%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "2.17", %%% date = "25 March 2012", %%% time = "08:20:27 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 = "64800 33540 162196 1696477", %%% 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 2.17, the year coverage looked %%% like this: %%% %%% 1976 ( 1) 1988 ( 0) 2000 ( 44) %%% 1977 ( 0) 1989 ( 106) 2001 ( 48) %%% 1978 ( 0) 1990 ( 64) 2002 ( 36) %%% 1979 ( 1) 1991 ( 86) 2003 ( 40) %%% 1980 ( 0) 1992 ( 50) 2004 ( 47) %%% 1981 ( 2) 1993 ( 58) 2005 ( 52) %%% 1982 ( 1) 1994 ( 103) 2006 ( 55) %%% 1983 ( 0) 1995 ( 52) 2007 ( 54) %%% 1984 ( 0) 1996 ( 50) 2008 ( 47) %%% 1985 ( 0) 1997 ( 88) 2009 ( 54) %%% 1986 ( 50) 1998 ( 49) 2010 ( 52) %%% 1987 ( 0) 1999 ( 41) %%% %%% Article: 3 %%% Book: 1 %%% InProceedings: 1286 %%% Proceedings: 41 %%% %%% Total entries: 1331 %%% %%% Regrettably, bibliographic data for most of %%% these conferences prior to 1989 are %%% inaccessible electronically. With an %%% estimated 60 papers at each conference, a %%% complete bibliography would have about 1800 %%% entries, so the coverage is only about 25%. %%% %%% This bibliography has been collected from %%% bibliographies in the author's personal %%% files, from the OCLC and IEEE INSPEC %%% (1989--1995) databases, and from the %%% computer science bibliography collection on %%% ftp.ira.uka.de in /pub/bibliography to %%% which many people of have contributed. The %%% snapshot of this collection was taken on %%% 5-May-1994, and it consists of 441 BibTeX %%% files, 2,672,675 lines, 205,289 entries, %%% and 6,375 String{} abbreviations, %%% occupying 94.8MB of disk space. %%% %%% 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 $$ for $w$ in $G$, finite $U$ contained in $G$, where $$ is the subgroup of $G$ generated by $U$. They describe $$ also by a rewrite system $S$ and define a rewrite relation $\mbox{implies}_{S,R}$ in such a way that $w$ implied by * $\mbox{implies}_{S,R} \lambda$ iff $w$ in $$ ($\lambda$ the empty word). For this rewrite relation the authors develop different critical pair criteria for $\mbox{implies}_{S,R}$ to be $\lambda$-confluent, i.e. confluent on the left-congruence class $(\lambda )$ of implied by * $\mbox{implies}_{S,R}$. Using any of these $\lambda$-confluence criteria they construct a completion procedure which stops for every input $S$ and computes a $\lambda$-confluent rewrite system equivalent to $S$. This leads to a decision procedure for GWP in G. Thus the authors give an explicit uniform algorithm for deciding GWP in polycyclic groups and a new proof based almost only on rewriting techniques for the decidability of this problem. Further, they define a rewrite relation $\mbox{implies}_{LM,U}$ which is stronger than $\mbox{implies}_{S,R}$. They show that if $G$ is given by a nilpotent string-rewriting system, then by a completion procedure the input $U$ can be transformed into $V$ such that $\mbox{implies}_{LM,V}$ is even confluent, not just $\lambda$-confluent.", acknowledgement = ack-nhfb, affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany", classification = "C1110 (Algebra); C4210 (Formal logic)", keywords = "$\Lambda$-confluent; algorithms; Canonical polycyclic string-rewriting system; Completion procedure; Critical pair criteria; Decidability; design; Explicit uniform algorithm; Generalized word problem; Group theory; Nilpotent string-rewriting system; Polycyclic groups; Rewrite relation; Rewriting techniques; theory", subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General.", thesaurus = "Decidability; Group theory; Rewriting systems; Symbol manipulation", } @InProceedings{Bajaj:1989:FRP, author = "C. Bajaj and J. Canny and T. Garrity and J. Warren", title = "Factoring rational polynomials over the complexes", crossref = "Gonnet:1989:PAI", pages = "81--90", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p81-bajaj/", abstract = "The authors give NC algorithms for determining the number and degrees of the absolute factors (factors irreducible over the complex numbers $C$) of a multivariate polynomial with rational coefficients. NC is the class of functions computable by logspace-uniform boolean circuits of polynomial size and polylogarithmic dept. The measures of size of the input polynomial are its degree $d$, coefficient length $c$, number of variables $n$, and for sparse polynomials, the number of nonzero coefficients $s$. For the general case, the authors give a random (Monte-Carlo) NC algorithm in these input measures. If $n$ is fixed, or if the polynomial is dense, they give a deterministic NC algorithm. The algorithm also works in random NC for polynomial represented by straight-line programs, provided the polynomial can be evaluated at integer points in NC. The authors discuss a method for obtaining an approximation to the coefficients of each factor whose running time is polynomial in the size of the original (dense) polynomial. These methods rely on the fact that the connected components of a complex hypersurface $P(z_1,\ldots{},z_n)=0$ minus its singular points correspond to the absolute factors of $P$.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Purdue Univ., Lafayette, IN, USA", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory)", keywords = "Absolute factors; algorithms; Complex numbers; Factorisation; Functions; Logspace-uniform boolean circuits; measurement; Monte-Carlo; Multivariate polynomial; NC algorithms; Rational coefficients; Rational polynomials; Set theory; theory; verification", subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving.", thesaurus = "Approximation theory; Computability; Computational complexity; Monte Carlo methods; Polynomials; Set theory; Symbol manipulation", xxauthor = "C. Bajaj and J. Canny and R. Garrity and J. Warren", } @InProceedings{Barkatou:1989:RLS, author = "M. A. Barkatou", title = "On the reduction of linear systems of difference equations", crossref = "Gonnet:1989:PAI", pages = "1--6", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p1-barkatou/", abstract = "The author deals with linear systems of difference equations whose coefficients admit generalized factorial series representations at $z=\infty$. He gives a criterion by which a given system is determined to have a regular singularity. He gives an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations on an irreducible form.", acknowledgement = ack-nhfb, affiliation = "Lab. TIM3-IMAG, Grenoble, France", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; Computer algebra system; Convergence; Generalized factorial series; Irreducible form; Linear difference equations; Regular singularity; theory", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", thesaurus = "Convergence; Difference equations; Linear differential equations; Mathematics computing; Matrix algebra; Series [mathematics]; Symbol manipulation", } @InProceedings{Barkatou:1989:RNA, author = "M. A. Barkatou", title = "Rational {Newton} algorithm for computing formal solutions of linear differential equations", crossref = "Gianni:1989:SAC", pages = "183--195", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents a new algorithm for solving linear differential equations in the neighbourhood of an irregular singular point. This algorithm is based upon the same principles as the Newton algorithm, however it has a lower cost and is more suitable for computing algebra.", acknowledgement = ack-nhfb, affiliation = "CNRS, INPG, IMAG, Grenoble, France", classification = "C1120 (Analysis); C4170 (Differential equations)", keywords = "Formal solutions; Irregular singular point; Linear differential equations; Neighbourhood; Rational Newton algorithm", thesaurus = "Linear differential equations", } @InProceedings{BoydelaTour:1989:FAS, author = "T. {Boy de la Tour} and R. Caferra", title = "A formal approach to some usually informal techniques used in mathematical reasoning", crossref = "Gianni:1989:SAC", pages = "402--406", year = "1989", bibdate = "Mon Dec 01 16:57:16 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "One of the striking characteristics of mathematical reasoning is the contrast between the formal aspects of mathematical truth and the informal character of the ways to that truth. Among the many important and usually informal mathematical activities the authors are interested in proof analogy (i.e. common pattern between proofs of different theorems) in the context of interactive theorem proving.", acknowledgement = ack-nhfb, affiliation = "LIFIA-INPG, Grenoble, France", classification = "C4210 (Formal logic)", keywords = "Formal approach; Informal character; Interactive theorem proving; Mathematical reasoning; Mathematical truth; Usually informal techniques", thesaurus = "Theorem proving", } @InProceedings{Bradford:1989:ETC, author = "R. J. Bradford and J. H. Davenport", title = "Effective tests for cyclotomic polynomials", crossref = "Gianni:1989:SAC", pages = "244--251", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present two efficient tests that determine if a given polynomial is cyclotomic, or is a product of cyclotomics. The first method uses the fact that all the roots of a cyclotomic polynomial are roots of unity, and the second the fact that the degree of a cyclotomic polynomial is a value of $\phi (n)$, for some $n$. The authors also find the cyclotomic factors of any polynomial.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C4130 (Interpolation and function approximation)", keywords = "Cyclotomic polynomials; Roots", thesaurus = "Polynomials", } @InProceedings{Bradford:1989:SRD, author = "R. Bradford", title = "Some results on the defect", crossref = "Gonnet:1989:PAI", pages = "129--135", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p129-bradford/", abstract = "The defect of an algebraic number field (or, more correctly, of a presentation of the field) is the largest rational integer that divides the denominator of any algebraic integer in the field when written using that presentation. Knowing the defect, or estimating it accurately is extremely valuable in many algorithms, the factorization of polynomials over algebraic number fields being a prime example. The author presents a few results that are a move in the right direction.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "Algebraic integer; Algebraic number field; algorithms; Defect; Factorization; Polynomials; Rational integer; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations.", thesaurus = "Computation theory; Number theory; Polynomials; Symbol manipulation", } @InProceedings{Bronstein:1989:FRR, author = "M. Bronstein", title = "Fast reduction of the {Risch} differential equation", crossref = "Gianni:1989:SAC", pages = "64--72", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Presents a weaker definition of weak-normality which: can always be obtained in a tower of transcendental elementary extensions, and gives an explicit formula for the denominator of $y$, so the equation $y'+fy=g$ can be reduced to a polynomial equation in one reduction step. As a consequence, a new algorithm is obtained for solving y'+fy=g. The algorithm is very similar to the one described by Rothstein (1976), except that the present one uses weak normality to prevent finite cancellation, rather than having to find integer roots of polynomials over the constant field of $K$ in order to detect it.", acknowledgement = ack-nhfb, affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1120 (Analysis); C4170 (Differential equations)", keywords = "Denominator; Explicit formula; Fast reduction; Polynomial equation; Reduction step; Risch differential equation; Transcendental elementary extensions; Weak-normality", thesaurus = "Differential equations", } @InProceedings{Bronstein:1989:SRE, author = "M. Bronstein", title = "Simplification of real elementary functions", crossref = "Gonnet:1989:PAI", pages = "207--211", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p207-bronstein/", abstract = "The author describes an algorithm, based on Risch's real structure theorem, that determines explicitly all the algebraic relations among a given set of real elementary functions. He provides examples from its implementation in the scratchpad computer algebra system that illustrate the advantages over the use of complex logarithms and exponentials.", acknowledgement = ack-nhfb, affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1110 (Algebra); C7310 (Mathematics)", keywords = "algorithms; Computer algebra system; Real elementary functions; Real structure theorem; Scratchpad; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", thesaurus = "Functions; Mathematics computing; Symbol manipulation", } @InProceedings{Brown:1989:SPP, author = "C. Brown and G. Cooperman and L. Finkelstein", title = "Solving permutation problems using rewriting systems", crossref = "Gianni:1989:SAC", pages = "364--377", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "A new approach is described for finding short expressions for arbitrary elements of a permutation group in terms of the original generators which uses rewriting methods. This forms an important component in a long term plan to find short solutions for `large' permutation problems (such as Rubik's cube), which are difficult to solve by existing search techniques. In order for this methodology to be successful, it is important to start with a short presentation for a finite permutation group. A new method is described for giving a presentation for an arbitrary permutation group acting on $n$ letters. This can be used to show that any such permutation group has a presentation with at most $n-1$ generators and $(n-1)^2$ relations. As an application of this method, an $O(n^4)$ algorithm is described for determining if a set of generators for a permutation group of $n$ letters is a strong generating set (in the sense of Sims). The `back end' includes a novel implementation of the Knuth--Bendix technique on symmetrization classes for groups.", acknowledgement = ack-nhfb, affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA, USA", classification = "C4210 (Formal logic)", keywords = "Knuth--Bendix technique; Permutation problems; Rewriting systems", thesaurus = "Rewriting systems", } @InProceedings{Butler:1989:CVU, author = "G. Butler and J. Cannon", title = "{Cayley}, version 4: the user language", crossref = "Gianni:1989:SAC", pages = "456--466", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Cayley, version 4, is a proposed knowledge-based system for modern algebra. The proposal integrates the existing powerful algorithm base of Cayley with modest deductive facilities and large sophisticated databases of groups and related algebraic structures. The outcome will be a revolutionary computer algebra system. The user language of Cayley, version 4, is the first stage of the project to develop a computer algebra system which integrates algorithmic, deductive, and factual knowledge. The language plays an important role in shaping the users' communication of their knowledge to the system, and in presenting the results to the user. The very survival of a system depends upon its acceptance by the users, so the language must be natural, extensible, and powerful. The major changes in the language (over version 3) are the definitions of algebraic structures, set constructors and associated control structures, the definitions of maps and homomorphisms, the provision of packages for procedural abstraction and encapsulation, database facilities, and other input/output. The motivation for these changes has been the need to provide facilities for a knowledge-based system; to allow sets to be defined by properties; and to remove semantic ambiguities of structure definitions.", acknowledgement = ack-nhfb, affiliation = "Sydney Univ., NSW, Australia", classification = "C6170 (Expert systems); C7310 (Mathematics)", keywords = "Algebra; Algebraic structures; Associated control structures; Cayley; Computer algebra system; Deductive facilities; Encapsulation; Factual knowledge; Homomorphisms; Knowledge-based system; Procedural abstraction; Set constructors; Sophisticated databases; User language; Version 4", thesaurus = "Knowledge based systems; Symbol manipulation", } @InProceedings{Cabay:1989:FRA, author = "S. Cabay and G. Labahn", title = "A fast, reliable algorithm for calculating {Pad{\'e}--Hermite} forms", crossref = "Gonnet:1989:PAI", pages = "95--100", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p95-cabay/", abstract = "The authors present a new fast algorithm for the calculation of a Pad{\'e}--Hermite form for a vector of power series. When the vector of power series is normal, the algorithm is shown to calculate a Pad{\'e}--Hermite form of type $(n_0, \ldots{}, n_k)$ in $O(k.(n_0^2+\ldots{} +n_k^2))$ operations. This complexity is the same as that of other fast algorithms for computing Pad{\'e}--Hermite approximants. However, unlike other algorithms, the new algorithm also succeeds in the nonnormal case, usually with only a moderate increase in cost.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Alberta Univ., Edmonton, Alta., Canada", classification = "C1120 (Analysis); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "algorithms; Complexity; Iterative methods; Nonnormal case; Pad{\'e}--Hermite approximants; Pad{\'e}--Hermite forms; theory; Vector of power series", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations.", thesaurus = "Computational complexity; Iterative methods; Linear differential equations; Series [mathematics]; Vectors", } @InProceedings{Canny:1989:GCP, author = "J. Canny", title = "Generalized characteristic polynomials", crossref = "Gianni:1989:SAC", pages = "293--299", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author generalises the notion of characteristic polynomial for a system of linear equations to systems of multivariate polynomial equations. The generalization is natural in the sense that it reduces to the usual definition when all the polynomials are linear. Whereas the constant coefficient of the characteristic polynomial of a linear system is the determinant, the constant coefficient of the general characteristic polynomial is the resultant of the system. This construction is applied to solve a traditional problem with efficient methods for solving systems of polynomial equations: the presence of infinitely many solutions `at infinity'. The author gives a single-exponential time method for finding all the isolated solution points of a system of polynomials, even in the presence of infinitely many solutions at infinity or elsewhere.", acknowledgement = ack-nhfb, affiliation = "Div. of Comput. Sci., California Univ., Berkeley, CA, USA", classification = "C4130 (Interpolation and function approximation)", keywords = "Generalised characteristic polynomials; Multivariate polynomial equations; Single-exponential time method; System of linear equations", thesaurus = "Polynomials", } @InProceedings{Canny:1989:SSN, author = "J. F. Canny and E. Kaltofen and L. Yagati", title = "Solving systems of non-linear polynomial equations faster", crossref = "Gonnet:1989:PAI", pages = "121--128", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p121-canny/", abstract = "Finding the solution to a system of $n$ non-linear polynomial equations in $n$ unknowns over a given field, say the algebraic closure of the coefficient field, is a classical and fundamental problem in computational algebra. The authors give a method that allows the computation of resultants and $u$-resultants of polynomial systems in essentially linear space and quadratic time. The algorithm constitutes the first improvement over Gaussian elimination-based methods for computing these fundamental invariants.", acknowledgement = ack-nhfb, affiliation = "Div. of Comp. Sci., California Univ., Berkeley, CA, USA", classification = "C1110 (Algebra); C1120 (Analysis); C4130 (Interpolation and function approximation); C4150 (Nonlinear and functional equations); C4240 (Programming and algorithm theory)", keywords = "Algebraic closure; algorithms; Coefficient field; Computational algebra; Computational complexity; Linear space; Nonlinear polynomial equations; Quadratic time; Resultants; theory; U-resultants", subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", thesaurus = "Computational complexity; Nonlinear equations; Polynomials; Symbol manipulation", } @InProceedings{Cantone:1989:DPE, author = "D. Cantone and V. Cutello and A. Ferro", title = "Decision procedures for elementary sublanguages of set theory. {XIV}. {Three} languages involving rank related constructs", crossref = "Gianni:1989:SAC", pages = "407--422", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present three decidability results for some quantifier-free and quantified theories of sets involving rank related constructs.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Courant Inst. of Math. Sci., New York Univ., NY, USA", classification = "C1160 (Combinatorial mathematics); C4210 (Formal logic)", keywords = "Decidability results; Decision procedures; Elementary sublanguages; Quantified theories; Quantifier-free; Rank related constructs; Set theory", thesaurus = "Decidability; Formal logic; Set theory", } @InProceedings{Caprasse:1989:CEB, author = "H. Caprasse and J. Demaret and E. Schrufer", title = "Can {EXCALC} be used to investigate high-dimensional cosmological models with nonlinear {Lagrangians}?", crossref = "Gianni:1989:SAC", pages = "116--124", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Recent work in cosmology is characterized by the extension of the traditional four-dimensional general relativity models in two directions: Kaluza--Klein type models which have more than four dimensions, and models with Lagrangians containing nonlinear terms in the Riemann curvature tensor and its contractions. The package EXCALC 2 seems particularly well suited to investigate these models further. The implementation of all operations of EXTERIOR CALCULUS opens the way to perform these calculations efficiently. The article presents the current stage of investigation in this direction.", acknowledgement = ack-nhfb, affiliation = "Inst. de Phys., Liege Univ., Belgium", classification = "A9575P (Mathematical and computer techniques); A9880D (Theoretical cosmology); C7350 (Astronomy and astrophysics)", keywords = "Contractions; Cosmology; EXCALC 2; Four-dimensional general relativity models; High-dimensional cosmological models; Kaluza--Klein type models; Nonlinear Lagrangians; Package; Riemann curvature tensor", thesaurus = "Astronomy computing; Astrophysics computing; Cosmology; Software packages", } @InProceedings{ChaffyCamus:1989:ARA, author = "C. Chaffy-Camus", title = "An application of {REDUCE} to the approximation of $f(x,y)$", crossref = "Gianni:1989:SAC", pages = "73--84", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Pad{\'e} approximants are an important tool in numerical analysis, to evaluate $f(x)$ from its power series even outside the disk of convergence, or to locate its singularities. The paper generalizes this process to the multivariate case and presents two applications of this method: the approximation of implicit curves and the approximation of double power series. Computations are carried out on a computer algebra system REDUCE.", acknowledgement = ack-nhfb, affiliation = "TIM3-INPG, Grenoble, France", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Approximation; Computer algebra system; Convergence; Double power series; Implicit curves; Multivariate case; Numerical analysis; Pad{\'e} approximants; Reduce; Singularities", thesaurus = "Approximation theory; Convergence of numerical methods; Mathematics computing; Software packages", } @InProceedings{Char:1989:ARA, author = "B. W. Char", title = "Automatic reasoning about numerical stability of rational expressions", crossref = "Gonnet:1989:PAI", pages = "234--241", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p234-char/", abstract = "While numerical (e.g. Fortran) code generation from computer algebra is nowadays relatively easy to do, the expressions as they are produced via computer algebra typically benefit from nontrivial reformulation for efficiency and numerical stability. To assist in automatic `expert reformulation', we desire good automated tools to assess the stability of a particular form of an expression. The author discusses an approach to proofs of numerical stability (with respect to roundoff error) of rational expressions. The proof technique is based upon the ability to propagate properties such as sign, exact representability, or a certain kind of numerical stability, to floating point results from properties of their antecedents. The qualitative approach to numerical stability lends itself to implementation as a backwards-chaining theorem prover. While it is not a replacement for alternative forms of stability analysis, it can sometimes discover stability and explain it straightforwardly.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN, USA", classification = "C4100 (Numerical analysis); C7310 (Mathematics)", keywords = "algorithms; Backwards-chaining theorem prover; Code generation; Computer algebra; Floating point; Numerical stability; Rational expressions; Roundoff error; theory", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", thesaurus = "Automatic programming; Convergence of numerical methods; Mathematics computing; Symbol manipulation", } @InProceedings{Char:1989:DIC, author = "B. W. Char and A. R. Macnaughton and P. A. Strooper", title = "Discovering inequality conditions in the analytical solutions of optimization problems", crossref = "Gianni:1989:SAC", pages = "109--115", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The Kuhn--Tucker conditions can provide an analytic solution to the problem of maximizing or minimizing a function subject to inequality constraints, if the artificial variables known as Lagrange multipliers can be eliminated. The paper describes an automated reasoning program that assists in the solution process. The program may also be useful for other problems involving algebraic reasoning with inequalities.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN, USA", classification = "C1180 (Optimisation techniques); C1230 (Artificial intelligence); C7310 (Mathematics)", keywords = "Algebraic reasoning; Analytic solution; Artificial variables; Automated reasoning program; Function maximization; Function minimization; Inequality conditions; Inequality constraints; Kuhn--Tucker conditions; Lagrange multipliers; Optimization problems", thesaurus = "Inference mechanisms; Mathematics computing; Optimisation", } @InProceedings{Chen:1989:CNF, author = "Guoting Chen", title = "Computing the normal forms of matrices depending on parameters", crossref = "Gonnet:1989:PAI", pages = "242--249", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p242-chen/", abstract = "The author considers an algorithm for the exact computation of the Frobenius, Jordan and Arnold's form of matrices depending holomorphically on parameters. The problem originates from the problem of formal resolution of a first order system of differential equations depending on parameter. This algorithm has been implemented in Macsyma.", acknowledgement = ack-nhfb, affiliation = "Equipe de Calcul Formel et Algorithmique Parallele, Laboratoire TIM3-IMAG, Grenoble, France", classification = "C1110 (Algebra); C1120 (Analysis); C4140 (Linear algebra); C4170 (Differential equations); C7310 (Mathematics)", keywords = "algorithms; design; Differential equations; Formal resolution; Macsyma; Matrices; Normal forms; theory", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", thesaurus = "Differential equations; Mathematics computing; Matrix algebra; Symbol manipulation", } @InProceedings{Collins:1989:PRP, author = "G. E. Collins and J. R. Johnson", title = "The probability of relative primality of {Gaussian} integers", crossref = "Gianni:1989:SAC", pages = "252--258", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors generalize, to an arbitrary number field, the theorem which gives the probability that two integers are relatively prime. The probability that two integers are relatively prime is $ 1/ \zeta (2)$, where $\zeta$ is the Riemann $\zeta$ function and $1/\zeta(2)=6/\pi^2$. The theorem for an arbitrary number field states that the probability that two ideals are relatively prime is the reciprocal of the $\zeta$ function of the number field evaluated at two. In particular, since the Gaussian integers are a unique factorization domain, the authors get the probability that two Gaussian integers are relatively prime is $1/\zeta_G(2)$ where $\zeta_G$ is the $\zeta$ function associated with the Gaussian integers. In order to calculate the Gaussian probability, they use a theorem that enables them to factor the $\zeta$ function into a product of the Riemann $\zeta$ function and a Dirichlet series called an L-series.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ., Columbus, OH, USA", classification = "C1140 (Probability and statistics); C1160 (Combinatorial mathematics)", keywords = "Arbitrary number field; Dirichlet series; Gaussian integers; L-series; Probability; Relative primality; Riemann $\zeta$ function", thesaurus = "Number theory; Probability", } @InProceedings{Collins:1989:QES, author = "G. E. Collins and J. R. Johnson", title = "Quantifier elimination and the sign variation method for real root isolation", crossref = "Gonnet:1989:PAI", pages = "264--271", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p264-collins/", abstract = "An important aspect of the construction of a cylindrical algebraic decomposition (CAD) is real root isolation. Root isolation involves finding disjoint intervals, each containing a single root, for all of the real roots of a given polynomial. Root isolation is used to construct a CAD of the real line, which serves as the base case in the construction of higher dimensional CAD's. It is also an essential part of the extension phase, which lifts an induced CAD to the next higher dimension. The authors reexamine the sign variation method of root isolation devised by Collins and Akritas (1976). A new proof of termination is given, which more accurately describes the behavior of the algorithm. This theorem is then sharpened for the special case of cubic polynomials. The result for cubic polynomials is obtained with the aid of Collins's CAD based quantifier elimination algorithm.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. and Inf. Sci., Ohio State Univ., Columbus, OH, USA", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation)", keywords = "algorithms; Cubic polynomials; Cylindrical algebraic decomposition; design; Disjoint intervals; Polynomial; Quantifier elimination; Real root isolation; Sign variation method; Symbol manipulation; theory", subject = "{\bf J.6} Computer Applications, COMPUTER-AIDED ENGINEERING. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Cooperman:1989:RGC, author = "G. Cooperman and L. Finkelstein and E. Luks", title = "Reduction of group constructions to point stabilizers", crossref = "Gonnet:1989:PAI", pages = "351--356", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p351-cooperman/", abstract = "The construction of point stabilizer subgroups is a problem which has been studied intensively. This work describes a general reduction of certain group constructions to the point stabilizer problem. Examples are given for the centralizer, the normal closure, and a restricted group intersection problem. For the normal closure problem, this work provides an alternative to current algorithms, which are limited by the need for repeated closures under conjugation. For the centralizer and restricted group intersection problems, one can use an existing point stabilizer sequence along with a recent base change algorithm to avoid generating a new point stabilizer sequence. This reduces the time complexity by at least an order of magnitude. Algorithms and theoretical time estimates for the special case of a small base are also summarized. An implementation is in progress.", acknowledgement = ack-nhfb, affiliation = "Coll. of Comput. Sci., Northeastern Univ., Boston, MA, USA", classification = "C1110 (Algebra); C4240 (Programming and algorithm theory)", keywords = "algorithms; Base change algorithm; Centralizer; Group constructions; Group intersection; Group theory; Normal closure; Point stabilizers; theory; Time complexity", subject = "{\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Permutations and combinations. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Mechanical theorem proving.", thesaurus = "Computational complexity; Group theory; Symbol manipulation", } @InProceedings{Deprit:1989:MPS, author = "A. Deprit and E. Deprit", title = "Massively parallel symbolic computation", crossref = "Gonnet:1989:PAI", pages = "308--316", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p308-deprit/", abstract = "A massively parallel processor proves to be a powerful tool for manipulating the very large Poisson series encountered in nonlinear dynamics. Exploiting the algebraic structure of Poisson series leads quite naturally to parallel data structures and algorithms for symbolic manipulation. Exercising the parallel symbolic processor on the solution of Kepler's equation reveals the need to reexamine the serial computational methods traditionally applied to problems in dynamics.", acknowledgement = ack-nhfb, affiliation = "Nat. Inst. of Stand. and Technol., Gaithersburg, MD, USA", classification = "C1120 (Analysis); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "Algebraic structure; algorithms; design; Massively parallel processor; Nonlinear dynamics; Parallel data structures; Symbolic manipulation; theory; Very large Poisson series", subject = "{\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf E.1} Data, DATA STRUCTURES. {\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf C.1.3} Computer Systems Organization, PROCESSOR ARCHITECTURES, Other Architecture Styles, Stack-oriented processors**.", thesaurus = "Data structures; Mathematics computing; Nonlinear equations; Parallel algorithms; Series [mathematics]; Symbol manipulation", } @InProceedings{Devitt:1989:UCA, author = "J. S. Devitt", title = "Unleashing computer algebra on the mathematics curriculum", crossref = "Gonnet:1989:PAI", pages = "218--227", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author presents examples of the actual use of a computer algebra system in the mathematics classroom. These methods and observations are based on the daily use of symbolic algebra during lectures. The potential for focusing student energies on the concepts and ideas of mathematical instead of just mimicking routine computations is enormous. Considerable work remains to make such tools widely accessible but the observations presented will help to make others aware of the great potential which exists for these and similar methods.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Saskatchewan Univ., Saskatoon, Sask., Canada", classification = "C7310 (Mathematics); C7810C (Computer-aided instruction)", keywords = "Computer algebra; Educational computing; Mathematics curriculum; Symbolic algebra", thesaurus = "Educational computing; Mathematics computing; Symbol manipulation", } @InProceedings{Dewar:1989:IIS, author = "M. C. Dewar", title = "{IRENA}: an integrated symbolic and numerical computation environment", crossref = "Gonnet:1989:PAI", pages = "171--179", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Computer algebra systems provide an extremely user-friendly and natural problem-solving environment, but are comparatively slow and limited in the scope of problems they can treat. Programs which call routines from numerical software libraries are fast, but require longer development and testing time, as well as forcing potential users to describe their problems in what is, to them, an unnatural form. Both approaches have advantages and disadvantages, but until now it has been rather difficult to mix the two. The author describes IRENA, an interface between the computer algebra system REDUCE and the NAG numerical subroutine library, which provides the NAG user with the advantages of a computer algebra system and the REDUCE user with the facilities of an extensive library of numerical software. He discusses how the two methods could be used side-by-side to solve problems in definite integration.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Bath Univ., UK", classification = "C4160 (Numerical integration and differentiation); C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "Computer algebra system; Definite integration; IRENA; NAG; Numerical software; Numerical subroutine library; REDUCE", thesaurus = "Integration; Mathematics computing; Symbol manipulation; User interfaces", } @InProceedings{Dicrescenzo:1989:AEA, author = "C. Dicrescenzo and D. Duval", title = "Algebraic extensions and algebraic closure in {Scratchpad II}", crossref = "Gianni:1989:SAC", pages = "440--446", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Many problems in computer algebra, as well as in high-school exercises, are such that their statement only involves integers but their solution involves complex numbers. For example, the complex numbers $\sqrt{2}$ and $-\sqrt{2}$ appear in the solutions of elementary problems in various domains. The authors describe an implementation of an algebraic closure domain constructor in the language Scratchpad II. In the first part they analyze the problem, and in the second part they describe a solution based on the D5 system.", acknowledgement = ack-nhfb, affiliation = "TIM3, INPG, Grenoble, France", classification = "C7310 (Mathematics)", keywords = "Algebraic closure domain constructor; D5 system; Language Scratchpad II", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Edelsbrunner:1989:TPS, author = "H. Edelsbrunner and F. P. Preparata and D. B. West", title = "Tetrahedrizing point sets in three dimensions", crossref = "Gianni:1989:SAC", pages = "315--331", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of $n$ points in general position in three dimensions, i.e. such that no four points are coplanar. It also presents an algorithm that in $O(n\log{}n)$ time constructs a tetrahedrization of a set of $n$ points consisting of at most $3n-11$ tetrahedra.", acknowledgement = ack-nhfb, affiliation = "Illinois Univ., Urbana, IL, USA", classification = "C4190 (Other numerical methods)", keywords = "Combinatorial results; Extremum problems; Tetrahedra; Tetrahedrization", thesaurus = "Computational geometry", } @InProceedings{Einwohner:1989:MPG, author = "T. H. Einwohner and R. J. Fateman", title = "A {MACSYMA} package for the generation and manipulation of {Chebyshev} series", crossref = "Gonnet:1989:PAI", pages = "180--185", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p180-einwohner/", abstract = "Techniques for a MACSYMA package for expanding an arbitrary univariate expression as a truncated series in Chebyshev polynomials and manipulating such expansions are described. A data structure is introduced to represent a truncated expansion in a set of orthogonal polynomials which contains the independent variable, the name of the orthogonal polynomial set, the number of terms retained, and a list of the expansion coefficients. The package converts a given expression into the aforementioned data structure. Special cases are the conversion of sums, products, the ratio, or the composition of truncated Chebyshev expansions. Another special case is converting an expression free of truncated Chebyshev expansions. The package generates exact expansion coefficients whenever possible. In addition to well-known Chebyshev expansions, such as for polynomials, the authors provide new methods for getting exact Chebyshev expansions for reciprocals of polynomials of degree one or two, meromorphic functions, arbitrary powers of a first-degree polynomial, the error-function, and generalized hypergeometric functions.", acknowledgement = ack-nhfb, affiliation = "Lawrence Livermore Lab., California Univ., CA, USA", classification = "C4130 (Interpolation and function approximation); C6120 (File organisation); C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "algorithms; Chebyshev polynomials; Chebyshev series; Data structure; MACSYMA; Orthogonal polynomials; theory; Univariate expression", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf E.1} Data, DATA STRUCTURES. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", thesaurus = "Chebyshev approximation; Data structures; Mathematics computing; Polynomials; Series [mathematics]; Software packages; Symbol manipulation", } @InProceedings{Fateman:1989:LTR, author = "R. J. Fateman", title = "Lookup tables, recurrences and complexity", crossref = "Gonnet:1989:PAI", pages = "68--73", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p68-fateman/", abstract = "The use of lookup tables can reduce the complexity of calculation of functions defined typically by mathematical recurrence relations. Although this technique has been adopted by several algebraic manipulation systems, it has not been examined critically in the literature. While the use of tabulation or `memoization' seems to be particularly simple and worthwhile technique in some areas, there are some negative consequences. Furthermore, the expansion of this technique to other areas (other than recurrences) has not been subjected to analysis. The paper examines some of the assumptions.", acknowledgement = ack-nhfb, affiliation = "California Univ., Berkeley, CA, USA", classification = "C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "Algebraic manipulation; algorithms; Complexity; Functions; Lookup tables; Mathematical recurrence relations; theory", subject = "{\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Computational complexity; Number theory; Recursive functions; Symbol manipulation; Table lookup", } @InProceedings{Fateman:1989:SSA, author = "R. J. Fateman", title = "Series solutions of algebraic and differential equations: a comparison of linear and quadratic algebraic convergence", crossref = "Gonnet:1989:PAI", pages = "11--16", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p11-fateman/", abstract = "Speed of convergence of Newton-like iterations in an algebraic domain can be affected heavily by the increasing cost of each step, so much so that a quadratically convergent algorithm with complex steps may be comparable to a slower one with simple steps. The author gives two examples: solving algebraic and first-order ordinary differential equations using the MACSYMA algebraic manipulation system, demonstrating this phenomenon. The relevant programs are exhibited in the hope that they might give rise to more widespread application of these techniques.", acknowledgement = ack-nhfb, affiliation = "California Univ., Berkeley, CA, USA", classification = "C4130 (Interpolation and function approximation); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algebraic equations; Algebraic manipulation system; algorithms; Convergence; Differential equations; Linear algebraic convergence; MACSYMA; Newton-like iterations; Polynomials; Quadratic algebraic convergence; Series solutions; theory", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Iterative methods. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Convergence of numerical methods; Differential equations; Iterative methods; Mathematics computing; Polynomials; Series [mathematics]; Symbol manipulation", } @InProceedings{Fitch:1989:CRB, author = "J. Fitch", title = "Can {REDUCE} be run in parallel?", crossref = "Gonnet:1989:PAI", pages = "155--162", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p155-fitch/", abstract = "In order to make a substantial improvement in the performance of algebra systems it will eventually be necessary to use a parallel execution system. This paper considers one approach to detecting parallelism, an automatic method related to compilation, and applies it to REDUCE, and to the factoriser in particular.", acknowledgement = ack-nhfb, classification = "C6130 (Data handling techniques); C6150C (Compilers, interpreters and other processors); C7310 (Mathematics)", keywords = "Algebra systems; algorithms; Automatic method; Compilation; Factoriser; measurement; Parallel execution system; Parallelism; REDUCE", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency. {\bf F.3.2} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics of Programming Languages.", thesaurus = "Mathematics computing; Parallel programming; Program compilers; Symbol manipulation", } @InProceedings{Freire:1989:ASC, author = "E. Freire and E. Gamero and E. Ponce and L. G. Franquelo", title = "An algorithm for symbolic computation of center manifolds", crossref = "Gianni:1989:SAC", pages = "218--230", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "A useful technique for the study of local bifurcations is part of the center manifold theory because a dimensional reduction is achieved. The computation of Taylor series approximations of center manifolds gives rise to several difficulties regarding the operational complexity and the computational effort. Previous works proceed in such a way that the computational effort is not optimized. In the paper an algorithm for center manifolds well suited to symbolic computation is presented. The algorithm is organized according to an iterative scheme making good use of the previous steps, thereby minimizing the number of operations. The results of two examples obtained through a REDUCE 3.2 implementation of the algorithm are included.", acknowledgement = ack-nhfb, affiliation = "Escuela Superior Ingenieros Ind., Sevilla, Spain", classification = "C1120 (Analysis); C4130 (Interpolation and function approximation); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Algorithm; Center manifold theory; Computational effort; Dimensional reduction; Iterative scheme; Local bifurcations; Operational complexity; REDUCE 3.2; Symbolic computation; Taylor series approximations", thesaurus = "Approximation theory; Differential equations; Mathematics computing; Symbol manipulation", } @InProceedings{Galligo:1989:GEC, author = "Andr\'e Galligo and Lo{\"\i}c Pottier and Carlo Traverso", title = "Greater easy common divisor and standard basis completion algorithms", crossref = "Gianni:1989:SAC", pages = "162--176", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The paper considers arithmetic complexity problems; the main problem is how to limit the growth of the coefficients in the algorithms and the complexity of the field operations involved. The problem is important with every ground field, with the obvious exception of finite fields.", acknowledgement = ack-nhfb, affiliation = "Nice Univ., France", classification = "C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "Algorithms; Arithmetic complexity problems; Coefficients; Field operations; Greater easy common divisor; Standard basis completion algorithms", thesaurus = "Computational complexity; Rewriting systems", } @InProceedings{Gaonzalez:1989:SS, author = "L. Gaonzalez and H. Lombardi and T. Recio and M.-F. Roy", title = "{Sturm--Habicht} sequence", crossref = "Gonnet:1989:PAI", pages = "136--146", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p136-gaonzalez/", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @InProceedings{Geddes:1989:HMO, author = "K. O. Geddes and G. H. Gonnet and T. J. Smedley", title = "Heuristic methods for operations with algebraic numbers", crossref = "Gianni:1989:SAC", pages = "475--480", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Algorithms for doing computations involving algebraic numbers have been known for quite some time and implementations now exist in many computer algebra systems. Many of these algorithms have been analysed and shown to run in polynomial time and space, but in spite of this many real problems take large amounts of time and space to solve. The authors describe a heuristic method which can be used for many operations involving algebraic numbers. They give specifics for doing algebraic number inverses, and algebraic number polynomial exact division and greatest common divisor calculation. The heuristic will not solve all instances of these problems, but it returns either the correct result or with failure very quickly, and succeeds for a very large number of problems.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Algebraic numbers; Heuristic methods; Polynomial", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Geddes:1989:NAC, author = "K. O. Geddes and G. H. Gonnet", title = "A new algorithm for computing symbolic limits using hierarchical series", crossref = "Gianni:1989:SAC", pages = "490--495", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors describe an algorithm for computing symbolic limits, i.e. limits of expressions in symbolic form, using hierarchical series. A hierarchical series consists of two levels: an inner level which uses a simple generalization of Laurent series with finite principal part and which captures the behaviour of subexpressions without essential singularities, and an outer level which captures the essential singularities. Once such a series has been computed for an expression at a given point, the limit of the expression at the point is determined by looking at the most significant term of the series. This algorithm solves the limit problem for a large class of expressions.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "Algorithm; Finite principal part; Hierarchical series; Laurent series; Limit problem; Singularities; Symbolic form; Symbolic limits", thesaurus = "Series [mathematics]; Symbol manipulation", } @InProceedings{Geddes:1989:RIM, author = "K. O. Geddes and L. Y. Stefanus", title = "On the {Risch--Norman} integration method and its implementation in {MAPLE}", crossref = "Gonnet:1989:PAI", pages = "212--217", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p212-geddes/", abstract = "Unlike the recursive Risch algorithm for the integration of transcendental elementary functions, the Risch--Norman method processes the tower of field extensions directly in one step. In addition to logarithmic and exponential field extensions, this method can handle extensions in terms of tangents. Consequently, it allows trigonometric functions to be treated without converting them to complex exponential form. The authors review this method and describe its implementation in MAPLE. A heuristic enhancement to this method is also presented.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Waterloo Univ., Ont., Canada", classification = "C1110 (Algebra); C1120 (Analysis); C4160 (Numerical integration and differentiation); C7310 (Mathematics)", keywords = "algorithms; Exponential field extensions; Logarithmic field extensions; MAPLE; Risch--Norman integration; Tangents; theory; Transcendental elementary functions; Trigonometric functions", subject = "{\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", thesaurus = "Functions; Integration; Mathematics computing; Symbol manipulation", } @InProceedings{Gianni:1989:DA, author = "P. Gianni and V. Miller and B. Trager", title = "Decomposition of algebras", crossref = "Gianni:1989:SAC", pages = "300--308", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors deal with the problem of decomposing finite commutative Q-algebras as a direct product of local Q-algebras. They solve this problem by reducing it to the problem of finding a decomposition of finite algebras over finite field. They show that it is possible to define a lifting process that allows to reconstruct the answer over the rational numbers. This lifting appears to be very efficient since it is a quadratic lifting that doesn't require stepwise inversions. It is easy to see that the Berlekamp--Hensel algorithm for the factorization of polynomials is a special case of this argument.", acknowledgement = ack-nhfb, affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", classification = "C1110 (Algebra); C4190 (Other numerical methods)", keywords = "Berlekamp--Hensel algorithm; Decomposing finite commutative Q-algebras; Lifting process", thesaurus = "Algebra; Computational geometry", } @InProceedings{Giusti:1989:ATP, author = "M. Giusti and D. Lazard and A. Valibouze", title = "Algebraic transformations of polynomial equations, symmetric polynomials and elimination", crossref = "Gianni:1989:SAC", pages = "309--314", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors define a general transformation of polynomials and study the following concrete problem: how to perform such a transformation using a standard system of computer algebra, providing the usual algebraic tools.", acknowledgement = ack-nhfb, affiliation = "Centre de Math., Ecole Polytech., Palaiseau, France", classification = "C4130 (Interpolation and function approximation); C6130 (Data handling techniques); C7310 (Mathematics)", keywords = "Algebraic tools; Algebraic transformations of polynomial equations; Computer algebra; Elimination; Symmetric polynomials", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Giusti:1989:CRC, author = "M. Giusti", title = "On the {Castelnuovo} regularity for curves", crossref = "Gonnet:1989:PAI", pages = "250--253", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p250-giusti/", abstract = "Let $k$ be a field of characteristic zero; let us consider an algebraic subvariety of the projective space $P_k^n$, defined by a homogeneous ideal I of the polynomial algebra $R=k(x_o,\ldots{},x_n)$. There exists different objects measuring the complexity of this subvariety. Some invariants are naturally intrinsic: the dimension and the degree of the subvariety, the Hilbert function and its regularity, and the Castelnuovo regularity. A natural question is to study the relationships between the integers, at least when the dimension is small (less or equal to one). The author gives a slightly different version of the Castelnuovo--Gruson--Lazarsfeld--Peskine theorem (1983), which relates the Castelnuovo regularity and the degree in the case of curves with more general hypotheses but unfortunately slightly weaker conclusion.", acknowledgement = ack-nhfb, affiliation = "Centre de Mathematiques, CNRS, Ecole Polytechnique, Palaiseau, France", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation)", keywords = "algorithms; Castelnuovo regularity; Complexity; Curves; design; Hilbert function; measurement; Polynomial algebra; Polynomials; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.1.3} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Measures and Classes.", thesaurus = "Computational complexity; Curve fitting; Polynomials", } @InProceedings{Gonzalez:1989:SS, author = "L. Gonzalez and H. Lombardi and T. Recio and M.-F. Roy", title = "{Sturm--Habicht} sequence", crossref = "Gonnet:1989:PAI", pages = "136--146", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Formal computations with inequalities is a subject of general interest in computer algebra. In particular it is fundamental in the parallelisation of basic algorithms and quantifier elimination for real closed fields. The authors give a generalisation of the Sturm theorem essentially due to Sylvester, which is the key for formal computations with inequalities. They study the subresultant sequence, precise some of the classical definitions in order to avoid problems and study specialisation properties. They introduce the Sturm--Habicht sequence, which generalizes Habicht's work (1948). This new sequence, obtained automatically from a subresultant sequence, has some remarkable properties: it gives the same information as the Sturm sequence, recovered by looking only at its principal coefficients; it can be computed by ring operations and exact divisions only, in polynomial time in case of integer coefficients, eventually by modular methods; it has good specialisation properties. Some information about applications and implementation of the Sturm--Habicht sequence is given.", acknowledgement = ack-nhfb, affiliation = "Dept. de Matematicas, Cantabria Univ., Spain", classification = "C1110 (Algebra); C4130 (Interpolation and function approximation); C4240 (Programming and algorithm theory)", keywords = "Computational complexity; Computer algebra; Inequalities; Integer coefficients; Modular methods; Parallelisation; Polynomial time; Quantifier elimination; Ring operations; Sturm theorem; Sturm--Habicht sequence", thesaurus = "Computational complexity; Parallel algorithms; Polynomials; Series [mathematics]; Symbol manipulation", } @InProceedings{Grigorev:1989:CCC, author = "D. Yu. Grigor'ev", title = "Complexity of computing the characters and the genre of a system of exterior differential equations", crossref = "Gianni:1989:SAC", pages = "534--543", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Let a system $(\sum_JA_{J,i}(dX_{j1},\ldots{},dX_{jm})=0)_{m,i}$ of exterior differential equations be given, where $A_{J,i}$ are polynomials in $n$ variables $X_1,\ldots{}, X_n$ of degrees less than $d$ and skew-symmetric relatively to multiindices $J=(j_1,\ldots{}, j_m)$, the square brackets denote the exterior product of the differentials $dX_{j1},\ldots{}, dX_{jm}$. E. Cartan (1945) introduced the characters and the genre $h$ of the system. Cauchy--Kovalevski theorem guarantees the existence of an integral manifold (and even of the general form) with the dimension less or equal to $h$ satisfying the given system. An algorithm for computing the characters and the genre is designed with the running time polynomial in $L$, $(dn)^n$, herein $L$ denotes the bit-size of the system. The algorithm involves the subexponential-time procedures for finding the irreducible components of an algebraic variety.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., V. A. Steklov Inst., Acad. of Sci., Leningrad, USSR", classification = "C4130 (Interpolation and function approximation); C4170 (Differential equations)", keywords = "Algebraic variety; Cauchy--Kovalevski theorem; Characters; Exterior differential equations; Integral manifold; Irreducible components; Polynomials", thesaurus = "Differential equations; Polynomials", } @InProceedings{Grossman:1989:LTE, author = "R. Grossman and R. G. Larson", title = "Labeled trees and the efficient computation of derivations", crossref = "Gonnet:1989:PAI", pages = "74--80", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p74-grossman/", abstract = "The paper is concerned with the effective parallel symbolic computation of operators under composition. Examples include differential operators under composition and vector fields under the Lie bracket. In general, such operators do not commute. An important problem is to find efficient algorithms to write expressions involving noncommuting operators in terms of operators which do commute. If the original expression enjoys a certain symmetry, then naive rewriting requires the computation of terms which in the end cancel. Previously, the authors gave an algorithm which in some cases is exponentially faster than the naive expansion of the noncommutating operators (1989). In this paper they show how that algorithm can be naturally parallelized.", acknowledgement = ack-nhfb, affiliation = "Illinois Univ., Chicago, IL, USA", classification = "C1120 (Analysis); C1160 (Combinatorial mathematics); C4210 (Formal logic); C4240 (Programming and algorithm theory)", keywords = "algorithms; Computational complexity; Data structures; Derivations; Differential operators; Labeled trees; Lie bracket; Noncommuting operators; Operators; Parallel algorithms; Parallel symbolic computation; theory; Vector fields", subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf F.1.2} Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation, Parallelism and concurrency.", thesaurus = "Computational complexity; Data structures; Differentiation; Parallel algorithms; Symbol manipulation; Trees [mathematics]", } @InProceedings{Hentzel:1989:VNA, author = "I. R. Hentzel and D. J. Pokrass", title = "Verification of non-identities in algebras", crossref = "Gianni:1989:SAC", pages = "496--507", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors present a computer assisted algorithm which establishes whether or not a proposed identity is a consequence of the defining identities of a variety of nonassociative algebras. When the nonassociative polynomial is not an identity, the algorithm produces a proof called a characteristic function. Like an ordinary counterexample, the characteristic function can be used to convince a verifier that the polynomial is not identically zero. However the characteristic function appears to be computationally easier to verify. Also, it reduces or eliminates problems with characteristic. The authors used this method to obtain and verify a new result in the theory of nonassociative algebras. Namely, in a free right alternative algebra $(a,a,b)^3 \ne 0$.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Iowa State Univ., Ames, IA, USA", classification = "C7310 (Mathematics)", keywords = "Algebras; Characteristic function; Computer assisted algorithm; Nonassociative polynomial; Nonidentities verification", thesaurus = "Mathematics computing; Symbol manipulation", } @InProceedings{Juozapavicius:1989:SCW, author = "A. Juozapavicius", title = "Symbolic computation for {Witt} rings", crossref = "Gianni:1989:SAC", pages = "271--273", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author considers bilinear and quadratic forms over polynomial rings, such that they can carry linear discrete orderings. The author defines the notion of reduced form and presents theorems concerning equivalence of forms to their reduced presentation. The proofs of these statements are based on the Buchberger's algorithms and their modifications to Gr{\"o}bner bases.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Vilnius State Univ., Lithuanian SSR, USSR", classification = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", keywords = "Bilinear forms; Symbolic computation; Witt rings; Quadratic forms; Polynomial rings; Linear discrete orderings; Reduced form; Gr{\"o}bner bases", thesaurus = "Polynomials; Symbol manipulation", } @InProceedings{Kaltofen:1989:ISM, author = "E. Kaltofen and L. Yagati", title = "Improved sparse multivariate polynomial interpolation algorithms", crossref = "Gianni:1989:SAC", pages = "467--474", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The authors consider the problem of interpolating sparse multivariate polynomials from their values. They discuss two algorithms for sparse interpolation, one due to Ben-Or and Tiwari (1988) and the other due to Zippel (1988). They present efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of equations, the use of which greatly improves the time complexities of the two interpolation algorithms.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C4130 (Interpolation and function approximation)", keywords = "Sparse multivariate polynomial interpolation algorithms; Time complexities; Toeplitz systems; Transposed Vandermonde systems of equations", thesaurus = "Interpolation; Polynomials", } @InProceedings{Kaltofen:1989:IVP, author = "E. Kaltofen and T. Valente and N. Yui", title = "An improved {Las Vegas} primality test", crossref = "Gonnet:1989:PAI", pages = "26--33", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p26-kaltofen/", abstract = "The authors present a modification of the Goldwasser--Kilian--Atkin primality test, which, when given an input $n$, outputs either prime or composite, along with a certificate of correctness which may be verified in polynomial time. Atkin's method computes the order of an elliptic curve whose endomorphism ring is isomorphic to the ring of integers of a given imaginary quadratic field $Q(\sqrt{-D})$. Once an appropriate order is found, the parameters of the curve are computed as a function of a root modulo $n$ of the Hilbert class equation for the Hilbert class field of $Q(\sqrt{-D})$. The modification proposed determines instead a root of the Watson class equation for $Q(\sqrt{-D})$ and applies a transformation to get a root of the corresponding Hilbert equation. This is a substantial improvement, in that the Watson equations have much smaller coefficients than do the Hilbert equations.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA", classification = "C1160 (Combinatorial mathematics); C4240 (Programming and algorithm theory); C7310 (Mathematics)", keywords = "algorithms; Certificate of correctness; Elliptic curve; Endomorphism ring; Goldwasser--Kilian--Atkin primality test; Hilbert equation; Imaginary quadratic field; Las Vegas primality test; Number theory; Polynomial time; Prime number; Programming theory; theory; Watson class equation", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Hyperbolic equations. {\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", thesaurus = "Computational complexity; Mathematics computing; Number theory; Program verification; Programming theory", } @InProceedings{Kirchner:1989:CER, author = "C. Kirchner and H. Kirchner", title = "Constrained equational reasoning", crossref = "Gonnet:1989:PAI", pages = "382--389", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p382-kirchner/", abstract = "The theory of constrained equational reasoning is outlined. Many questions and prolongations of this work arise.", acknowledgement = ack-nhfb, classification = "C4210 (Formal logic)", keywords = "algorithms; Constrained equational reasoning; Formal logic; Theorem proving; theory", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Logic and constraint programming. {\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computational logic.", thesaurus = "Formal logic; Theorem proving", } @InProceedings{Kobayashi:1989:SSA, author = "H. Kobayashi and S. Moritsugu and R. W. Hogan", title = "Solving systems of algebraic equations", crossref = "Gianni:1989:SAC", pages = "139--149", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Shows an algorithm for computing all the solutions with their multiplicities of a system of algebraic equations. The algorithm previously proposed by the authors for the case where the ideal is zero-dimensional and radical seems to have practical efficiency. The authors present a new method for solving systems which are not necessarily radical. The set of all solutions is partitioned into subsets each of which consists of mutually conjugate solutions having the same multiplicity.", acknowledgement = ack-nhfb, affiliation = "Dept. of Math., Coll. of Sci. and Technol., Nihon Univ., Tokyo, Japan", classification = "C1110 (Algebra); C4210 (Formal logic)", keywords = "Algebraic equations; Algorithm; Ideal; Multiplicities; Mutually conjugate solutions; Radical; Subsets; Zero-dimensional", thesaurus = "Algebra; Problem solving; Theorem proving", } @InProceedings{Kredel:1989:SDC, author = "H. Kredel", title = "Software development for computer algebra or from {ALDES\slash SAC-2} to {WEB\slash Modula-2}", crossref = "Gianni:1989:SAC", pages = "447--455", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author defines a new concept for developing computer algebra software. The development system will integrate a documentation system, a programming language, algorithm libraries, and an interactive calculation facility. The author exemplifies the workability of this concept by applying it to the well known ALDES/SAC-2 system. The ALDES Translator is modified to help in converting ALDES/SAC-2 Code to Modula-2. The implementation and module setup of the SAC-2 basic system, list processing system and arithmetic system in Modula-2 are discussed. An example gives a first idea of the performance of the system. The WEB System of Structured Documentation is used to generate documentation with {\TeX}.", acknowledgement = ack-nhfb, affiliation = "Passau Univ., West Germany", classification = "C6110B (Software engineering techniques); C7310 (Mathematics)", keywords = "ALDES/SAC-2 system; Algorithm libraries; Computer algebra software; Documentation system; Interactive calculation facility; Performance; Programming language; WEB/Modula-2", thesaurus = "Mathematics computing; Software engineering; Symbol manipulation", } @InProceedings{Kuhn:1989:MEC, author = "N. Kuhn and K. Madlener", title = "A method for enumerating cosets of a group presented by a canonical system", crossref = "Gonnet:1989:PAI", pages = "338--350", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p338-kuhn/", abstract = "The application of rewriting techniques to enumerate cosets of subgroups in groups is investigated. Given a class of groups $G$ having canonical string rewriting presentations the authors consider the GWP for this class which is defined by $GWP(w,U)$ iff $w$ in $$ for $w$ in finite $U$ contained in $G$, $G \in G$, where $$ is the subgroup of $G$ generated by $U$. They show how to associate to $U$ two rewriting relations to $-{}_U$ and implies $-{}_U$ on strings such that $w$ in $$ iff $w$ from $*$ to $-{}_U\lambda$ iff $w$ implied by $*\mbox{implies}-_U\lambda$ ($\lambda$ the empty word), both representing the left congruence generated by $$. They derive general critical pair criteria for confluence and $\lambda$-confluence for these relations. Using these criteria completion procedures can be constructed which enumerate cosets like the Todd--Coxeter algorithm without explicit definition of all cosets. The procedures are shown to be terminating if the index of the subgroup is finite or for groups with finite canonical monadic group presentations. If the completion procedure terminates it returns a prefix rewriting system which is confluent on $\Sigma *$, thus deciding the GWP and the index problem for this class of groups. The normal forms of the rewriting relations form a minimal Schreier-representative system of $$ in $G$.", acknowledgement = ack-nhfb, affiliation = "Fachbereich Inf., Kaiserslautern Univ., West Germany", classification = "C1110 (Algebra); C4210 (Formal logic)", keywords = "$\Lambda$-confluence; algorithms; Canonical string rewriting presentations; Completion procedures; Confluence; Cosets; Critical pair criteria; Decidability; Finite canonical monadic group presentations; Generalized word problem; Group theory; Minimal Schreier-representative system; Rewriting relations; Rewriting techniques; Subgroups; theory; Todd--Coxeter algorithm", subject = "{\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems. {\bf F.4.2} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Grammars and Other Rewriting Systems, Decision problems. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems.", thesaurus = "Decidability; Group theory; Rewriting systems; Symbol manipulation", } @InProceedings{Kutzler:1989:CAT, author = "B. Kutzler", title = "Careful algebraic translations of geometry theorems", crossref = "Gonnet:1989:PAI", pages = "254--263", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p254-kutzler/", abstract = "Modern application areas like computer-aided design and robotics have revived interest in geometry. The algorithmic techniques of computer algebra are important tools for solving large classes of nonlinear geometric problems. However, their application requires a translation of geometric problems into algebraic form. So far, this algebraization process has not gained special attention, since it was considered `obvious'. In the context of automated geometry theorem proving, the use of algebraic deduction techniques led to very promising results, but it seemed to change the nature of proof problems from deciding the validity of a theorem to finding nondegeneracy conditions under which the theorem holds. A careful analysis shows, that this is mainly due to the `careless' translation method. A careful translation technique is presented that resolves this defect. The usefulness of the new algebraization method is demonstrated on concrete examples. A practical comparison with the former `careless' translation is done.", acknowledgement = ack-nhfb, affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria", classification = "C1160 (Combinatorial mathematics); C4190 (Other numerical methods); C4210 (Formal logic); C4290 (Other computer theory); C7310 (Mathematics)", keywords = "Algebraic deduction; algorithms; Automated geometry theorem proving; Computer algebra; experimentation; Geometry theorems; Nonlinear geometric problems; theory", subject = "{\bf I.2.0} Computing Methodologies, ARTIFICIAL INTELLIGENCE, General. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics.", thesaurus = "Computational geometry; Symbol manipulation; Theorem proving", } @InProceedings{MacCallum:1989:ODE, author = "M. A. H. MacCallum", title = "An ordinary differential equation solver for {REDUCE}", crossref = "Gianni:1989:SAC", pages = "196--205", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "Progress and plans for the implementation of an ordinary differential equation solver in REDUCE 3.3 are reported; the aim is to incorporate the best available methods for obtaining closed-form solutions, and to aim at the `best possible' alternative when this fails. It is hoped that this will become a part of the standard REDUCE program library. Elementary capabilities have already been implemented, i.e. methods for first order differential equations of simple types and linear equations of any order with constant coefficients. The further methods to be used include: for first-order equations, an adaptation of Shtokhamer's MACSYMA program; for higher-order linear equations, factorisation of the operator where possible; and for nonlinear equations, the exploitation of Lie symmetries.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math. Sci., Queen Mary Coll., London, UK", classification = "C1120 (Analysis); C4170 (Differential equations); C7310 (Mathematics)", keywords = "Closed-form solutions; Factorisation; First-order equations; Lie symmetries; MACSYMA program; Nonlinear equations; Ordinary differential equation solver; REDUCE 3.3; REDUCE program library", thesaurus = "Differential equations; Mathematics computing; Software packages; Subroutines", } @InProceedings{Menezes:1989:SCA, author = "A. J. Menezes and P. C. {van Oorschot} and S. A. Vanstone", title = "Some computational aspects of root finding in ${GF}(q^m)$", crossref = "Gianni:1989:SAC", pages = "259--270", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "This paper is an implementation report comparing several variations of a deterministic algorithm for finding roots of polynomials in finite extension fields. Running times for problem instances in fields $\mbox{GF}(2^m)$, including $m>1000$, are given. Comparisons are made between the variations, and improvements achieved in running times are discussed.", acknowledgement = ack-nhfb, affiliation = "Waterloo Univ., Ont., Canada", classification = "C4130 (Interpolation and function approximation)", keywords = "Computational aspects; Root finding; Roots of polynomials", thesaurus = "Polynomials", } @InProceedings{Miller:1989:PGE, author = "B. R. Miller", title = "A program generator for efficient evaluation of {Fourier} series", crossref = "Gonnet:1989:PAI", pages = "199--206", year = "1989", bibdate = "Thu Mar 12 08:33:50 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/74540/p199-miller/", abstract = "Many fields require the evaluation of large multi-variate Fourier series, but the naive method of calling sine and cosine for each term can be prohibitive where computing resources are constrained or the series are extremely large (30000 terms). Although the number of such calls can be reduced by using trigonometric identities, such a reduction is usually not possible by hand. Indeed, even when it is carried out by computer, care must be taken to generate compact programs and avoid generating large numbers of intermediate terms. The author describes an algorithm for automatically generating very efficient Fortran programs directly from the mathematical description of the series to be evaluated. The resulting Fortran programs are 5-7 times faster than the naive version and sometimes significantly more compact.", acknowledgement = ack-nhfb, affiliation = "Nat. Inst. of Stand. and Technol., Gaithersbury, MD, USA", classification = "C6115 (Programming support); C7310 (Mathematics)", keywords = "algorithms; design; Fortran programs; Fourier series; languages; Program generator", subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic, Computability theory. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf D.3.3} Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Procedures, functions, and subroutines.", thesaurus = "Automatic programming; Mathematics computing; Series [mathematics]; Symbol manipulation", } @InProceedings{Mora:1989:GBN, author = "T. Mora", title = "{Gr{\"o}bner} bases in noncommutative algebras", crossref = "Gianni:1989:SAC", pages = "150--161", year = "1989", bibdate = "Thu Sep 26 06:21:35 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib", abstract = "The author has studied, in 1988, the concept of standard and Gr{\"o}bner bases and algorithms for their computation in a very wide algebraic context (graded structures). It is easy to show that if $R=k/H$, where $H$ is the ideal generated by $(X_jX_j-c_{ij}X_iX_j-p_{ij})$ and $\deg(p_{ij})<\deg(X_iX_j)$ for each $i,j$, then $R$ is such a graded structure; so his previous techniques can be applied to it in order to define a concept of Gr{\"o}bner basis and to produce an algorithm for their computation, provided that if $J$ is the ideal generated by $(X_jX_i-c_{ij}X_iX_j:i$, homogeneous for the graduation defined above and containing J, is finitely generated; (2) For each homogeneous ideal $(h_1, \ldots{}, h_s)$ in $k/J$, it is possible to compute a finite set of syzygies, which together with the trivial ones, generate the module of syzygies; and (3) For each homogeneous ideal $(h_1, \ldots{}, h_s)$ and each homogeneous element $h$ in $k/J$, it is possible to decide whether $h$ in $(h_1,\ldots{},h_s)$, in which case it is possible to compute a representation of $h$ in terms of $(h_1,\ldots{},h_s)$. It turns out that the above conditions hold whenever for no $i