential code to improve speed. They are developing techniques to derive parallel procedures, based on high-level user input, to exploit parallel computer architectures. An experimental software system called P-FINGER is under development to derive key finite element routines for the Warp systolic array computer. A separate parallel code generation package is used to render the symbolically derived parallel procedures into code for the Warp parallel computer.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. Sci., Kent State Univ., OH, USA", classification = "C4100 (Numerical analysis); C7400 (Engineering)", keywords = "Automatic derivation; Automatic generation; Computer science; Engineering; Experimental software system; Finite element analysis; Finite element computations; Finite element routines; P-FINGER; Parallel architectures; Parallel code; Parallel code generation package; Parallel computer architectures; Parallel procedures; Parallel routines; Symbolic derivation; Symbolically derived parallel procedures; Warp parallel computer; Warp systolic array computer", thesaurus = "Engineering computing; Finite element analysis; Parallel processing", } @InProceedings{Siebert-Roch:1989:PAH, author = "F. Siebert-Roch", title = "Parallel algorithms for {Hermite} normal form of an integer matrix", crossref = "Gonnet:1989:PAI", pages = "317--321", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p317-siebert-roch/", abstract = "The main problem in integral matrices triangularization is the `intermediate coefficients swell'. This aspect limits the dimension of treated matrices. The lliopoulos algorithm computes the Hermite normal form of an integer matrix controlling the coefficients growth by means of the determinant. The author presents two parallelizations of this algorithm and their implementations on a MIMD machine, with 16 processors.", acknowledgement = ack-nhfb, affiliation = "Laboratoire TIM3-IMAG, Grenoble, France", classification = "C1110 (Algebra); C4140 (Linear algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Determinant; Hermite normal form; Integer matrix; Integral matrices triangularization; Intermediate coefficients swell; Lliopoulos algorithm; MIMD; Parallel algorithms; Parallelizations; theory", subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Computational complexity; Determinants; Mathematics computing; Matrix algebra; Parallel algorithms; Symbol manipulation", } @InProceedings{Singer:1989:LFI, author = "M. F. Singer", title = "{Liouvillian} first integrals of differential equations", crossref = "Gianni:1989:SAC", pages = "57--63", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The system of differential equations $x=P(x,y),y=Q(x,y)$ has a Liouvillian first integral if and only if the differential form $Q(x,y)dx-P(x,y)dy$ has an integrating factor of the form $R(x,y)=exp(\int{}U(x,y)dx+V(x,y)dy)$ where $U$ and $V$ are rational functions and $U_y=V_x$. This theorem shows that if a Liouvillian first integral exists, then there is a Liouvillian first integral of a very special form, but it does not show how to find one. Before turning to this latter question, the author discusses how this theorem is placed in the setting of differential algebra and the tools used to prove it.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., North Carolina State Univ., Raleigh, NC, USA", classification = "C1120 (Analysis); C4170 (Differential equations); C4180 (Integral equations)", keywords = "Differential algebra; Differential equations; Differential form; Integrating factor; Liouvillian first integrals; Rational functions", thesaurus = "Differential equations; Integral equations", } @InProceedings{Smedley:1989:NMA, author = "T. J. Smedley", title = "A new modular algorithm for computation of algebraic number polynomial gcds", crossref = "Gonnet:1989:PAI", pages = "91--94", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p91-smedley/", abstract = "Euclid's algorithm for finding the greatest common divisor of two polynominals when applied to polynomials over an algebraic extension field, tends to be very slow. In the case of polynomials with integer coefficients, one approach to solving this problem is to use a modular algorithm. This approach has been extended to algebraic number fields by Langemyr and McCallum (1987). Another approach for algebraic numbers is to use a heuristic method (Geddes, Gonnett and Smedley, 1988). The paper shows that this heuristic method can be made into an algorithm.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci. Waterloo Univ., Ont., Canada", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory)", keywords = "Algebraic number polynomial gcds; algorithms; Euclid; Heuristic method; Integer coefficients; Modular algorithm; Symbol manipulation; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Computation theory; Polynomials; Symbol manipulation", } @InProceedings{Stifter:1989:GRM, author = "S. Stifter", title = "A generalization of the {Roider} method to solve the robot collision problem in {3D}", crossref = "Gianni:1989:SAC", pages = "332--343", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The Roider method is a method to test by means of computational geometry whether two convex, compact objects, say $A$ and $B$, in two dimensions intersect. Roughly, this iterative method constructs a witness to disjointness (a wedge formed by a pair of touching-lines from some $P(\in A)$ to $B$ that separates $A$ and $B$) if the objects are disjoint. If the objects intersect then a witness to intersection, i.e. a point in common to both objects, is constructed. The author generalizes the Roider method in two aspects: Firstly, he generalizes the algorithm such that it is also applicable to convex, compact objects in three dimensions. Secondly, he generalizes the method such that it can be used to test whether a non-moving object A collides with a moving object $B$.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Keples Univ., Linz, Austria", classification = "C3120C (Spatial variables); C4190 (Other numerical methods)", keywords = "3D; Computational geometry; Disjointness; Iterative method; Robot collision problem; Roider method", thesaurus = "Computational geometry; Position control", } @InProceedings{Teitelbaum:1989:CCR, author = "J. Teitelbaum", title = "On the computational complexity of the resolution of plane curve singularities", crossref = "Gianni:1989:SAC", pages = "285--292", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author describes an algorithm which computes the resolution of a plane curve singularity-that is, a singularity at the origin defined by a formal power series $F$ in two variables $x$ and $y$ over a field $k$. The algorithm requires that $k$ be of characteristic zero (or at least of `large' characteristic) but this hypothesis can certainly be removed at the expense of some complications. The algorithm obtains explicit equations for the blowing-up of the singularity, and therefore yields all of the interesting invariants of the singularity, such as its conductor and its Milnor number. The author also provides upper bounds for the number of $k$-operations needed for the operation of the algorithm.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Michigan Univ., Ann Arbor, MI, USA", classification = "C4240 (Programming and algorithm theory)", keywords = "Computational complexity; Formal power series; Resolution of plane curve singularities", thesaurus = "Computational complexity; Series [mathematics]", } @InProceedings{Todd:1989:SAP, author = "P. H. Todd and G. W. Cherry", title = "Symbolic analysis of planar drawings", crossref = "Gianni:1989:SAC", pages = "344--355", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "A method is described for performing a symbolic analysis of planar drawings. The method takes input in the form of a dimensioned (i.e. labeled) drawing and determines whether the coordinates of all of the points in the drawing can be uniquely written in terms of the specified labels. If it is possible to determine the coordinates of the points (i.e. the drawing is consistently dimensioned), then they are calculated. Otherwise the algorithm returns a flag specifying whether the drawing is underdimensioned or overdimensioned. The method employs standard constructions from geometry such as the construction of a line from two distinct points or the construction of a line from a given line, a point and an angle. In order to determine whether some sequence of given constructions can be used to calculate the coordinates of each point the authors construct and analyse an undirected graph called the dimension graph of the drawing. If such a sequence exists, then the calculations are performed by calling symbolic routines which correspond to the various constructions. An implementation is described and examples are given.", acknowledgement = ack-nhfb, affiliation = "Tektronix Labs., Beaverton, OR, USA", classification = "C1160 (Combinatorial mathematics); C4190 (Other numerical methods); C6130 (Data handling techniques)", keywords = "Coordinates; Dimension graph; Geometry; Labeled drawing; Planar drawings; Symbolic analysis; Symbolic routines; Undirected graph", thesaurus = "Computational geometry; Graph theory; Symbol manipulation", } @InProceedings{Traverso:1989:EGB, author = "C. Traverso and L. Donati", title = "Experimenting the {Gr{\"o}bner} basis algorithm with the {A1PI} system", crossref = "Gonnet:1989:PAI", pages = "192--198", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p192-traverso/", abstract = "The AlPI (Algoritmi Pisa) system is a small polynomial algebra system. It was designed and implemented by the first author in MuLISP-86. It is now (almost) ported by the second author in lucid COMMON-LISP, in such a way that only a few macros are needed to transport it in any COMMON-LISP dialect (MuLISP included). Its main aim is the experimentation on the Buchberger Gr{\"o}bner basis completion algorithm with its different versions, and on the Mora tangent cone algorithm. It is driven by a menu, and has a series of facilities to manipulate lists of polynomials. After a description of the system and of the versions of the algorithms presently implemented, the authors give a series of experimental results (for the MuLISP version). These results, and results of the same kind to obtain with further experimentation, can give suggestions on the versions of the algorithm to choose as default for other implementations of the algorithms.", acknowledgement = ack-nhfb, affiliation = "Dipartmento di Matematica, Pisa Univ., Italy", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "algorithms; experimentation; theory; User interfaces; Gr{\"o}bner basis algorithm; AlPI system; Algoritmi Pisa; Polynomial algebra system; MuLISP-86; Macros; Buchberger Gr{\"o}bner basis; Completion algorithm; Mora tangent cone algorithm", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Mathematics computing; Polynomials; Symbol manipulation", xxtitle = "Experimenting the {Gr{\"o}bner} basis algorithm with the {AlPI} system", } @InProceedings{Traverso:1989:GTA, author = "C. Traverso", title = "{Gr{\"o}bner} trace algorithms", crossref = "Gianni:1989:SAC", pages = "125--138", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Practical computing experience on Gr{\"o}bner bases has shown that computing with rational numbers or integers, very frequently one has very large coefficients in the intermediate computations, and that often the final result is of more moderate size. Sometimes it happens that the size of these numbers, which have to be kept up to the end, is such that memory overflow or excessive paging occurs. The author's approach gives a series of algorithms, based on the concept of Gr{\"o}bner trace; these algorithms are mainly probabilistic (Monte Carlo); they include a series of tests (still probabilistic) to check the probable correctness; he also describes deterministic tests that unfortunately are sometimes as costly as a direct Gr{\"o}bner basis computation, but sometimes instead very rapid.", acknowledgement = ack-nhfb, affiliation = "Dipartimento di Matematica, Pisa Univ., Italy", classification = "C1140G (Monte Carlo methods); C4210 (Formal logic)", keywords = "Gr{\"o}bner trace algorithms; Gr{\"o}bner bases; Rational numbers; Integers; Probabilistic; Monte Carlo; Probable correctness; Deterministic tests", thesaurus = "Monte Carlo methods; Rewriting systems", } @InProceedings{Valibouze:1989:RSF, author = "A. Valibouze", title = "Resolvents and symmetric functions", crossref = "Gonnet:1989:PAI", pages = "390--399", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p390-valibouze/", abstract = "A model of transformations of polynomial equations (direct image model) is studied. The model expresses some minimal polynomials and some resolvents relative to the Galois group of a polynomial in order to use a general algorithm of resolution. This algorithm can be effectively computed in MACSYMA with the extension SYM that manipulates symmetric polynomials. Examples obtained by specializing the general algorithm for the Galois resolvent are given.", acknowledgement = ack-nhfb, affiliation = "Univ. Pierre et Marie Curie, Paris, France", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "algorithms; Direct image model; Galois group; MACSYMA; Minimal polynomials; Polynomial equations; Resolution; Resolvents; SYM; Symmetric polynomials; theory; Transformations", language = "French", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Functions; Mathematics computing; Polynomials; Symbol manipulation", } @InProceedings{vanHulzen:1989:COP, author = "J. A. {van Hulzen} and B. J. A. Hulshof and B. L. Gates and M. C. {van Heerwaarden}", title = "A code optimization package for {REDUCE}", crossref = "Gonnet:1989:PAI", pages = "163--170", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p163-van_hulzen/", abstract = "A survey of the strategy behind and the facilities of a code optimization package for REDUCE are given. The authors avoid a detailed discussion of the different algorithms and concentrate on the user aspects of the package. Examples of straightforward and more advanced usage are shown.", acknowledgement = ack-nhfb, affiliation = "Twente Univ., Dept. of Comput. Sci., Enschede, Netherlands", classification = "C6130 (Data handling techniques); C6150C (Compilers, interpreters and other processors); C7310 (Mathematics)", keywords = "algorithms; Code optimization package; Compilers; REDUCE; theory; User aspects", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.2.2} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Compilers.", thesaurus = "Mathematics computing; Optimisation; Program compilers; Symbol manipulation", } @InProceedings{Vinette:1989:USC, author = "F. Vinette and J. Cizek", title = "The use of symbolic computation in solving some nonrelativistic quantum mechanical problems", crossref = "Gianni:1989:SAC", pages = "85--95", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Stresses the importance of symbolic computation languages as a new research tool in applied mathematics. The treatment of some non-relativistic quantum mechanical problems are presented as illustrations of the use of the symbolic computation language MAPLE developed at the University of Waterloo. Emphasis is given on the possibility to manipulate expressions symbolically, to perform rapidly tedious operations as well as to work in rational arithmetic. Another important feature will consist in the interface of MAPLE and FORTRAN.", acknowledgement = ack-nhfb, affiliation = "Dept. of Appl. Math., Waterloo Univ., Ont., Canada", classification = "A0365D (Functional analytical methods); C7320 (Physics and Chemistry)", keywords = "Applied mathematics; Expression manipulation; FORTRAN; Interface; MAPLE; Nonrelativistic quantum mechanical problems; Symbolic computation languages; Symbolic manipulation", thesaurus = "High level languages; Physics computing; Quantum theory; Symbol manipulation", } @InProceedings{Watt:1989:FPM, author = "S. M. Watt", title = "A fixed point method for power series computation", crossref = "Gianni:1989:SAC", pages = "206--217", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents a novel technique for manipulating structures which represent infinite power series. The technique described allows a power series to be defined in a very natural but computationally inefficient way and transforms it to an equivalent, efficient form. This is achieved by using a fixed point operator on the delayed part to remove redundant calculations. The paper describes this fixed point method and the class of problems to which it is applicable. It has been used in Scratchpad II to improve the performance of a number of operations on infinite series, including division, reversion, special functions and the solution of linear and non-linear ordinary differential equations. A few examples are given of the method and of the speed up obtained. To illustrate, the computation of the first $n$ terms of $\exp(u)$ for a dense, infinite series $u$ is reduced from $O(n^4)$ to $O(n^2)$ coefficient operations, the same as required by the standard on-line algorithms.", acknowledgement = ack-nhfb, affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Delayed part; Fixed point method; Fixed point operator; Infinite power series; Power series computation; Redundant calculations; Scratchpad II", thesaurus = "Computational complexity; Mathematics computing", } @InProceedings{Weerawarana:1989:GPC, author = "S. Weerawarana and P. S. Wang", title = "{GENCRAY}: a portable code generator for {Cray} {Fortran}", crossref = "Gonnet:1989:PAI", pages = "186--191", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p186-weerawarana/", abstract = "The authors have applied these concepts to finite element analysis. Their research resulted in the software systems FINGER and GENTRAN, both written in Franz LISP. FINGER, derives element strain-displacement matrices and stiffness matrices based on user-supplied parameters. The derived codes involve declarations, expressions, arrays, functions and subroutines. These quantities are represented by LISP internal data structures that must be generated into numerical code by a code translation process. This is the function of GENTRAN which can translate MACSYMA representations into f77, ratfor, or C. GENCRAY is a code generation package similar to GENTRAN but different in many respects. The output of GENCRAY is f77 or Cray Fortran-77 (CFT77) code. CFT77 is a superset of f77 and is the standard Fortran used on Cray supercomputers. The authors present the design of GENCRAY, the steps of code translation, its implementation, features for generating vectorizable and parallel code for the Cray, and how a user can customize GENCRAY to suite different purposes.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. Sci., Kent State Univ., OH, USA", classification = "C6115 (Programming support); C6130 (Data handling techniques); C6150C (Compilers, interpreters and other processors); C7310 (Mathematics)", keywords = "algorithms; Code generation package; Code translation; Cray Fortran; Data structures; FINGER; Finite element analysis; GENCRAY; GENTRAN; Portable code generator; Supercomputers; theory", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Automatic programming; Finite element analysis; Mathematics computing; Parallel programming; Program interpreters; Software portability; Symbol manipulation", } @InProceedings{Weispfenning:1989:EDP, author = "V. Weispfenning", title = "Efficient decision procedures for locally finite theories. {II}", crossref = "Gianni:1989:SAC", pages = "262--273", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", note = "For pt. I, see AECC-3, Grenoble, Springer LNCS, vol. 229,", abstract = "Let $T$ be a finitely axiomatized, universal theory in a finite, first-order language $L$, and suppose $T$ has a model companion $T'$ with only finitely many countable models. $T$ is uniformly locally finite, say with generating function $g: N$ to $N$. The author shows the existence of a further function $am: N$ to $N$ measuring the extent to which $\mbox{Mod(T)}$ fails to satisfy the amalgamation property. The main result is as follows: There exist explicitly described uniform decision and quantifier elimination procedures for $T'$, whose asymptotic complexity can be bounded from above by an elementary recursive function in $g$ and am, without any further reference to $T$ or $T'$. A corresponding result (with $g$ replaced by $d$) holds, if $T$ is not finitely axiomatized, provided there is a function $d: N$ to $N$ bounding the size of suitable descriptions of $n$-generated $T$-models.", acknowledgement = ack-nhfb, affiliation = "Lehrstuhl fur Math., Passau Univ., West Germany", classification = "C1140E (Game theory); C4210 (Formal logic)", keywords = "Asymptotic complexity; Decision procedures; First-order language; Generating function; Locally finite theories; Quantifier elimination procedures", thesaurus = "Decision theory; Formal logic", } @InProceedings{White:1989:CF, author = "N. L. White and T. McMillan", title = "{Cayley} factorization", crossref = "Gianni:1989:SAC", pages = "521--533", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "An important problem in computer-aided geometric reasoning is to automatically find geometric interpretations for algebraic expressions. For projective geometry this question can be reduced to the Cayley factorization problem. A Cayley factorization of a homogeneous bracket polynomial $P$ is a Cayley algebra expression (using only the join and meet operations) which evaluates to P. The authors give an introduction to both Cayley algebra and bracket algebra. The main result of the paper is an algorithm which solves the Cayley factorization problem in the important special case that $P$ is multilinear.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Florida Univ., Gainesville, FL, USA", classification = "C4210 (Formal logic); C7310 (Mathematics)", keywords = "Algebraic expressions; Bracket algebra; Cayley factorization; Computer-aided geometric reasoning; Homogeneous bracket polynomial; Projective geometry", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Winkler:1989:GDA, author = "F. Winkler", title = "A geometrical decision algorithm based on the {Gr{\"o}bner} bases algorithm", crossref = "Gianni:1989:SAC", pages = "356--363", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Gr{\"o}bner bases have been used in various ways for dealing with the problem of geometry theorem proving as posed by Wu (1978). Kutzler and Stifter (1986) have proposed a procedure centered around the computation of a basis for the module of syzygies of the geometrical hypotheses. The author elaborates this approach and extends it to a complete decision procedure. Also, in geometry theorem proving the problem of constructing subsidiary (or degeneracy) conditions arises. Such subsidiary conditions usually are not uniquely determined and obviously one wants to keep them as simple as possible. This problem, however, has not received enough attention in the geometry theorem proving literature. The author's algorithm is able to construct the simplest subsidiary conditions with respect to certain predefined criteria, such as lowest degree or dependence on a given set of variables.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C4190 (Other numerical methods); C4210 (Formal logic)", keywords = "Geometrical decision algorithm; Gr{\"o}bner bases algorithm; Geometry theorem proving; Complete decision procedure; Subsidiary conditions", thesaurus = "Computational geometry; Theorem proving", } @InProceedings{Winkler:1989:KPB, author = "F. Winkler", title = "{Knuth--Bendix} procedure and {Buchberger} algorithm-a synthesis", crossref = "Gonnet:1989:PAI", pages = "55--67", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p55-winkler/", abstract = "The Knuth--Bendix procedure for the completion of a rewrite rule system and the Buchberger algorithm for computing a Gr{\"o}bner basis of a polynomial ideal are very similar in two respects: they both start with an arbitrary specification of an algebraic structure (axioms for an equational theory and a basis for a polynomial ideal, respectively) which is transformed to a very special specification of this algebraic structure (a complete rewrite rule system and a Gr{\"o}bner basis of the polynomial ideal, respectively). This special specification allows many problems concerning the given algebraic structure to be decided. Moreover, both algorithms achieve their goals by employing the same basic concepts: formation of critical pairs and completion. Although the two methods are obviously related, the exact nature of this relation remains to be clarified. The author shows how the Knuth--Bendix procedure and the Buchberger algorithm can be seen as special cases of a more general completion procedure.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "algorithms; theory; Decidability; Programming theory; Knuth--Bendix procedure; Rewrite rule system; Buchberger algorithm; Gr{\"o}bner basis; Polynomial; Algebraic structure; Equational theory", subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving.", thesaurus = "Decidability; Polynomials; Programming theory; Rewriting systems; Set theory", } @InProceedings{Wissmann:1989:ART, author = "D. Wissmann", title = "Applying rewriting techniques to groups with power-commutation-presentations", crossref = "Gianni:1989:SAC", pages = "378--389", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author applies rewriting techniques to certain types of string-rewriting systems related to power-commutation-presentations for finitely generated (f.g.) abelian groups, f.g. nilpotent groups, f.g. supersolvable groups and f.g. polycyclic groups. The author develops a modified version of the Knuth--Bendix completion procedure which transforms such a string-rewriting system into an equivalent canonical system of the same type. This completion procedure terminates on all admissible inputs and works with a fixed reduction ordering on strings. Since canonical string-rewriting systems have decidable word problem this procedure shows that the systems above have uniformly decidable word problem. In addition, this result yields a new purely combinatorial proof for the well-known uniform decidability of the work problem for the corresponding groups.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Kaiserslautern Univ., West Germany", classification = "C1160 (Combinatorial mathematics); C4210 (Formal logic)", keywords = "Abelian groups; Combinatorial proof; Decidable word problem; Knuth--Bendix completion; Nilpotent groups; Polycyclic groups; Power-commutation-presentations; Rewriting techniques; String-rewriting systems; Supersolvable groups; Uniform decidability", thesaurus = "Decidability; Group theory; Rewriting systems", } @InProceedings{Aberer:1990:NFF, author = "K. Aberer", title = "Normal forms in function fields", crossref = "Watanabe:1990:IPI", pages = "1--7", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p1-aberer/", abstract = "Considers function fields of functions of one variable augmented by the binary operation of composition of functions. It is shown that the straightforward axiomatization of this concept allows the introduction of a normal form for expressions denoting elements in such fields. While the description of this normal form seems relatively intuitive, it is surprisingly difficult to prove this fact. The author presents an algorithm for the normalization of expressions, formulated in the symbolic computer algebra language Mathematica. This allows us to effectively decide compositional identities in such fields. Examples are given.", acknowledgement = ack-nhfb, affiliation = "ETH, Zurich, Switzerland", classification = "C1100 (Mathematical techniques); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Axiomatization; Binary operation; Compositional identities; Function fields; languages; Mathematica; Symbolic computer algebra language", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Algebra; Functions; Symbol manipulation", } @InProceedings{Adamchik:1990:ACI, author = "V. S. Adamchik and O. I. Marichev", title = "The algorithm for calculating integrals of hypergeometric type functions and its realization in {REDUCE} system", crossref = "Watanabe:1990:IPI", pages = "212--224", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p212-adamchik/", abstract = "The most effective and the simplest algorithm for analytical integration was made by O. I. Marichev (1983). This algorithm allows one to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type. It embraces about 70 per cent of integrals which are included in the world reference-literature. It allows one to calculate many other integrals too. The article contains a short description of this algorithm and its realization in the REDUCE system during the process of creation of the INTEGRATOR system.", acknowledgement = ack-nhfb, affiliation = "Byelorussian Univ., Minsk, Byelorussian SSR, USSR", classification = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", keywords = "algorithms; Analytical integration; Convergence; Hypergeometric type functions; INTEGRATOR system; languages; Pascal; REDUCE system; Residue number theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Pascal.", thesaurus = "Convergence of numerical methods; Integration", } @InProceedings{Baaz:1990:SPR, author = "M. Baaz and A. Leitsch", title = "A strong problem reduction method based on function introduction", crossref = "Watanabe:1990:IPI", pages = "30--37", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p30-baaz/", abstract = "Although problem reduction is a very important tool in mathematical practice, relatively little attention has been paid to problem reduction in automated theorem proving. The authors propose problem reduction based on a splitting rule of the form $C$ implies $C'$, where $C\approx{}C_1vC_2,C'\approx{}C_1vC_2',C_2'\approx{}C_2$ $(x\mbox{from}f(y_1,\ldots{},y_n)),(x,y_1,\ldots{},y_n)$ is the set of variables both in $C_1$ and $C_2$ and $f$ is a new function symbol up to this point not occurring in any clause. Finally the authors construct a sequence of clause sets $C_n$ having resolution proofs exponential in $n$ only, but application of the new reduction rule reduces the problem to two problems linear in $n$. Thus it turns out that the introduction of (elementary) quantificational rules into clause logic can strongly influence the structure of proofs and the performance of theorem provers", acknowledgement = ack-nhfb, affiliation = "Inst. fur Algebra und Diskrete Math., Tech. Univ. Wien, Austria", classification = "C4210 (Formal logic)", keywords = "algorithms; Automated theorem proving; Clause logic; Problem reduction; Quantificational rules; Theorem provers; theory", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic. {\bf I.2.3} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and Theorem Proving. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Functions; Theorem proving", xxauthor = "M. Baaz and A. Leitsh", } @InProceedings{Belmesk:1990:EME, author = "M. Belmesk", title = "An execution model for exploiting and-or parallelism in logic programs (abstract)", crossref = "Watanabe:1990:IPI", pages = "288--288", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p288-belmesk/", abstract = "Several models have been developed for parallel execution of logic programming languages. Most of them involve variations of two basic mechanisms: and parallelism and or parallelism. The model developed exploits both the and -and or- parallelism using a compile-time program-level and clause-level data dependence analysis to generate an execution graph that embodies the possible parallel executions. The execution graph is a directed acyclic graph, containing one node per atom of the clause body and two nodes for the head clause. Simple tests on the terms provided at run-time determine which of the different possible executions graph is to be used.", acknowledgement = ack-nhfb, affiliation = "Lifia-Inst. IMAG, Grenoble, France", classification = "C4240 (Programming and algorithm theory)", keywords = "algorithms; And-or parallelism; Execution graph; Execution model; Logic programming languages; Parallel execution", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Logic and constraint programming. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency.", thesaurus = "Logic programming; Parallel programming", } @InProceedings{Bini:1990:PPC, author = "D. Bini and V. Pan", title = "Parallel polynomial computations by recursive processes", crossref = "Watanabe:1990:IPI", pages = "294--294", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p294-bini/", abstract = "Let $\lg$ stand for $\log_2$, $\lg^{(0)}n=n$, $\lg^{(h)}n=\lg\lg^{(h-1)}n,h=1,\ldots{},\lg*n,\lg*n=\min(h,\lg^{(h)}n<=1)$. Given natural $N$, $h$, $1<=h<=\lg*N$, and polynomial $p(x), p(0) \ne 0$, the authors compute $r(x)=p(x)^{-1}\bmod{}x^N$ for the cost $O_A(t,P),t=h\lg{}N, P=(N/h)\lg^{(h)}N$, under the PRAM arithmetic model, that is, the authors need $O(t)$ steps and $O(P)$ processors (with $t$ and $P$ as above), provided $DFT(m)$ costs $O_A(\lg{}m,m)$. For $h=\lg*N$, the cost bounds turn into $O_A(\lg{}N\lg*N,N/\lg*N)$. The results apply to various related computations.", acknowledgement = ack-nhfb, affiliation = "Pisa Univ., Italy", classification = "C4240 (Programming and algorithm theory)", keywords = "algorithms; Computational complexity; Parallel computations; Polynomial computations; PRAM arithmetic model; Recursive processes", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.", thesaurus = "Computational complexity; Parallel algorithms; Polynomials; Recursive functions", } @InProceedings{Bradford:1990:PBA, author = "R. Bradford", title = "A parallelization of the {Buchberger} algorithm", crossref = "Watanabe:1990:IPI", pages = "296--296", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p296-bradford/", abstract = "Describes experiments with a little elementary parallelism applied to Buchberger's algorithm. This is in contrast to Ponder (1988) and Vidal (1990) as gains can be achieved by using the method even on a single processor.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory)", keywords = "algorithms; Buchberger's algorithm; experimentation; languages; Parallelism", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", thesaurus = "Parallel algorithms; Polynomials; Symbol manipulation", } @InProceedings{Cantone:1990:DFE, author = "D. Cantone and V. Cutello", title = "A decidable fragment of the elementary theory of relations and some applications", crossref = "Watanabe:1990:IPI", pages = "24--29", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p24-cantone/", abstract = "The class of purely universal formulae of the elementary theory of relations with equality is shown to have an NP-complete satisfiability problem, under the assumption that there is an a priori bound on the length of quantifier prefixes and the arities of relation variables. In the second part of the paper the authors discuss possible applications in the field of theorem proving in set and graph theory and of consistency checking for queries in relational databases.", acknowledgement = ack-nhfb, affiliation = "Archimedes SRL, Catania, Italy", classification = "C4210 (Formal logic); C4250 (Database theory)", keywords = "algorithms; Consistency checking; Decidable; Elementary theory of relations; Graph theory; Relational databases; Satisfiability; Theorem proving; theory", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computability theory. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", thesaurus = "Database theory; Decidability; Relational databases; Theorem proving", } @InProceedings{Char:1990:PRS, author = "B. W. Char", title = "Progress report on a system for general-purpose parallel symbolic algebraic computation", crossref = "Watanabe:1990:IPI", pages = "96--103", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p96-char/", abstract = "Discusses on-going work on large-grained parallel symbolic computation using a system based on Maple and Linda. The prototype runs on a Sequent Balance. The approach can be used with most existing algebra/symbol manipulation systems and provides the potential to deliver of parallel symbolic computation on a variety of architectures (e.g. shared memory, hypercubes, networked workstations). Parallel speedup was achieved on a variety of algebraic problems, although many significant improvements in efficiency remain to be achieved.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN, USA", classification = "C4240 (Programming and algorithm theory)", keywords = "Algebraic computation; design; languages; Large-grained; Linda; Maple; Parallel symbolic computation; performance; Sequent Balance; Symbol manipulation systems", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Linda. {\bf D.1.3} Software, PROGRAMMING TECHNIQUES, Concurrent Programming.", thesaurus = "Parallel processing; Symbol manipulation", } @InProceedings{Chen:1990:ACF, author = "Guoting Chen", title = "An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point", crossref = "Watanabe:1990:IPI", pages = "231--235", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p231-chen/", abstract = "Discusses an algorithm for the computation of the formal solutions of differential systems in the neighborhood of an irregular singular point. In the reduction of the differential systems, the author uses its Arnold--Wasow's canonical form. He discusses also an algorithm for the reduction of the differential system to its Arnold--Wasow's canonical form. Then he discusses the results of a shearing transformation on this canonical form and gets the convergence of the algorithm. This paper consists of a complete study of the problem of computations of the formal solutions of differential systems in the neighborhood of a singular point (regular or irregular).", acknowledgement = ack-nhfb, affiliation = "LMC, IMAG INPC CNRS, Grenoble, France", classification = "C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; Computation; Convergence; Differential systems; Formal solutions; Irregular singular point; languages; Shearing transformation", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.", thesaurus = "Convergence of numerical methods; Differential equations; Symbol manipulation", } @InProceedings{Chen:1990:IAM, author = "G. Chen and I. Gil", title = "The implementation of an algorithm in {Macsyma}: computing the formal solutions of differential systems in the neighborhood of regular singular point", crossref = "Watanabe:1990:IPI", pages = "307--307", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p307-chen/", abstract = "Discusses the problems arising in the implementation in Macsyma of a direct algorithm for computing the formal solutions of differential systems in the neighborhood of regular singular point. The differential system to be considered is of the form $x^h dy/dx=A(x)y$ with $A(x)=A_0+A_1x+\ldots{}$ is an $n$ by $n$ matrices of formal series.", acknowledgement = ack-nhfb, affiliation = "Equipe de Calcul Parallele et Calcul Formel, Grenoble, France", classification = "C4170 (Differential equations)", keywords = "algorithms; Differential systems; Formal solutions; Macsyma; Regular singular point", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", thesaurus = "Differential equations; Symbol manipulation", } @InProceedings{Cherief:1990:AMP, author = "F. Cherief", title = "An algebraic model for the parallel interpretation of equationally defined functions (abstract)", crossref = "Watanabe:1990:IPI", pages = "285--285", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p285-cherief/", abstract = "Summary form only given. Algebraic Languages are well suited for rapid prototyping. Their operational semantics is given by means of term rewriting systems. Here, the author proposes a new approach for the parallel interpretation of term rewriting systems by mapping every defined function into parallel processes. The target language is HAL, a new process algebra where parallel computations are described as a set of interconnected processes which communicate through the explicit sending and receiving of messages. HAL is derived from LOTOS, FP2 and CCS. In HAL an event is a set of simultaneous communications. Each communication within an event transports one term along one connector. When two connectors are linked, the corresponding communication unifies the two terms. This essential feature makes it possible to perform all computations via communications (computation=communication). In the case considered here unification reduces to matching.", acknowledgement = ack-nhfb, affiliation = "LIFIA-IMAG, Grenoble, France", classification = "C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "Algebraic model; algorithms; HAL; Interconnected processes; languages; Operational semantics; Parallel interpretation; Prototyping; Simultaneous communications; Target language; Term rewriting systems", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.3.2} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics of Programming Languages, Algebraic approaches to semantics.", thesaurus = "Formal languages; Parallel languages; Rewriting systems", } @InProceedings{Chou:1990:ARG, author = "Shang-Ching Chou", title = "Automated reasoning in geometries using the characteristic set method and {Gr{\"o}bner} basis method", crossref = "Watanabe:1990:IPI", pages = "255--260", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p255-chou/", abstract = "Presents an overview of the applications of the characteristic set method and the Gr{\"o}bner basis method to automated reasoning in elementary geometries, differential geometries, and mechanics.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA", classification = "C4190 (Other numerical methods); C4290 (Other computer theory); C7310 (Mathematics)", keywords = "Characteristic set method; Gr{\"o}bner basis method; Automated reasoning; Elementary geometries; Differential geometries; algorithms; verification", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving.", thesaurus = "Computational geometry; Inference mechanisms; Symbol manipulation", } @InProceedings{Chou:1990:MMG, author = "Shang-Ching Chou and Xiao-Shan Gao", title = "Methods for mechanical geometry formula deriving", crossref = "Watanabe:1990:IPI", pages = "265--270", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p265-chou/", abstract = "A precise formulation for the relations among certain variables under a set of polynomial equations and a set of polynomial inequations (to exclude certain special cases which cannot be excluded by the selection of parameters alone) is given. Several methods are presented to find such relations. The methods have been implemented and used to find geometry formulas, to discover geometry theorems, and to find geometry locus equations. About 120 non-trivial problems have been solved using the methods.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Texas Univ., Austin, TX, USA", classification = "C1120 (Analysis); C7310 (Mathematics)", keywords = "algorithms; Geometry formulas; Geometry locus equations; Geometry theorems; Mechanical geometry; Polynomial equations; Polynomial inequations", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", thesaurus = "Computational geometry; Polynomials; Symbol manipulation", } @InProceedings{Codognet:1990:EDU, author = "P. Codognet", title = "Equations, disequations and unsolvable subsets (abstract)", crossref = "Watanabe:1990:IPI", pages = "289--289", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p289-codognet/", abstract = "Presents a framework for solving a system of equations and disequations that allow to determine, upon unsolvability, the `cause' of the failure, i.e. the minimal unsolvable subsets of equations and disequations responsible of it.", acknowledgement = ack-nhfb, affiliation = "INRIA, Le Chesnay, France", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Disequations; Equations; Failure; Unsolvability; Unsolvable subsets", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computability theory. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", thesaurus = "Algebra; Symbol manipulation", } @InProceedings{Cooperman:1990:RBC, author = "G. Cooperman and L. Finkelstein and N. Sarawagi", title = "A random base change algorithm for permutation groups", crossref = "Watanabe:1990:IPI", pages = "161--168", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p161-cooperman/", abstract = "A new random base change algorithm is presented for a permutation group $G$ acting on $n$ points whose worst case asymptotic running time is better for groups with a small to moderate size base than any known deterministic algorithm. To achieve this time bound, the algorithm requires a \mbox{Rand}om generator $\mbox{Rand}(G)$ producing a Random element of $G$ with the uniform distribution and so that each call to $\mbox{Rand}(G)$ takes time $O(\log(\bmod{}G\bmod{})n)$. The random base change algorithm has probability $1-1/\bmod{}G\bmod{}^2$ of completing in time $ O(\log^2(\bmod{}G\bmod{})n)$ and outputting a data structure for representing the point stabilizer sequence relative to the new ordering which requires $O(\log(\bmod{}g\bmod{})n)$ space and which can be used to test group membership in time $O(\log(\bmod{}G\bmod{})n)$. The time to build a data structure for computing a $\mbox{Rand}(G)$ with the above properties from a strong generating set for $G$ is dominated by the time to construct the strong generating set of from the original set of generators.", acknowledgement = ack-nhfb, affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA, USA", classification = "C4240 (Programming and algorithm theory)", keywords = "algorithms; Asymptotic running time; Data structure; Deterministic algorithm; Permutation groups; Point stabilizer sequence; Random base change algorithm; Random generator; Space complexity; Time complexity", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", thesaurus = "Algorithm theory; Computational complexity; Data structures; Group theory; Random functions", } @InProceedings{Doleh:1990:SSI, author = "Y. Doleh and P. S. Wang", title = "{SUI}: a system independent user interface for an integrated scientific computing environment", crossref = "Watanabe:1990:IPI", pages = "88--95", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p88-doleh/", abstract = "The design and implementation of a Scientific User Interface is presented. Written in the C language, SUI is a window-menu-mouse oriented graphical user interface that is designed to provide a modern and integrated computing environment for scientific work. SUI can serve multiple client systems in parallel including symbolic, numeric, graphics and document formatting systems. SUI achieves hardware and operating system independence as well as network transparency by employing the X11 protocols and achieves client system independence by defining a client-SUI protocol that is simple and effective. Features of SUI includes input editing, history, 2-D mathematical expression display, interactive selection of subexpressions, interactive display and manipulation of 2-D and 3-D plots of mathematical functions, cut and paste with syntax translation, command templates, incremental 2-D display of mathematical input, and interactive configuration.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH, USA", classification = "C6180 (User interfaces)", keywords = "2-D display; 3-D plots; C language; Command templates; Cut and paste; Document formatting; Graphical user interface; Graphics; History; Input editing; Integrated computing environment; Integrated scientific computing environment; Interactive display; languages; Mathematical expression display; Mathematical functions; Network transparency; Numeric; Scientific User Interface; SUI; Symbolic; Syntax translation; Window-menu-mouse oriented", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C. {\bf I.3.6} Computing Methodologies, COMPUTER GRAPHICS, Methodology and Techniques, Interaction techniques. {\bf I.3.1} Computing Methodologies, COMPUTER GRAPHICS, Hardware Architecture, Input devices. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Graphical user interfaces; Symbol manipulation", } @InProceedings{Fateman:1990:ATD, author = "R. J. Fateman", title = "Advances and trends in the design and construction of algebraic manipulation systems", crossref = "Watanabe:1990:IPI", pages = "60--67", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p60-fateman/", abstract = "Compares and contrast several techniques for the implementation of components of an algebraic manipulation system. On one hand is the mathematical algebraic approach which characterizes (for example) IBM's Scratchpad II. On the other hand is the more ad hoc approach which characterizes many other popular systems (for example, Macsyma, Reduce, Maple, and Mathematica). While the algebraic approach has generally positive results, careful examination suggests that there are significant remaining problems, especially in the representation and manipulation of analytical, as opposed to algebraic mathematics. The author describes some of these problems, and some general approaches for solutions.", acknowledgement = ack-nhfb, affiliation = "California Univ., Berkeley, CA, USA", classification = "C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Algebraic manipulation systems; Algebraic mathematics; design; languages; Macsyma; Maple; Mathematica; Mathematical algebraic; Reduce; Scratchpad II", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.", thesaurus = "Algebra; Symbol manipulation", } @InProceedings{Faure:1990:MS, author = "C. Faure", title = "A {Meta} simplifier", crossref = "Watanabe:1990:IPI", pages = "290--290", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p290-faure/", abstract = "The simplification process is a key point in computer algebra systems. The author presents a model of a simplifier based on two ideas: homogenizing the computation over numerical and formal expressions, and building a simplifier completely reachable by the user. In order to evaluate numerical expressions, the simplifier calls functions which compute the result or raise a runtime type error. Formal expressions are transformed modulo the properties of the operators. For homogenizing those two processes, three basic mechanisms come out: simplification by properties, type checking, evaluation. Moreover a fourth mechanism using rewriting rules is necessary to compute nonstandard transformations needed by the user.", acknowledgement = ack-nhfb, affiliation = "INRIA, Centre de Sophia-Antipolis, Valbonne, France", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Computer algebra systems; design; Evaluation; Homogenization; Meta amplifier; Nonstandard transformations; Rewriting rules; Run-time error; Runtime type error; Simplification; Type checking", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", thesaurus = "Algebra; Rewriting systems; Symbol manipulation", } @InProceedings{Fee:1990:CCC, author = "G. J. Fee", title = "Computation of {Catalan}'s constant using {Ramanujan}'s formula", crossref = "Watanabe:1990:IPI", pages = "157--160", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p157-fee/", abstract = "The author uses some formulas due to Ramanujan for the multiple precision computation of Catalan's constant $C=0.915\ldots{}$. The algorithm has been implemented in Maple and $C$ has been computed to 20000 decimal places. The resulting program is very simple yet efficient. It computes $N$ digits of $C$ in $O(N^2)$ time and $O(N)$ space.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "B0290D (Functional analysis); C4120 (Functional analysis); C4240 (Programming and algorithm theory)", keywords = "algorithms; C; Catalan constant; Function evaluation; languages; Maple; Ramanujan formula", subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational complexity; Function evaluation", } @InProceedings{Fitch:1990:DSR, author = "J. Fitch", title = "A delivery system for {REDUCE}", crossref = "Watanabe:1990:IPI", pages = "76--81", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p76-fitch/", abstract = "A nonLISP delivery system for REDUCE is described and compared with other implementations of REDUCE for speed and size, as well as ease of porting. The mechanism for this delivery system is direct compilation of the REDUCE sources into ANSI C, which is then compiled and linked together with some support code for arithmetic and space administration. The resulting system is compared with a number of other implementations of true REDUCE, and is shown to be similar in size, but faster. The time to port the system is measured in hours. Also considered are the difficulties in this method of delivering LISP code, and an assessment of the loss of flexibility.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C7310 (Mathematics)", keywords = "algorithms; Delivery system; languages; LISP code; REDUCE", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, LISP. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Compilers.", thesaurus = "Algebra; Symbol manipulation", } @InProceedings{Franova:1990:PIC, author = "M. Franov{\'a}", title = "{PRECOMAS}. {An} implementation of constructive matching methodology", crossref = "Watanabe:1990:IPI", pages = "16--23", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p16-franova/", abstract = "The system PRECOMAS (PRoofs Educed by COnstructive MATching of Synthesis) implements the Constructive Matching methodology for automatic constructions of programs from formal specifications. The author describes briefly the goal of PRECOMAS, its logical background and the CM method applied to proving atomic formulae. She shows how the user of the system is involved in solving a program synthesis problem. She shows that this interaction does not concern the problem of guiding the program synthesis process, this being solved by CM. The experimental version serves to confirm that the system is worth being developed.", acknowledgement = ack-nhfb, affiliation = "CNRS, Univ. Paris Sud, Orsay, France", classification = "C4240 (Programming and algorithm theory); C6115 (Programming support)", keywords = "algorithms; Atomic formulae; Constructive Matching; design; Formal specifications; PRECOMAS; Program synthesis; theory", subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf D.1.2} Software, PROGRAMMING TECHNIQUES, Automatic Programming.", thesaurus = "Formal logic; Programming environments", } @InProceedings{Ganzha:1990:ARS, author = "V. G. Ganzha and S. V. Meleshko and V. P. Shelest", title = "Application of {REDUCE} system for analyzing consistency of systems of {PDE}'s", crossref = "Watanabe:1990:IPI", pages = "301--301", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p301-ganzha/", abstract = "Summary form only given. A consistency analysis of differential equation systems involves a sequence of differential-algebraic operations. At present there are known two methods: the Cartan's and the Riquier--Janet--Kuranishi (RJK) method which are equivalent. The implementation of the both of the methods with the purpose of their practical application leads to large symbolic computations which often cannot be performed without a computer.", acknowledgement = ack-nhfb, affiliation = "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR", classification = "C4170 (Differential equations); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Consistency; Consistency analysis; Differential equation systems; Partial differential equations; Riquier--Janet--Kuranishi method; RJK method", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", thesaurus = "Computational complexity; Partial differential equations; Symbol manipulation", } @InProceedings{Ganzha:1990:LAS, author = "V. G. Ganzha and M. Yu. Shashkov", title = "Local approximation study of difference operators by means of {REDUCE} system", crossref = "Watanabe:1990:IPI", pages = "185--192", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p185-ganzha/", abstract = "Describes new algorithms and programs in the REDUCE system for the automated study of a local order of the approximation of difference operator written on non-orthogonal meshes. The performance of the program is demonstrated by local approximation of several difference operators in one and two-dimensional cases.", acknowledgement = ack-nhfb, affiliation = "Inst. of Theor. and Appl. Mech., Novosibirsk, USSR", classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation); C4170 (Differential equations)", keywords = "algorithms; Approximation; Difference operators; languages; Local order; Nonorthogonal meshes; Numerical methods; performance; REDUCE system", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Difference equations; Function approximation", } @InProceedings{Gatemann:1990:SSP, author = "K. Gatemann", title = "Symbolic solution polynomial equation systems with symmetry", crossref = "Watanabe:1990:IPI", pages = "112--119", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p112-gatemann/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Gatermann:1990:SSP, author = "K. Gatermann", title = "Symbolic solution of polynomial equation systems with symmetry", crossref = "Watanabe:1990:IPI", pages = "112--119", year = "1990", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Systems of polynomial equations often have symmetry. The Buchberger algorithm which may be used for the solution ignores this symmetry. It is restricted to moderate problems unless factorizing polynomials are found leading to several smaller systems. Therefore two methods are presented which use the symmetry to find factorizing polynomials, decompose the ideal and thus decrease the complexity of the system a lot. In a first approach projections determine factorizing polynomials as input for the solution process, if the group contains reflections with respect to a hyperplane. Two different ways are described for the symmetric group $S_m$ and the dihedral group $D_m$. While for $S_m$ subsystems are ignored if they have the same zeros modulo $G$ as another subsystem, for the dihedral group $D_m$ polynomials with more than two factors are generated with the help of the theory of linear representations and restrictions are used as well. These decomposition algorithms are independent of the finally used solution technique. The author uses the REDUCE package Gr{\"o}bner to solve examples which illustrate the efficiency of the REDUCE program. A short introduction to the theory of linear representations is given. In a second approach problems of another class are transformed such that more factors are found during the computation; these transformations are based on the theory of linear representations. Examples illustrate these approaches. The range of solvable problems is enlarged significantly.", acknowledgement = ack-nhfb, affiliation = "Konrad Zuse Zentrum fur Inf. Berlin, Germany", classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", keywords = "Symbolic solution; Polynomial equation systems; Buchberger algorithm; Factorizing polynomials; Symmetry; Complexity; Symmetric group; Dihedral group; Linear representations; REDUCE package; Gr{\"o}bner; Solvable problems", thesaurus = "Computational complexity; Polynomials; Symbol manipulation", } @InProceedings{Gerdt:1990:CGN, author = "V. P. Gerdt and A. Yu. Zharkov", title = "Computer generation of necessary integrability conditions for polynomial nonlinear evolution systems", crossref = "Watanabe:1990:IPI", pages = "250--254", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p250-gerdt/", abstract = "Uses the symmetry approach to establish an efficient program in REDUCE for verifying necessary integrability conditions for polynomial-nonlinear evolution equations and systems in one-spatial and one-temporal dimensions. These conditions follow from the existence of higher infinitesimal symmetries and conservation law densities. The authors briefly consider the mathematical background of the symmetry approach to the problem of integrability. In the description of the algorithms and their implementation in REDUCE they present in particular the basic algorithm for reversing the operator of the total derivative with respect to the spatial variable. One of the most interesting applications of the present program is the problem of classification when the complete list of integrable equations from a given multiparametric family is needed. In this case the program generates necessary integrability conditions in form of a system of nonlinear algebraic equations in the parameters present in the initial equations. In spite of their often complicated structure, there are systems for which the solution can be found in exact form by applying the technique of Gr{\"o}bner basis. The authors present three examples of evolution equations for which this system can in fact be solved.", acknowledgement = ack-nhfb, affiliation = "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Integrability; Polynomial nonlinear evolution systems; REDUCE; Symmetry approach; Spatial variable; Nonlinear algebraic equations; Gr{\"o}bner basis; algorithms; languages; verification", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Differential equations; Symbol manipulation", } @InProceedings{Gerdt:1990:SAS, author = "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov", title = "Solving algebraic systems which arise as necessary integrability conditions for polynomial-nonlinear evolution equations", crossref = "Watanabe:1990:IPI", pages = "299--299", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p299-gerdt/", abstract = "The investigation of the problem of integrability of polynomial-nonlinear evolution equations in particular, verifying the existence of the higher symmetries and conservation laws can often be reduced to the problem of finding the exact solution of a complicated system of nonlinear algebraic equations. It is remarkable that these algebraic equations can be not only obtained completely automatically by computer but also often not only completely solved by computer, in spite of their complicated structure and often infinitely many solutions. The authors demonstrate this fact using the Gr{\"o}bner basis method and obtain all (infinitely many) solutions of the systems of algebraic equations which are equivalent to integrability of three different multiparametric families of NLEEs: the seventh order scalar KdV-like equations, the seventh order MKdV-like equations, and the third order coupled KdV-like systems.", acknowledgement = ack-nhfb, affiliation = "Lab. of Comput. Tech. and Autom., JINR, Moscow, USSR", classification = "C4170 (Differential equations); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Algebraic systems; Integrability; Polynomial-nonlinear evolution equations; Nonlinear algebraic equations; Gr{\"o}bner basis; Algebraic equations; NLEEs; verification", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf K.8} Computing Milieux, PERSONAL COMPUTING, IBM PC.", thesaurus = "Differential equations; Nonlinear equations; Polynomials; Symbol manipulation", } @InProceedings{Glueck:1990:AMT, author = "R. Glueck and V. F. Turchin", title = "Application of metasystem transition to function inversion and transformation", crossref = "Watanabe:1990:IPI", pages = "286--287", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p286-glueck/", abstract = "The authors prove by construction an application considered theoretically by Turchin (1972) that self-application of metacomputation will allow the automatic construction of inverse algorithms, in particular the algorithm of binary subtraction from the algorithm of binary addition. Further, they present results concerning the algorithmic construction of an efficient pattern matcher, which leads to the Knuth, Morris and Pratt algorithm. These results were achieved with the first working model of a self-applicable supercompiler system, implementing the concept of metacomputation.", acknowledgement = ack-nhfb, affiliation = "Univ. of Technol. Vienna, Austria", classification = "C4240 (Programming and algorithm theory)", keywords = "Algorithmic construction; algorithms; Function inversion; Inverse algorithms; Metacomputation; Metasystem transition; Pattern matcher; theory; Transformation; verification", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Pattern matching.", thesaurus = "Algorithm theory; Computation theory; Symbol manipulation", } @InProceedings{Grigoriev:1990:CIT, author = "D. Yu. Grigoriev", title = "Complexity of irreducibility testing for a system of linear ordinary differential equations", crossref = "Watanabe:1990:IPI", pages = "225--230", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p225-grigoriev/", abstract = "Let a system of linear ordinary differential equations of the first order $Y'=AY$ be given, where $A$ is $n*n$ matrix over a field $F(X)$, assume that the degree $deg_X(A)<d$ and the size of any coefficient occurring in $A$ is at most $M$. The system $Y'=AY$ is called reducible if it is equivalent (over the field $F(X)$) to a system $Y'_1=A_1Y_1$. An algorithm is described for testing irreducibility of the system, with an expression for the time complexity.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci., Leningrad, USSR", classification = "C4170 (Differential equations); C4240 (Programming and algorithm theory)", keywords = "algorithms; Irreducibility; Irreducibility testing; Linear ordinary differential equations; Time complexity", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational complexity; Differential equations", } @InProceedings{Grigoriev:1990:HTS, author = "D. Yu. Grigoriev", title = "How to test in subexponential time whether two points can be connected by a curve in a semialgebraic set", crossref = "Watanabe:1990:IPI", pages = "104--105", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p104-grigoriev/", abstract = "A subexponential-time algorithm is designed which finds the number of connected components of a semialgebraic set given by a quantifier-free formula of the first-order theory of real closed fields. Moreover, the algorithm allows for any two points from the semialgebraic set to test, whether they belong to the same connected component. Decidability of the mentioned problems follows from the quantifier elimination method in the first-order theory of real closed fields. However, complexity bound of this method is nonelementary, in particular, one cannot estimate it by any finite iteration of the exponential function. G. Collins (1975) has proposed a construction of cylindrical algebraic decomposition which allows to solve these problems in exponential time.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. V.A Steklov, Inst. of Acad. of Sci., Leningrad, USSR", classification = "C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "algorithms; Complexity; Connected components; Cylindrical algebraic decomposition; Decidability; Real closed fields; Semialgebraic set; Subexponential time; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational complexity; Computational geometry; Decidability; Symbol manipulation", } @InProceedings{Hong:1990:IPO, author = "Hooh Hong", title = "An improvement of the projection operator in cylindrical algebraic decomposition", crossref = "Watanabe:1990:IPI", pages = "261--264", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p261-hong/", abstract = "The Cylindrical Algebraic Decomposition (CAD) method of Collins (1975) decomposes $r$-dimensional Euclidean space into regions over which a given set of polynomials have constant signs. An important component of the CAD method is the projection operation: given a set A of $r$-variate polynomials, the projection operation produces a set $P$ of $(r-1)$-variate polynomials such that a CAD of $r$-dimensional space for $A$ can be constructed from a CAD of $(r-1)$-dimensional space for $P$. The author presents an improvement to the projection operation. By generalizing a lemma on which the proof of the original projection operation is based, he is able to find another projection operation which produces a smaller number of polynomials.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Ohio State Univ., Columbus, OH, USA", classification = "C4190 (Other numerical methods); C4290 (Other computer theory); C7310 (Mathematics)", keywords = "algorithms; CAD; Cylindrical Algebraic Decomposition; Euclidean space; Polynomials; Projection operator", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Computational geometry; Polynomials; Symbol manipulation", } @InProceedings{Kalkbrener:1990:SSB, author = "M. Kalkbrener", title = "Solving systems of bivariate algebraic equations by using primitive polynomial remainder sequences", crossref = "Watanabe:1990:IPI", pages = "295--295", year = "1990", bibdate = "Sat Apr 25 12:58:10 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p295-kalkbrener/", abstract = "Let $K$ be a field, $K$ the algebraic closure of $K$ and $f=q_m(x)y^m+ \cdots{} +q_o(x)$ a polynomial in $K(x,y)$ with $q_m \ne 0$. The polynomial $q_m$ is called the leading coefficient of $f$, abbreviated $lc(f)$. The degree of $f$ in $y$ is denoted by $\deg(f)$. Let $f_1, f_2,\ldots{}, f_k$ be the primitive polynomial remainder sequence of the primitive polynomials $f_1$ and $f_2$ in $K(x,y)$, abbreviated $pprs(f_1,f_2)$. For every $i$ in $(2,\ldots{},k-1)$ let $c_i$ be the content of the pseudoremainder of $f_{i-}1$ and $f_i,l_i:=lc(f_i)^{deg(fi-1)-deg(fi)+1},M_i:=(p\in{}K(x)-K\bmod{}p)$ is irreducible, monic and there exists a $j$ in $N$ such that $p^j$ divides $c_2\ldots{}c_i$ but not $l_2\ldots{}l_i$, $(\pi,1,\ldots{},\pi,s_i):=(p\in{}Mi\bmod{}p\in{}M_r {\rm for } r=2,\ldots{},i-1)$ and $e_i:=\pi,1\ldots{}pis_i.e_2,\ldots{},e_k-1$ is called the elimination sequence of $f_1$ and $f_2$, abbreviated $\mbox{elimseq}(f_1, f_2)$. Theorem 1 Let $a=(a_1,a_2)$ be an element of $K^2$. $f_1(a)=f_2(a)=0$ iff $f_k(a)=0$ or there exists an $i$ in $(2,\ldots{},k-1)$ with $(f_i/f_k)(a)=e_i(a)=0$. The correctness of bsolve is based on this result. By using this algorithm arbitrary systems of bivariate algebraic equations can be solved.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Algebraic closure; Algorithm correctness; algorithms; Bivariate algebraic equations; Bsolve; Primitive polynomial remainder sequences", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Algebra; Program verification; Symbol manipulation", } @InProceedings{Kaltofen:1990:MRS, author = "E. Kaltofen and {Lakshman Y. N.} and J.-M. Wiley", title = "Modular rational sparse multivariate polynomial interpolation", crossref = "Watanabe:1990:IPI", pages = "135--139", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p135-kaltofen/", abstract = "The problem of interpolating multivariate polynomials whose coefficient domain is the rational numbers is considered. The effect of intermediate number growth on a speeded Ben-Or and Tiwari algorithm (1988) is studied. Then the newly developed modular algorithm is presented. The computing times for the speeded Ben-Or and Tiwari and the modular algorithm are compared, and it is shown that the modular algorithm is markedly superior.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Computing times; Modular algorithm; Multivariate polynomials; Polynomial interpolation; Rational numbers; Rational sparse polynomials; Symbolic expressions; Time complexity", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational complexity; Interpolation; Polynomials", } @InProceedings{Kapur:1990:RPG, author = "D. Kapur and H. K. Wan", title = "Refutational proofs of geometry theorems via characteristic set computation", crossref = "Watanabe:1990:IPI", pages = "277--284", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p277-kapur/", abstract = "A refutational approach to geometry theorem proving using Ritt--Wu's algorithm for computing a characteristic set is discussed. A geometry problem is specified as a quantifier-free formula consisting of a finite set of hypotheses implying a conclusion, where each hypothesis is either a geometry relation or a subsidiary condition ruling out degenerate cases, and the conclusion is another geometry relation. The conclusion is negated, and each of the hypotheses (including the subsidiary conditions) and the negated conclusion is converted to a polynomial equation. Characteristic set computation is used for checking the inconsistency of a finite set of polynomial equations over an algebraic closed field. The method is contrasted with a related refutational method that used Buchberger's Gr{\"o}bner basis algorithm for the inconsistency check.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., State Univ. of New York, Albany, NY, USA", classification = "C1110 (Algebra); C4210 (Formal logic); C7310 (Mathematics)", keywords = "Algebraic closed field; algorithms; Characteristic set computation; Geometry theorem proving; Polynomial equations; Refutational approach; Ritt--Wu's algorithm; verification", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications.", thesaurus = "Computational geometry; Polynomials; Theorem proving", } @InProceedings{Kohno:1990:RPT, author = "M. Kohno", title = "Reduction problems in the theory of differential equations", crossref = "Watanabe:1990:IPI", pages = "244--249", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p244-kohno/", abstract = "In studying the theory of differential equations, it seems to be better to treat systems of differential equations rather than single differential equations, since the latter are included in a class of the former and the theory can be made clear through full use of matrix calculus. Even some specialists of numerical analysis of differential equations recommend to deal with systems rather than single equations in practical calculation of approximate solutions. The objective of this report is to show an attempt to solve the reduction problems, illustrating some algorithms to be applied by algebraic manipulation system.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Kumamoto Univ., Japan", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algebraic manipulation system; algorithms; Differential equations; Matrix calculus; Reduction problems; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Differential equations; Symbol manipulation", } @InProceedings{Kolyada:1990:SSC, author = "S. V. Kolyada", title = "Systems for symbolic computations in {Boolean} algebra", crossref = "Watanabe:1990:IPI", pages = "291--291", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p291-kolyada/", abstract = "Boolean algebra as scientific discipline has a few features. It is a pure mathematical theory and, on the other hand, an applied mathematical theory too. Boolean algebra is applied, for instance, to improve intelligence of software, to automate integrated circuit design and theorem proving as it can be used to model situation analysis and decision making. Computer algebra system for boolean algebra (APAL-PC) allows one to write and process logical formulae in usual manner. The system APAL-PC is developed for IBM PC personal computers on the basis of the programming language C and universal formula processing tools implemented at Glushkov Institute of Cybernetics. The experience of development of a similar system APAL-ES (implemented in OS/360 environment) is taken into consideration in designing of the APAL-PC.", acknowledgement = ack-nhfb, affiliation = "Glushkov Inst. of Cybernetics, Kiev, USSR", classification = "C4210 (Formal logic); C7310 (Mathematics)", keywords = "APAL-PC; Boolean algebra; design; IBM PC; languages; Symbolic computations", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic.", thesaurus = "Boolean algebra; IBM computers; Symbol manipulation", } @InProceedings{Kuhn:1990:TLC, author = "N. Kuhn and K. Madlener and F. Otto", title = "A test for $\lambda$-confluence for certain prefix rewriting systems with applications to the generalized word problem", crossref = "Watanabe:1990:IPI", pages = "8--15", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p8-kuhn/", abstract = "Applies rewriting techniques to the generalized word problem for groups. Let $R$ be a finite string-rewriting system on an alphabet $\Sigma$ such that the monoid $M_R$ presented by $(\Sigma:R)$ is a group, and let $U$ contained in $\Sigma ^+$ be a finite set. The generalized word problem GWP is defined by $GWP(w,U)$ iff $w \in (U)$, where $(U)$ is the subgroup of $M_R$ generated by $U$. With $U$ we associate a prefix rewriting relation $\mbox{implies}_P$ on $\Sigma*$ such that $w$ implies/implied by $-{}_P$ $\lambda$ iff $GWP(w,U)$ holds. If $\mbox{implies} _P$ is $\lambda$-confluent then $w\mbox{implies}_P\lambda$ iff $w \in (U)$. Then $\mbox{implies} _P$ yields a decision procedure for GWP. For groups given through confluent string-rewriting systems $R$ the authors develop a necessary and sufficient condition for $\mbox{implies}_P$ being $\lambda$-confluent and show that this condition becomes decidable in case of $R$ being length-reducing, in addition.", acknowledgement = ack-nhfb, affiliation = "Fachbereich Inf., Kaiserslautern Univ., Germany", classification = "C4210 (Formal logic)", keywords = "$\Lambda$-confluence; algorithms; Decidable; Generalized word problem; languages; Length-reducing; Prefix rewriting systems; Rewriting; String-rewriting system; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", thesaurus = "Decidability; Rewriting systems", } @InProceedings{Letichevsky:1990:APA, author = "A. A. Letichevsky and J. V. Kapitonova", title = "Algebraic programming in the {APS} system", crossref = "Watanabe:1990:IPI", pages = "68--75", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p68-letichevsky/", abstract = "System APS (algebraic programming system) which was developed in the Glushkov Institute of Cybernetics of the Ukrainian Acadamy of Sciences is an instrumental tool for designing applied systems by means of algebraic programming. Systems of rewriting rules may be interpreted in APS by means of different computational strategies. This approach allows the use of not only canonical (confluent and noetherian) but any other systems of equalities, and algebraic programs may be designed by combining rewriting rules with different strategies of their applications. Another peculiarity of APS is the possibility to combine procedural and algebraic methods of programming.", acknowledgement = ack-nhfb, affiliation = "Glushkov Inst. of Cybernetics, Acad. of Sci., Kiev, Ukrainian SSR, USSR", classification = "C6115 (Programming support)", keywords = "Algebraic programming; algorithms; APS system; Computational strategies; languages; Rewriting rules", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf F.3.2} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics of Programming Languages, Algebraic approaches to semantics.", thesaurus = "Programming environments; Symbol manipulation", } @InProceedings{Liska:1990:FRP, author = "R. Liska and L. Drska", title = "{FIDE}: a {REDUCE} package for automation of {FInite} difference method for solving {pDE}", crossref = "Watanabe:1990:IPI", pages = "169--176", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p169-liska/", abstract = "Discusses the automation of the process of numerical solving of partial differential equations systems (PDES) by means of computer algebra. For solving PDES the finite difference method is applied. The computer algebra system REDUCE and the numerical programming language FORTRAN are used in the methodology presented, its main aim being to speed up the process of preparing numerical programs for solving PDES. Quite often, especially for complicated systems, this process is a tedious and time consuming task. In the process several stages can be found in which computer algebra can be used for performing routine analytical calculations, namely: transformation of differential equations into different coordinate systems, discretization of differential equations, analysis of difference schemes, and generation of numerical programs. The FIDE package is applied to two physical problems. The first one is the nonlinear Schr{\"o}dinger equation. The second one is the Fokker--Planck equation. The numerical programs have been tested and compared with similar published calculations.", acknowledgement = ack-nhfb, affiliation = "Fac. of Nucl. Sci. and Phys. Eng., Tech. Univ. of Prague, Czechoslovakia", classification = "C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; Computer algebra; Coordinate systems; Discretization; FIDE; FInite difference method; Fokker--Planck equation; FORTRAN; Integro-interpolation; languages; Nonlinear Schr{\"o}dinger equation; Numerical solving; Partial differential equations; PDE; REDUCE package", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite difference methods. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", thesaurus = "Difference equations; Partial differential equations; Software packages; Symbol manipulation", xxauthor = "R. Liska and L. Drsda", } @InProceedings{Liu:1990:AFA, author = "Zhuo-jun Liu", title = "An algorithm for finding all isolated zeros of polynomial systems", crossref = "Watanabe:1990:IPI", pages = "300--300", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p300-liu/", abstract = "Solving algebraic equations is desired for many problems appearing in applied science. Sometimes, finding all isolated solutions is enough. Suppose a set of polynomials (abbr. polset), denoted by PS, to be given. As a usual convention, by Zero(PS) and ISZero(PS), we respectively denote the zeros and isolated zeros defined by PS. Recently, the homotopy continuation method was widely used to find all isolated zeros of polset. However, that method is not good enough to find the isolated zeros of any polset. Here, based on Wu's method, the author introduces a new algorithm to solve this problem.", acknowledgement = ack-nhfb, affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "Algorithm; algorithms; Isolated zeros; Polset; Polynomial systems; Polynomials; Wu's method", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Poles and zeros; Polynomials; Symbol manipulation", } @InProceedings{Llovet:1990:MAC, author = "J. Llovet and J. R. Sendra", title = "A modular approach to the computation of the number of real roots", crossref = "Watanabe:1990:IPI", pages = "298--298", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p298-llovet/", abstract = "The problem of computing the number of distinct real roots of a real polynomial can be solved analyzing the sign variations of the sequence of principal minors of the Hankel matrix associated with the given polynomial. In this paper, the authors present a modular algorithm to achieve this goal. In this approach, the principal minors sequence of the associated Hankel matrix is computed using modular methods. The computing time analysis shows that the maximum computing time function of the modular algorithm is $O(n^5l^2)$, where $n$ is the degree of the polynomial and $l$ its length.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Alcala Univ., Madrid, Spain", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Associated Hankel matrix; Computing time; Distinct real roots; Hankel matrix; Modular algorithm; Principal minors; Real polynomial", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Computational complexity; Polynomials; Symbol manipulation", } @InProceedings{Manocha:1990:RCP, author = "D. Manocha", title = "Regular curves and proper parametrizations", crossref = "Watanabe:1990:IPI", pages = "271--276", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p271-manocha/", abstract = "Presents an algorithm for determining whether a given rational parametric curve, defined as vector valued function over a finite domain, has a regular parametrization. A curve has a regular parametrization if it has no cusps in its defining interval. It has been known that the vanishing of the derivative vector is a necessary condition for the existence of cusps. The author shows that if a curve is properly parametrized, then the vanishing of the derivative vector is a necessary and sufficient condition for the existence of cusps. If a curve has no cusps in its defining interval, its proper parametrization is a regular parametrization. He presents a simple algorithm to compute the proper parametrization of a polynomial parametric curve which is used to analyze for cusps and later on reduce the problem of detecting cusps in a rational curve to that of a polynomial curve.", acknowledgement = ack-nhfb, affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA, USA", classification = "C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "algorithms; Cusps; Polynomial curve; Polynomial parametric curve; Proper parametrization; Rational parametric curve; Vector valued function", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages, and systems.", thesaurus = "Computational geometry; Symbol manipulation", } @InProceedings{Mazurik:1990:SCS, author = "S. I. Mazurik and E. V. Vorozhtsov", title = "Symbolic-numerical computations in the stability analyses of difference schemes", crossref = "Watanabe:1990:IPI", pages = "177--184", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p177-mazurik/", abstract = "The authors propose a number of symbolic-numeric approaches to the computer-aided construction of the stability domains of difference schemes approximating the partial differential equations with constant coefficients. They use the Fourier method, the algebraic methods of the Routh--Hurwitz and Schur--Cohn theories for the localization of the polynomial zeros, the methods of optimization theory as well as the means of computer algebra, digital image processing and computer graphics. The efficiency of the approaches is demonstrated at the practical examples of difference schemes for fluid dynamics problems.", acknowledgement = ack-nhfb, affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci., Novosibirsk, USSR", classification = "C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algebraic methods; algorithms; Computer algebra; Computer graphics; Difference schemes; Digital image processing; Fluid dynamics problems; Fourier method; Optimization theory; Partial differential equations; Polynomial zeros; Routh--Hurwitz; Schur--Cohn theories; Stability analyses; Symbolic-numeric approaches; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite difference methods. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Convergence of numerical methods; Difference equations; Mathematics computing; Partial differential equations; Symbol manipulation", } @InProceedings{Mishra:1990:ARA, author = "B. Mishra and P. Pedersen", title = "Arithmetic with real algebraic numbers is in {NC}", crossref = "Watanabe:1990:IPI", pages = "120--126", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p120-mishra/", abstract = "The authors describe NC algorithms for doing exact arithmetic with real algebraic numbers in the sign-coded representation introduced by Coste and Roy (1988). They present polynomial sized circuits of depth $O(\log^3N)$ for the monadic operations $-\alpha,1/\alpha$, as well as $\alpha +r$, $\alpha\cdot{}r$, and $\mbox{sgn} (\alpha -r)$, where $r$ is rational and $\alpha$ is real algebraic. They also present polynomial sized circuits of depth $O(\log^7N)$ for the dyadic operations $\alpha+\beta$, $\alpha\cdot\beta$, and $\mbox{sgn}(\alpha-\beta)$, where $\alpha$ and $\beta$ are both real algebraic. The algorithms employ a strengthened form of the NC polynomial-consistency algorithm of Ben-Or, Kozen, and Reif (1986).", acknowledgement = ack-nhfb, affiliation = "New York Univ., NY, USA", classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", keywords = "algorithms; Dyadic operations; Exact arithmetic; Fast parallel algorithms; Monadic operations; NC algorithms; NC polynomial-consistency algorithm; Polynomial sized circuits; Real algebraic numbers; Sign-coded representation", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Parallel algorithms; Polynomials", } @InProceedings{Murray:1990:RIT, author = "N. V. Murray and E. Rosenthal", title = "Reexamining intractability of tableau methods", crossref = "Watanabe:1990:IPI", pages = "52--59", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p52-murray/", abstract = "Considers the class of formulas on which the method of analytic tableaux was first shown to be intractable, and shows that the applications of the ordinary distributive law tableau methods admit linear time proofs for this class. The authors introduce a new class of formulas that are intractable for tableaux (even with the distributive law), and demonstrate that path dissolution admits linear proofs of these formulas. Modifications of the tableau method are described that would render this class tractable. Since dissolution is linear on this class, these results demonstrate that dissolution cannot be $p$-simulated by the method of analytic tableau.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., State Univ. of New York, Albany, NY, USA", classification = "C4210 (Formal logic)", keywords = "algorithms; Analytic tableaux; Dissolution; Linear proofs; Linear time proofs; Path dissolution; Tableau methods; theory; verification", subject = "{\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.2.3} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and Theorem Proving, Deduction.", thesaurus = "Formal logic", } @InProceedings{Noda:1990:SHI, author = "Matu-Tarow T. Noda and E. Miyahiro", title = "On the symbolic\slash numeric hybrid integration", crossref = "Watanabe:1990:IPI", pages = "304--304", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p304-noda/", abstract = "Integrating a given function is one of the most important areas in the mathematical computing. Both numerical and symbolic integration methods have been developed and widely used. Numerical methods, however, have some defects such as (1) formal integrals are not obtained, (2) wrong answers are given for pathological integrand and (3) error estimates depend on types of integrands. Symbolic methods have also difficulties on (1) restrictions on an integrand and (2) uses of wasteful big-number computation. To avoid difficulties, some attempts in which both methods are combined have been proposed, called hybrid methods. The authors propose new hybrid integration method for a rational function, (say $q/r$, $q$ and $r$ are polynomials) with floating point but real coefficients.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Ehime Univ., Matsuyama, Japan", classification = "C4160 (Numerical integration and differentiation)", keywords = "algorithms; Floating point; Hybrid integration; Numerical; Numerical integration; Rational function; Symbolic integration", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation.", thesaurus = "Integration; Numerical methods; Symbol manipulation", } @InProceedings{Norman:1990:CBI, author = "A. C. Norman", title = "A critical-pair\slash completion based integration algorithm", crossref = "Watanabe:1990:IPI", pages = "201--205", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p201-norman/", abstract = "The presentation re-expresses the 1976 Risch method in terms of rewrite rules, and thus exposes the major problem it suffers from as a manifestation of the fact that in certain circumstances the set of rewrites generated is not confluent. This difficulty is then attacked using a critical-pair/completion (CPC) approach. For very many integrands it is then easy to see that the initial set of rewrites used in the early implementations do not need any extension, and this fact explains the high level of competence of the programs involved despite their shaky theoretical foundations. For a further large collection of problems even a simple CPC scheme converges rapidly; when the techniques are applied to the REDUCE integration test suite in all applicable cases a short computation succeeds in completing the set of rewrites and hence gives a secure basis for testing for integrability. This paper describes the implementation of the CPC process and discusses current limitations to and possible future extended applications of it.", acknowledgement = ack-nhfb, affiliation = "Trinity Coll., Cambridge, UK", classification = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", keywords = "algorithms; Convergence; CPC scheme; Critical-pair/completion based integration algorithm; experimentation; Integrability; REDUCE integration test suite; Rewrite rules; Transcendental functions", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", thesaurus = "Convergence of numerical methods; Integration; Rewriting systems", } @InProceedings{Okubo:1990:GTO, author = "K. Okubo", title = "Global theory of ordinary differential equations and formula manipulation", crossref = "Watanabe:1990:IPI", pages = "193--200", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p193-okubo/", abstract = "The author discusses the fundamental domain of the monodromy group for hypergeometric equations. One can classify these triangles formed by circular arcs with the sum of inner angles greater, equal or less than $\pi$. The domains have been classified into three classes, those on the unit sphere, those on the open complex plane and those on the unit disk. Any algebraically integrable solution of a hypergeometric equation is expressed by invariants of the groups of five platonic solids or dipyramids. One can express the key in terms of non-Euclidean expression by the sum of inner angles of triangles. The authors rephrases this into quadratic invariant of definite, degenerate or indefinite sign. The quadratic invariants may be of help as the key to the classification in higher dimensions.", acknowledgement = ack-nhfb, affiliation = "Univ. of Electro-Commun., Chofu, Tokyo, Japan", classification = "B0290P (Differential equations); C4170 (Differential equations)", keywords = "Algebraically integrable solution; Circular arcs; Dipyramids; Five platonic solids; Formula manipulation; Gauss equation; Hypergeometric equations; Inner angles; Monodromy group; Open complex plane; Ordinary differential equations; Quadratic invariant; Unit disk; Unit sphere", thesaurus = "Differential equations; Symbol manipulation", } @InProceedings{Padget:1990:UPS, author = "J. Padget and A. Barnes", title = "Univariate power series expansions in {Reduce}", crossref = "Watanabe:1990:IPI", pages = "82--87", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p82-padget/", abstract = "Describes the development of a formal power series expansion package for Reduce which takes advantage of Reduce's domain mechanism to make for a seamless integration of series values with the rest of the Reduce system. Consequently, series values may be manipulated with the same algebraic operators as other algebraic objects. To create the illusion of infinite power series a simulated lazy-evaluation mechanism has been used. The paper reports experience of using the Reduce domain mechanism and documents the algorithms and data structures that can be used to implement and to represent power series.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C7310 (Mathematics)", keywords = "Algebraic operators; Algorithms; algorithms; Data structures; Domain mechanism; languages; Lazy-evaluation mechanism; Power series expansions; Reduce; Series values", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.", thesaurus = "Series [mathematics]; Symbol manipulation", } @InProceedings{Scott:1990:SAM, author = "T. C. Scott and G. J. Fee", title = "Some applications of {Maple} symbolic computation to scientific and engineering problems", crossref = "Watanabe:1990:IPI", pages = "302--303", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p302-scott/", abstract = "Presents a survey of use of the Maple symbolic computation system at the University of Waterloo. This represents only a sample of what has and can be done with symbolic computation. However, these examples have been chosen from a broad spectrum of areas which includes: Quantum theory, general and special relativity, audio engineering and asbestos fiber analysis (an application of fluid and magneto-dynamics). They represent new avenues of research and illustrate the large untapped potential of symbolic computation.", acknowledgement = ack-nhfb, affiliation = "Maple Symbolic Comput. Group, Waterloo Univ., Ont., Canada", classification = "C7300 (Natural sciences); C7400 (Engineering)", keywords = "Asbestos fiber analysis; Audio engineering; design; General relativity; Maple; Quantum theory; Special relativity; Symbolic computation; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple.", thesaurus = "Engineering computing; Natural sciences computing; Symbol manipulation", } @InProceedings{Shirayanagi:1990:IPF, author = "K. Shirayanagi", title = "On the isomorphism problem for finite-dimensional binomial algebras", crossref = "Watanabe:1990:IPI", pages = "106--111", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p106-shirayanagi/", abstract = "Binomial algebras are finitely presented algebras defined by monomials or binomials. Given two binomial algebras, one important problem is to decide whether or not they are isomorphic as algebras. The author studies an algorithm for solving this problem, when both algebras are finite-dimensional over a field. In particular, when they are monomial algebras (i.e binomial algebras defined by monomials only), the problem has already been completely solved by the presentation uniqueness. The author provides some necessary conditions in terms of partially ordered sets for two certain binomial algebras to be isomorphic. In other words, invariants of the binomial algebras are presented. These conditions together serve as an effective procedure for solving the isomorphism problem.", acknowledgement = ack-nhfb, affiliation = "NTT Software Lab., Tokyo, Japan", classification = "C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "algorithms; Binomial algebras; Binomials; Finitely presented algebras; Monomials; Partially ordered sets; Presentation uniqueness; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Algebra; Set theory; Symbol manipulation", } @InProceedings{Smedley:1990:DAD, author = "T. J. Smedley", title = "Detecting algebraic dependencies between unnested radicals (abstract)", crossref = "Watanabe:1990:IPI", pages = "292--293", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p292-smedley/", abstract = "There are a number of known methods for checking for dependencies between unnested radicals. However, these methods usually have one or both of the following disadvantages: 1. They rely on integer factorisation, or 2. They generate an algebraic extension field of degree higher than is necessary to express the input. The first disadvantage is not generally too important, as the integers involved are usually quite small and can be easily factored. However, the second disadvantage can cause real problems. Since the degree of the algebraic extension has a large influence on the cost of algorithms involving algebraic numbers, the author wants a method which detects dependencies but keeps the degree of the extension field as low as possible.", acknowledgement = ack-nhfb, affiliation = "Delaware Univ., Newark, DE, USA", classification = "C4240 (Programming and algorithm theory)", keywords = "Algebraic dependencies; Algebraic extension; Algebraic numbers; Unnested radicals; verification", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Computational complexity; Symbol manipulation", } @InProceedings{Stachniak:1990:RPS, author = "Z. Stachniak", title = "Resolution proof systems with weak transformation rules", crossref = "Watanabe:1990:IPI", pages = "38--43", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p38-stachniak/", abstract = "In previous papers the author defined and explored a formal methodological framework on the basis of which resolution proof systems for strongly-finite logics can be introduced and studied. In the present paper he extends this approach to a wider class of so-called resolution logics.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., York Univ., North York, Ont., Canada", classification = "C4210 (Formal logic)", keywords = "algorithms; Formal methodological framework; Resolution logics; Resolution proof systems; Strongly-finite logics; theory; verification; Weak transformation rules", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic. {\bf I.2.3} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Deduction and Theorem Proving, Deduction. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic.", thesaurus = "Formal logic", } @InProceedings{Takayama:1990:ACI, author = "N. Takayama", title = "An algorithm of constructing the integral of a module-an infinite dimensional analog of {Gr{\"o}bner} basis", crossref = "Watanabe:1990:IPI", pages = "206--211", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p206-takayama/", abstract = "Let $U$ be a left ideal of Weyl algebra: $A_n=K(x_1,\ldots{},x_n,\delta_1,\ldots{},\delta_n)$. Put $M=A_n/U$. M is a left $A_n$ module. The paper presents an explicit construction of the left $A_{n-1}$ module by introducing an analog of Gr{\"o}bner basis of a submodule of a kind of infinite dimensional free module. The author gives a complete algorithm. The algorithm is an answer to the research problem of the paper (AZ).", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Kobe Univ., Japan", classification = "B0290R (Integral equations); C4180 (Integral equations)", keywords = "algorithms; Integral; Gr{\"o}bner basis; Left ideal; Weyl algebra", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Integral equations; Symbol manipulation", } @InProceedings{Takayama:1990:GBI, author = "N. Takayama", title = "{Gr{\"o}bner} basis, integration and transcendental functions", crossref = "Watanabe:1990:IPI", pages = "152--156", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p152-takayama/", abstract = "It is well known that Gr{\"o}bner basis is a fundamental and powerful tool to solve problems of polynomials. One can use the Gr{\"o}bner basis of Weyl algebra to solve the problems of integration and formula verification of transcendental functions. The paper surveys the theory of the Gr{\"o}bner basis of the ring of differential operators and its applications to the following problems: computation of differential equations for a definite integral with parameters; zero recognition of an expression that contains special functions or binomial coefficients etc., i.e. formula verification by a computer; derivations of some of special function identities; solving a definite integral or obtaining an asymptotic expansion of a definite integral with parameters.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Kobe Univ., Japan", classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", keywords = "Transcendental functions; Gr{\"o}bner basis; Polynomials; Weyl algebra; Integration; Formula verification; Differential operators; Differential equations; Definite integral; Zero recognition; Binomial coefficients; Special function identities; Asymptotic expansion; algorithms; verification", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Differential equations; Function approximation; Integration; Polynomials; Symbol manipulation", } @InProceedings{Tan:1990:OTS, author = "H. Q. Tan and X. Dong", title = "Optimization techniques for symbolic equation solver in engineering applications", crossref = "Watanabe:1990:IPI", pages = "305--305", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p305-tan/", abstract = "In MACSYMA, there are procedures for solving systems of equations, such as solve and linsolve. Because the systems of equations we are dealing with are mostly sparse, the application of Gaussian elimination which is used in linsolve produces results that are usually lengthy and inefficient. The authors have implemented a new derivation procedure to solve the problem of expression growth and increase the computational efficiency. The underlying concept is the identification of the smallest full subsystems contained within the original and then subsequent remaining systems, labeling common terms by intermediate variables. Gaussian elimination is employed to solve these subsystems independently and sequentially instead of the complete system.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. Sci., Akron Univ., OH, USA", classification = "C7310 (Mathematics)", keywords = "algorithms; Derivation procedure; Gaussian elimination; Symbolic equation solver", subject = "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Algebra; Symbol manipulation", } @InProceedings{Tao:1990:SAM, author = "Qingsheng Tao", title = "Symbolic and algebraic manipulation for formulae of interpolation and quadrature", crossref = "Watanabe:1990:IPI", pages = "306--306", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p306-tao/", abstract = "Computer algebra has been used for construction and analysis of algorithms of numerical computation. In the paper, an attempt has been made to derive the formulae of interpolation and quadrature with Computer Algebra. In REDUCE language, the formula manipulation system for interpolation INTEP and for quadrature QUADRAT are developed. The two formula manipulators can be used to derive Lagrange, Hermite and Birkhoff interpolation formulae with any degree of polynomials and to derive Newton--Cotes quadrature formulae and the quadrature formulae involving the derivatives of the integrand.", acknowledgement = ack-nhfb, affiliation = "Dept. of Mech., Zhejiang Univ., Hangzhou, China", classification = "C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", keywords = "Algebraic manipulation; algorithms; Birkhoff; Computer Algebra; Formula manipulators; Hermite; INTEP; Interpolation; Interpolation formulae; Lagrange; languages; Newton--Cotes quadrature formulae; QUADRAT; Quadrature; Symbolic manipulation", subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Integration; Interpolation; Symbol manipulation", } @InProceedings{Ulmer:1990:LSH, author = "F. Ulmer and J. Calmet", title = "On {Liouvillian} solutions of homogeneous linear differential equations", crossref = "Watanabe:1990:IPI", pages = "236--243", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p236-ulmer/", abstract = "Deals with the problem of finding Liouvillian solutions of an $n$-th order homogeneous linear differential equation $L(y)=0$ with coefficients in a differential field $k$ whose field of constants is $C$. For second order linear differential equations such an algorithm has been given by J. Kovacic (1986) and implemented. A general decision procedure for finding Liouvillian solutions of $n$-th order equations has been given by M. F. Singer (1981), but the resulting algorithm, although constructive, is not in implementable form even for second order equations. The algorithm uses the fact that, if $L(y)=0$ has a Liouvillian solution, then, $L(y)=0$ has a solution $z$ such that $u=z'/z$ is algebraic over $k$, which means that $L(y)$ has a solution $z$ of the form $e^{\int{}u}$, where $u$ is algebraic over $k$. Since the logarithmic derivative $u=z'/z$ of a solution $z$ is a solution of the Riccati equation $R(y)=0$ associated to $L(y)=0$, the problem thus reduces to find an algebraic solution $u$ of $R(y)=0$. This task is now split into two parts: (i) to find the set DEG(n) of possible degrees $N$ for the minimal polynomial $P(x)=0$ of $u$ over $k$, (ii) to compute, for each possible degree of $P(x)$, the possible coefficients of $P(x)$. If we donate $c(ii)$ the complexity of the second step and Hash DEG($n$) the size of the set DEG($n$), one sees that the complexity of the whole procedure is of the form $c(ii)^{Hash DEG(n)}$ and thus exponential in Hash DEG($n$). This shows that the only way to make the procedure effective is to get sharp bounds on the size of the set DEG($n$), which is the scope of this paper.", acknowledgement = ack-nhfb, affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe Univ., Germany", classification = "C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algebraic solution; algorithms; Complexity; Homogeneous; Linear differential equations; Liouvillian solutions; Sharp bounds", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Computational complexity; Differential equations; Symbol manipulation", } @InProceedings{vonzurGathen:1990:PFF, author = "J. {von zur Gathen}", title = "Polynomials over finite fields with large images", crossref = "Watanabe:1990:IPI", pages = "140--144", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p140-von_zur_gathen/", abstract = "A polynomial $f$ in $F_q(x)$, over a finite field $F_q$ with $q$ elements, is $\rho$-large if its image in $F_q$ contains at least $q-\rho$ elements. The article presents an efficient probabilistic test for this property, using expected time polynomial in $\deg{}f$, $\log{}q$, and $\rho$.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Toronto Univ., Ont., Canada", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Expected time polynomial; Finite fields; Large images; Polynomial; Probabilistic test; Time complexity", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Probabilistic computation.", thesaurus = "Computational complexity; Polynomials", } @InProceedings{Wang:1990:PUP, author = "P. S. Wang", title = "Parallel univariate polynomial factorization on shared-memory multiprocessors", crossref = "Watanabe:1990:IPI", pages = "145--151", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p145-wang/", abstract = "Using parallelism afforded by shared-memory multiprocessors to speed up systems for polynomial factorization is discussed. The approach is to take the fastest known factoring algorithm for practical purposes and parallelize key parts of it. The univariate factoring algorithm consists of two major tasks (a) factoring modulo small integer primes and (b) EEZ lifting and recovery of true factors. A C coded system PFACTOR that implements (a) in parallel is described in detail. PFACTOR is a stand-alone parallel factorizer that can take input from a file, a pipe or a socket connection over a network. It can also be used interactively as a UNIX command. PFACTOR consists of parallel selection of primes, automatic balancing of work, parallel Berlekamp algorithm, and parallel reconciliation of degrees of factors modulo different primes. Actual timings on the Encore Multimax show the effectiveness of the approach.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH, USA", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; C coded system; EEZ lifting; Encore Multimax; Modulo small integer primes; Parallel Berlekamp algorithm; Parallel reconciliation; Parallelism; performance; PFACTOR; Polynomial factorization; Shared-memory multiprocessors; Time complexity; Univariate factoring algorithm; UNIX command", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency.", thesaurus = "Computational complexity; Parallel algorithms; Polynomials", } @InProceedings{Yamasaki:1990:DLP, author = "S. Yamasaki", title = "Dataflow for logic program as substitution manipulator", crossref = "Watanabe:1990:IPI", pages = "44--51", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p44-yamasaki/", abstract = "Shows a method of constructing a dataflow, which denotes the deductions of a logic program, by means of a sequence domain based on equivalence classes of substitutions. The dataflow involves fair merge functions to represent unions of atom subsets over a sequence domain, as well as functions as manipulations of unifiers for the deductions of clauses. A continuous functional is associated with the dataflow on condition that the dataflow completely and soundly denotes the atom generation in terms of equivalent substitutions sets. Its least fixpoint is interpreted as denoting the whole atom generation based on manipulations of equivalent substitutions sets.", acknowledgement = ack-nhfb, affiliation = "Dept. of Inf. Technol., Okayama Univ., Japan", classification = "C4240 (Programming and algorithm theory)", keywords = "algorithms; Continuous functional; Dataflow; Equivalence classes; Fair merge functions; Logic program; Sequence domain; Substitution manipulator; theory", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Logic and constraint programming. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic.", thesaurus = "Logic programming; Programming theory", } @InProceedings{Yokoyama:1990:DSP, author = "K. Yokoyama and M. Noro and T. Takeshima", title = "On determining the solvability of polynomials", crossref = "Watanabe:1990:IPI", pages = "127--134", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p127-yokoyama/", abstract = "Landau and Miller (1985) presented a method for determining the solvability of a monic irreducible polynomial over integers in polynomial time. In their method, a series of polynomials is constructed so that the original problem is reduced to determining the solvability of new polynomials. The authors present an improved method for finding such a series of polynomials efficiently. More precisely, they introduce a new notion on a series of blocks in the set of all roots of the original polynomial under the action of its Galois group, and then present an efficient method for finding such a series of blocks by modifying Landau and Miller's method for finding minimal imprimitive blocks.", acknowledgement = ack-nhfb, affiliation = "IIAS-SIS, Fujitsu Ltd., Numazu, Japan", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Galois group; Minimal imprimitive blocks; Monic irreducible polynomial; Polynomials; Problem complexity; Solvability; Time complexity", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.", thesaurus = "Computability; Computational complexity; Polynomials", } @InProceedings{Yokoyama:1990:FMP, author = "Kazuhiro Yokoyama and Masayuki Noro and Taku Takeshima", title = "On factoring multi-variate polynomials over algebraically closed fields (abstract)", crossref = "Watanabe:1990:IPI", pages = "297--297", year = "1990", bibdate = "Thu Mar 12 08:36:58 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/96877/p297-yokoyama/", abstract = "For a problem how to find an extension field over which we can obtain an absolutely irreducible factor, Kaltofen gave an answer in 1983 and explicitly in 1985 by employing analytic argument for showing his answer, and Chistov and Grigor'ev also gave the same answer in 1983 by algebraic arguments. Here the authors give an alternative proof for Kaltofen's answer in algebraic way, independently to Chistov and Grigor'ev, and by the benefit of new way, they also give several extensions of his answer and properties of absolutely irreducible factors. They also discuss usage of their results for actual computation of absolutely irreducible factors. They restrict themselves to bi-variate polynomials with integer (or rational) coefficients.", acknowledgement = ack-nhfb, affiliation = "IIAS-SIS, Fujitsu Ltd., Japan", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "Actual computation; Algebraic arguments; Algebraically closed fields; Bi-variate polynomials; Irreducible factor; Multi-variate polynomials; theory; verification", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Abramov:1991:FAS, author = "S. A. Abramov and K. Yu. Kvashenko", title = "Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients", crossref = "Watt:1991:IPI", pages = "267--270", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p267-abramov/", abstract = "The paper is concerned with some ways for an improvement with regard to solving the linear ordinary differential equations of the form $\sum_0^na_i(x)y^{(i)}(x)=b(x)$ where $a_0(x),\ldots{},a_n(x),b(x)$ in $K(x)$ ($K$ is the constant field), $a_n(x) \neq 0$. The authors consider one after another of the problems of finding all the polynomial and rational solutions of equation. They consider the simplest approach and then its improvement.", acknowledgement = ack-nhfb, affiliation = "Comput. Center, Acad. of Sci., Moscow, USSR", classification = "C4170 (Differential equations)", keywords = "algorithms; Linear differential equations; Polynomial coefficients; Rational solutions; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Linear differential equations; Symbol manipulation", } @InProceedings{Amirkhanov:1991:BOV, author = "I. V. Amirkhanov and E. P. Zhidkov and I. E. Zhidkova", title = "The betatron oscillations in the vicinity of nonlinear resonance in cyclic accelerator investigation", crossref = "Watt:1991:IPI", pages = "452--453", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p452-amirkhanov/", abstract = "Motion of charged particle in given fields in a cyclic accelerator has been investigated. The nonlinear problem of finding stable trajectories in the vicinity of a resonance has been solved. The equations of motion for charged particle deviation from ideal orbit or the betatron oscillations equations (which are lateral to the closed orbit oscillations with the frequencies $\nu_x, \nu_z$) are studied using REDUCE-3.2. The study of the equations formed by computer is applied to two types of accelerators: (1) the averaged equations in the vicinity of 19 resonances for a weakly focusing accelerator (WFA) and (2) those in the vicinity of 24 resonances-for a strong focusing accelerator (SFA).", acknowledgement = ack-nhfb, affiliation = "JINR, Moscow, USSR", classification = "A2920F (Betatrons); B7410 (Accelerators); C7320 (Physics and Chemistry)", keywords = "algorithms; Betatron oscillations; Charged particle deviation; Cyclic accelerator; Nonlinear resonance; REDUCE-3.2; Strong focusing accelerator; Weakly focusing accelerator", subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics.", thesaurus = "Betatrons; Physics computing", } @InProceedings{Apel:1991:FAA, author = "Joachim Apel and Uwe Klaus", title = "{FELIX}: an assistant for algebraists", crossref = "Watt:1991:IPI", pages = "382--389", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p382-apel/", abstract = "FELIX is a special computer algebra system designed for calculations with elements of algebraic structures as well as with substructures and homomorphisms. It covers both commutative polynomial rings and modules and non-commutative structures. Buchberger's algorithm for the computation of Gr{\"o}bner bases is fundamental for many of the included operations. The articles contains a short description of the system FELIX and illustrates the sensitivity of Buchberger's algorithm against changes of selection strategies.", acknowledgement = ack-nhfb, affiliation = "Leipzig Univ., Germany", classification = "C7310 (Mathematics)", keywords = "algorithms; design; FELIX; Computer algebra system; Algebraic structures; Substructures; Homomorphisms; Commutative polynomial rings; Modules; Non-commutative structures; Buchberger's algorithm; Gr{\"o}bner bases", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Astrelin:1991:BDI, author = "A. V. Astrelin", title = "A bound of degree of irreducible eigenpolynomial of some differential operator", crossref = "Watt:1991:IPI", pages = "265--266", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p265-astrelin/", abstract = "Consider the following problem: for the differential operator $D=P \delta / \delta x+Q \delta / \delta y$ find an integer $K$, such that any irreducible polynomial $f$ dividing $Df$ has degree $\deg{}f<=K$. This problem arises when one wants to find the symbolic solution of a differential equation $dy/dx=R(x,y)$ where $R$ is a rational function. A solution when $P$ and $Q$ are homogeneous polynomials of equal degrees i.e. $P(x,y)=x^mp(x/y),Q(x,y)=x^mq(x,y)$ for some $m$ is proposed.", acknowledgement = ack-nhfb, affiliation = "Dept. of Mech. and Math., Moscow State Univ., USSR", classification = "C1110 (Algebra); C1120 (Analysis); C4170 (Differential equations)", keywords = "algorithms; Differential equation; Differential operator; Homogeneous polynomials; Irreducible eigenpolynomial; Irreducible polynomial; Rational function; Symbolic solution", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Differential equations; Polynomials", } @InProceedings{Babai:1991:NLT, author = "L{\'a}szl{\'o} Babai and Gene Cooperman and Larry Finkelstein and {\'A}kos Seress", title = "Nearly linear time algorithms for permutation groups with a small base", crossref = "Watt:1991:IPI", pages = "200--209", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p200-babai/", abstract = "A base of a permutation group $G$ is a subset $B$ of the permutation domain such that only the identity of $G$ fixes $B$ pointwise. The permutation representations of important classes of groups, including all finite simple groups other than the alternating groups, admit $O(\log{}n)$ size bases, where $n$ is the size of the permutation domain. Groups with very small bases dominate the work on permutation groups in much of computational group theory. A series of new combinatorial results allows us to present Monte Carlo algorithms achieving $O(n \log^cn)$ ($c$ a constant) time and space performance for such groups with respect to the fundamental operations of finding order and testing membership. (The input is a list of generators of the group). Previous methods have achieved similar space performance only at the expense of increased time performance. Adaptations of a `cube-doubling' technique (L. Babai, E. Szemeredi, 1984) and a local expansion property of groups (L. Babai, 1991) are the key to theoretically reducing the time complexity to $O(n \log^c n)$. The shared principal novelty of the new ideas is in their ability to build and manipulate certain chains of subsets of a group, which are not themselves subgroups, in order to build the point stabilizer subgroup chain. Further combinatorial ideas are used to lower the constant $c$. Comparative timing estimates, based on asymptotic worst-case analysis, lead us to expect a new implementation to be faster than previous implementations for groups of high degree.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comp. Sci. Chicago Univ., IL, USA", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory)", keywords = "algorithms; Alternating groups; Asymptotic worst-case analysis; Computational group theory; Cube-doubling; Finite simple groups; Fundamental operations; Group order determination; Local expansion property; Membership testing; Monte Carlo algorithms; Permutation domain; Permutation group; Point stabilizer subgroup chain; Shared principal novelty; theory; Time complexity", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms.", thesaurus = "Computational complexity; Group theory", } @InProceedings{Backelin:1991:HWP, author = "J{\"o}rgen Backelin and Ralf Fr{\"o}berg", title = "How we proved that there are exactly 924 cyclic 7-roots", crossref = "Watt:1991:IPI", pages = "103--111", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p103-backelin/", abstract = "The following problem has become some sort of test problem for Gr{\"o}bner bases techniques: find all solutions to $Sn=z_1+z_2+\ldots{}+z_{n-1}+z_n=0$, $z_1z_2+z_2z_3+\ldots{}+z_{n-1}z_n+z_nz_1=0$, \ldots{} $z_1z_2\ldots{}z_{n-1}+z_2z_3\ldots{}z_n+\ldots{}+z_{n-1}z_n\ldots{}z_{n-3}+z_nz_1\ldots{}z_{n-2}=0$, $z_1z_2\ldots{}z_n=1$. The solutions are called cyclic $n$-roots. In order to solve the problem one of the authors constructed a new characteristic 0 Gr{\"o}bner basis programme, Bergman. The authors describe some features of Bergman, in particular its graph component algorithm. They make some theoretical analysis and practical tests of the differences in performance between Bergman and some other Buchberger based algorithms, mainly the Gebauer--Moller algorithm. With the help of Bergman and some commutative algebra they succeeded to prove: there are exactly 924 cyclic 7-roots. Each of them has multiplicity 1.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Stockholm Univ., Sweden", classification = "C4130 (Interpolation and function approximation)", keywords = "algorithms; verification; Exact proof; Cyclic 7-roots; Cyclic $n$-roots; Characteristic 0 Gr{\"o}bner basis programme; Bergman; Graph component algorithm; Gebauer--Moller algorithm; Multiplicity", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Polynomials", } @InProceedings{Becker:1991:CRP, author = "Thomas Becker and Volker Weispfenning", title = "The {Chinese} remainder problem, multivariate interpolation, and {Gr{\"o}bner} bases", crossref = "Watt:1991:IPI", pages = "64--69", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p64-becker/", abstract = "Let $K(X)$ be a multivariate polynomial ring over a field $K, I_1, \ldots{}, I_m$ ideals in $K(X)$, $U$ contained in $X$. Using a single Gr{\"o}bner basis in an extension ring of $K(X)$, the authors solve the following problems effectively. Given $f_1,\ldots{},f_m$ in $K(X)$, put $A_f=\cap_{k=1}^m(I_k+f_k)$. (1) Decide whether $A_f\cap{}K(U)\ne0$ and if so, construct some element of $A_f\cap{}K(U)$. (2) For given $g$ in $K(U)$, decide whether $g\in{}A_f$. (3) Construct all elements of $A_f\cap{}K(U)$. Taking for $I^k$ a suitable vanishing ideal of some parametrized hypersurface in $K^n(1<=k<=m)$, this solves a generalized Hermite and spline interpolation problem.", acknowledgement = ack-nhfb, affiliation = "Fakultat fur Math. und Inf., Passau Univ., Germany", classification = "C4130 (Interpolation and function approximation)", keywords = "algorithms; theory; Hermite problem; Chinese remainder problem; Multivariate interpolation; Gr{\"o}bner bases; Multivariate polynomial ring; Extension ring; Vanishing ideal; Parametrized hypersurface; Spline interpolation", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations.", thesaurus = "Interpolation; Polynomials; Splines [mathematics]", } @InProceedings{Belkov:1991:RUC, author = "Alexander A. Bel'kov and Alexander V. Lanyov", title = "{REDUCE} usage for calculation of low-energy process amplitudes in chiral {QCD} model", crossref = "Watt:1991:IPI", pages = "454--455", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p454-bel_kov/", abstract = "Describes the extension of REDUCE capabilities for the calculations of strong and weak meson processes within the chiral Lagrangians with higher derivatives. The main non-trivial difficulty is to obtain the process amplitude from the Lagrangian, describing these interactions. Another one is to overcome some REDUCE deficiencies such as the lack of arguments in the matrix data type as well as of some physical operations with the particle operators. This package of procedures allows one to calculate the amplitudes of the strong and weak processes by simple specifying the particles involved and their momenta.", acknowledgement = ack-nhfb, affiliation = "Particle Phys. Lab., JINR, Moscow, USSR", classification = "A0270 (Computational techniques); A1110 (Field theory); A1130R (Chiral symmetries); A1235C (General properties of quantum chromodynamics (dynamics, confinement, etc.)); C7320 (Physics and Chemistry)", keywords = "algorithms; Chiral Lagrangians; Meson processes; REDUCE capabilities", subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Chiral symmetries; Colour model; Meson field theory; Physics computing; Symbol manipulation", } @InProceedings{Berndt:1991:ACA, author = "R. Berndt and A. Lock and G. Witte and C. h. W{\"o}ll", title = "Application of computer algebra to surface lattice dynamics", crossref = "Watt:1991:IPI", pages = "433--438", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p433-berndt/", abstract = "Lattice dynamical calculations for surfaces and in particular for stepped and absorbed covered surfaces are commonly hampered by the complexity of the dynamical matrix for these systems. The authors propose the use of computer algebra programs to set up the dynamical matrix. In the present implementation the dynamical matrix is calculated fully analytically within the framework of a force constant-mode and partially analytically for other interaction models such as the shell model or the bond charge model.", acknowledgement = ack-nhfb, affiliation = "Max-Planck Inst. fur Stromungsforschung, Gottingen, Germany", classification = "A6830 (Dynamics of solid surfaces and interface vibrations); A6845 (Solid-fluid interface processes); C4140 (Linear algebra); C7320 (Physics and Chemistry)", keywords = "Absorbed covered surfaces; algorithms; Bond charge model; Computer algebra; Dynamical matrix; Force constant-mode; Interaction models; languages; Shell model; Surface lattice dynamics", subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", thesaurus = "Adsorbed layers; Crystal surface and interface vibrations; Matrix algebra; Phonon dispersion relations; Physics computing; Symbol manipulation", } @InProceedings{Beth:1991:FGN, author = "T. Beth and W. Geiselmann and F. Meyer", title = "Finding (good) normal bases in finite fields", crossref = "Watt:1991:IPI", pages = "173--178", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p173-beth/", abstract = "An algorithm to generate low complexity normal bases in finite fields is presented. This algorithm generalizes the method of Ash et al. to fields of arbitrary characteristic. It can be applied to most finite fields and produces (under certain conditions) the multiplication matrix for the normal basis multiplication of $\mbox{GF}(q^n):\mbox{GF}(q)$ in $O(n^2 \log^2 n \log{}q)$ bit-operations.", acknowledgement = ack-nhfb, affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe Univ., Germany", classification = "C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Finite fields; Low complexity normal bases; Multiplication matrix; Normal basis multiplication", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Computational complexity; Number theory", } @InProceedings{Bosma:1991:CFG, author = "Wieb Bosma and Michael Pohst", title = "Computations with finitely generated modules over {Dedekind} rings", crossref = "Watt:1991:IPI", pages = "151--156", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p151-bosma/", abstract = "In computer algebra the use of normal forms for matrices is of eminent importance. Especially, Hermite and Smith normal form techniques are frequently used for various computational problems over Euclidean rings. The paper discusses a generalization of these concepts to Dedekind rings. It considers the problem of normal forms for matrices in the context of basis transformations for finitely generated modules.", acknowledgement = ack-nhfb, affiliation = "Dept. of Pure Math., Sydney Univ., NSW, Australia", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)", keywords = "algorithms; Basis transformations; Computer algebra; Dedekind rings; Euclidean rings; Finitely generated modules; Hermite normal form; Matrices; Smith normal form; theory; verification", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Matrix algebra; Number theory", } @InProceedings{Bronstein:1991:RDE, author = "Manuel Bronstein", title = "The {Risch} differential equation on an algebraic curve", crossref = "Watt:1991:IPI", pages = "241--246", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p241-bronstein/", abstract = "The author presents a new rational algorithm for solving Risch differential equations over algebraic curves. This algorithm can also be used to solve $n^{\mbox{th}}$-order linear ordinary differential equations with coefficients in an algebraic extension of the rational functions. In the general (`mixed function') case, this algorithm finds the denominator of any solution of the equation. The algorithm has been implemented in the Maple and Scratchpad computer algebra systems.", acknowledgement = ack-nhfb, affiliation = "Inf. ETH-Zentrum, Zurich, Switzerland", classification = "C4170 (Differential equations); C7310 (Mathematics)", keywords = "$N^{th}$-order linear ordinary differential equations; Algebraic curve; algorithms; Computer algebra systems; Maple; Rational algorithm; Rational functions; Risch differential equation; Scratchpad", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, SCRATCHPAD. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple.", thesaurus = "Differential equations; Symbol manipulation", } @InProceedings{Buchmann:1991:CNP, author = "Johannes Buchmann and Volker M{\"u}ller", title = "Computing the number of points of elliptic curves over finite fields", crossref = "Watt:1991:IPI", pages = "179--182", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p179-buchmann/", abstract = "The authors study the problem of counting the points on an elliptic curve over a prime field. Although Schoof (1985) proves that the cardinality of an elliptic curve group over a finite field can be computed in polynomial time, his algorithm is extremely inefficient in practice. On the other hand, the application of Shanks' babystep giantstep idea (1970) to the problem yields an algorithm which is efficient for medium size prime numbers but of exponential complexity. So far no experimental results concerning those algorithms have been published. The authors present a practical improvement of the algorithm of Shanks which is based on the ideas of Schoof. It turns out to be very efficient.", acknowledgement = ack-nhfb, affiliation = "FB 14 Inf., Saarlandes Univ., Saarbrucken, Germany", classification = "C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Cardinality; Elliptic curves; Finite fields; Medium size prime numbers; Prime field", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational complexity; Number theory", } @InProceedings{Bundgen:1991:CIP, author = "Reinhard B{\"u}ndgen", title = "Completion of integral polynomials by {AC-term} completion", crossref = "Watt:1991:IPI", pages = "70--78", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p70-bundgen/", abstract = "The article presents a canonical term rewriting system RX whose ground normal forms can directly be mapped to integral polynomials in distributive normal form. Completing RX and a set of ground equations simulates the Gr{\"o}bner base computation for the ideal presented by the ground equations. With this approach, it clearly shows the correspondence of the key features of algebraic completion procedures for integral polynomial ideals and their simulation in a term rewriting environment.", acknowledgement = ack-nhfb, affiliation = "Wilhelm-Schickard-Inst., Tubingen Univ., Germany", classification = "C4130 (Interpolation and function approximation); C4210 (Formal logic)", keywords = "algorithms; AC-term completion; Canonical term rewriting system; Ground normal forms; Distributive normal form; Ground equations; Gr{\"o}bner base computation; Algebraic completion procedures; Integral polynomial ideals", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Polynomials; Rewriting systems", } @InProceedings{Burge:1991:SRI, author = "William H. Burge", title = "{Scratchpad} and the {Rogers--Ramanujan} identities", crossref = "Watt:1991:IPI", pages = "189--190", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p189-burge/", abstract = "This note sketches the part played by Scratchpad in obtaining new proofs of Euler's theorem and the Rogers--Ramanujan Identities.", acknowledgement = ack-nhfb, affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "algorithms; Euler theorem; Infinite series; Restricted partition pairs; Rogers--Ramanujan identities; Scratchpad", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, SCRATCHPAD.", thesaurus = "Mathematics computing; Number theory; Symbol manipulation", } @InProceedings{Butler:1991:DDG, author = "Greg Butler and Sridhar S. Iyer and Susan H. Ley", title = "A deductive database of the groups of order dividing 128", crossref = "Watt:1991:IPI", pages = "210--218", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p210-butler/", abstract = "The paper describes the design and implementation of a deductive database for the 2668 groups of order $2^n$, ($n<=7$). The system was implemented in NU-Prolog, a Prolog system with built-in functions for creating and using deductive databases. In addition to the database, a simple query language was written. This enables database users to assess the data using a simpler and more familiar set-theoretic syntax than that provided by the Prolog interpreter.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Sydney Univ., NSW, Australia", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C6160Z (Other DBMS); C6170 (Expert systems); C7310 (Mathematics)", keywords = "Built-in functions; Deductive database; design; languages; NU-Prolog; Query language; Set-theoretic syntax", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Prolog.", thesaurus = "Deductive databases; Group theory; Knowledge based systems; Mathematics computing; Set theory", } @InProceedings{Canny:1991:OCD, author = "John Canny and J. Maurice Rojas", title = "An optimal condition for determining the exact number of roots of a polynomial system", crossref = "Watt:1991:IPI", pages = "96--102", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p96-canny/", abstract = "It was shown by Bernshtein (1975) that the number of roots in $(C*)^n$ of a polynomial system depends only on the Newton polytopes of the system, for almost all specializations of the coefficients. This result, referred to as the BKK bound, gives an upper bound on the number of roots of a polynomial system. The BKK bound is often much better than the Bezout bound for the same system, but the original theorem gives an exact bound only if all the coefficients corresponding to Newton polytope boundaries are generically chosen. The current paper shows that the BKK bound is exact under much weaker assumptions: only coefficients corresponding to certain vertices of the Newton polytopes need be generic. This result allows application of the BKK bound to many practical problems.", acknowledgement = ack-nhfb, affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA, USA", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; BKK bound; Newton polytopes; Optimal condition; Polynomial system; Roots; theory; Upper bound; verification; Vertices", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational complexity; Polynomials", } @InProceedings{Chen:1991:NNF, author = "Guoting Chen and Jean Della Dora and Laurent Stolovitch", title = "Nilpotent normal form via {Carleman} linearization (for systems of ordinary differential equations)", crossref = "Watt:1991:IPI", pages = "281--288", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p281-chen/", abstract = "Considers in this paper the normal formal problem for systems of nonlinear ordinary differential equations with singularity at the origin. The problem has its origin in the classical work of Poincare. The authors define a normal form for differential systems whose linear part is nilpotent which is called nilpotent normal form. They give an algorithm for the computation of the normal form and the transformation that leads a system to its normal form. The elementary notations and methods used in the paper are the Carleman linearizations of differential systems and formal diffeomorphisms.", acknowledgement = ack-nhfb, affiliation = "Dept. de Math., Univ. Louis Pasteur, Strasbourg, France", classification = "C4170 (Differential equations)", keywords = "algorithms; Carleman linearizations; Formal diffeomorphisms; Nilpotent normal form; Nonlinear ordinary differential equations; Normal form; Singularity; Transformation", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Nonlinear differential equations", } @InProceedings{Cohen:1991:OES, author = "Ian Cohen and Karl-Erik E. Thylwe", title = "Obtaining exact steady-state responses in driven undamped oscillators", crossref = "Watt:1991:IPI", pages = "319--320", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p319-cohen/", abstract = "Exact solutions are very scarce in non-linear applied mathematics. However, exact solutions can be an invaluable aid to understanding how well an approximate method is working. It can also be used as a `stepping off' solution into parameter regions where no exact solutions exist. Most importantly however, each exact solution is a potential candidate for a new area of research as it can contain new insights into the physics of the equation under investigation or may be used to replace numerical methods in an investigation. Another important motivation is the synthesis in this project of Gr{\"o}bner bases with dynamical systems research, two areas at the forefront of modern research.", acknowledgement = ack-nhfb, affiliation = "Dept. of Mech., R. Inst. of Technol., Stockholm, Sweden", classification = "C4170 (Differential equations)", keywords = "algorithms; Steady-state responses; Undamped oscillators; Gr{\"o}bner bases; Dynamical systems", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", thesaurus = "Differential equations; Nonlinear systems", } @InProceedings{Crouch:1991:CID, author = "Peter Crouch and Robert Grossman and Richard Larson", title = "Computations involving differential operators and their actions on functions", crossref = "Watt:1991:IPI", pages = "301--307", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p301-crouch/", abstract = "Further develops the authors algorithms for rewriting expressions involving differential operators. The differential operators considered arise in the local analysis of nonlinear dynamical systems. The authors extend these algorithms in two different directions: they generalize the algorithms so that they apply to differential operators on groups and develop the data structures and algorithms to compute symbolically the action of differential operators on functions. Both of these generalizations are needed for applications. The paper is preliminary: a final paper containing proofs and a further analysis of the algorithm will appear elsewhere.", acknowledgement = ack-nhfb, affiliation = "Arizona State Univ., Tempe, AZ, USA", classification = "C6120 (File organisation); C7310 (Mathematics)", keywords = "algorithms; Data structures; Differential operators; Nonlinear dynamical systems; Rewriting expressions; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", thesaurus = "Rewriting systems; Symbol manipulation", } @InProceedings{Czapor:1991:HSS, author = "S. R. Czapor", title = "A heuristic selection strategy for lexicographic {Gr{\"o}bner} bases?", crossref = "Watt:1991:IPI", pages = "39--48", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p39-czapor/", abstract = "It is well known that the computation of lexicographic Gr{\"o}bner bases using the Buchberger's algorithm is more difficult than the computation of Gr{\"o}bner bases with respect to total degree orderings. The lexicographic algorithm is particularly susceptible to the problem of intermediate expression swell; that is, intermediate polynomials may be far larger than those which make up the final basis. To some extent, this is a function of `selection strategy', i.e. the order in which S-polynomials are used to extend a partial basis. The paper argues and provides empirical evidence that for the lexicographic ordering (in direct contrast to the case of degree orderings), a simple heuristic strategy will in practice control intermediate growth more effectively than the normal strategy based on the lexicographic term ordering alone. The results is usually a much more efficient computation, even for nonzero dimension ideals.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Stat. and Comput. Sci., Dalhousie Univ., Halifax, NS, Canada", classification = "C4130 (Interpolation and function approximation)", keywords = "algorithms; Heuristic selection strategy; Lexicographic Gr{\"o}bner bases; Buchberger's algorithm; Intermediate expression swell; Intermediate polynomials; S-polynomials; Partial basis; Lexicographic ordering; Intermediate growth; Nonzero dimension ideals", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf F.2.0} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, General.", thesaurus = "Polynomials", } @InProceedings{Davenport:1991:SVA, author = "J. H. Davenport and P. Gianni and B. M. Trager", title = "{Scratchpad}'s view of algebra. {II}. {A} categorical view of factorization", crossref = "Watt:1991:IPI", pages = "32--38", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p32-davenport/", abstract = "For pt.I see Proc. DISCO 1990 (p.40-54). The paper explains how Scratchpad solves the problem of presenting a categorical view of factorization in unique factorization domains, i.e. a view which can be propagated by functors such as SparseUnivariatePolynomial or Fraction. This is not easy, as the constructive version of the classical concept of UniqueFactorizationdomain cannot be so propagated. The solution adopted is based largely on the Seidenberg conditions ($F$) and ($P$), but there are several additional points that have to be borne in mind to produce reasonably efficient algorithms in the required generality. The consequence of the algorithms and interfaces presented is that Scratchpad can factorize in any extension of the integers or finite fields by any combination of polynomial, fraction and algebraic extensions: a capability far more general than any other computer algebra system possesses.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math., Bath Univ., Claverton Down, UK", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Algebraic extensions; algorithms; Categorical view; Computer algebra system; Factorization; Finite fields; Fraction; Integers; Polynomial; Scratchpad; Seidenberg conditions", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields.", thesaurus = "Mathematics computing; Polynomials; Symbol manipulation", } @InProceedings{deJager:1991:SCZ, author = "Bram de Jager", title = "Symbolic calculation of zero dynamics for nonlinear control systems", crossref = "Watt:1991:IPI", pages = "321--322", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p321-de_jager/", abstract = "The calculation of the zero dynamics of a nonlinear system is of advantage in the design of controllers for this system. Because the calculation is difficult to do by hand, symbolic algebra programs are used. To access the usefulness of these programs and to solve some design problems, a MAPLE procedure, ZERODYN, is written to calculate the zero dynamics symbolically. The procedure can, however, not solve all problems, mainly because general symbolic algebra programs have insufficient capabilities to solve sets of nonlinear equations and partial differential equations. A realistic analysis problem shows this.", acknowledgement = ack-nhfb, affiliation = "Dept. of Mech. Eng., Eindhoven Univ. of Technol., Netherlands", classification = "C1340K (Nonlinear systems); C7310 (Mathematics)", keywords = "algorithms; experimentation; MAPLE procedure; Nonlinear control systems; Nonlinear system; Partial differential equations; Symbolic algebra; Zero dynamics; ZERODYN", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple.", thesaurus = "Nonlinear control systems; Symbol manipulation", } @InProceedings{Diaz:1991:DSD, author = "A. Diaz and E. Kaltofen and K. Schmitz and T. Valente and M. Hitz and A. Lobo and P. Smyth", title = "{DSC}: a system for distributed symbolic computation", crossref = "Watt:1991:IPI", pages = "323--332", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p323-diaz/", abstract = "DSC is a general purpose tool that allows the distribution of a computation over a network of Unix workstations. Its control mechanisms automatically start up daemon processes on the participating workstations in order to communicate data by the standard IP/TCP/UDP protocols. The user's program distributes either remote procedure calls or source code of programs and their corresponding input data files by calling a DSC library function. The authors have tested DSC with a primarily test for large integers and with a factorization algorithm for polynomials over large finite fields and observed significant speed-ups over executing the best-known methods on a single workstation computation. These experiments have been carried out not only on our local area network but also on off-site workstations at the University of Delaware.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C7310 (Mathematics)", keywords = "algorithms; Distributed symbolic computation; DSC; experimentation; Factorization algorithm; Large integers; Polynomials; Primarily test; Unix workstations", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and Techniques, User interfaces.", thesaurus = "Distributed processing; Software packages; Symbol manipulation", } @InProceedings{Faradzev:1991:CCC, author = "I. A. Faradzev and M. H. Klin", title = "For computations with coherent configurations", crossref = "Watt:1991:IPI", pages = "219--223", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p219-faradzev/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Permutations and combinations.", } @InProceedings{Faradzev:1991:CPC, author = "I. A. Faradzev and M. H. Klin", title = "Computer package for computations with coherent configurations", crossref = "Watt:1991:IPI", pages = "219--223", year = "1991", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "A collection of computer programs based on the Galois correspondence between coherent configurations and permutation groups is described. A number of examples of application of this package for construction of combinatorial objects with interesting properties and for solving some group theoretical problems (extension of a permutation group and intersection of subgroups) are presented.", acknowledgement = ack-nhfb, affiliation = "inst. for Syst. Studies, Acad. of Sci., Moscow, USSR", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "Coherent configurations; Combinatorial objects; Computer programs; Galois correspondence; Group theoretical problems; Permutation groups", thesaurus = "Group theory; Mathematics computing; Software packages; Symbol manipulation", } @InProceedings{Fateman:1991:CRL, author = "Richard J. Fateman", title = "Canonical representations in {Lisp} and applications to computer algebra systems", crossref = "Watt:1991:IPI", pages = "360--369", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p360-fateman/", abstract = "Lisp, as well as many other programming languages, provides for the creation of compound data-structures or objects. What if one follows a discipline in which any time one constructs an object which happens to be isomorphic to one previously stored, the constructor function simply returns the same location in memory as the first? The author discusses some of the advantages and show how an implementation fits neatly into Common Lisp. Some of the results are especially relevant for the design and implementation of efficient `general representation' computer algebra systems. The author gives some experimental results showing speedups of a factor of ten or more in basic operations such as simplification of sums.", acknowledgement = ack-nhfb, affiliation = "Dept. of Electron. Eng. and Comput. Sci., California Univ., Berkeley, CA, USA", classification = "C6120 (File organisation); C6140D (High level languages); C7310 (Mathematics)", keywords = "algorithms; Canonical representation; Computer algebra systems; experimentation; languages; Lisp", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Common Lisp. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Data structures; LISP; Symbol manipulation", } @InProceedings{Gaal:1991:RIF, author = "I. Ga{\'a}l and A. Peth{\"o} and M. Pohst", title = "On the resolution of index form equations", crossref = "Watt:1991:IPI", pages = "185--186", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p185-gaal/", abstract = "For practical applications it is very important to know a power integral basis of the algebraic number field $K$. The solutions of the index form equation, $I(x_2,\ldots{},x_n)=\pm 1$ in $x_2,\ldots{},x_n$ in $Z$ enable one to determine all power integral bases of $K$. If there are no power integral bases, then the best is to determine all integral elements of $K$, having the least possible index, i.e. to determine the least positive $m$ in $Z$ for which $I(x_2,\ldots{},x_n)=\pm m$ in $x_2,\ldots{},x_n$ in $Z$ is soluble and to compute all solutions of this equation to find all integral elements with least index. The authors discuss their attempts at constructing algorithms to solve the equations and results obtained.", acknowledgement = ack-nhfb, affiliation = "Kossuth Lajos Univ., Debrecen, Hungary", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)", keywords = "algorithms; Index form equations; Power integral basis", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", thesaurus = "Algebra; Number theory", } @InProceedings{Ganzha:1991:SAD, author = "V. G. Ganzha and B. Yu. Scobelev and E. V. Vorozhtsov", title = "Stability analysis of difference schemes by the catastrophe theory methods and by means of computer algebra", crossref = "Watt:1991:IPI", pages = "427--428", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p427-ganzha/", abstract = "A new method for determining the stability domains of difference schemes(d.s.) is based on the Fourier method and the methods of catastrophe theory. In the paper the authors propose a symbolic-numerical approach to a realization of the method of the work.", acknowledgement = ack-nhfb, affiliation = "Inst. of Theor. and Appl. Mech., Acad. of Sci., Novosibirsk, USSR", classification = "C4170 (Differential equations)", keywords = "algorithms; Catastrophe theory; Computer algebra; Difference schemes; Stability analysis; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Catastrophe theory; Convergence of numerical methods; Difference equations; Symbol manipulation", } @InProceedings{Gao:1991:CPE, author = "Xiao-Shan Gao and Shang-Ching Chou", title = "Computations with parametric equations", crossref = "Watt:1991:IPI", pages = "122--127", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p122-gao/", abstract = "The authors present a complete method of implicitization for general rational parametric equations. They also present a method to decide whether the parameters of a set of parametric equations (PEs) are independent, and if not, to reparameterize the PEs so that the new PEs have independent parameters. They give a method to compute the inversion maps of the PEs with independent parameters, and as a consequence, they can decide whether the PEs are proper. A new method to find a proper reparameterization for a set of improper PEs of algebraic curves is presented.", acknowledgement = ack-nhfb, affiliation = "Inst. of Syst. Sci., Acad. Sinica, Beijing, China", classification = "C4130 (Interpolation and function approximation)", keywords = "Algebraic curves; algorithms; Implicitization; Independent parameters; Inversion maps; Rational parametric equations; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Polynomials", } @InProceedings{Gatermann:1991:MSS, author = "Karin Gatermann", title = "Mixed symbolic-numeric solution of symmetrical nonlinear systems", crossref = "Watt:1991:IPI", pages = "431--432", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p431-gatermann/", abstract = "The mixed symbolic-numeric algorithm SYMCON for the fully automatic treatment of equivariant systems is presented. The global aspects of the theory of Vanderbauwhede (1982) for these systems are viewed with regard to the full bifurcation scenario containing solution paths with different isotropy groups and symmetry preserving and symmetry breaking bifurcation points. The advanced exploitation of symmetry in the numerical computations causes a comprehensive symmetry analysis and complicated organization of numerical work which is done by the symbolic part of the algorithm.", acknowledgement = ack-nhfb, affiliation = "Konrad-Zuse-Zentrum Berlin, Germany", classification = "C1340K (Nonlinear systems); C4150 (Nonlinear and functional equations)", keywords = "algorithms; Bifurcation points; Equivariant systems; Symbolic-numeric algorithm; SYMCON; Symmetrical nonlinear systems; Symmetry analysis; theory", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Nonlinear systems; Symbol manipulation", } @InProceedings{Gebauer:1991:CCA, author = "R. Gebauer and M. Kalkbrener and B. Wall and F. Winkler", title = "{CASA}: a computer algebra package for constructive algebraic geometry", crossref = "Watt:1991:IPI", pages = "403--410", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p403-gebauer/", abstract = "The program package CASA is designed to enhance the power of a traditional computer algebra system by adding programs for constructive algebraic geometry. The objects that CASA works with are algebraic sets in affine or projective spaces over a field. The geometric objects may be given in various different representations. CASA is able to analyse properties of algebraic sets, such as to compute their dimensions, compute their irreducible components, determine singular points, determine intersection properties and the like. The user can also create 2- and 3-dimensional pictures of curves and surfaces.", acknowledgement = ack-nhfb, affiliation = "Johannes Kepler Univ., Linz, Austria", classification = "C4190 (Other numerical methods)", keywords = "Algebraic geometry; Algebraic sets; algorithms; CASA; Computer algebra; Computer algebra package; Constructive algebraic geometry; Intersection properties; Irreducible components; Singular points", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Computational geometry; Symbol manipulation", } @InProceedings{Gerdt:1991:LSC, author = "V. P. Gerdt and N. V. Khutornoy and A. Yu. Zharkov", title = "{Lie--B{\"a}cklund} symmetries of coupled nonlinear {Schr{\"o}dinger} equations", crossref = "Watt:1991:IPI", pages = "313--314", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p313-gerdt/", abstract = "Applies computer-aided symmetry approach to an investigation of an eight-parametric system of two coupled nonlinear Schr{\"o}dinger equations. Symmetry approach allows one not only to verify the necessary integrability conditions which follow from the existence of a higher infinitesimal or Lie--B{\"a}cklund symmetry but often to find an explicit form of the latter. The corresponding necessary conditions in the form of existence of the series of the local conservation laws lead to the system of nonlinear algebraic equations in numeric parameters. As a result of the first two necessary integrability conditions the REDUCE program provided with some new additional facilities, generates the three set of algebraic equations.", acknowledgement = ack-nhfb, affiliation = "JINR, Moscow, USSR", classification = "C4170 (Differential equations)", keywords = "algorithms; Lie--B{\"a}cklund symmetry; Nonlinear Schr{\"o}dinger equations", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", thesaurus = "Schr{\"o}dinger equation; Symbol manipulation", } @InProceedings{Giovini:1991:OSC, author = "Alessandro Giovini and Teo Mora and Gianfranco Niesi and Lorenzo Robbiano and Carlo Traverso", title = "`One sugar cube, please' or selection strategies in the {Buchberger} algorithm", crossref = "Watt:1991:IPI", pages = "49--54", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p49-giovini/", abstract = "The paper describes some experimental findings on selection strategies for Gr{\"o}bner basis computation with the Buchberger algorithm. In particular, the results suggest that the sugar flavor of the normal selection is the best choice for a selection strategy. It has to be combined with the straightforward simplification strategy and with a special form of the Gebauer--Moller criteria to obtain the best results. The idea of the sugar flavor is the following: the Buchberger algorithm for homogeneous ideals, with degree-compatible term ordering and normal selection strategy, usually works fine. Homogenizing the basis of the ideal is good for the strategy, but bad for the basis to be computed. The sugar flavor computes, for every polynomial in the course of the algorithm, `the degree that it would have if computed with the homogeneous algorithm', and uses this phantom degree (the sugar) only for the selection strategy.", acknowledgement = ack-nhfb, affiliation = "Dipartimento di Matematica, Genova Univ., Italy", classification = "C4130 (Interpolation and function approximation)", keywords = "algorithms; experimentation; Selection strategies; Buchberger algorithm; Gr{\"o}bner basis computation; Sugar flavor; Normal selection; Straightforward simplification strategy; Gebauer--Moller criteria; Homogeneous ideals; Degree-compatible term ordering; Polynomial; Homogeneous algorithm; Phantom degree", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Polynomials", } @InProceedings{Gonzalez-Vega:1991:STM, author = "Laureano Gonz{\'a}lez-Vega", title = "A subresultant theory for multivariate polynomials", crossref = "Watt:1991:IPI", pages = "79--85", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p79-gonzalez-vega/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Gonzalez-Vega:1991:WRA, author = "Laureano Gonz{\'a}lez-Vega", title = "Working with real algebraic plane curves in {REDUCE} the {GCUR} package", crossref = "Watt:1991:IPI", pages = "397--402", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p397-gonzalez-vega/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.", } @InProceedings{GonzalezVega:1991:STM, author = "L. {Gonzalez Vega}", title = "A subresultant theory for multivariate polynomials", crossref = "Watt:1991:IPI", pages = "79--85", year = "1991", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "In computer algebra, subresultant theory provides a powerful method to construct algorithms solving problems for polynomials in one variable in an optimal way. The paper extends the subresultant theory to the multivariate case. In order to achieve this, first of all, it introduces the definition of a subresultant sequence associated to two polynomials in one variable with coefficients in an integral domain, describing the properties of this sequence that one would like to extend to the multivariate case. In the second section it generalizes the definition of a subresultant polynomial to the multivariate case, showing that many of the properties obtained in the one variable case work also in the multivariate case. In this way it shows how these subresultants can be used to get a greatest common divisor of $n$ polynomials in $D(x_1,\ldots{},x_{n-1})$ where $D$ is an integral domain. The paper then applies this subresultant theory to get a determinantal formula for the solution set of almost all $0$-dimensional ideals defined by $n$ polynomials in $D(x_1, \ldots{}, x_n)$, with $D$ an integral domain. Finally, some open problems related with this construction are shown.", acknowledgement = ack-nhfb, affiliation = "Dept. de Matematicas, Cantabria Univ., Santander, Spain", classification = "C4130 (Interpolation and function approximation)", keywords = "0-Dimensional ideals; Computer algebra; Determinantal formula; Greatest common divisor; Integral domain; Multivariate polynomials; Solution set; Subresultant polynomial; Subresultant sequence; Subresultant theory", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{GonzalezVega:1991:WRA, author = "L. {Gonzalez Vega}", title = "Working with real algebraic plane curves in {REDUCE}: the {GCUR} package", crossref = "Watt:1991:IPI", pages = "397--402", year = "1991", bibdate = "Sat Apr 25 12:53:35 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents an implementation in Reduce of a package to get topological and geometric information about real algebraic plane curves defined as the real zeros of polynomials in $Z(x, y)$. More precisely, if $P$ in $Z(x,y)$ the output using the package GCUR will be a plane graph homeomorphic to the set: $C(P)=((\alpha,\beta) {\rm in } R^2/P(\alpha,\beta)=0)$.", acknowledgement = ack-nhfb, affiliation = "Dept. Mat., Cantabria Univ., Santander, Spain", classification = "C4190 (Other numerical methods)", keywords = "Algebraic plane curves; GCUR; Geometric information; Plane graph; REDUCE; Topological information", thesaurus = "Computational geometry; Poles and zeros; Polynomials; Symbol manipulation; Topology", } @InProceedings{Grigoriev:1991:ASR, author = "Dima Yu. u. Grigoriev and Marek Karpinski", title = "Algorithms for sparse rational interpolation", crossref = "Watt:1991:IPI", pages = "7--13", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p7-grigoriev/", abstract = "Presents two algorithms for interpolating sparse rational functions. The first is the interpolation algorithm in a sense of sparse partial fraction representation of rational functions. The second is the algorithm for computing the entier and the remainder of a rational function. The first algorithm works without a priori known bound on the degree of a rational function, the second one is in the parallel class NC provided that the degree is known.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Bonn Univ., Germany", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Entier; Interpolation algorithm; NC; Parallel class; Remainder; Sparse partial fraction representation; Sparse rational functions", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Computational complexity; Interpolation; Parallel algorithms", } @InProceedings{Grudtsin:1991:ISI, author = "S. N. Grudtsin and V. N. Larin", title = "Integrated system {INTERCOMP} and computer language for physicists", crossref = "Watt:1991:IPI", pages = "377--381", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p377-grudtsin/", abstract = "Contains a description of a general approach to physics related integrated software elaborations. A development history and modern stage of the INTERCOMP system, containing a large set of language and program means for a description and computer analysis of physical models are also described. The system has a high level interpreted language and includes a powerful symbolic algebraic computation subsystem, a numeric algorithms library, a relational DBMS, a graphic package, editor and text processor.", acknowledgement = ack-nhfb, affiliation = "Inst. for High Energy Phys., Protvino, USSR", classification = "C6140D (High level languages); C7320 (Physics and Chemistry)", keywords = "Algebraic; Computer analysis; Computer language; Graphic package; Integrated software elaborations; INTERCOMP; languages; Numeric algorithms; Physical models; Relational DBMS; Symbolic computation", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "High level languages; Physics computing; Symbol manipulation", } @InProceedings{Havas:1991:CES, author = "George Havas", title = "Coset enumeration strategies", crossref = "Watt:1991:IPI", pages = "191--199", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p191-havas/", abstract = "A primary reference on computer implementation of coset enumeration procedures is a 1973 paper of Cannon, Dimino, Havas and Watson. Programs and techniques described there are updated in this paper. Improved coset definition strategies, space saving techniques and advice for obtaining improved performance are included. New coset definition strategies for Felsch-type methods give substantial reductions in total cosets defined for some pathological enumerations. Significant time savings are achieved for coset enumeration procedures in general. Statistics on performance are presented, both in terms of time and in terms of maximum and total cosets defined for selected enumerations.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Queensland Univ., St. Lucia, Qld., Australia", classification = "C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "Coset definition strategies; Coset enumeration procedures; Felsch-type methods; Pathological enumerations; performance; Subgroups", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, CAYLEY.", thesaurus = "Mathematics computing; Set theory", } @InProceedings{Hietarinta:1991:SIP, author = "Jarmo Hietarinta", title = "Searching for integrable {PDE}'s by testing {Hirota}'s three-soliton condition", crossref = "Watt:1991:IPI", pages = "295--300", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p295-hietarinta/", abstract = "The search for integrable PDE's has been an active research subject with computer algebra as a necessary tool. The author describes a search method based on the requirement that standard type three- and four-soliton solution exist in the bilinear formalism of Hirota. The existence of $N$-soliton solutions can be formulated as a requirement that a certain high degree polynomial in $N*M$ variables vanishes on an affine manifold defined by $N$ polynomials of $M$ variables each. An exhaustive search has been carried out for certain classes of typical equations and several new equations have been found.", acknowledgement = ack-nhfb, affiliation = "Dept. of Phys., Turku Univ., Finland", classification = "A0230 (Function theory, analysis); A0340K (Waves and wave propagation: general mathematical aspects)", keywords = "algorithms; Bilinear formalism; Computer algebra; Integrable PDE's; Search method; theory; Three-soliton condition", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Partial differential equations; Search problems; Solitons; Symbol manipulation", } @InProceedings{Ilyin:1991:PIF, author = "V. A. Ilyin and A. P. Kryukov and A. Ya. Rodionov and A. Yu. Taranov", title = "{PC} implementation of fast {Dirac} matrix trace calculations", crossref = "Watt:1991:IPI", pages = "456--457", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p456-ilyin/", abstract = "Presents an implementation of a fast algorithm for Dirac matrix trace calculations. This implementation is made for IBM compatible PC and works under REDUCE 3.3.1. Name of package is CVIT. The algorithm is based on intense use of Fierz identities in N-dimensional space ($N$ is arbitrary natural number or symbol) and may be considered as an extension of well known Kahane algorithm on higher space dimensions.", acknowledgement = ack-nhfb, affiliation = "Inst. for Nucl. Phys., Moscow State Univ., USSR", classification = "C7320 (Physics and Chemistry)", keywords = "algorithms; CVIT; Dirac matrix trace calculations; Fierz identities; IBM compatible PC; Kahane algorithm; N-dimensional space; REDUCE 3.3.1", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics.", thesaurus = "IBM computers; Matrix algebra; Physics computing; Symbol manipulation", } @InProceedings{Ilyin:1991:SST, author = "V. A. Ilyin and A. P. Kryukov", title = "Symbolic simplification of tensor expressions using symmetries, dummy indices and identities", crossref = "Watt:1991:IPI", pages = "224--228", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p224-ilyin/", abstract = "The algorithm based on simple geometrical ideas is suggested for simplification of tensor expressions which takes into account symmetries, dummy indices, and linear identities with many terms. The results of the realization in REDUCE system are adduced. The Riemann tensor is used as an example.", acknowledgement = ack-nhfb, affiliation = "Inst. for Nucl. Phys., Moscow State Univ., USSR", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "algorithms; Dummy indices; Geometrical ideas; Linear identities; REDUCE; Simplification; Symbolic simplification; Symmetries; Tensor expressions", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Kleczka:1991:SCA, author = "W. Kleczka and E. Kreuzer", title = "Systematic computer-aided analysis of dynamic systems", crossref = "Watt:1991:IPI", pages = "429--430", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p429-kleczka/", abstract = "An automated numerical-symbolical analysis concept for dynamic systems in engineering mechanics is outlined. Besides the computerized generation of symbolic equations of motion, the subsequent analysis is also performed by means of computer algebra in combination with well-established numerical methods.", acknowledgement = ack-nhfb, affiliation = "Meerestech. II, Tech. Univ., Hamburg-Harburg, Germany", classification = "C1210 (General system theory); C7440 (Civil and mechanical engineering)", keywords = "algorithms; Computer-aided analysis; Dynamic systems; Engineering mechanics; Numerical-symbolical analysis; Symbolic equations", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues and eigenvectors (direct and iterative methods).", thesaurus = "Computer aided analysis; Convergence of numerical methods; Mechanical engineering computing; Symbol manipulation", } @InProceedings{Kornyak:1991:PSA, author = "V. V. Kornyak and W. I. Fushchich", title = "A program for symmetry analysis of differential equations", crossref = "Watt:1991:IPI", pages = "315--316", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p315-kornyak/", abstract = "Proposes in this work a program for determining Lie--B{\"a}cklund (LB) symmetries of (partial or ordinary) differential equations and for classification of equations containing arbitrary functions and parameters with respect to symmetries of this kind. The program was implemented in Turbo C language and designed in such a way to be more effective for systems of equations with multidimensional spaces of independent and dependent variables. The internal data structures for representation of expressions are right-threaded binary trees. The program reduces input system of equations to the passive form, computes the differential consequences of equations up to the needed order, constructs the invariance conditions for a given order LB symmetries, eliminates the dependencies between the invariance conditions using differential manifold, separates the determining equations and tries to integrate them.", acknowledgement = ack-nhfb, affiliation = "Dept. of Appl. Res., Acad. of Sci., Kiev, Ukrainian SSR, USSR", classification = "C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; Differential equations; languages; Lie--B{\"a}cklund symmetries; Symmetry analysis", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Turbo C.", thesaurus = "Differential equations", } @InProceedings{Kuchlin:1991:MCI, author = "Wolfgang K{\"u}chlin", title = "On the multi-threaded computation of integral polynomial greatest common divisors", crossref = "Watt:1991:IPI", pages = "333--342", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p333-kuchlin/", abstract = "Reports experiences and practical results from parallelizing the Brown--Collins polynomial g.c.d. algorithm, starting from Collins' SAC-2 implementation IPGCDC. The parallelization environment is PARSAC-2, a multi-threaded version of SAC-2 programmed in C with the parallelization constructs of the C Threads library. IPGCDC computes the g.c.d. and its co-factors of two polynomials in $Z(x_1,\ldots{},x_r)$, by first reducing the problem to multiple calculations of modular polynomial g.c.d.'s in $Z_p(x_1,\ldots{},x_r)$, and then recovering the result by Chinese remaindering. After studying timings of the SAC-2 algorithm, the author first parallelizes the Chinese remainder algorithm, and then parallelizes the main loop of IPGCDC by executing the modular g.c.d. computations concurrently. Finally, he determines speed-up's and speed-up efficiencies of our parallel algorithms over a wide range of polynomials. The experiments were conducted on a 12 processor Encore Multimax under Mach.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ., Columbus, OH, USA", classification = "C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Brown--Collins polynomial g.c.d. algorithm; Chinese remaindering; Encore Multimax; Multi-threaded computation; PARSAC-2; Polynomial greatest common divisors", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C.", thesaurus = "Mathematics computing; Parallel algorithms; Symbol manipulation", } @InProceedings{Langemyr:1991:ASA, author = "Lars Langemyr", title = "An analysis of the subresultant algorithm over an algebraic number field", crossref = "Watt:1991:IPI", pages = "167--172", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p167-langemyr/", abstract = "The author shows that one can compute the subresultant polynomial remainder sequence over an algebraic number field in $O((n^5m^3+n^4m^5) \log^2(nDE^m))$ binary operations, where the generator of the field is given by a monic irreducible polynomial of degree $m$ with integer coefficients bounded by $E$ in absolute value, and where the two input polynomials are of degree at most $n$ and with integer coefficients bounded by $D$ in absolute value.", acknowledgement = ack-nhfb, affiliation = "Numerical Anal. and Comput. Sci., R. Inst. of Technol., Stockholm, Sweden", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Algebraic number field; algorithms; Greatest common division; Integer coefficients; Monic irreducible polynomial; Subresultant polynomial remainder sequence", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Algebra; Computational complexity; Mathematics computing; Number theory; Polynomials", } @InProceedings{Letichevsky:1991:APO, author = "A. A. Letichevsky and J. V. Kapitonova and S. V. Konozenko", title = "Algebraic programs optimization", crossref = "Watt:1991:IPI", pages = "370--376", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p370-letichevsky/", abstract = "Algebraic program is a system of relations (equalities of data algebra) with a given strategy for applying these relations as rewriting rules. An algebraic program may be optimized by transforming a system of relations or by transforming a strategy. Only second case of optimization is considered in the paper. The problem of algebraic program optimization is investigated in the context of programming in the APS-1 system.", acknowledgement = ack-nhfb, affiliation = "Glushkov Inst. of Cybern., Acad. of Sci., Kiev, Ukrainian SSR, USSR", classification = "C6110 (Systems analysis and programming); C7310 (Mathematics)", keywords = "Algebraic program optimization; algorithms; APS-1; Data algebra; languages; Programming; Rewriting rules; System of relations", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", thesaurus = "Optimisation; Programming; Symbol manipulation", } @InProceedings{Liska:1991:ADS, author = "Richard Liska and Michail Yu. u. Shashkov", title = "Algorithms for difference schemes construction on non-orthogonal logically rectangular meshes", crossref = "Watt:1991:IPI", pages = "419--426", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p419-liska/", abstract = "Deals with the formalization of the basic operator method for construction of difference schemes for the numerical solving of partial differential equations. The strength of the basic operator method lies in the fact that it produces fully conservative difference schemes. The difference mesh can be non-orthogonal but has to be logically orthogonal. Algorithms for working with grid functions and grid operators in symbolic form which are necessary in the basic operator method are described. The algorithms have been implemented in the computer algebra system REDUCE.", acknowledgement = ack-nhfb, affiliation = "Fac. of Nucl. Sci. and Phys. Eng., Czech Tech. Univ., Prague, Czechoslovakia", classification = "C4170 (Differential equations)", keywords = "algorithms; Basic operator method; Computer algebra; Difference mesh; Difference schemes; Grid functions; Grid operators; Logically orthogonal; Numerical solving; Partial differential equations; Rectangular meshes; REDUCE", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Numerical methods; Partial differential equations; Symbol manipulation", } @InProceedings{Manocha:1991:ETM, author = "Dinesh Manocha and John Canny", title = "Efficient techniques for multipolynomial resultant algorithms", crossref = "Watt:1991:IPI", pages = "86--95", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p86-manocha/", abstract = "The paper presents efficient techniques for applying multipolynomial resultant algorithms and shows their effectiveness for manipulating systems of polynomial equations. In particular, it presents efficient algorithms for computing the resultant of a system of polynomial equations (whose coefficients may be symbolic variables). These algorithms can be used for interpolating polynomials from their values and expanding symbolic determinants. Moreover, it uses multipolynomial resultants for computing the real or complex solutions of nonlinear polynomial equations. It also discusses the implementation of these algorithms in the context of certain applications.", acknowledgement = ack-nhfb, affiliation = "Comput. Sci. Div., California Univ., Berkeley, CA, USA", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Complex solutions; Efficient algorithms; Multipolynomial resultant algorithms; Nonlinear polynomial equations; Polynomial interpolation; Real solutions; Symbolic determinants; Symbolic variables", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", thesaurus = "Algorithm theory; Interpolation; Polynomials", } @InProceedings{Marinari:1991:GBI, author = "M. G. Marinari and H. M. M{\"o}ller and T. Mora", title = "{Gr{\"o}bner} bases of ideals given by dual bases", crossref = "Watt:1991:IPI", pages = "55--63", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p55-marinari/", abstract = "In 1982, Buchberger and Moller proposed an algorithm which, given a finite number of rational points in the affine $n$-dimensional space, computes a Gr{\"o}bner basis for the ideal I of the polynomials vanishing at the points. In 1988, Faugere, Gianni, Lazard and Mora supplied an algorithm, which, given the reduced Gr{\"o}bner basis w.r.t. some term-ordering $<_1$ of a 0-dim. ideal I, returns its reduced Gr{\"o}bner basis w.r.t. some other term-ordering $<_2$. The paper systematizes and generalizes the common properties of the Buchberger--M{\"o}ller and the FGLM algorithms to the frame of ideals defined by functionals. It gives two algorithms to compute the Gr{\"o}bner basis of an ideal defined by functionals, together with a set of biorthogonal polynomials: the first one is a direct generalization of the B-M and the FGLM algorithms; the second one iteratively for each $i$ solves the question for the ideals defined by $L_1,\ldots{}, L_i$. It then measures the complexity of the algorithms in terms of the number of additions+multiplications in $K$ which they require and proves that both have a complexity of $1/2 s^3+s^2 b+f s (s+b)<=O (n s^3+f n s^2)$.", acknowledgement = ack-nhfb, affiliation = "Dipartimento di Matematica, Genova Univ., Italy", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Gr{\"o}bner bases; Ideals; Dual bases; Rational points; Affine $n$-dimensional space; Term-ordering; Functionals; Biorthogonal polynomials; Complexity", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", thesaurus = "Computational complexity; Polynomials", } @InProceedings{Marzinkewitsch:1991:OCA, author = "Reiner Marzinkewitsch", title = "Operating computer algebra systems by handprinted input", crossref = "Watt:1991:IPI", pages = "411--413", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p411-marzinkewitsch/", abstract = "Nearly twenty years have passed since the first computer algebra systems (CAS) came up in the beginning of the seventies. Since then CAS have gained a lot of computational power. In contrast to this fact CAS have not experienced the deserved widespread use by potential users. The main reason for this discrepancy is the unnatural operation of CAS by artificial linearized notations, which tend to give little comprehensive survey of the problem under work. Calculation with pencil and paper not only offers many efficient techniques but also appeals to the user's ease. Especially occasional users need a familiar i.e. paperlike interface to CAS. In this paper an integrated system is presented, which offers the demanded facilities: Calculating by hand in a traditional, `two dimensional' fashion with the computational support of a CAS.", acknowledgement = ack-nhfb, affiliation = "Fachbereich 14, Saarlandes Univ., Saarbrucken, Germany", classification = "C5260B (Computer vision and picture processing); C5530 (Pattern recognition and computer vision equipment); C5540 (Terminals and graphic displays); C7310 (Mathematics)", keywords = "algorithms; CAS; Computer algebra systems; design; Handprinted input", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf H.5.2} Information Systems, INFORMATION INTERFACES AND PRESENTATION, User Interfaces, Interaction styles.", thesaurus = "Character recognition; Neural nets; Symbol manipulation; Workstations", } @InProceedings{Molenkamp:1991:IAA, author = "J. H. J. Molenkamp and V. V. Goldman and J. A. {van Hulzen}", title = "An improved approach to automatic error cumulation control", crossref = "Watt:1991:IPI", pages = "414--418", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p414-molenkamp/", abstract = "For evaluation of arithmetical expressions using multiple precision floating-point arithmetic, a method is given to automatically perform error cumulation control prior to the actual computations. Individual errors and their effects are identified, and it is shown how to compute these effects efficiently via automatic differentiation. In the presented approach these effects are used to determine which precisions have to be chosen during the real computations, in order to limit error cumulation to admissible, user chosen error bounds.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Twente Univ., Enschede, Netherlands", classification = "C4110 (Error analysis in numerical methods); C5230 (Digital arithmetic methods)", keywords = "algorithms; Arithmetical expressions; Computations; Error bounds; Error cumulation control; Multiple precision floating-point arithmetic", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", thesaurus = "Digital arithmetic; Error analysis", } @InProceedings{Oevel:1991:YES, author = "Walter Oevel and Klaus Strack", title = "The {Yang--Baxter} equation and a systematic search for {Poisson} brackets on associative algebras", crossref = "Watt:1991:IPI", pages = "229--236", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p229-oevel/", abstract = "Starting with an associative algebra equipped with a linear map solving the Yang--Baxter equation three Poisson brackets may be constructed admitting a common hierarchy of functions in involution. Realizations of the algebra lead to various integrable hierarchies known to admit an infinite number of invariant Poisson brackets. In all cases three of these brackets are known to originate from the three abstract brackets defined on the algebra. A systematic search for abstract versions of the higher Poisson brackets is performed using computer algebra. It is shown that apart from the three known brackets no further relevant abstract brackets of a certain `local' form may be constructed from solutions of the Yang--Baxter equations.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. Sci., Univ. of Technol., Loubhborough, UK", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "Abstract brackets; algorithms; Associative algebras; Computer algebra; Integrable hierarchies; Poisson brackets; Yang--Baxter equation", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Algebra; Mathematics computing", } @InProceedings{Pecelli:1991:FMD, author = "Giampiero Pecelli", title = "Formal methods in delay-differential equations", crossref = "Watt:1991:IPI", pages = "317--318", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p317-pecelli/", abstract = "Studies formal methods in the solution of delay-differential equations (DDEs). The motivation for such study comes from the introduction of Hopf bifurcation techniques and the method of averaging to the study of stable oscillations in such systems. The author concentrates on the formal aspects associated with the construction of solutions required for an application of the methods. These classes of solutions are quite simple, being solutions to linear systems. The paper concentrates on completing the formalization and showing that an automated system is possible.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Lowell Univ., MA, USA", classification = "C4170 (Differential equations)", keywords = "algorithms; DDEs; Delay-differential equations; Formal methods; Hopf bifurcation; Stable oscillations", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple.", thesaurus = "Differential equations", } @InProceedings{Petho:1991:AGB, author = "Attila Peth{\"o}", title = "Application of {Gr{\"o}bner} bases to the resolution of systems of norm equations", crossref = "Watt:1991:IPI", pages = "144--150", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p144-petho/", abstract = "Let $K$ be a cubic extension of the rational number field $Q$. Denote by $Z_K$ the ring of integers of $K$ and by $N_KQ/(\gamma )$ the norm of $\gamma$ in $K$. Let $P(x)=x^2+cx+d$ in $Z(x)$ and $a,b,n_1,n_2,n_3$, in $Z$. The paper gives necessary and sufficient conditions for the existence of cubic number fields $K$ and elements $\eta$ in $Z_K$ such that $N_KQ/(\eta)=n_1,N_KQ/(\eta-a)=n_2,N_KQ/(\eta-b)=n_3$; or $N_KQ/(\eta)=n_1,N_KQ/(P(\eta))=n_2$.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Kossuth Lajos Univ., Debrecen, Hungary", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)", keywords = "algorithms; theory; Gr{\"o}bner bases; Norm equations; Cubic extension; Rational number field; Integers; Necessary and sufficient conditions; Cubic number fields", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Number theory; Polynomials", } @InProceedings{Reid:1991:RSD, author = "G. J. Reid and A. Boulton", title = "Reduction of systems of differential equations to standard form and their integration using directed graphs", crossref = "Watt:1991:IPI", pages = "308--312", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p308-reid/", abstract = "Discusses an algorithm developed in earlier work which has been implemented in MACSYMA that reduces systems of partial differential equations to a simplified standard form by eliminating redundances and including all integrability conditions. Once a system has been put in standard form the authors show how directed graphs representing the dependencies amongst the system's variables can be used to simplify the problem of explicitly or numerically integrating the system.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., British Columbia Univ., Vancouver, BC, Canada", classification = "C1160 (Combinatorial mathematics); C4160 (Numerical integration and differentiation); C4170 (Differential equations)", keywords = "algorithms; Directed graphs; Integration; MACSYMA; Partial differential equations; Standard form", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA.", thesaurus = "Directed graphs; Integration; Partial differential equations", } @InProceedings{Renner:1991:NEE, author = "Friedrich Renner", title = "Nonlinear evolution equations and the {Painleve} analysis: a constructive approach with {REDUCE}", crossref = "Watt:1991:IPI", pages = "289--294", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p289-renner/", abstract = "A number of necessary conditions for a class of nonlinear partial differential equations to pass the Painleve test with the Kruskal ansatz is given. Using these one can (theoretically) construct all evolution equations of certain form and this property with a computer algebra package based on REDUCE.", acknowledgement = ack-nhfb, affiliation = "Kassel Univ., Germany", classification = "C4170 (Differential equations)", keywords = "algorithms; Computer algebra package; Evolution equations; Kruskal ansatz; Nonlinear partial differential equations; Painleve test; REDUCE; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Nonlinear differential equations; Partial differential equations; Symbol manipulation", } @InProceedings{Richardson:1991:TCN, author = "Daniel Richardson", title = "Towards computing nonalgebraic cylindrical decompositions", crossref = "Watt:1991:IPI", pages = "247--255", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p247-richardson/", abstract = "Non algebraic cylindrical decompositions are discussed. False derivatives and local Sturm sequences are defined as tools for computing them. The crucial fact in the algebraic case is that one can characterize the number of distinct real roots of a polynomial $p(y)$ by a condition on the coefficients. An attempt is made to obtain an analogous characterization for nonalgebraic functions such as polynomials in monomials which are defined by algebraic differential equations. An example would be an exponential polynomial $p(y,e^y)$. The difficulties of applying this characterization are described, using the example of exponential polynomials in two variables, $p(x,e^y,y,e^y)$. The characterization obtained does not lead to quantifier elimination.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Bath Univ., UK", classification = "C1110 (Algebra); C1120 (Analysis); C7310 (Mathematics)", keywords = "Algebraic differential equations; algorithms; Cylindrical decompositions; Differential geometry; Distinct real roots; Exponential polynomials; Local Sturm sequences; Monomials; Nonalgebraic functions; theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms.", thesaurus = "Algebra; Differential equations; Polynomials", } @InProceedings{Roch-Siebert:1991:PFE, author = "Fran{\c{c}}oise Roch-Siebert and Gilles Villard", title = "{PAC}: first experiments on a 128 transputers m{\'e}ganode", crossref = "Watt:1991:IPI", pages = "343--351", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p343-roch-siebert/", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf C.1.2} Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Multiple-instruction-stream, multiple-data-stream processors (MIMD).", } @InProceedings{RochSiebert:1991:PFE, author = "F. Roch-Siebert and G. Villard", title = "{PAC}: first experiments on a 128 transputers meganode", crossref = "Watt:1991:IPI", pages = "343--351", year = "1991", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "From its beginning three years ago, the PAC project: parallel algebraic computing, has been exploiting a 16 processors hypercube to validate some algebraic computation algorithms, and to justify the use of parallelism. Going further, the authors begin to generalize the previous results and study new problems. Experiments are now held on a more massively parallel computer: a 128 Transputers network. The authors present the first results have obtained: as an example, they have been interested in applying the Chinese remainder theorem in linear algebra. For a fixed number of processors, they show how the behaviour of an algorithm is influenced by the chosen network topology. They point out the communication costs and the constraints due to the storage requirements.", acknowledgement = ack-nhfb, affiliation = "Equipe Calcul Parallele et Calcul Formel, CNRS, Grenoble, France", classification = "C4140 (Linear algebra); C7310 (Mathematics)", keywords = "Algebraic computation; Chinese remainder theorem; Linear algebra; Network topology; PAC project; Parallel algebraic computing; Parallelism", thesaurus = "Linear algebra; Parallel algorithms; Symbol manipulation", } @InProceedings{Roelofs:1991:IMO, author = "Marcel Roelofs and Peter K. H. Gragert", title = "Implementation of multilinear operators in {REDUCE} and applications in mathematics", crossref = "Watt:1991:IPI", pages = "390--396", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p390-roelofs/", abstract = "Introduces and implement a concept for dealing with mathematical bases of linear spaces and mappings (multi)linear with respect to such bases, in REDUCE (cf. (1)). Using this concept the authors give some examples how to implement some well known (multi)linear mappings in mathematics with very little effort. Moreover they implement a procedure operatorcoeff similar to the standard REDUCE procedure coeff, but now for linear spaces instead of polynomial rings.", acknowledgement = ack-nhfb, affiliation = "Dept. of Appl. Math., Twente Univ., Enschede, Netherlands", classification = "C4140 (Linear algebra); C7310 (Mathematics)", keywords = "algorithms; Linear spaces; Mappings; Multilinear operators; REDUCE", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions.", thesaurus = "Linear algebra; Symbol manipulation", } @InProceedings{Roque:1991:QRD, author = "W. L. Roque and R. P. {dos Santos}", title = "Qualitative reasoning, dimensional analysis and computer algebra", crossref = "Watt:1991:IPI", pages = "460--461", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p460-roque/", abstract = "In this short application report the authors discuss qualitative reasoning about physical processes under the framework of dimensional analysis. The symbolic system QDR-Qualitative Dimensional Reasoner-has been developed to automate the whole qualitative reasoning analysis.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C1230 (Artificial intelligence)", keywords = "algorithms; Computer algebra; Dimensional analysis; languages; Physical processes; Qualitative reasoning; Reasoning; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems.", thesaurus = "Inference mechanisms; Symbol manipulation", } @InProceedings{Rudenko:1991:ACA, author = "V. M. Rudenko and V. V. Leonov and A. F. Bragazin and I. P. Shmyglevsky", title = "Application of computer algebra to the investigation of the orbital satellite motion", crossref = "Watt:1991:IPI", pages = "450--451", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p450-rudenko/", abstract = "Presents the features of a program package `Polymech-symbol' helping to solve some laborious mechanical problems. The package was written by means of the REDUCE system and contains several algorithms in a form of REDUCE procedures. The authors consider the problems of navigation and center of mass motion on board a satellite.", acknowledgement = ack-nhfb, affiliation = "Inst. for Problems of Mech., Acad. of Sci., Moscow, USSR", classification = "C7460 (Aerospace engineering)", keywords = "algorithms; Center of mass motion; Computer algebra; Navigation; Orbital satellite motion; Polymech-symbol; REDUCE system", subject = "{\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Aerospace.", thesaurus = "Aerospace computing; Artificial satellites; Symbol manipulation", } @InProceedings{Rybowicz:1991:ACI, author = "Marc Rybowicz", title = "An algorithm for computing integral bases of an algebraic function field", crossref = "Watt:1991:IPI", pages = "157--166", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p157-rybowicz/", abstract = "The author presents a new algorithm for function fields which borrows techniques from previous methods and works in any characteristic. Theorem 5 allows one to reduce the problem to the factorization of rational primes via some standard linear algebra techniques. He, in turn, reduces this factorization problem to study how two branches of the underlying curve intersect. This latter task is achieved with the help of the `Hamburger--Noether Development', a special type of local parametrization. He expects the algorithm to be more efficient than Zassenhaus' global approach and to highlight the classical local approach. Moreover, the techniques presented allow one to build a function with specified zeros in any characteristic and could be applied to other problems. Although the algorithm is complete, some steps clearly need to be improved and studied more carefully before attempting any implementation. In particular, he assumes that the constant field is algebraically closed, but a `rational' extension of the algorithm would be welcome.", acknowledgement = ack-nhfb, affiliation = "Symbolic Comput. Group, Waterloo Univ., Ont., Canada", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "Algebraic function field; algorithms; Factorization; Hamburger--Noether Development; Integral bases; Linear algebra; Local parametrization; Rational primes", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Group theory; Mathematics computing; Number theory; Symbol manipulation", } @InProceedings{Schlegel:1991:DRS, author = "H. Schlegel", title = "Determination of the root system of semisimple {Lie} algebras from the {Dynkin} diagram", crossref = "Watt:1991:IPI", pages = "239--240", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p239-schlegel/", abstract = "One way to represent the properties of the Lie algebra for calculations is by means of the commutation relations, i.e. the structure constants. The paper shows a way of the calculation of the Cartan--Weyl basis for all simple Lie algebras starting from the Dynkin diagram. The package DYNKIN written in REDUCE implements the described relations and can as an application be used to perform the calculations for a specified Lie algebra.", acknowledgement = ack-nhfb, affiliation = "Zentralinstitut fur Elektronenphys., Berlin, Germany", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "algorithms; Cartan--Weyl basis; Commutation relations; Dynkin diagram; Root system; Semisimple Lie algebras; Simple Lie algebras; Structure constants", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Algebra; Diagrams; Mathematics computing", } @InProceedings{Schmitt:1991:EAA, author = "Joacheim Schmitt", title = "An embedding algorithm for algebraic congruence function fields", crossref = "Watt:1991:IPI", pages = "187--188", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p187-schmitt/", abstract = "Provides an analogue of the Round 4 algorithm of Ford/Zassenhaus (1978) for algebraic congruence function fields. The reduction steps can also be used in other embedding algorithms. The algorithm is implemented within the computer algebra system SIMATH. The corresponding programs are written in C. The results can be used in integration and cryptography.", acknowledgement = ack-nhfb, affiliation = "Saarlandes Univ., Saarbrucken, Germany", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics)", keywords = "Algebraic congruence function fields; algorithms; Computer algebra system; Cryptography; Embedding algorithms; Integration; Round 4 algorithm; SIMATH", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Number theory", } @InProceedings{Schonhage:1991:FRC, author = "Arnold Sch{\"o}nhage", title = "Fast reduction and composition of binary quadratic forms", crossref = "Watt:1991:IPI", pages = "128--133", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p128-schonhage/", abstract = "Similar to the fast computation of integer gcd's, reduction of binary quadratic forms $ax^2+bxy+cy^2$ with integral coefficients $a, b, c$ bounded by $2^n$ is possible in time $O (\mu (n) \log{}n)$, where $\mu(n)$ is a time bound for $n$-bit integer multiplication. This result is obtained by a corresponding algorithm for the monotone reduction of positive forms. The same time bound holds for the composition of forms. Moreover, finding a reduced form is shown to be at least as difficult as extended gcd computation, up to terms of order $\mu (n)$.", acknowledgement = ack-nhfb, affiliation = "Bonn Univ., Germany", classification = "C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory)", keywords = "algorithms; Binary quadratic forms; Integer multiplication; Integral coefficients; Monotone reduction; Positive forms; Time bound", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation.", thesaurus = "Computational complexity; Number theory", } @InProceedings{Schulze-Pillot:1991:ACG, author = "Rainer Schulze-Pillot", title = "An algorithm for computing genera of ternary and quaternary quadratic forms", crossref = "Watt:1991:IPI", pages = "134--143", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p134-schulze-pillot/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", } @InProceedings{SchulzePillot:1991:ACG, author = "R. Schulze-Pillot", title = "An algorithm for computing genera of ternary and quaternary quadratic forms", crossref = "Watt:1991:IPI", pages = "134--143", year = "1991", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The paper reports on an algorithm for computing genera of ternary and quaternary positive definite quadratic forms over Z. It is well known that due to the simple shape of the reduction conditions in these dimensions it is in principle no problem to compute representatives of all classes of such quadratic forms whose discriminant is below a given bound. It is, however, sometimes desirable to be able to quickly determine representatives of all classes in some fixed genus of quadratic forms of possibly high discriminant without having to generate along the way all forms of smaller discriminant. An obvious attempt in such a case is to use Kneser's method of neighbouring or adjacent lattices. The paper draws attention to the fact that it is indeed not difficult to use this method in dimensions 3 and 4 as the basis of an algorithm that serves the purpose. With almost no extra work one obtains at the same time the adjacency graph of the classes determined; this has interesting arithmetic and graph theoretic applications. It is intended to use the algorithm for the experimental investigation of the Fourier and Fourier--Jacobi coefficients of certain linear combinations of Siegel $\theta$ series of quaternary quadratic forms.", acknowledgement = ack-nhfb, affiliation = "Fakultat fur Math., Bielefeld Univ., Germany", classification = "C1160 (Combinatorial mathematics)", keywords = "Adjacency graph; Adjacent lattices; Discriminant; Fourier--Jacobi coefficients; Genera; Linear combinations; Neighbouring lattices; Quaternary positive definite quadratic forms; Reduction conditions; Siegel $\theta$ series; Ternary positive definite quadratic forms", thesaurus = "Number theory", } @InProceedings{Schwarz:1991:ETP, author = "Fritz Schwarz", title = "Existence theorems for polynomial first integrals", crossref = "Watt:1991:IPI", pages = "256--264", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p256-schwarz/", abstract = "In various areas of applied mathematics there occur autonomous systems of ordinary differential equations of the form $x_i= \omega _i(x,c), i=1,\ldots{}n$ where the right hand sides are polynomial in all arguments $x=(x_1,\ldots{}x_n)$ and $c=(c_1,c_2,\ldots{})$; the latter variables are parameters which are a priori unspecified. There arises the following question: Do first integrals of a certain type, e.g. polynomial first integrals? The computer algebra package DYNSYS allows one to find all polynomial first integrals up to a given highest degree $D$ but does not provide any information beyond $D$. To obtain a complete answer these packages should be complemented by rigorous results concerning the possible existence of first integrals of any degree. Theorems of this kind are obtained. The basic principle for obtaining them is to identify subsystems of the determining system which have a certain structure independent of $D$. This method is applied to several two- and three-dimensional systems. It is shown for example that the famous Lorenz system in general does not allow any polynomial first integrals. Furthermore some ideas are presented on how these methods may be converted into algorithms such that a machine may perform the necessary analysis.", acknowledgement = ack-nhfb, affiliation = "GMD, Inst. F1, St. Augustin, Germany", classification = "C1120 (Analysis); C4170 (Differential equations); C4180 (Integral equations)", keywords = "algorithms; Applied mathematics; Autonomous systems; Computer algebra package; DYNSYS; Lorenz system; Ordinary differential equations; Polynomial first integrals; theory; Three-dimensional systems", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems.", thesaurus = "Differential equations; Integral equations; Polynomials", } @InProceedings{Shoup:1991:FDA, author = "Victor Shoup", title = "A fast deterministic algorithm for factoring polynomials over finite fields of small characteristic", crossref = "Watt:1991:IPI", pages = "14--21", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p14-shoup/", abstract = "Presents a new algorithm for factoring polynomials over finite fields. The algorithm is deterministic, and its running time is `almost' quadratic when the characteristic is a small fixed prime. As such, the algorithm is asymptotically faster than previously known deterministic algorithms for factoring polynomials over finite fields of small characteristic.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Toronto Univ., Toronto, Ont., Canada", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Deterministic algorithm; Finite fields; Polynomial factorisation; Small characteristic; Small fixed prime; theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields.", thesaurus = "Computational complexity; Polynomials", } @InProceedings{Sit:1991:TPL, author = "William Y. Sit", title = "A theory for parametric linear systems", crossref = "Watt:1991:IPI", pages = "112--121", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p112-sit/", abstract = "Presents a theoretical foundation for studying parametric systems of linear equations and proves an efficient algorithm for identifying all parametric values (including degenerate cases) for which the system is consistent. The algorithm gives a small set of regimes where for each regime, the solutions of the specialized systems may be given uniformly. For homogeneous systems, or for systems where the right hand side is arbitrary, this small set is irredundant. A complexity analysis of the Gaussian elimination method is given and compared with the algorithm.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., City Coll. of New York, NY, USA", classification = "C4140 (Linear algebra); C4240 (Programming and algorithm theory)", keywords = "algorithms; Complexity analysis; Degenerate cases; Gaussian elimination; Homogeneous systems; Linear equations; Parametric systems; Parametric values; Regimes; Right hand side; Specialized systems; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", thesaurus = "Computational complexity; Linear algebra", } @InProceedings{Stein:1991:ADR, author = "Andreas Stein and Horst G{\"u}nter Zimmer", title = "An algorithm for determining the regulator and the fundamental unit of a hyperelliptic congruence function field", crossref = "Watt:1991:IPI", pages = "183--184", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p183-stein/", abstract = "A continued fraction algorithm (baby steps) is described by B. Weis, H. G. Zimmer (Mitt. Math. Ges: Hamburg, 1991) for determining the regulator and the fundamental unit of the congruence function field $K/k$ with respect to the indeterminate $X$. The algorithm is based on work of Artin (Math Z vol. 19, p. 153--246, 1924) and was implemented within the computer algebra system SIMATH. The authors show how the algorithm can be substantially improved by applying to the function field case D. Shanks' (1972) idea of the infrastructure of a real quadratic number field. The improved version of this algorithm has been implemented within the computer algebra system SIMATH, too.", acknowledgement = ack-nhfb, affiliation = "Saarlandes Univ., Saarbrucken, Germany", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "algorithms; Baby steps; Computer algebra system; Congruence function field; Continued fraction algorithm; Function field; Fundamental unit; Hyperelliptic congruence function field; Indeterminate; Real quadratic number field; Regulator; SIMATH", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", thesaurus = "Algebra; Number theory; Symbol manipulation", } @InProceedings{Surguladze:1991:APC, author = "Levan R. Surguladze and Mark A. Samuel", title = "Algebraic perturbative calculations in high energy physics. {Methods}, algorithms, computer programs and physical applications", crossref = "Watt:1991:IPI", pages = "439--447", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p439-surguladze/", abstract = "The methods and algorithms for high order algebraic perturbative calculations in theoretical high energy physics are briefly reviewed. The SCHOONSCHIP program MINCER and the REDUCE program LOOPS for analytical computation of arbitrary massless, one-, two- and three-loop Feynman diagrams of the propagator type are described. The version of the program LOOPS for personal computers and the extended version of the program MINCER for four-loop renormalization group calculations are presented. The new program for algebraic perturbative calculations is also discussed. This program is written on the new algebraic programming system FORM. Some recent results of application to the high energy physics are given.", acknowledgement = ack-nhfb, affiliation = "Inst. for Nucl. Res., Acad. of Sci., Moscow, USSR", classification = "A0270 (Computational techniques); A1110G (Renormalization); C7320 (Physics and Chemistry)", keywords = "Algebraic perturbative calculations; algorithms; Feynman diagrams; High energy physics; LOOPS; MINCER; REDUCE; SCHOONSCHIP program", subject = "{\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", thesaurus = "Feynman diagrams; Physics computing; Renormalisation; Symbol manipulation", } @InProceedings{Trenkov:1991:ARS, author = "I. Trenkov and M. Spiridonova and M. Daskalova", title = "An application of the {REDUCE} system for solving a mathematical geodesy problem", crossref = "Watt:1991:IPI", pages = "448--449", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p448-trenkov/", abstract = "A REDUCE program package for solving some mathematical geodesy problems now under development includes capabilities for solving the problem: the geographical coordinates (the geographical density $B_p$ and the geographical longitude $L_p$) of a point $P$ on the earthly ellipsoid are to be calculated when $n$ different points $C_i(i=1, 2, \ldots{}, n)$ with their geographical coordinates $B_i$ and $L_i$ are given and the azimuths $A_{ip}$ in all points $C_i$ to the point $P$ are measured.", acknowledgement = ack-nhfb, affiliation = "Central Lab. for Geodesy, Bulgarian Acad. of Sci., Sofia, Bulgaria", classification = "A9110B (Mathematical geodesy: general theory); C7310 (Mathematics); C7340 (Geophysics)", keywords = "algorithms; Geographical coordinates; Mathematical geodesy; Program package; REDUCE system", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Mathematics and statistics. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Earth and atmospheric sciences.", thesaurus = "Computational geometry; Geodesy; Geophysics computing; Symbol manipulation", } @InProceedings{Trevisan:1991:PFU, author = "Vilmar Trevisan and Paul Wang", title = "Practical factorization of univariate polynomials over finite fields", crossref = "Watt:1991:IPI", pages = "22--31", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p22-trevisan/", abstract = "The research presented is part of an effort to establish state-of-the-art factoring routines for polynomials. The foundation of such algorithms lies in the efficient factorization over a finite field $\mbox{GF}(p^k)$. The Cantor--Zassenhaus algorithm together with innovative ideas suggested by others is compared with the Berlekamp algorithm. The studies led to the design of a hybrid algorithm that combines the strengths of the different approaches. The algorithms are also implemented and machine timings are obtained to measure the performance of these algorithms.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. and Comput. Sci., Kent State Univ., OH, USA", classification = "C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Berlekamp algorithm; Cantor--Zassenhaus algorithm; Factoring routines; Factorization; Finite fields; Hybrid algorithm; performance; Univariate polynomials", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms.", thesaurus = "Computational complexity; Polynomials", } @InProceedings{Vinette:1991:FSC, author = "F. Vinette", title = "Features of symbolic computation exploited in the calculation of lower energy bounds of cyclic polyene models", crossref = "Watt:1991:IPI", pages = "458--459", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p458-vinette/", abstract = "Symbolic computation has been applied in many scientific disciplines and has proved to be a very valuable research tool. In earlier studies, features of symbolic computation including algebraic manipulations and high decimal precision, were shown to be very useful to solve nonrelativistic quantum mechanical problems. The author illustrates the valuable assistance of symbolic computation in solving quantum chemical problems. The symbolic computational language MAPLE is used throughout this study. The computational aspects of the application of Lowdin's Optimized Inner Projection (OIP) to determine lower bounds to the ground state energy of the Pariser--Parr--Pople (PPP) model of cyclic polyenes, is briefly presented. A diagrammatic approach for evaluating the required matrix elements is needed: this method is often used in quantum chemistry. The evaluation of Brandow diagrams, which is very tedious and almost impossible to do by hand, is easily obtained using MAPLE.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math. and Stat., York Univ., North York, Ont., Canada", classification = "A3115 (General mathematical and computational developments); A3120 (Specific calculations and results); C7320 (Physics and Chemistry)", keywords = "algorithms; Brandow diagrams; Cyclic polyene models; Ground state energy; languages; Lower energy bounds; MAPLE; Optimized Inner Projection; Pariser--Parr--Pople; Quantum chemical problems; Symbolic computation", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf J.2} Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Chemistry. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", thesaurus = "Chemistry computing; Molecular energy level calculations; Organic compounds; Quantum chemistry; Symbol manipulation", } @InProceedings{Wang:1991:TMI, author = "Dongming Wang", title = "A toolkit for manipulating indefinite summations with application to neural networks", crossref = "Watt:1991:IPI", pages = "462--463", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p462-wang/", abstract = "Presents the design of some rules and the implementation of an application-oriented toolkit in Macsyma by amending some of its incorrect computations for the manipulation of indefinite summations. The application of this toolkit to the analysis and derivation of neural networks is briefly discussed.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C6115 (Programming support); C6170 (Expert systems)", keywords = "algorithms; Application-oriented toolkit; design; Indefinite summations; Macsyma; Neural networks", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, MACSYMA. {\bf I.2.6} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Learning, Connectionism and neural nets.", thesaurus = "Neural nets; Software tools; Symbol manipulation", } @InProceedings{Weibel:1991:AP, author = "Trudy Weibel and Gaston H. Gonnet", title = "An algebra of properties", crossref = "Watt:1991:IPI", pages = "352--359", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p352-weibel/", abstract = "The purpose of the paper is to build a framework and give algorithms to solve queries of the form obj in Prop where the object obj is expressible in terms of other given objects. The authors develop an algebra of properties, PROP, in which we carry out computations. They present a set of rules (axioms Ax1-Ax7) for the behaviour of the basic functions on properties. In addition, they represent the algorithmic components such as if and while by the algebra operations meet and join. They conclude by proposing an implementation of the algebra PROP.", acknowledgement = ack-nhfb, affiliation = "Inst. for Theor. Comput. Sci., Zurich, Switzerland", classification = "C4100 (Numerical analysis); C7310 (Mathematics)", keywords = "Algebra; Algebra of properties; Algorithmic components; algorithms; PROP", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous.", thesaurus = "Symbol manipulation", } @InProceedings{Yakubovich:1991:EIS, author = "S. B. Yakubovich and Yu. F. Luchko", title = "The evaluation of integrals and series with respect to indices (parameters) of hypergeometric functions", crossref = "Watt:1991:IPI", pages = "271--280", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p271-yakubovich/", abstract = "A general method for the evaluation of some integrals of hypergeometric functions, and programming package, which works on the basis of this method, were described in Adamchik, Luchko, Marichev (1990). But many integrals which have appeared in practice don't belong to the class of convolution type integrals and, consequently, one can't use the previous method for the evaluation of such integrals. In particular, one needs original methods for the evaluation of integrals and series with respect to indices of special functions.", acknowledgement = ack-nhfb, affiliation = "Byelorussian State Univ., Minsk, Byelorussian SSR, USSR", classification = "C4160 (Numerical integration and differentiation)", keywords = "algorithms; Evaluation of integrals; Hypergeometric functions; Indices; Integrals; Special functions; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", thesaurus = "Integration; Series [mathematics]", } @InProceedings{Ziel:1991:RFD, author = "Richard Ziel", title = "Rational function decomposition", crossref = "Watt:1991:IPI", pages = "1--6", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p1-zippel/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", } @InProceedings{Zippel:1991:RFD, author = "R. Zippel", title = "Rational function decomposition", crossref = "Watt:1991:IPI", pages = "1--6", year = "1991", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents a polynomial time algorithm for determining whether a given univariate rational function over an arbitrary field is the composition of two rational functions over that field, and finds them if so.", acknowledgement = ack-nhfb, affiliation = "Cornell Univ., Ithaca, NY, USA", classification = "C4130 (Interpolation and function approximation)", keywords = "Arbitrary field; Polynomial time algorithm; Univariate rational function", thesaurus = "Polynomials", } @InProceedings{Zolotykh:1991:PCS, author = "A. A. Zolotykh", title = "A package for computations in simple {Lie} algebra representations", crossref = "Watt:1991:IPI", pages = "237--238", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p237-zolotykh/", abstract = "The author present a software package for calculations of some numerical characteristics of simple Lie algebras of rank not more than 12 and their irreducible finite-dimensional representations over algebraically closed fields of characteristic zero (for example, over the field of complex numbers). Times of some computations on an IBM PC/AT (processor 286) are given: the times of character computations and times of tensor square computations for the fundamental (basic) representation of exceptional Lie algebras and of 12-rank Lie algebras. The table contains also the dimensions of corresponding fundamental representations.", acknowledgement = ack-nhfb, affiliation = "Dept. of Mech. and Math., Moscow State Univ., USSR", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "Algebraically closed fields; algorithms; IBM PC/AT; Irreducible finite-dimensional representations; Numerical characteristics; Simple Lie algebra representations; Tensor square computations; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems.", thesaurus = "Algebra; Mathematics computing; Microcomputer applications", xxtitle = "A package for computation in simple {Lie} algebra representations", } @InProceedings{Bischof:1992:AAD, author = "Christian Bischof and Alan Carle and George Corliss and Andreas Griewank", title = "{ADIFOR}: {Automatic} differentiation in a source translator environment", crossref = "Wang:1992:PII", pages = "294--302", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p294-bischof/", acknowledgement = ack-nhfb, keywords = "algorithms; design; experimentation; languages", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", } @InProceedings{Bronstein:1992:LOD, author = "Manuel Bronstein", title = "Linear ordinary differential equations: breaking through the order 2 barrier", crossref = "Wang:1992:PII", pages = "42--48", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib; Theory/cathode.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p42-bronstein/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", } @InProceedings{Burnel:1992:CCY, author = "A. Burnel and H. Caprasse", title = "The computation of $1$-loop contributions in {Y.M.} theories with class {III} nonrelativistic gauges and {REDUCE}", crossref = "Wang:1992:PII", pages = "103--107", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p103-burnel/", acknowledgement = ack-nhfb, keywords = "algorithms; theory; Yang--Mills", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", } @InProceedings{Butler:1992:ECA, author = "Greg Butler", title = "Experimental comparison of algorithms for {Sylow} subgroups", crossref = "Wang:1992:PII", pages = "251--262", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p251-butler/", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous.", } @InProceedings{Cetinkaya:1992:SAL, author = "Cetin Cetinkaya", title = "On stability analysis of linear stochastic and time-varying deterministic systems", crossref = "Wang:1992:PII", pages = "278--283", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p278-cetinkaya/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues and eigenvectors (direct and iterative methods). {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @InProceedings{Codutti:1992:NNL, author = "M. Codutti", title = "{NODES}: non linear ordinary differential equations solver", crossref = "Wang:1992:PII", pages = "69--79", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib; Theory/cathode.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p69-codutti/", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @InProceedings{Collins:1992:EAI, author = "George E. Collins and Werner Krandick", title = "An efficient algorithm for infallible polynomial complex root isolation", crossref = "Wang:1992:PII", pages = "189--194", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p189-collins/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Cook:1992:CGA, author = "Grant O. {Cook, Jr.}", title = "Code generation in {ALPAL} using symbolic techniques", crossref = "Wang:1992:PII", pages = "27--35", year = "1992", DOI = "https://doi.org/10.1145/143242.143260", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p27-cook/", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation.", } @InProceedings{Cooperman:1992:FCB, author = "Gene Cooperman and Larry Finkelstein", title = "A fast cyclic base change for permutation groups", crossref = "Wang:1992:PII", pages = "224--232", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p224-cooperman/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo).", } @InProceedings{Crouch:1992:ECI, author = "P. E. Crouch and R. L. Grossman", title = "The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees", crossref = "Wang:1992:PII", pages = "89--94", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p89-crouch/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms.", } @InProceedings{Dalmas:1992:PFL, author = "St{\'e}phane Dalmas", title = "A polymorphic functional language applied to symbolic computation", crossref = "Wang:1992:PII", pages = "369--375", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p369-dalmas/", acknowledgement = ack-nhfb, keywords = "algorithms; design; languages", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems. {\bf F.3.3} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies of Program Constructs, Type structure. {\bf F.3.3} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies of Program Constructs, Functional constructs. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, SCRATCHPAD.", } @InProceedings{Davenport:1992:PTR, author = "J. H. Davenport", title = "Primality testing revisited", crossref = "Wang:1992:PII", pages = "123--129", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p123-davenport/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations.", } @InProceedings{Dewar:1992:UCA, author = "Michael C. Dewar", title = "Using computer algebra to select numerical algorithms", crossref = "Wang:1992:PII", pages = "1--8", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p1-dewar/", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", } @InProceedings{Fateman:1992:HPG, author = "Richard Fateman", title = "Honest plotting, global extrema, and interval arithmetic", crossref = "Wang:1992:PII", pages = "216--223", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p216-fateman/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.2.2} Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.", } @InProceedings{Ganzha:1992:NSA, author = "V. G. Ganzha and E. V. Vorozhtsov and J. A. {van Hulzen}", title = "A new symbolic-numeric approach to stability analysis of difference schemes", crossref = "Wang:1992:PII", pages = "9--15", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p9-ganzha/", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Finite difference methods. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.", } @InProceedings{Gao:1992:SPA, author = "Xiao-Shan Gao and Shang-Ching Chou", title = "Solving parametric algebraic systems", crossref = "Wang:1992:PII", pages = "335--341", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p335-gao/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Geddes:1992:HSI, author = "K. O. Geddes and G. J. Fee", title = "Hybrid symbolic-numeric integration in {MAPLE}", crossref = "Wang:1992:PII", pages = "36--41", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p36-geddes/", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @InProceedings{Gil:1992:CJC, author = "Isabelle Gil", title = "Computation of the {Jordan} canonical form of a square matrix (using the {Axiom} programming language)", crossref = "Wang:1992:PII", pages = "138--145", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p138-gil/", acknowledgement = ack-nhfb, keywords = "algorithms; languages; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues and eigenvectors (direct and iterative methods). {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", } @InProceedings{Grigoriev:1992:ESP, author = "Dima Y. u. Grigoriev and Marek Karpinski and Andrew M. Odlyzko", title = "Existence of short proofs for nondivisibility of sparse polynomials under the extended {Riemann} hypothesis", crossref = "Wang:1992:PII", pages = "117--122", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p117-grigoriev/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial).", } @InProceedings{Gutierrez:1992:PIT, author = "Jaime Gutierrez and Tomas Recio", title = "A practical implementation of two rational function decomposition algorithms", crossref = "Wang:1992:PII", pages = "152--157", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p152-gutierrez/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Hietarinta:1992:SCQ, author = "Jarmo Hietarinta", title = "Solving the constant quantum {Yang--Baxter} equation in $2$ dimensions with massive use of factorizing {Gr{\"o}bner} basis computations", crossref = "Wang:1992:PII", pages = "350--357", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p350-hietarinta/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @InProceedings{Hong:1992:SSF, author = "Hoon Hong", title = "Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination", crossref = "Wang:1992:PII", pages = "177--188", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p177-hong/", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.4} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Applications.", } @InProceedings{Johnson:1992:RAN, author = "J. R. Johnson", title = "Real algebraic number computation using interval arithmetic", crossref = "Wang:1992:PII", pages = "195--205", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p195-johnson/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", } @InProceedings{Kajler:1992:CPE, author = "Norbert Kajler", title = "{CAS\slash PI}: a portable and extensible interface for computer algebra systems", crossref = "Wang:1992:PII", pages = "376--386", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p376-kajler/", acknowledgement = ack-nhfb, keywords = "algorithms; design; languages", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf H.5.2} Information Systems, INFORMATION INTERFACES AND PRESENTATION, User Interfaces. {\bf D.2.2} Software, SOFTWARE ENGINEERING, Design Tools and Techniques, User interfaces. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.", } @InProceedings{Kaltofen:1992:CDM, author = "Erich Kaltofen", title = "On computing determinants of matrices without divisions", crossref = "Wang:1992:PII", pages = "342--349", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p342-kaltofen/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", } @InProceedings{Kirrinnis:1992:FCN, author = "Peter Kirrinnis", title = "Fast computation of numerical partial fraction decompositions and contour integrals of rational functions", crossref = "Wang:1992:PII", pages = "16--26", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p16-kirrinnis/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @InProceedings{Kuhn:1992:CPS, author = "Norbert Kuhn and Klaus Madlener and Friedrich Otto", title = "Computing presentations for subgroups of context-free groups", crossref = "Wang:1992:PII", pages = "240--250", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p240-kuhn/", acknowledgement = ack-nhfb, keywords = "algorithms; languages; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems, Decision problems. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes.", } @InProceedings{Lamagna:1992:DUI, author = "Edmund A. Lamagna and Michael B. Hayden and Catherine W. Johnson", title = "The design of a user interface to a computer algebra system for introductory calculus", crossref = "Wang:1992:PII", pages = "358--368", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p358-lamagna/", acknowledgement = ack-nhfb, keywords = "algorithms; human factors", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Maple. {\bf H.5.2} Information Systems, INFORMATION INTERFACES AND PRESENTATION, User Interfaces, Interaction styles. {\bf H.5.2} Information Systems, INFORMATION INTERFACES AND PRESENTATION, User Interfaces, Input devices and strategies.", } @InProceedings{Lempken:1992:SPS, author = "W. Lempken and R. Staszewski", title = "The structure of the {PIMs} of {SL(3,4)} in characteristic 2", crossref = "Wang:1992:PII", pages = "233--239", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p233-lempken/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial).", } @InProceedings{Manocha:1992:MRL, author = "Dinesh Manocha and John F. Canny", title = "Multipolynomial resultants and linear algebra", crossref = "Wang:1992:PII", pages = "158--167", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p158-manocha/", acknowledgement = ack-nhfb, subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @InProceedings{Marinuzzi:1992:LNS, author = "Francesco Marinuzzi and Stefano Soliani", title = "{LISA}: {A} new symbolic package for the definition, analysis and resolution of {Markovian} processes: symbolic and inductive techniques", crossref = "Wang:1992:PII", pages = "303--311", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p303-marinuzzi/", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, LISP. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic.", } @InProceedings{Moller:1992:GBC, author = "H. Michael M{\"o}ller and Teo Mora and Carlo Traverso", title = "Gr{\"o}bner bases computation using syzygies", crossref = "Wang:1992:PII", pages = "320--328", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p320-moller/", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.1.1} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Expressions and Their Representation, Simplification of expressions. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", } @InProceedings{Morain:1992:ENE, author = "F. Morain", title = "Easy numbers for the elliptic curve primality proving algorithm", crossref = "Wang:1992:PII", pages = "263--268", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p263-morain/", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous.", } @InProceedings{Mutrie:1992:AFE, author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W. Char", title = "An approach for floating-point error analysis using computer algebra", crossref = "Wang:1992:PII", pages = "284--293", year = "1992", bibdate = "Thu Mar 12 08:39:32 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/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