%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.23",
%%% date = "11 December 2023",
%%% time = "12:04:13 MST",
%%% filename = "axiom.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 = "https://www.math.utah.edu/~beebe",
%%% checksum = "52261 5161 25920 246667",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography; AXIOM; Fricas; OpenAxiom;
%%% Scratchpad; symbolic algebra",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This file contains a bibliography of
%%% publications about the AXIOM (formerly
%%% known as Scratchpad) symbolic algebra
%%% system. It also covers publications about
%%% Scratchpad and a few about MathCAD.
%%%
%%% At version 1.23, the year coverage looked
%%% like this:
%%%
%%% 1971 ( 3) 1987 ( 5) 2003 ( 3)
%%% 1972 ( 3) 1988 ( 8) 2004 ( 1)
%%% 1973 ( 0) 1989 ( 18) 2005 ( 9)
%%% 1974 ( 1) 1990 ( 7) 2006 ( 2)
%%% 1975 ( 1) 1991 ( 16) 2007 ( 6)
%%% 1976 ( 1) 1992 ( 16) 2008 ( 1)
%%% 1977 ( 1) 1993 ( 10) 2009 ( 0)
%%% 1978 ( 0) 1994 ( 11) 2010 ( 0)
%%% 1979 ( 0) 1995 ( 7) 2011 ( 0)
%%% 1982 ( 0) 1998 ( 1) 2014 ( 0)
%%% 1983 ( 0) 1999 ( 2) 2015 ( 0)
%%% 1984 ( 6) 2000 ( 0) 2016 ( 0)
%%% 1985 ( 2) 2001 ( 1) 2017 ( 1)
%%% 1986 ( 4) 2002 ( 1)
%%%
%%% Article: 34
%%% Book: 18
%%% InCollection: 1
%%% InProceedings: 48
%%% Manual: 1
%%% MastersThesis: 2
%%% Proceedings: 28
%%% TechReport: 16
%%%
%%% Total entries: 148
%%%
%%% Scratchpad and AXIOM were developed at IBM
%%% research laboratories over many years before
%%% they were offered as supported products.
%%% Today, AXIOM is marketed for several
%%% platforms by the Numerical Algorithms Group,
%%% Inc. (NAG) (Downer's Grove, IL, USA. and
%%% Oxford, UK), and versions are available in
%%% late 1995 for Hewlett--Packard 9000 (HP-UX),
%%% IBM RS/6000 (AIX), and Sun (SunOS) systems,
%%% with ports to other systems under
%%% development.
%%%
%%% Further information on AXIOM licensing
%%% can be found at http://www.nag.com/ and
%%% http://www.nag.co.uk/1h/symbolic/AX.html.
%%%
%%% NAG maintains an AXIOM code and documentation
%%% repository at http://www.nag.co.uk/symbolic/
%%% AX/Upload_Readme.html. All of the NAG
%%% technical reports listed in this bibliography
%%% can be found at that address.
%%%
%%% In 2006, AXIOM became free software, with a
%%% Web site at
%%%
%%% http://www.axiom-developer.org
%%%
%%% This bibliography has been collected from the
%%% author's personal bibliography files, from
%%% the very large computer science bibliography
%%% collection on ftp.ira.uka.de in
%%% /pub/bibliography to which many people of
%%% have contributed, and from several
%%% Internet-accessible library catalogs, notably
%%% those of the University of California,
%%% Library of Congress, OCLC, plus the IEEE
%%% INSPEC (1989--1995) database.
%%%
%%% This bibliography is sorted by year, and
%%% within each year, by author and title key,
%%% with ``bibsort -byyear''. Cross-referenced
%%% proceedings entries appear at the end,
%%% because of a restriction in the current
%%% BibTeX.
%%%
%%% 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.",
%%% }
%%% ====================================================================
%%% 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|https://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Institution abbreviations:
@String{inst-NAG = "Numerical Algorithms Group, Inc."}
@String{inst-NAG:adr = "Downer's Grove, IL, USA and Oxford,
UK"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-COED = "CoED"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-ELECTRONIK = "Elektronik"}
@String{j-IFIP-TRANS-A = "IFIP Transactions. A. Computer Science and
Technology"}
@String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-MATH-COMP-EDU = "Mathematics and computer education"}
@String{j-SIGPLAN = "ACM SIG{\-}PLAN Notices"}
@String{j-SIGSAM = "SIGSAM Bulletin (ACM Special Interest
Group on Symbolic and Algebraic
Manipulation)"}
@String{j-STAT-COMP = "Statistics and Computing"}
@String{j-THEOR-COMP-SCI = "Theoretical Computer Science"}
@String{j-TOMS = "ACM Transactions on Mathematical Software"}
@String{j-ZEIT-ANGE-MATH-PHYS = "Zeitschrift fur Angewandte Mathematik
und Physik"}
%%% ====================================================================
%%% Publisher abbreviations:
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
@String{pub-AP = "Academic Press"}
@String{pub-AP:adr = "New York, NY, USA"}
@String{pub-DEKKER = "Marcel Dekker"}
@String{pub-DEKKER:adr = "New York, NY, USA"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-VIEWEG = "Friedrich Vieweg und Sohn"}
@String{pub-VIEWEG:adr = "Braunschweig, Germany"}
%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNCS = "Lecture Notes in Computer Science"}
%%% ====================================================================
%%% Bibliography entries:
@InProceedings{Griesmer:1971:SIF,
author = "J. H. Griesmer and R. D. Jenks",
title = "{SCRATCHPAD/1} --- an interactive facility for
symbolic mathematics",
crossref = "Petrick:1971:PSS",
pages = "42--58",
year = "1971",
DOI = "https://doi.org/10.1145806266",
bibdate = "Thu Jul 26 08:45:53 2001",
bibsource = "/usr/local/src/bib/bibliography/Theory/obscure.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://delivery.acm.org/10.1145/810000/806266/p42-griesmer.pdf",
}
@TechReport{Jenks:1971:MPS,
author = "R. D. Jenks",
title = "{META\slash PLUS}: The Syntax Extension Facility for
{SCRATCHPAD}",
type = "Research Report",
number = "RC 3259",
institution = "International Business Machines Inc., Thomas J. Watson
Research Center",
address = "Yorktown Heights, NY, USA",
pages = "??",
month = feb,
year = "1971",
bibdate = "Sat Dec 30 08:53:02 1995",
bibsource = "/usr/local/src/bib/bibliography/Ai/lisp.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InProceedings{Griesmer:1972:EOSb,
author = "J. Griesmer and R. Jenks",
title = "Experience with an online symbolic math. system
{SCRATCHPAD}",
crossref = "Online:1972:OCP",
pages = "??--??",
year = "1972",
bibsource = "/usr/local/src/bib/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
bydate = "Le",
byrev = "Le",
date = "00/00/00",
descriptors = "Formula manipulation",
enum = "1209",
language = "English",
location = "PKI-OG: Li-Ord.Le",
references = "0",
revision = "21/04/91",
}
@Article{Griesmer:1972:SCV,
author = "James H. Griesmer and Richard D. Jenks",
title = "{SCRATCHPAD}: {A} capsule view",
journal = j-SIGPLAN,
volume = "7",
number = "10",
pages = "93--102",
year = "1972",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145807019",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Jul 26 10:33:16 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "Proceedings of the symposium on Two-dimensional
man-machine communication, Mark B. Wells and James B.
Morris (eds.)",
acknowledgement = ack-nhfb,
bookpages = "iii + 160",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Jenks:1974:SL,
author = "R. D. Jenks",
title = "The {SCRATCHPAD} language",
journal = j-SIGPLAN,
volume = "9",
number = "4",
pages = "101--111",
month = apr,
year = "1974",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145807051",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C7310 (Mathematics
computing)",
conflocation = "Santa Monica, CA, USA; 28-29 March 1974",
conftitle = "ACM SIGPLAN Symposium on Very High Level Languages",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "formal description; formal programming language; high
level programming language; interactive system;
mathematical algorithms; natural sciences applications
of computers; online problem solving; problem oriented
languages; SCRATCHPAD language; symbolic mathematical
computation; user language",
sponsororg = "ACM",
treatment = "A Application; P Practical",
}
@Article{Norman:1975:CFP,
author = "A. C. Norman",
title = "Computing with Formal Power Series",
journal = j-TOMS,
volume = "1",
number = "4",
pages = "346--356",
month = dec,
year = "1975",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 00:22:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "Scratchpad",
}
@InProceedings{Jenks:1976:PC,
author = "Richard D. Jenks",
editor = "Richard D. Jenks",
booktitle = "Symsac '76: proceedings of the 1976 ACM Symposium on
Symbolic and Algebraic Computation, August 10--12,
1976, Yorktown Heights, New York",
title = "A pattern compiler",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "60--65",
year = "1976",
DOI = "https://doi.org/10.1145806324",
ISBN = "????",
ISBN-13 = "????",
LCCN = "QA155.7.E4 .A15 1976; QA9.58 .A11 1976",
bibdate = "Thu Jul 26 08:56:43 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
bookpages = "384",
keywords = "Scratchpad",
}
@MastersThesis{Lueken:1977:UIF,
author = "E. Lueken",
title = "{Ueberlegungen zur Implementierung eines
Formelmanipulationssystemes}",
school = "Technischen Universit{\"{a}}t Carolo-Wilhelmina zu
Braunschweig",
address = "Braunschweig, Germany",
pages = "??",
year = "1977",
bibsource = "/usr/local/src/bib/bibliography/Misc/TUBScsd.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
descriptor = "Alpak, Altran, Formac, Funktion, G.g.t., Kanonische
Darstellung von Polynomen, Macsyma, Mathlab, Polynom,
Rationale Funktion, Reduce, Sac-1, Scratchpad",
}
@InProceedings{Andrews:1984:RS,
author = "George E. Andrews",
title = "{Ramanujan} and {SCRATCHPAD}",
crossref = "Golden:1984:PMU",
pages = "383--??",
year = "1984",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@Manual{Davenport:1984:S,
author = "J. Davenport and P. Gianni and R. Jenks and V. Miller
and S. Morrison and M. Rothstein and C. Sundaresan and
R. Sutor and B. Trager",
title = "{Scratchpad}",
organization = "Mathematical Sciences Department",
address = "IBM Thomas Watson Research Center",
pages = "??",
year = "1984",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InProceedings{Jenks:1984:NSL,
author = "Richard D. Jenks",
title = "The New {SCRATCHPAD} Language and System for Computer
Algebra",
crossref = "Golden:1984:PMU",
pages = "409--??",
year = "1984",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InProceedings{Jenks:1984:PKN,
author = "Richard D. Jenks",
title = "A primer: 11 keys to {New Scratchpad}",
crossref = "Fitch:1984:E",
pages = "123--147",
year = "1984",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InProceedings{Sutor:1985:SIC,
author = "R. S. Sutor",
title = "The {Scratchpad II} Computer Algebra Language and
System",
crossref = "Buchberger:1985:EEC",
pages = "32--33",
year = "1985",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InProceedings{Gebauer:1986:BAS,
author = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
editor = "Bruce W. Char",
booktitle = "Proceedings of the 1986 Symposium on Symbolic and
Algebraic Computation: Symsac '86, July 21--23, 1986,
Waterloo, Ontario",
title = "{Buchberger}'s algorithm and staggered linear bases",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "218--221",
year = "1986",
DOI = "https://doi.org/10.1145.32482",
ISBN = "0-89791-199-7",
ISBN-13 = "978-0-89791-199-3",
LCCN = "QA155.7.E4 A281 1986",
bibdate = "Thu Jul 26 09:06:12 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "ACM order number 505860.",
acknowledgement = ack-nhfb,
bookpages = "254",
}
@TechReport{Jenks:1986:SIA,
author = "Richard D. Jenks and Robert S. Sutor and Stephen M.
Watt",
title = "Scratchpad {II}: an abstract datatype system for
mathematical computation",
type = "Research Report",
number = "RC 12327 (\#55257)",
institution = "International Business Machines Inc., Thomas J. Watson
Research Center",
address = "Yorktown Heights, NY, USA",
pages = "23",
year = "1986",
bibdate = "Thu Oct 31 17:23:28 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
keywords = "Abstract data types (Computer science); Operating
systems (Computers)",
}
@InProceedings{Lucks:1986:FIP,
author = "Michael Lucks",
editor = "Bruce W. Char",
booktitle = "Proceedings of the 1986 Symposium on Symbolic and
Algebraic Computation: Symsac '86, July 21--23, 1986,
Waterloo, Ontario",
title = "A fast implementation of polynomial factorization",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "228--232",
year = "1986",
DOI = "https://doi.org/10.1145.32485",
ISBN = "0-89791-199-7",
ISBN-13 = "978-0-89791-199-3",
LCCN = "QA155.7.E4 A281 1986",
bibdate = "Thu Jul 26 09:06:12 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "ACM order number 505860.",
acknowledgement = ack-nhfb,
keywords = "Scratchpad",
}
@InProceedings{Purtilo:1986:ASI,
author = "J. Purtilo",
editor = "Bruce W. Char",
booktitle = "Proceedings of the 1986 Symposium on Symbolic and
Algebraic Computation: Symsac '86, July 21--23, 1986,
Waterloo, Ontario",
title = "Applications of a software interconnection system in
mathematical problem solving environments",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "16--23",
year = "1986",
DOI = "https://doi.org/10.1145.32443",
ISBN = "0-89791-199-7",
ISBN-13 = "978-0-89791-199-3",
LCCN = "QA155.7.E4 A281 1986",
bibdate = "Thu Jul 26 09:26:18 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "ACM order number 505860.",
acknowledgement = ack-nhfb,
keywords = "Scratchpad",
}
@TechReport{Burge:1987:ISS,
author = "W. Burge and S. Watt",
title = "Infinite Structures in {SCRATCHPAD II}",
number = "RC 12794 (\#57573)",
institution = "IBM Thomas J. Watson Research Center",
address = "Bos 218, Yorktown Heights, NY 10598, USA",
pages = "??",
year = "1987",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@TechReport{Senechaud:1987:SIP,
author = "P. Senechaud and F. Siebert and G. Villard",
title = "Scratchpad {II}: Pr{\'e}sentation d'un nouveau langage
de calcul formel",
number = "640-M",
institution = "TIM 3 (IMAG)",
address = "Grenoble, France",
pages = "??",
month = feb,
year = "1987",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@TechReport{Sutor:1987:TICa,
author = "Robert S. Sutor and Richard D. Jenks",
title = "The type inference and coercion facilities in the
{Scratchpad II} interpreter",
type = "Research Report",
number = "RC 12595 (\#56575)",
institution = "IBM Thomas J. Watson Research Center",
address = "Yorktown Heights, NY, USA",
pages = "11",
year = "1987",
bibdate = "Sat Dec 30 08:25:26 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
keywords = "Abstract data types (Computer science); Programming
languages (Electronic computers)",
}
@InProceedings{Sutor:1987:TICb,
author = "R. S. Sutor and R. D. Jenks",
title = "The Type Inference and Coercion Facilities in the
{Scratchpad II} Interpreter",
crossref = "Wexelblat:1987:IIT",
pages = "56--63",
year = "1987",
bibsource = "/usr/local/src/bib/bibliography/Compiler/bevan.bib;
/usr/local/src/bib/bibliography/Misc/sigplan.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The Scratchpad II system is an abstract datatype
programming language, a compiler for the language, a
library of packages of polymorphic functions and
parameterized abstract datatypes, and an interpreter
that provides sophisticated type inference and coercion
facilities. Although originally designed for the
implementation of symbolic mathematical algorithms,
Scratchpad II is a general purpose programming
language. This paper discusses aspects of the
implementation of the interpreter and how it attempts
to provide a user friendly ad relatively weakly typed
front end for the strongly typed programming
language.",
acknowledgement = ack-nhfb,
checked = "19940516",
keywords = "scratchpad",
refs = "8",
subject = "D.3.4 Software, PROGRAMMING LANGUAGES, Processors,
Interpreters \\ I.1.3 Computing Methodologies,
ALGEBRAIC MANIPULATION, Languages and Systems,
SCRATCHPAD \\ D.3.3 Software, PROGRAMMING LANGUAGES,
Language Constructs, Abstract data types",
}
@InProceedings{Andrews:1988:ASP,
author = "G. E. Andrews",
title = "Application of {Scratchpad} to problems in special
functions and combinatorics",
crossref = "Janssen:1988:TCA",
pages = "158--??",
year = "1988",
bibdate = "Fri Dec 29 18:28:25 1995",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@Book{Davenport:1988:CA,
author = "J. H. Davenport and Y. Siret and E. Tournier",
title = "Computer Algebra: Systems and Algorithms for Algebraic
Computation",
publisher = pub-AP,
address = pub-AP:adr,
pages = "xix + 267",
year = "1988",
ISBN = "0-12-204230-1",
ISBN-13 = "978-0-12-204230-0",
LCCN = "QA155.7.E4 D38 1988",
bibdate = "Fri Dec 29 18:14:51 1995",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
notes = "{\footnotesize Dies ist die englische Ausgabe des
urspr{\"u}nglich bei Masson 1987 erschienen Buches {\em
Calcul Formel}. Es ist die erste Monographie {\"u}ber
Computeralgebra. Es wird in etwa die Theorie behandelt,
die heute in den gr{\"o}{\ss}eren Systemen wie MACSYMA,
MAPLE, REDUCE oder SCRATCHPAD II realisiert ist. Das
erste Kapitel ist der Diskussion verschiedener \CA\
Systeme mit Beispielen gewidmet. Die wichtige Frage der
Repr{\"a}sentation der mathematischen Objekte auf einem
Computer ist das Thema des zweiten Kapitels. Der
Algorithmus von Buchberger, zylindrische Dekomposition,
Berechnung von gr{\"o}{\ss}ten gemeinsamen Teilern,
p-adische Methoden und Faktorisierung,
Differentialgleichungen und Stammfunktionen sind die
wichtigsten behandelten Gegenst{\"a}nde des Buches, das
mit einer ausf{\"u}hrlichen Bibliographie und einer
Beschreibung von REDUCE im Anhang endet. \hfill J.
Grabmeier}",
}
@Article{Gebauer:1988:IBA,
author = "R. Gebauer and H. M. M{\"o}ller",
title = "On an installation of {Buchberger}'s algorithm",
journal = j-J-SYMBOLIC-COMP,
volume = "6",
number = "2-3",
pages = "275--286",
month = oct # "--" # dec,
year = "1988",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Sep 17 08:24:38 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Buchberger's algorithm calculates Gr{\"o}bner bases of
polynomial ideals. Its efficiency depends strongly on
practical criteria for detecting superfluous
reductions. Buchberger recommends two criteria. The
more important one is interpreted in this paper as a
criterion for detecting redundant elements in a basis
of a module of syzygies The authors present a method
for obtaining a reduced, nearly minimal basis of that
module. The simple procedure for detecting (redundant
syzygies and) superfluous reductions is incorporated
now in the installation of Buchberger's algorithm in
SCRATCHPAD II and REDUCE 3.3. The paper concludes with
statistics stressing the good computational properties
of these installations.",
acknowledgement = ack-nhfb,
affiliation = "Springer-Verlag, New York, NY, USA",
classification = "C4130 (Interpolation and function approximation);
C6130 (Data handling techniques); C7310 (Mathematics)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Buchberger algorithm installation; Gr{\"o}bner bases;
Polynomial ideals; Superfluous reductions; Redundant
elements; Module of syzygies; SCRATCHPAD II; REDUCE
3.3; Computational properties",
language = "English",
pubcountry = "UK",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Jenks:1988:SIA,
author = "R. D. Jenks and R. S. Sutor and S. M. Watt",
title = "{Scratchpad II}: An Abstract Datatype System for
Mathematical Computation",
crossref = "Janssen:1988:TCA",
pages = "12--37",
year = "1988",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InCollection{Schwarz:1988:PAD,
author = "F. Schwarz",
title = "Programming with abstract data types: the symmetry
package {SPDE} in {Scratchpad}",
crossref = "Janssen:1988:TCA",
pages = "167--176",
year = "1988",
bibsource = "/usr/local/src/bib/bibliography/Theory/cathode.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@Article{Shannon:1988:UGB,
author = "D. Shannon and M. Sweedler",
title = "Using {Gr{\"o}bner} bases to determine algebra
membership, split surjective algebra homomorphisms
determine birational equivalence",
journal = j-J-SYMBOLIC-COMP,
volume = "6",
number = "2-3",
pages = "267--273",
month = oct # "--" # dec,
year = "1988",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Sep 17 06:48:10 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "This paper presents a simple algorithm, based on
Gr{\"o}bner bases, to test if a given polynomial g of
k(X/sub 1/,\ldots{}, X/sub n/) lies in k(f/sub
1/,\ldots{}, f/sub m/) where k is a field, X/sub
i/,\ldots{}, X/sub n/ are indeterminates over k and
f/sub 1/,\ldots{}, f/sub m/ in k(X/sub 1/,\ldots{},
X/sub n/). If so, the algorithm produces a polynomial P
of m variables where g=P(f/sub 1/,\ldots{}, f/sub m/).
Say omega:B to k(X/sub 1/,\ldots{}, X/sub n/) is a
homomorphism where omega (b/sub i/)=f/sub i/, for
algebra generators (b/sub i/) contained in/implied by
B. If omega is onto, the algorithm gives a homomorphism
lambda:k(X/sub 1/,\ldots{}, X/sub n/) to B, where the
composite omega lambda is the identity map. In
particular, the algorithm computes the inverse of
algebra automorphisms of the polynomial ring. A
variation of the test if k(f/sub 1/,\ldots{}, f/sub
m/)=k(X/sub 1/,\ldots{}, X/sub n/), tells if k(f/sub
1/,\ldots{}, f/sub m/)=k(X/sub 1/,\ldots{}, X/sub n/).
Existing computer algebra systems, such as IBM'S
SCRATCHPAD II, have Gr{\"o}bner basis packages which
allow the user to specify a term ordering sufficient to
carry out the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Transylvania Univ., Lexington, KY,
USA",
classification = "C4130 (Interpolation and function approximation);
C6130 (Data handling techniques); C7310 (Mathematics)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "IBM; Gr{\"o}bner bases; Algebra membership; Split
surjective algebra homomorphisms; Birational
equivalence; Polynomial; Homomorphism; Algebra
generators; Identity map; Algebra automorphisms;
Computer algebra systems; SCRATCHPAD II",
language = "English",
pubcountry = "UK",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Sutor:1988:SIA,
author = "R. D. Jenks R. S. Sutor and S. M. Watt",
title = "{Scratchpad II}: {An} abstract Datatype system for
mathematical computation",
crossref = "Janssen:1988:TCA",
pages = "12--??",
year = "1988",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@Article{Boehm:1989:TIP,
author = "Hans-J. Boehm",
title = "Type inference in the presence of type abstraction",
journal = j-SIGPLAN,
volume = "24",
number = "7",
pages = "192--206",
month = jul,
year = "1989",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 13 12:31:07 MDT 1999",
bibsource = "http://www.acm.org/pubs/contents/proceedings/pldi/73141/index.html;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/73141/p192-boehm/",
abstract = "A number of recent programming language designs
incorporate a type checking system based on the
Girard--Reynolds polymorphic \$lambda@-calculus. This
allows the construction of general purpose, reusable
software without sacrificing compile-time type
checking. A major factor constraining the
implementation of these languages is the difficulty of
automatically inferring the lengthy type information
that is otherwise required if full use is made of these
languages. There is no known algorithm to solve any
natural and fully general formulation of this `type
inference' problem. One very reasonable formulation of
the problem is known to be undecidable. Here we define
a restricted version of the type inference problem and
present an efficient algorithm for its solution. We
argue that the restriction is sufficiently weak to be
unobtrusive in practice.",
acknowledgement = ack-nhfb,
affiliationaddress = "Houston, TX, USA",
annote = "Published as part of the Proceedings of PLDI'89.",
classification = "723",
conference = "Proceedings of the SIGPLAN '89 Conference on
Programming Language Design and Implementation",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "Abstract Data Types (ADT); algorithms; Computer
Programming Languages--Design; Data Processing; Data
Structures; design; languages; Scratchpad; theory",
meetingaddress = "Portland, OR, USA",
meetingdate = "Jun 21--23 1989",
meetingdate2 = "06/21--23/89",
sponsor = "ACM, Special Interest Group on Programming Languages,
New York; SS NY, USA",
subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
AND FORMAL LANGUAGES, Mathematical Logic. {\bf F.3.3}
Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
Studies of Program Constructs, Type structure.",
}
@InProceedings{Bronstein:1989:SRE,
author = "M. Bronstein",
title = "Simplification of real elementary functions",
crossref = "ACM:1989:PAI",
pages = "207--211",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
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 = "Computer algebra system; Real elementary functions;
Real structure theorem; Scratchpad",
language = "English",
thesaurus = "Functions; Mathematics computing; Symbol
manipulation",
}
@InProceedings{Burge:1989:ISS,
author = "W. H. Burge and S. M. Watt",
title = "Infinite structures in {Scratchpad} {II}",
crossref = "Davenport:1989:EEC",
pages = "138--148",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "An infinite structure is a data structure which cannot
be fully constructed in any fixed amount of space.
Several varieties of infinite structures are currently
supported in Scratchpad II: infinite sequences, radix
expansions, power series and continued fractions. Two
basic methods are employed to represent infinite
structures: self-referential data structures and lazy
evaluation. These may be employed either separately or
in conjunction. This paper presents recently developed
facilities in Scratchpad II for manipulating infinite
structures. General techniques for manipulating
infinite structures are covered, as well as the higher
level manipulations on the various types of
mathematical objects represented by infinite
structures.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C6120 (File organisation); C7310 (Mathematics)",
keywords = "Continued fractions; Higher level manipulations;
Infinite sequences; Infinite structure; Lazy
evaluation; Mathematical objects; Power series; Radix
expansions; Scratchpad II; Self-referential data
structures",
language = "English",
thesaurus = "Algebra; Data structures; Mathematics computing;
Series [mathematics]; Software packages; Symbol
manipulation",
}
@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 = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.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",
language = "English",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@InProceedings{Gianni:1989:ASS,
author = "P. Gianni and T. Mora",
title = "Algebraic solution of systems of polynomial equations
using {Gr{\"o}bner} bases",
crossref = "Huguet:1989:AAA",
pages = "247--257",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "One of the most important applications of Buchberger's
algorithm for Gr{\"o}bner basis computation is the
solution of systems of polynomial equations (having
finitely many roots), i.e. the computation of zeros of
0-dimensional polynomial ideals. It is based on a
relation between Gr{\"o}bner bases w.r.t. a
lexicographical ordering and elimination ideals. The
algorithms discussed in this paper are implemented in
SCRATCHPAD II. In the first section the authors recall
some well-known properties of Gr{\"o}bner bases and
properties on the structure of Gr{\"o}bner bases of
zero-dimensional ideals; in the second section they
recall the Gr{\"o}bner basis algorithm for solving
systems of algebraic equations. The original results
are then presented. The authors first take advantage of
the obvious fact that density can be controlled
performing `small' changes of coordinates: they show
that such approach is possible during a Gr{\"o}bner
basis computation, in such a way that computations done
before a change of coordinates are valid also after it;
they propose a `linear algebra' approach to obtain the
Gr{\"o}bner basis w.r.t. the lexicographical ordering
from the one w.r.t. the total-degree ordering; and
finally they present a zero-dimensional radical
algorithm and show how to apply it to the present
problem.",
acknowledgement = ack-nhfb,
affiliation = "Pisa Univ., Italy",
classification = "C1110 (Algebra); C4140 (Linear algebra); C7310
(Mathematics)",
keywords = "Coordinate changes; Polynomial equations; Gr{\"o}bner
bases; Buchberger's algorithm; Gr{\"o}bner basis
computation; Zeros; 0-Dimensional polynomial ideals;
Lexicographical ordering; Elimination ideals;
SCRATCHPAD II; Algebraic equations; Linear algebra;
Total-degree ordering; Zero-dimensional radical
algorithm",
language = "English",
thesaurus = "Equations; Linear algebra; Mathematics computing;
Poles and zeros; Polynomials",
}
@InProceedings{Kusche:1989:IGT,
author = "K. Kusche and B. Kutzler and H. Mayr",
title = "Implementation of a geometry theorem proving package
in {SCRATCHPAD} {II}",
crossref = "Davenport:1989:EEC",
pages = "246--257",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The problem of automatically proving geometric
theorems has gained a lot of attention in the last two
years. Following the general approach of translating a
given geometric theorem into an algebraic one, various
powerful provers based on characteristic sets and
Gr{\"o}bner bases have been implemented by groups at
Academia Sinica Beijing (China), U. Texas at Austin
(USA), General Electric Schenectady (USA), and Research
Institute for Symbolic Computation Linz (Austria). So
far, fair comparisons of the various provers were not
possible, because the underlying hardware and the
underlying algebra systems differed greatly. This paper
reports on the first uniform implementation of all
these provers in the computer algebra system and
language SCRATCHPAD II. The authors summarize the
recent achievements in the area of automated geometry
theorem proving, shortly review the SCRATCHPAD II
system, describe the implementation of the geometry
theorem proving package, and finally give computing
time statistics of 24 examples.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., RISC-LINZ, Johannes
Kepler Univ., Linz, Austria",
classification = "C1230 (Artificial intelligence); C7310
(Mathematics)",
keywords = "Geometry theorem proving package; SCRATCHPAD II;
Characteristic sets; Gr{\"o}bner bases; Computer
algebra system; Computing time statistics",
language = "English",
thesaurus = "Algebra; Computational geometry; Mathematics
computing; Symbol manipulation; Theorem proving",
}
@Article{Mathews:1989:SCA,
author = "J. Mathews",
title = "Symbolic computational algebra applied to {Picard}
iteration",
journal = j-MATH-COMP-EDU,
volume = "23",
number = "2",
pages = "117--122",
month = "Spring",
year = "1989",
CODEN = "MCEDDA",
ISSN = "0730-8639",
bibdate = "Tue Sep 17 06:48:10 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Picard iteration occurs in differential equations as a
constructive procedure for establishing the existence
of a solution to a differential equation. This
application of Picard iteration illustrates how to use
a computer to generate a sequence of functions which
converges to a solution. The article shows the step by
step process in translating mathematical theory into
the symbolic manipulation setting. Systems such as
MACSYMA, ALTRAN, REDUCE, SMP, MAPLE, SCRATCHPAD, and
muMATH are being introduced in undergraduate
mathematics courses to assist in keeping track of
equations during complicated manipulations. The product
muMATH is illustrated because of its availability. It
runs on all 16-bit computers which are IBM compatible.
The way has been opened to see how computers can be
used as a symbol cruncher.",
acknowledgement = ack-nhfb,
affiliation = "California State Univ., Fullerton, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C4170 (Differential equations); C6130 (Data handling
techniques); C7310 (Mathematics)",
fjournal = "Mathematics and computer education",
keywords = "Differential equations; IBM compatible; Mathematical
theory; Mathematics computing; MuMATH; Picard
iteration; Symbol cruncher; Symbolic manipulation;
Undergraduate mathematics",
language = "English",
pubcountry = "USA",
thesaurus = "Differential equations; Iterative methods; Mathematics
computing; Microcomputer applications; Symbol
manipulation",
}
@InProceedings{Ollivier:1989:IRM,
author = "F. Ollivier",
title = "Inversibility of rational mappings and structural
identifiability in automatics",
crossref = "ACM:1989:PAI",
pages = "43--54",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The author investigates different methods for testing
whether a rational mapping f from k/sup n/ to k/sup m/
admits a rational inverse, or whether a polynomial
mapping admits a polynomial one. He gives a new
solution, which seems much more efficient in practice
than previously known ones using `tag' variables and
standard basis, and a majoration for the degree of the
standard basis calculations which is valid for both
methods in the case of a polynomial map which is
birational. He shows that a better bound can be given
for the method, under some assumption on the form of f.
The method can also extend to check whether a given
polynomial belongs to the subfield generated by a
finite set of fractions. The author illustrates the
algorithm with an application to structural
identifiability. The implementation has been done in
the IBM computer algebra system Scratchpad II.",
acknowledgement = ack-nhfb,
affiliation = "Lab. d'Inf. de l'X, Ecole Polytech., Palaiseau,
France",
classification = "C1110 (Algebra); C1120 (Analysis); C7310
(Mathematics)",
keywords = "Computer algebra system; Fractions; IBM;
Inversibility; Polynomial inverse; Polynomial mapping;
Rational inverse; Rational mappings; Scratchpad II;
Structural identifiability",
language = "English",
thesaurus = "Inverse problems; Mathematics computing; Polynomials;
Set theory; Symbol manipulation",
}
@TechReport{Salvy:1989:EAA,
author = "B. Salvy",
title = "Examples of automatic asymptotic expansions",
number = "114",
institution = "Inst. Nat. Recherche Inf. Autom.",
address = "Le Chesnay, France",
pages = "18",
month = dec,
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Describes the current state of a Maple library, gdev,
designed to perform asymptotic expansions for a large
class of expressions. Many examples are provided, along
with a short sketch of the underlying principles. A
striking feature of these examples is that none of them
can be computed directly with any of the most
widespread symbolic computation systems (Macsyma,
Mathematica, Maple or Scratchpad II).",
acknowledgement = ack-nhfb,
classification = "C1120 (Analysis); C6130 (Data handling techniques);
C7310 (Mathematics)",
keywords = "Asymptotic expansions; Gdev; Maple library; Symbolic
computation systems",
language = "English",
pubcountry = "France",
thesaurus = "Mathematical analysis; Mathematics computing;
Subroutines; Symbol manipulation",
}
@InProceedings{Schwarz:1989:FAL,
author = "F. Schwarz",
title = "A factorization algorithm for linear ordinary
differential equations",
crossref = "ACM:1989:PAI",
pages = "17--25",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The reducibility and factorization of linear
homogeneous differential equations are of great
theoretical and practical importance in mathematics.
Although it has been known for a long time that
factorization is in principle a decision procedure, its
use in an automatic differential equation solver
requires a more detailed analysis of the various steps
involved. Especially important are certain auxiliary
equations, the so-called associated equations. An upper
bound for the degree of its coefficients is derived.
Another important ingredient is the computation of
optimal estimates for the size of polynomial and
rational solutions of certain differential equations
with rotational coefficients. Applying these results,
the design of the factorization algorithm LODEF and its
implementation in the Scratchpad II Computer Algebra
System is described.",
acknowledgement = ack-nhfb,
affiliation = "GMD, Inst. F1, St. Augustin, West Germany",
classification = "C1120 (Analysis); C4170 (Differential equations);
C7310 (Mathematics)",
keywords = "Associated equations; Automatic differential equation
solver; Factorization algorithm; Linear ordinary
differential equations; LODEF; Optimal estimates;
Polynomial solutions; Rational solutions; Rotational
coefficients; Scratchpad II Computer Algebra System;
Upper bound",
language = "English",
thesaurus = "Linear differential equations; Mathematics computing;
Polynomials; Symbol manipulation",
}
@InProceedings{Sit:1989:GAS,
author = "W. Y. Sit",
title = "On {Goldman}'s algorithm for solving first-order
multinomial autonomous systems",
crossref = "Mora:1989:AAA",
pages = "386--395",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "A brief exposition of a method for finding first
integrals for first order multinomial autonomous
systems (FOMAS) of ordinary differential equations with
constant coefficients is given. The method is a
simplified as well as a redesigned version based on a
paper of Goldman (1987). The author shows how it can be
applied to FOMAS with parametric coefficients. The
algorithm is currently being implemented using the
SCRATCHPAD II computer algebra language and system at
the IBM TJ Watson Research Center.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., City Coll. of New York, NY, USA",
classification = "B0290P (Differential equations); B0290R (Integral
equations); C4170 (Differential equations); C4180
(Integral equations); C7310 (Mathematics)",
keywords = "Computer algebra language; Constant coefficients;
First integrals; First order multinomial autonomous
systems; FOMAS; Goldman algorithm; IBM; Ordinary
differential equations; SCRATCHPAD II",
language = "English",
thesaurus = "Differential equations; Integral equations;
Mathematics computing",
}
@Article{Wang:1989:PCL,
author = "D. Wang",
title = "A program for computing the {Liapunov} functions and
{Liapunov} constants in {Scratchpad} {II}",
journal = j-SIGSAM,
volume = "23",
number = "4",
pages = "25--31",
month = oct,
year = "1989",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "/usr/local/src/bib/bibliography/Theory/sigsam.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The report describes the implementation and use of a
program for computing the Liapunov functions and
Liapunov constants for a class of differential systems
in Scratchpad II.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1320 (Stability); C4170 (Differential equations);
C7420 (Control engineering)",
fjournal = "SIGSAM Bulletin",
keywords = "Differential systems, design; Liapunov constants;
Liapunov functions; performance; Scratchpad II",
language = "English",
pubcountry = "USA",
subject = "E.4 Data, CODING AND INFORMATION THEORY, Data
compaction and compression \\ G.2.0 Mathematics of
Computing, DISCRETE MATHEMATICS, General",
thesaurus = "Control system CAD; Differential equations; Lyapunov
methods; Polynomials",
}
@InProceedings{Watt:1989:FPM,
author = "S. M. Watt",
title = "A fixed point method for power series computation",
crossref = "Gianni:1989:SAC",
pages = "206--217",
month = "",
year = "1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Presents a novel technique for manipulating structures
which represent infinite power series. The technique
described allows a power series to be defined in a very
natural but computationally inefficient way and
transforms it to an equivalent, efficient form. This is
achieved by using a fixed point operator on the delayed
part to remove redundant calculations. The paper
describes this fixed point method and the class of
problems to which it is applicable. It has been used in
Scratchpad II to improve the performance of a number of
operations on infinite series, including division,
reversion, special functions and the solution of linear
and non-linear ordinary differential equations. A few
examples are given of the method and of the speed up
obtained. To illustrate, the computation of the first n
terms of exp(u) for a dense, infinite series u is
reduced from O(n/sup 4/) to O(n/sup 2/) coefficient
operations, the same as required by the standard
on-line algorithms.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Delayed part; Fixed point method; Fixed point
operator; Infinite power series; Power series
computation; Redundant calculations; Scratchpad II",
language = "English",
thesaurus = "Computational complexity; Mathematics computing",
}
@InProceedings{Davenport:1990:SVA,
author = "J. H. Davenport and B. M. Trager",
title = "{Scratchpad}'s View of Algebra {I}: Basic Commutative
Algebra",
crossref = "Miola:1990:DIS",
pages = "40--54",
month = "",
year = "1990",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "auch in: {AXIOM} Technical Report, ATR/1, NAG Ltd.,
Oxford, 1992.",
abstract = "The paper describes the constructive theory of
commutative algebra which underlies that part of
Scratchpad which deals with commutative algebra. The
authors begin by explaining the background that led the
Scratchpad group to construct such a general theory.
They contrast the general theory in Scratchpad with
Reduce-3's theory of domains, which is in many ways
more limited, but is the closest approach to an
implemented general theory to be found outside
Scratchpad. This leads them to describe the general
Scratchpad view of data types and categories, and the
possibilities it offers. They then digress a little to
ask what criteria should be adopted in choosing what
types to define. Having discussed the philosophical
issues, they then discuss commutative algebra proper,
breaking this up into the sections `up to Ring',
`Integral Domain', `Gcd Domain' and `Euclidean
Domain'.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math. Sci., Bath Univ., UK",
classification = "C1110 (Algebra); C7310 (Mathematics)",
keywords = "Categories; Commutative algebra; Constructive theory;
Data types; Euclidean Domain; Gcd Domain; Greatest
common divisors; Integral Domain; Philosophical issues;
Ring; Scratchpad",
language = "English",
thesaurus = "Algebra; Software packages; Symbol manipulation",
}
@InProceedings{Fateman:1990:ATD,
author = "R. J. Fateman",
title = "Advances and trends in the design and construction of
algebraic manipulation systems",
crossref = "Watanabe:1990:IPI",
pages = "60--67",
year = "1990",
DOI = "https://doi.org/10.1145.96895",
bibdate = "Thu Jul 26 09:04:25 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Compares and contrasts several techniques for the
implementation of components of an algebraic
manipulation system. On one hand is the mathematical
algebraic approach which characterizes (for example)
IBM's Scratchpad II. On the other hand is the more ad
hoc approach which characterizes many other popular
systems (for example, Macsyma, Reduce, Maple, and
Mathematica). While the algebraic approach has
generally positive results, careful examination
suggests that there are significant remaining problems,
especially in the representation and manipulation of
analytical, as opposed to algebraic mathematics. The
author describes some of these problems, and some
general approaches for solutions.",
acknowledgement = ack-nhfb,
affiliation = "California Univ., Berkeley, CA, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
keywords = "Algebraic manipulation systems; Algebraic mathematics;
Macsyma; Maple; Mathematica; Mathematical algebraic;
Reduce; Scratchpad II",
language = "English",
thesaurus = "Algebra; Symbol manipulation",
}
@InProceedings{Fortenbacher:1990:ETI,
author = "A. Fortenbacher",
title = "Efficient type inference and coercion in computer
algebra",
crossref = "Miola:1990:DIS",
pages = "56--60",
month = "",
year = "1990",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Computer algebra systems of the new generation, like
Scratchpad, are characterized by a very rich type
concept, which models the relationship between
mathematical domains of computation. To use these
systems interactively, however, the user should be
freed of type information. A type inference mechanism
determines the appropriate function to call. All known
models which define a semantics for type inference
cannot express the rich `mathematical' type structure,
so presently type inference is done heuristically. The
following paper defines a semantics for a subproblem,
namely coercion, which is based on rewrite rules. From
this definition, an efficient coercion algorithm for
Scratchpad is constructed using graph techniques.",
acknowledgement = ack-nhfb,
affiliation = "Sci. Center Heidelberg, IBM Deutschland GmbH,
Germany",
classification = "C1110 (Algebra); C4210 (Formal logic); C6120 (File
organisation); C7310 (Mathematics)",
keywords = "Coercion algorithm; Computer algebra; Graph
techniques; Rewrite rules; Scratchpad; Type inference
mechanism",
language = "English",
thesaurus = "Algebra; Data structures; Inference mechanisms;
Mathematics computing; Rewriting systems; Symbol
manipulation",
}
@TechReport{Fouche:1990:ILK,
author = "Francois Fouche",
title = "Une Implantation de l'algorithme de {Kovacic} en
{Scratchpad}",
institution = "Institut de Recherche Math{\'{e}}matique
Avanc{\'{e}}e",
address = "Strasbourg, France",
pages = "31",
year = "1990",
bibdate = "Sat Dec 30 08:25:26 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
}
@Article{Melachrinoudis:1990:TAT,
author = "E. Melachrinoudis and D. L. Rumpf",
title = "Teaching advantages of transparent computer software
--- {MathCAD}",
journal = j-COED,
volume = "10",
number = "1",
pages = "71--76",
month = jan # "--" # mar,
year = "1990",
CODEN = "CWLJDP",
ISSN = "0736-8607",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The case is presented for using mathematical
scratchpad software, such as MathCAD, in undergraduate
and graduate engineering courses. The pedagogical
benefits, especially relative to the usual black box
engineering software, are described. Several examples
of student written projects are presented. The projects
solve problems in operations research, control theory
and statistical regression analysis.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Ind. Eng., Northeastern Univ., Boston, MA,
USA",
classification = "C7110 (Education); C7310 (Mathematics); C7400
(Engineering); C7810C (Computer-aided instruction)",
fjournal = "CoED",
keywords = "Black box engineering software; Control theory;
Graduate engineering courses; MathCAD; Mathematical
scratchpad software; Operations research; Pedagogical
benefits; Statistical regression analysis; Student
written projects; Transparent computer software;
Undergraduate",
language = "English",
pubcountry = "USA",
thesaurus = "CAD; Educational computing; Engineering computing;
Mathematics computing; Teaching",
}
@InProceedings{Augot:1991:MDS,
author = "D. Augot and P. Charpin and N. Sendrier",
title = "The minimum distance of some binary codes via the
{Newton}'s identities",
crossref = "Cohen:1991:EIS",
pages = "65--73",
month = "",
year = "1991",
bibdate = "Tue Sep 17 06:41:20 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The authors propose a natural way of deciding whether
a given cyclic code contains a word of given weight.
The method is based on the manipulation of the locators
and of the locator polynomial of a codeword x. Because
of the dimensions of the problem, one needs to use
symbolic computation software, like Maple or Scratchpad
II. The method can be ineffective when the length is
too large. The paper is in two parts: In the first
part, they present the main definitions and properties
needed. In the second part, they explain how to use
these properties, and, as illustration, prove the three
following facts: the dual of the BCH code of length 63
and designed distance 9 has true minimum distance 14
(which was already known). The BCH code of length 1023
and designed distance 253 has minimum distance 253. The
cyclic codes of length 2/sup 11/, 2/sup 13/, 2/sup 17/,
with generator polynomial m/sub 1/(x) and m/sub 7/(x)
have minimum distance 4.",
acknowledgement = ack-nhfb,
affiliation = "Paris 6 Univ., France",
classification = "B6120B (Codes)",
keywords = "BCH code; Binary codes; Codeword; Cyclic codes;
Generator polynomial; Locator polynomial; Minimum
distance; Newton identities; Symbolic computation",
language = "English",
thesaurus = "Codes",
}
@InProceedings{Bronstein:1991:RDE,
author = "M. Bronstein",
title = "The {Risch} differential equation on an algebraic
curve",
crossref = "Watt:1991:PIS",
pages = "241--246",
month = "",
year = "1991",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The author presents a new rational algorithm for
solving Risch differential equations over algebraic
curves. This algorithm can also be used to solve n/sup
th/-order linear ordinary differential equations with
coefficients in an algebraic extension of the rational
functions. In the general ('mixed function') case, this
algorithm finds the denominator of any solution of the
equation. The algorithm has been implemented in the
Maple and Scratchpad computer algebra systems.",
acknowledgement = ack-nhfb,
affiliation = "Inf. ETH-Zentrum, Zurich, Switzerland",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
keywords = "Algebraic curve; Computer algebra systems; Maple;
N/sup th/-order linear ordinary differential equations;
Rational algorithm; Rational functions; Risch
differential equation; Scratchpad",
language = "English",
thesaurus = "Differential equations; Symbol manipulation",
}
@InProceedings{Burge:1991:SRI,
author = "W. H. Burge",
title = "{Scratchpad} and the {Rogers--Ramanujan} identities",
crossref = "Watt:1991:PIS",
pages = "189--190",
month = "",
year = "1991",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "This note sketches the part played by Scratchpad in
obtaining new proofs of Euler's theorem and the
Rogers--Ramanujan Identities.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C1160 (Combinatorial mathematics); C7310
(Mathematics)",
keywords = "Euler theorem; Infinite series; Restricted partition
pairs; Rogers--Ramanujan identities; Scratchpad",
language = "English",
thesaurus = "Mathematics computing; Number theory; Symbol
manipulation",
}
@InProceedings{Davenport:1991:SVA,
author = "J. H. Davenport and P. Gianni and B. M. Trager",
title = "{Scratchpad}'s view of algebra. {II}. {A} categorical
view of factorization",
crossref = "Watt:1991:PIS",
pages = "32--38",
month = "",
year = "1991",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "auch in: {AXIOM} Technical Report, ATR/2, NAG Ltd.,
Oxford, 1992.",
abstract = "For pt.I see Proc. DISCO 1990 (p.40-54). The paper
explains how Scratchpad solves the problem of
presenting a categorical view of factorization in
unique factorization domains, i.e. a view which can be
propagated by functors such as
SparseUnivariatePolynomial or Fraction. This is not
easy, as the constructive version of the classical
concept of UniqueFactorizationdomain cannot be so
propagated. The solution adopted is based largely on
the Seidenberg conditions (F) and (P), but there are
several additional points that have to be borne in mind
to produce reasonably efficient algorithms in the
required generality. The consequence of the algorithms
and interfaces presented is that Scratchpad can
factorize in any extension of the integers or finite
fields by any combination of polynomial, fraction and
algebraic extensions: a capability far more general
than any other computer algebra system possesses.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Bath Univ., Claverton Down, UK",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Algebraic extensions; Categorical view; Computer
algebra system; Factorization; Finite fields; Fraction;
Integers; Polynomial; Scratchpad; Seidenberg
conditions",
language = "English",
thesaurus = "Mathematics computing; Polynomials; Symbol
manipulation",
}
@InProceedings{Goodwin:1991:UMT,
author = "B. M. Goodwin and R. A. Buonopane and A. Lee",
title = "Using {MathCAD} in teaching material and energy
balance concepts",
crossref = "Anonymous:1991:PAC",
pages = "345--349 (vol. 1)",
year = "1991",
bibdate = "Tue Sep 17 06:37:45 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The authors show how PC-based applications software,
specifically MathCAD, is used in the teaching of
material and energy balance concepts. MathCAD is a
microcomputer software package which acts as a
mathematical scratchpad. It has proven to be a very
useful instructional tool in introductory chemical
engineering courses. MathCAD solutions to typical
course problems are presented.",
acknowledgement = ack-nhfb,
affiliation = "Northeastern Univ., Boston, MA, USA",
classification = "C7450 (Chemical engineering); C7810C (Computer-aided
instruction)",
keywords = "Energy balance concepts; Instructional tool;
Introductory chemical engineering courses; MathCAD;
Mathematical scratchpad; PC-based applications
software",
language = "English",
thesaurus = "Chemical engineering computing; Computer aided
instruction; Microcomputer applications; Spreadsheet
programs",
}
@TechReport{Grabmeier:1991:CSA,
author = "J. Grabmeier and K. Huber and U. Krieger",
title = "{Das Computeralgebra-System AXIOM bei kryptologischen
und verkehrstheoretischen Untersuchungen des
Forschungsinstituts der Deutschen Bundespost TELEKOM}",
type = "Technischer Report",
number = "TR 75.91.20",
institution = "IBM Wissenschaftliches Zentrum",
address = "Heidelberg, Germany",
pages = "??",
year = "1991",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@Article{Koseleff:1991:WGF,
author = "P.-V. Koseleff",
title = "Word games in free {Lie} algebras: several bases and
formulas",
journal = j-THEOR-COMP-SCI,
volume = "79",
number = "1",
pages = "241--256",
month = feb,
year = "1991",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The author compares the efficiency of many methods
which allow calculations in Lie algebras. Many
construction methods exist for the base of free Lie
algebras developed from finite sets. They use two
algorithms for calculation of several
Campbell--Hausdorf formulas. Diverse implementations
are realised in LISP on Scratchpad II.",
acknowledgement = ack-nhfb,
affiliation = "IBM, Paris, France",
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "Bases; Campbell--Hausdorf formulas; Finite sets; Free
Lie algebras; LISP; Scratchpad II",
language = "English",
pubcountry = "Netherlands",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@Article{Lambe:1991:RHP,
author = "L. A. Lambe",
title = "Resolutions via homological perturbation",
journal = j-J-SYMBOLIC-COMP,
volume = "12",
number = "1",
pages = "71--87",
month = jul,
year = "1991",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "There is a trade-off between the size of the
resolutions which arise from the perturbation method
and the complexity of the new differential. In order to
keep the modules relatively small, there is a
considerable increase in the algebraic complexity of
the resulting differentials. In order to study such
complexes systematically, examples are needed. To
facilitate such study, the Scratchpad system was used
to set up and perform the necessary calculations.
Because of the way Scratchpad is organized, this could
be done in a way that minimizes programming effort and
provides the natural mathematical environment for such
calculations. The author discusses some of the general
theory behind homological perturbation theory, gives an
idea of what is needed to make calculations within that
theory in Scratchpad, and calculates a resolution of
the integers over the integral group ring of the 4*4
upper triangular matrices with ones along the
diagonal.",
acknowledgement = ack-nhfb,
affiliation = "Illinois Univ., Chicago, IL, USA",
classification = "C4240 (Programming and algorithm theory); C7310
(Mathematics)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Algebraic complexity; Complexity; Homological
perturbation; Integers; Mathematical environment;
Resolutions; Scratchpad system",
language = "English",
pubcountry = "UK",
thesaurus = "Computational complexity; Perturbation theory; Symbol
manipulation",
}
@InProceedings{LeBlanc:1991:UMT,
author = "S. E. LeBlanc",
title = "The use of {MathCAD} and {Theorist} in the {ChE}
classroom",
crossref = "Anonymous:1991:PAC",
pages = "287--299 (vol. 1)",
year = "1991",
bibdate = "Tue Sep 17 06:37:45 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "MathCAD and Theorist are two powerful mathematical
packages available for instruction in the ChE
classroom. MathCAD is advertised as an `electronic
scratchpad' and it certainly lives up to its billing.
It is an extremely user-friendly collection of
numerical routines that eliminates the drudgery of
solving many of the types of problems encountered by
undergraduate ChE's (and engineers in general). MathCAD
is available for both the Macintosh and IBM PC
compatibles. The PC version is available as a
full-functioned student version for around US\$40 (less
than many textbooks). Theorist is a symbolic
mathematical package for the Macintosh. Many
interesting and instructive things can be done with it
in the ChE curriculum. One of its many attractive
features includes the ability to generate high quality
three dimensional plots that can be very instructive in
examining the behavior of an engineering system. The
author discusses the application and use of these
packages in chemical engineering and give example
problems and their solutions for a number of courses
including stoichiometry, unit operations,
thermodynamics and design.",
acknowledgement = ack-nhfb,
affiliation = "Toledo Univ., OH, USA",
classification = "C7450 (Chemical engineering); C7810C (Computer-aided
instruction)",
keywords = "Chemical engineering; MathCAD; Mathematical packages;
Numerical routines; Stoichiometry; Symbolic
mathematical package; Theorist; Thermodynamics; Unit
operations",
language = "English",
thesaurus = "Chemical engineering computing; Computer aided
instruction; Spreadsheet programs; Symbol
manipulation",
}
@Article{Lynch:1991:NQM,
author = "R. Lynch and H. A. Mavromatis",
title = "New quantum mechanical perturbation technique using an
`electronic scratchpad' on an inexpensive computer",
journal = j-AMER-J-PHYSICS,
volume = "59",
number = "3",
pages = "270--273",
month = mar,
year = "1991",
CODEN = "AJPIAS",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The authors have developed a new method for doing
numerical quantum mechanical perturbation theory. It
has the flavor of Rayleigh--Schr{\"o}dinger
perturbation theory (division of the Hamiltonian into
an unperturbed Hamiltonian and a perturbing term, use
of the basis formed by the eigenfunctions of the
unperturbed Hamiltonian) while turning out to be a
variational technique. Furthermore, it is easily
implemented by means of the widely used `electronic
scratchpad,' MathCAD 2.0, using an inexpensive
computer. As an example of the method, the problem of a
harmonic oscillator with a quartic perturbing term is
examined.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Phys., King Fahd Univ. of Pet. and Miner.,
Dhahran, Saudi Arabia",
classification = "A0150H (Instructional computer use); A0210 (Algebra,
set theory, and graph theory); A0230 (Function theory,
analysis); A0365D (Functional analytical methods);
A0365F (Algebraic methods); A0365G (Solutions of wave
equations: bound state); C7810C (Computer-aided
instruction)",
fjournal = "American Journal of Physics",
keywords = "Electronic scratchpad; Eigenvalues; Eigenfunctions;
Quantum mechanical perturbation technique;
Rayleigh--Schr{\"o}dinger perturbation theory;
Hamiltonian; Variational technique; MathCAD 2.0;
Harmonic oscillator",
language = "English",
pubcountry = "USA",
thesaurus = "Computer aided instruction; Eigenvalues and
eigenfunctions; Harmonic oscillators; Perturbation
theory; Quantum theory; Variational techniques",
}
@Article{Salvy:1991:EAA,
author = "B. Salvy",
title = "Examples of automatic asymptotic expansions",
journal = j-SIGSAM,
volume = "25",
number = "2",
pages = "4--17",
month = apr,
year = "1991",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Describes the current state of a Maple library, gdev,
designed to perform asymptotic expansions for a large
class of expressions. Many examples are provided, along
with a short sketch of the underlying principles. At
the time when this report is written, a striking
feature of these examples is that none of them can be
computed directly with any of today's most widespread
symbolic computation systems (Macsyma, Mathematica,
Maple or Scratchpad II).",
acknowledgement = ack-nhfb,
affiliation = "LIX, Ecole Polytech., Palaiseau, France",
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
fjournal = "SIGSAM Bulletin",
keywords = "Automatic asymptotic expansions; Expressions; Gdev;
Maple library; Symbolic computation systems",
language = "English",
pubcountry = "USA",
thesaurus = "Symbol manipulation",
}
@Article{Schwarz:1991:MOG,
author = "F. Schwarz",
title = "Monomial orderings and {Gr{\"o}bner} bases",
journal = j-SIGSAM,
volume = "25",
number = "1",
pages = "10--23",
month = jan,
year = "1991",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Let there be given a set of monomials in n variables
and some order relations between them. The following
fundamental problem of monomial ordering is considered.
Is it possible to decide whether these ordering
relations are consistent and if so to extend them to an
admissible ordering for all monomials? The answer is
given in terms of the algorithm MACOT which constructs
a matrix of so-called cotes which establishes the
desired ordering relations. The main area of
application of this algorithm, i.e. the construction of
Gr{\"o}bner bases for different orderings and of
universal Gr{\"o}bner bases, is presented. An
implementation in Scratchpad is also briefly
described.",
acknowledgement = ack-nhfb,
affiliation = "GMD Inst., St. Augustin, Germany",
classification = "C1110 (Algebra); C4140 (Linear algebra); C7310
(Mathematics)",
fjournal = "SIGSAM Bulletin",
keywords = "Computer algebra; Thomas theorem; Multivariate
polynomial; Gr{\"o}bner bases; Monomial ordering;
Ordering relations; Admissible ordering; MACOT; Matrix;
Cotes; Scratchpad",
language = "English",
pubcountry = "USA",
thesaurus = "Algebra; Matrix algebra; Polynomials; Symbol
manipulation",
}
@Article{Wang:1991:MMC,
author = "Dongming Wang",
title = "Mechanical manipulation for a class of differential
systems",
journal = j-J-SYMBOLIC-COMP,
volume = "12",
number = "2",
pages = "233--254",
month = aug,
year = "1991",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "/usr/local/src/bib/bibliography/Theory/cathode.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The author describes a mechanical procedure for
computing the Liapunov functions and Liapunov constants
for a class of differential systems. These functions
and constants are used for establishing the stability
criteria, the conditions for the existence of a center
and for the investigation of limit cycles. Some
problems for handling the computer constants, which are
usually large polynomials in terms of the coefficients
of the differential system, and an approach towards
their solution by using computer algebraic methods are
proposed. This approach has been successfully applied
to check some known results mechanically. The author
has implemented a system DEMS on an HP1000 and in
Scratchpad II on an IBM4341 for computing and
manipulating the Liapunov functions and Liapunov
constants. As examples, two particular cubic systems
are discussed in detail. The explicit algebraic
relations between the computed Liapunov constants and
the conditions given by Saharnikov are established,
which leads to a rediscovery of the incompleteness of
his conditions. A class of cubic systems with 6-tuple
focus is presented to demonstrate the feasibility of
the approach for finding systems with higher multiple
focus.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
Univ., Linz, Austria",
classification = "C1320 (Stability); C4170 (Differential equations);
C7420 (Control engineering)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "6-Tuple focus; Computer algebraic methods; Cubic
systems; DEMS; Differential systems; HP1000; IBM4341;
Incompleteness; Large polynomials; Liapunov constants;
Liapunov functions; Limit cycles; Limit cycles
SCRATCHPAD, Nonlinear DEs; Mechanical procedure;
Scratchpad II; Stability criteria",
language = "English",
pubcountry = "UK",
thesaurus = "Control system analysis computing; Lyapunov methods;
Nonlinear differential equations; Stability; Symbol
manipulation",
}
@Article{Anonymous:1992:PEH,
author = "Anonymous",
title = "Programming Environments for High-Level Scientific
Problem Solving. {IFIP} {TC2}\slash {WG} 2.5 Working
Conference",
journal = j-IFIP-TRANS-A,
volume = "A-2",
pages = "??--??",
year = "1992",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Tue Sep 17 06:41:20 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "23--27 Sept. 1991",
conflocation = "Karlsruhe, Germany",
confsponsor = "IFIP",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
pubcountry = "Netherlands",
}
@TechReport{Camion:1992:PCG,
author = "Paul Camion and Bernard Courteau and Andre Montpetit",
title = "Un probl{\`e}me combinatoire dans les graphes de
{Hamming} et sa solution en {Scratchpad}. ({English}:
{A} combinatorial problem in {Hamming} graphs and its
solution in {Scratchpad})",
type = "Rapports de recherche",
number = "1586",
institution = "Institut National de Recherche en Informatique et en
Automatique",
address = "Le Chesnay, France",
pages = "12",
month = jan,
year = "1992",
bibdate = "Sat Dec 30 08:42:16 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "We present a combinatorial problem which arises in the
determination of the complete weight coset enumerators
of error-correcting codes [1]. In solving this problem
by exponential power series with coefficients in a ring
of multivariate polynomials, we fall on a system of
differential equations with coefficients in a field of
rational functions. Thanks to the abstraction
capabilities of Scratchpad this differential equation
may be solved simply and naturally, which seems not to
be the case for the other computer algebra systems now
available.",
acknowledgement = ack-nhfb,
}
@InProceedings{Dalmas:1992:PFL,
author = "S. Dalmas",
title = "A polymorphic functional language applied to symbolic
computation",
crossref = "Wang:1992:ISS",
pages = "369--375",
month = "",
year = "1992",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The programming language in which to describe
mathematical objects and algorithms is a fundamental
issue in the design of a symbolic computation system.
XFun is a strongly typed functional programming
language. Although it was not designed as a specialized
language, its sophisticated type system can be
successfully applied to describe mathematical objects
and structures. After illustrating its main features,
the author sketches how it could be applied to symbolic
computation. A comparison with Scratchpad II is
attempted. XFun seems to exhibit more flexibility
simplicity and uniformity.",
acknowledgement = ack-nhfb,
affiliation = "Inst. Nat. de Recherche d'Inf. et d'Autom., Valbonne,
France",
classification = "C6140D (High level languages); C7310 (Mathematics)",
keywords = "Mathematical objects; Polymorphic functional language;
Scratchpad II; Symbolic computation; XFun",
language = "English",
thesaurus = "Functional programming; High level languages; Symbol
manipulation",
}
@TechReport{Davenport:1992:AS,
author = "J. H. Davenport",
title = "The {AXIOM} System",
type = "AXIOM Technical Report",
number = "TR5/92 (ATR/3) (NP2492)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
month = dec,
year = "1992",
bibdate = "Fri Dec 29 16:31:49 1995",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
acknowledgement = ack-nhfb,
}
@TechReport{Davenport:1992:HDO,
author = "J. H. Davenport",
title = "How Does One Program in the {AXIOM} System?",
type = "AXIOM Technical Report",
number = "TR6/92 (ATR/4) (NP2493)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
month = dec,
year = "1992",
bibdate = "Fri Dec 29 16:31:49 1995",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
acknowledgement = ack-nhfb,
}
@TechReport{Davenport:1992:SVAa,
author = "J. H. Davenport and B. M. Trager",
title = "{Scratchpad}'s View of Algebra {I}: Basic Commutative
Algebra",
number = "TR3/92 (ATR/1) (NP2490)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
month = dec,
year = "1992",
bibdate = "Fri Dec 29 16:31:49 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
acknowledgement = ack-nhfb,
}
@TechReport{Davenport:1992:SVAb,
author = "J. H. Davenport and P. Gianni and B. M. Trager",
title = "{Scratchpad}'s View of Algebra {II}: {A} Categorical
View of Factorization",
number = "TR4/92 (ATR/2) (NP2491)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
month = dec,
year = "1992",
bibdate = "Fri Dec 29 16:31:49 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
acknowledgement = ack-nhfb,
}
@Article{Duval:1992:EPS,
author = "D. Duval and F. Jung",
title = "Examples of problem solving using computer algebra",
journal = j-IFIP-TRANS-A,
volume = "A-2",
pages = "133--141, 143",
month = "",
year = "1992",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Tue Sep 17 06:41:20 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Computer algebra, in contrast with numerical analysis,
aims at returning exact solutions to given problems.
One consequence is that the shape of the solutions may,
at first, look somewhat surprising. The authors present
two examples of problem solving using computer algebra,
with emphasis on the shape of the solutions. The first
example is the resolution of linear differential
equations with polynomial coefficients, and the second
one is the resolution of polynomial equations in one
variable. In the first example the solution may look
useless since it makes use of divergent series, and in
the second example the solution may look rather
awkward. But in both examples it is shown that these
solutions are in the right shape for a lot of
applications, including numerical ones. It is also
shown that some features of the computer algebra system
Scratchpad, especially strong typing and genericity,
are useful for the implementation of a method for a
second problem, i.e. for the implementation of the
`dynamic' algebraic closure of a field.",
acknowledgement = ack-nhfb,
affiliation = "Lab. de Theorie des Nombres et Algorithmique, Limoges
Univ., France",
classification = "C7310 (Mathematics)",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
keywords = "Algebraic closure; Computer algebra; Divergent series;
Exact solutions; Genericity; Linear differential
equations; Polynomial coefficients; Polynomial
equations; Problem solving; Scratchpad; Strong typing",
language = "English",
thesaurus = "Linear differential equations; Polynomials; Symbol
manipulation",
}
@InProceedings{Gil:1992:CJC,
author = "I. Gil",
title = "Computation of the {Jordan} canonical form of a square
matrix (using the {Axiom} programming language)",
crossref = "Wang:1992:ISS",
pages = "138--145",
month = "",
year = "1992",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Presents an algorithm for computing: the Jordan form
of a square matrix with coefficients in a field K using
the computer algebra system Axiom. This system presents
the advantage of allowing generic programming. That is
to say, the algorithm can first be implemented for
matrices with rational coefficients and then
generalized to matrices with coefficients in any field.
Therefore the author presents the general method which
is essentially based on the use of the Frobenius form
of a matrix in order to compute its Jordan form; and
then restricts attention to matrices with rational
coefficients. On the one hand the author streamlines
the algorithm froben which computes the Frobenius form
of a matrix, and on the other she examines in some
detail the transformation from the Frobenius form to
the Jordan form, and gives the so called algorithm
Jordform. The author studies in particular, the
complexity of this algorithm and proves that it is
polynomial when the coefficients of the matrix are
rational. Finally the author gives some experiments and
a conclusion.",
acknowledgement = ack-nhfb,
affiliation = "LMC, IMAG, Grenoble, France",
classification = "C4130 (Interpolation and function approximation);
C4140 (Linear algebra); C4240 (Programming and
algorithm theory); C7310 (Mathematics)",
keywords = "Axiom programming language; Complexity; Computer
algebra system; Froben; Frobenius form; Generic
programming; Jordan canonical form; Jordform;
Polynomial; Rational coefficients; Square matrix",
language = "English",
thesaurus = "Computational complexity; Matrix algebra; Polynomials;
Symbol manipulation",
}
@TechReport{Grabmeier:1992:FFA,
author = "J. Grabmeier and A. Scheerhorn",
title = "Finite Fields in {AXIOM}",
type = "AXIOM Technical Report",
number = "TR7/92 (ATR/5) (NP2522)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
month = dec,
year = "1992",
bibdate = "Fri Dec 29 16:31:49 1995",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
acknowledgement = ack-nhfb,
}
@Book{Jenks:1992:ASC,
author = "Richard D. Jenks and Robert S. Sutor",
title = "{AXIOM}: The Scientific Computation System",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiv + 742",
year = "1992",
DOI = "https://doi.org/10.1007/978-1-4612-2940-7",
ISBN = "0-387-97855-0 (New York), 3-540-97855-0 (Berlin)",
ISBN-13 = "978-0-387-97855-0 (New York), 978-3-540-97855-8
(Berlin)",
LCCN = "QA76.95.J46 1992",
MRclass = "68Q40 (68-04 68N15)",
MRnumber = "95k:68089",
MRreviewer = "P. D. F. Ion",
bibdate = "Fri Dec 29 18:16:15 1995",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
URL = "http://link.springer.com/10.1007/978-1-4612-2940-7",
ZMnumber = "0758.68010",
abstract = "Recent advances in hardware performance and software
technology have made possible a wholly different
approach to computational mathematics. Symbolic
computation systems have revolutionized the field,
building upon established and recent mathematical
theory to open new possibilities in virtually every
industry. Formerly dubbed Scratchpad, AXIOM is a
powerful new symbolic and numerical system developed at
the IBM Thomas J. Watson Research Center. AXIOM's
scope, structure, and organization make it outstanding
among computer algebra systems. AXIOM: The Scientific
Computation System is a companion to the AXIOM system.
The text is written in a straightforward style and
begins with a spirited foreword by David and Gregory
Chudnovsky. The book gives the reader a technical
introduction to AXIOM, interacts with the system's
tutorial, accesses algorithms newly developed by the
symbolic computation community, and presents advanced
programming and problem solving techniques. Eighty
illustrations and eight pages of color inserts
accompany text detailing methods used in the 2D and 3D
interactive graphics system, and over 2500 example
input lines help the reader solve formerly intractable
problems.",
acknowledgement = ack-nhfb,
subject = "Axiom (Computer file); Axiom (Computer file);
Mathematics; Data processing; Mathematics; Data
processing.; AXIOM (computerprogramma); Mathematics.;
Physical Sciences and Mathematics.; Mathematical
Theory.",
tableofcontents = "Foreword / David V. Chudnovsky and Gregory V.
Chudnovsky / vii \\
Contributors Introduction to AXIOM / 1 \\
A Technical Introduction to AXIOM / 9 \\
I Basic Features of AXIOM / 17 \\
1 An Overview of AXIOM / 19 \\
1.1 Starting Up and Winding Down / 19 \\
1.2 Typographic Conventions 2 / 1 \\
1.3 The AXIOM Language 2 / 2 \\
1.4 Graphics / 28 \\
1.5 Numbers / 29 \\
1.6 Data Structures / 33 \\
1.7 Expanding to Higher Dimensions / 38 \\
1.8 Writing Your Own Functions / 39 \\
1.9 Polynomials / 43 \\
1.10 Limits / 44 \\
1.11 Series / 45 \\
1.12 Derivatives / 47 \\
1.13 Integration / 49 \\
1.14 Differential Equations / 52 \\
1.15 Solution of Equations / 53 \\
1.16 System Commands / 55 \\
2 Using Types and Modes / 59 \\
2.1 The Basic Idea / 59 \\
2.2 Writing Types and Modes / 66 \\
2.3 Declarations / 69 \\
2.4 Records / 71 \\
2.5 Unions / 73 \\
2.6 The ``Any'' Domain / 77 \\
2.7 Conversion / 78 \\
2.8 Subdomains Again / 80 \\
2.9 Package Calling and Target Types / 83 \\
2.10 Resolving Types / 86 \\
2.11 Exposing Domains and Packages / 87 \\
2.12 Commands for Snooping / 89 \\
3 Using HyperDoc / 93 \\
3.1 Headings / 94 \\
3.2 Scroll Bars / 94 \\
3.3 Input Areas / 95 \\
3.4 Buttons / 96 \\
3.5 Search Strings / 96 \\
3.6 Example Pages / 97 \\
3.7 X Window Resources for HyperDoc / 97 \\
4 Input Files and Output Styles / 99 \\
4.1 Input Files / 99 \\
4.2 The axiom.input File / 100 \\
4.3 Common Features of Using Output Formats / 101 \\
4.4 Monospace Two-Dimensional Mathematical Format / 102
\\
4.5 TeX Format / 103 \\
4.6 IBM Script Formula Format / 104 \\
4.7 FORTRAN Format / 104 \\
5 Introduction to the AXIOM Interactive Language / 109
\\
5.1 Immediate and Delayed Assignments / 109 \\
5.2 Blocks 11 / 2 \\
5.3 if-then-else 11 / 5 \\
5.4 Loops / 117 \\
5.5 Creating Lists and Streams with Iterators / 130 \\
5.6 An Example: Streams of Primes / 132 \\
6 User-Defined Functions, Macros and Rules / 135 \\
6.1 Functions vs. Macros / 135 \\
6.2 Macros / 136 \\
6.3 Introduction to Functions / 138 \\
6.4 Declaring the Type of Functions / 140 \\
6.5 One-Line Functions / 141 \\
6.6 Declared vs. Undeclared Functions / 142 \\
6.7 Functions vs. Operations / 143 \\
6.8 Delayed Assignments vs. Functions with No Arguments
/ 144 \\
6.9 How AXIOM Determines What Function to Use / 145 \\
6.10 Compiling vs. Interpreting / 146 \\
6.11 Piece-Wise Function Definitions / 148 \\
6.12 Caching Previously Computed Results / 153 \\
6.13 Recurrence Relations / 155 \\
6.14 Making Functions from Objects / 157 \\
6.15 Functions Defined with Blocks / 159 \\
6.16 Free and Local Variables / 162 \\
6.17 Anonymous Functions / 165 \\
6.18 Example: A Database / 168 \\
6.19 Example: A Famous Triangle / 170 \\
6.20 Example: Testing for Palindromes / 171 \\
6.21 Rules and Pattern Matching / 173 \\
7 Graphics / 179 \\
7.1 Two-Dimensional Graphics / 180 \\
7.2 Three-Dimensional Graphics / 196 \\
II Advanced Problem Solving and Examples / 225 \\
8 Advanced Problem Solving / 227 \\
8.1 Numeric Functions / 227 \\
8.2 Polynomial Factorization / 236 \\
8.3 Manipulating Symbolic Roots of a Polynomial / 239
\\
8.4 Computation of Eigenvalues and Eigenvectors / 241
\\
8.5 Solution of Linear and Polynomial Equations / 244
\\
8.6 Limits / 249 \\
8.7 Laplace Transforms 25 / 1 \\
8.8 Integration / 252 \\
8.9 Working with Power Series / 255 \\
8.10 Solution of Differential Equations / 269 \\
8.11 Finite Fields / 276 \\
8.12 Primary Decomposition of Ideals / 294 \\
8.13 Computation of Galois Groups / 296 \\
8.14 Non-Associative Algebras and Modelling Genetic
Laws / 303 \\
9 Some Examples of Domains and Packages / 309 \\
9.1 AssociationList / 309 \\
9.2 BalancedBinaryTree 31 / 1 \\
9.3 BinaryExpansion / 312 \\
9.4 BinarySearchTree / 313 \\
9.5 CardinalNumber / 315 \\
9.6 CartesianTensor / 317 \\
9.7 Character / 325 \\
9.8 CharacterClass / 326 \\
9.9 CliffordAlgebra / 328 \\
9.10 Complex / 333 \\
9.11 ContinuedFraction / 335 \\
9.12 CycleIndicators / 339 \\
9.13 DeRhamComplex / 346 \\
9.14 DecimalExpansion / 350 \\
9.15 DistributedMultivariatePolynomial / 352 \\
9.16 EqTable / 353 \\
9.17 Equation / 354 \\
9.18 Exit / 355 \\
9.19 Factored / 356 \\
9.20 FactoredFunctions2 / 361 \\
9.21 File / 362 \\
9.22 FileName / 364 \\
9.23 FlexibleArray / 366 \\
9.24 Float / 368 \\
9.25 Fraction / 373 \\
9.26 GeneralSparseTable / 375 \\
9.27 GroebnerFactorizationPackage / 376 \\
9.28 Heap / 378 \\
9.29 HexadecimalExpansion / 379 \\
9.30 Integer / 380 \\
9.31 IntegerLinearDependence / 385 \\
9.32 IntegerNumberTheoryFunctions / 387 \\
9.33 KeyedAccessFile / 390 \\
9.34 Library / 393 \\
9.35 LinearOrdinaryDifferentialOperator / 394 \\
9.36 List / 404 \\
9.37 MakeFunction / 409 \\
9.38 MappingPackage / 411 \\
9.39 Matrix / 414 \\
9.40 MultiSet / 420 \\
9.41 MultivariatePolynomial 42 / 1 \\
9.42 None / 423 \\
9.43 Octonion / 423 \\
9.44 OneDimensionalArray / 425 \\
9.45 Operator / 426 \\
9.46 OrderlyDifferentialPolynomial / 429 \\
9.47 PartialFraction / 433 \\
9.48 Permanent / 436 \\
9.49 Polynomial / 436 \\
9.50 Quaternion / 442 \\
9.51 RadixExpansion / 444 \\
9.52 RomanNumeral / 446 \\
9.53 Segment / 447 \\
9.54 SegmentBinding / 448 \\
9.55 Set / 449 \\
9.56 SmallFloat / 452 \\
9.57 Smalllnteger / 453 \\
9.58 SparseTable / 455 \\
9.59 SquareMatrix / 456 \\
9.60 Stream / 457 \\
9.61 String / 458 \\
9.62 StringTable / 462 \\
9.63 Symbol / 462 \\
9.64 Table / 465 \\
9.65 TextFile / 468 \\
9.66 TwoDimensionalArray / 469 \\
9.67 UnivariatePolynomial / 472 \\
9.68 UniversalSegment / 477 \\
9.69 Vector / 478 \\
9.70 Void / 480 \\
III Advanced Programming in AXIOM 48 / 1 \\
10 Interactive Programming / 483 \\
10.1 Drawing Ribbons Interactively / 483 \\
10.2 A Ribbon Program / 487 \\
10.3 Coloring and Positioning Ribbons / 488 \\
10.4 Points, Lines, and Curves / 489 \\
10.5 A Bouquet of Arrows / 492 \\
10.6 Drawing Complex Vector Fields / 493 \\
10.7 Drawing Complex Functions / 495 \\
10.8 Functions Producing Functions / 497 \\
10.9 Automatic Newton Iteration Formulas / 497 \\
11 Packages / 501 \\
11.1 Names, Abbreviations, and File Structure / 502 \\
11.2 Syntax / 503 \\
11.3 Abstract Datatypes / 504 \\
11.4 Capsules / 504 \\
11.5 Input Files vs. Packages / 505 \\
11.6 Compiling Packages / 506 \\
11.7 Parameters / 507 \\
11.8 Conditionals / 509 \\
11.9 Testing 51 / 1 \\
11.10 How Packages Work / 512 \\
12 Categories / 515 \\
12.1 Definitions / 516 \\
12.2 Exports / 517 \\
12.3 Documentation / 518 \\
12.4 Hierarchies / 519 \\
12.5 Membership / 519 \\
12.6 Defaults / 520 \\
12.7 Axioms 52 / 1 \\
12.8 Correctness / 522 \\
12.9 Attributes / 522 \\
12.10 Parameters / 524 \\
12.11 Conditionals / 524 \\
12.12 Anonymous Categories / 525 \\
13 Domains / 527 \\
13.1 Domains vs. Packages / 527 \\
13.2 Definitions / 528 \\
13.3 Category Assertions / 529 \\
13.4 A Demo / 530 \\
13.5 Browse 53 / 1 \\
13.6 Representation / 532 \\
13.7 Multiple Representations / 532 \\
13.8 Add Domain / 533 \\
13.9 Defaults / 534 \\
13.10 Origins / 535 \\
13.11 Short Forms / 535 \\
13.12 Example 1 : Clifford Algebra / 536 \\
13.13 Example 2: Building A Query Facility / 537 \\
14 Browse / 547 \\
14.1 The Front Page: Searching the Library / 547 \\
14.2 The Constructor Page / 551 \\
14.3 Miscellaneous Features of Browse / 562 \\
Appendices / 569 \\
A AXIOM System Commands / 571 \\
A.1 Introduction / 571 \\
A.2 )abbreviation / 572 \\
A.3 )boot / 573 \\
A.4 )cd / 574 \\
A.5 )clear / 574 \\
A.6 )compile / 575 \\
A.7 )display / 577 \\
A.8 )edit / 578 \\
A.9 )fin / 578 \\
A.10 )frame / 579 \\
A.11 )help / 580 \\
A.12 )history / 580 \\
A.13 )lisp / 582 \\
A.14 )load / 583 \\
A.15 )ltrace / 584 \\
A.16 )pquit / 584 \\
A.17 )quit / 585 \\
A.18 )read / 585 \\
A.19 )set / 586 \\
A.20 )show : / 586 \\
A.21 )spool / 587 \\
A.22 )synonym / 587 \\
A.23 )system / 588 \\
A.24 )trace / 589 \\
A.25 )undo / 592 \\
A.26 )what / 592 \\
B Categories / 595 \\
C Domains / 601 \\
D Packages / 619 \\
E Operations / 627 \\
F Programs for AXIOM Images / 691 \\
F.1 images1.input / 691 \\
F.2 images2.input / 692 \\
F.3 images3.input / 692 \\
F.4 images5.input / 692 \\
F.5 images6.input / 693 \\
F.6 images7.input / 694 \\
F.7 images8.input / 694 \\
F.8 conformal.input / 695 \\
F.9 tknot.input / 697 \\
F.10 ntube.input / 697 \\
F.11 dhtri.input / 699 \\
F.12 tetra.input / 700 \\
F.13 antoine.input / 701 \\
F.14 scherk.input / 702 \\
G Glossary / 703 \\
Index / 717",
}
@InProceedings{Lambe:1994:NGC,
author = "Larry Lambe",
editor = "Mats Gyllenberg and Lars Erik Persson",
booktitle = "{Analysis, algebra, and computers in mathematical
research: proceedings of the Twenty-first Nordic
Congress of Mathematicians, Lule{\aa} University of
Technology, Sweden, 1992}",
title = "Next generation computer algebra systems {AXIOM} and
the {Scratchpad} concept: Applications to research in
algebra",
volume = "156",
publisher = pub-DEKKER,
address = pub-DEKKER:adr,
pages = "201--222",
year = "1994",
ISBN = "0-8247-9217-3",
ISBN-13 = "978-0-8247-9217-6",
LCCN = "QA299.6 .N67 1992",
MRclass = "18-04 (Machine computation, programs (category
theory)) 68W30 (Symbolic computation and algebraic
computation) 20-04 (Machine computation, programs
(group theory)) 18G15 (Ext and Tor, generalizations)
18G35 (Chain complexes (homological algebra)) 55U15
(Chain complexes) 20J05 (Homological methods in group
theory) 16E40 (Homology and cohomology theories for
assoc. rings)",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
series = "Lecture Notes in Pure and Applied Mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0647/94002464-d.html",
ZMnumber = "0832.18001",
abstract = "One way in which mathematicians deal with infinite
amounts of data is symbolic representation. A simple
example is the quadratic equation $ x = {- b \pm \sqrt
{b^2 - 4a} c \over 2a} $, a formula which uses symbolic
representation to describe the solutions to an infinite
class of equations. Most computer algebra systems can
deal with polynomials with symbolic coefficients, but
what if symbolic exponents are called for (e.g., $ 1 +
t^i) $ ? What if symbolic limits on summations are also
called for (e.g., $ 1 + t + \cdots + t^i = \sum_j t^j)
$ ? The ``Scratchpad concept'' is a theoretical ideal
which allows the implementation of objects at this
level of abstraction and beyond in a mathematically
consistent way. The AXIOM computer algebra system is an
implementation of a major part of the Scratchpad
concept. AXIOM (formerly called Scratchpad) is a
language with extensible parameterized types and
generic operators which is based on the notion of
domains and categories [{\it R. D. Jenks} and {\it R.
S. Sutor}, Axiom. The scientific computation system,
Springer, Berlin etc. (1992; Zbl 0758.68010)]. By
examining some aspects of the AXIOM system, the
Scratchpad concept will be illustrated. It will be
shown how some complex problems in homological algebra
[cf. the author, Contemp. Math. 134, 183-218 (1992; Zbl
0798.16028), J. Pure Appl. Algebra 84, No. 3, 311-329
(1993; Zbl 0766.55015)] were solved through the use of
this system.",
bookpages = "ix + 408",
keywords = "AXIOM; bar construction; computer algebra; domains;
Ext; generic operators; parameterized types;
perturbation lemma; Scratchpad; symbolic exponents;
symbolic limits; Tor",
language = "English",
}
@InProceedings{Rioboo:1992:RAC,
author = "Renaud Rioboo",
title = "Real algebraic closure of an ordered field,
implementation in {Axiom}",
crossref = "Wang:1992:ISS",
pages = "206--215",
year = "1992",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Real algebraic numbers appear in many computer algebra
problems. For instance the determination of a
cylindrical algebraic decomposition for an Euclidian
space requires computing with real algebraic numbers.
This paper describes an implementation for computations
with the real roots of a polynomial. This process is
designed to be recursively used, so the resulting
domain of computation is the set of all real algebraic
numbers. An implementation for the real algebraic
closure has been done in Axiom (previously called
Scratchpad).",
acknowledgement = ack-nhfb,
affiliation = "LITP, Univ. Pierre et Marie Curie, Paris, France",
classification = "C4130 (Interpolation and function approximation);
C6130 (Data handling techniques); C7310 (Mathematics)",
keywords = "Axiom; Computer algebra; Cylindrical algebraic
decomposition; Euclidian space; Ordered field;
Polynomial; Real algebraic closure",
language = "English",
thesaurus = "Polynomials; Symbol manipulation",
}
@Article{Sit:1992:ASP,
author = "W. Y. Sit",
title = "An algorithm for solving parametric linear systems",
journal = j-J-SYMBOLIC-COMP,
volume = "13",
number = "4",
pages = "353--394",
month = apr,
year = "1992",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Sep 17 06:41:20 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The author presents a theoretical foundation for
studying parametric systems of linear equations and
proves an efficient algorithm for identifying all
parametric values (including degenerate cases) for
which the system is consistent. The algorithm gives a
small set of regimes where for each regime, the
solutions of the specialized systems may be given
uniformly. For homogeneous linear systems, or for
systems where the right hand side is arbitrary, this
small set is irredundant. He discusses in detail
practical issues concerning implementations, with
particular emphasis on simplification of results.
Examples are given based on a close implementation of
the algorithm in SCRATCHPAD II. He also gives a
complexity analysis of the Gaussian elimination method
and compares that with the algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., City Coll. of New York, NY, USA",
classification = "B0290H (Linear algebra); C4140 (Linear algebra);
C4240 (Programming and algorithm theory); C7310
(Mathematics)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Complexity analysis; Efficient algorithm; Gaussian
elimination method; Linear equations; Parametric linear
systems; SCRATCHPAD II",
language = "English",
pubcountry = "UK",
thesaurus = "Computational complexity; Matrix algebra; Symbol
manipulation",
}
@InProceedings{Smedley:1992:UPO,
author = "Trevor J. Smedley",
editor = "Hal Berghel and others",
booktitle = "Applied computing --- technological challenges of the
1990's: proceedings of the 1992 ACM\slash SIGAPP
Symposium on Applied Computing, Kansas City Convention
Center, March 1--3, 1992",
title = "Using pictorial and object oriented programming for
computer algebra",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "1243--1247",
year = "1992",
DOI = "https://doi.org/10.1145.130154",
ISBN = "0-89791-502-X",
ISBN-13 = "978-0-89791-502-1",
LCCN = "QA76.76.A65 S95 1992",
bibdate = "Thu Jul 26 09:02:03 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
bookpages = "xiii + 1257 (2 volumes)",
keywords = "Scratchpad",
}
@MastersThesis{Zenger:1992:GFD,
author = "Ch. Zenger",
title = "{Gr{\"o}bnerbasen f{\"u}r Differentialformen und ihre
Implementierung in AXIOM}",
type = "Diplomarbeit",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1992",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
@InProceedings{Bronstein:1993:FPF,
author = "Manuel Bronstein and Bruno Salvy",
title = "Full Partial Fraction Decomposition of Rational
Functions",
crossref = "Bronstein:1993:IPI",
pages = "157--160",
year = "1993",
bibdate = "Thu Mar 12 08:40:26 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p157-bronstein/",
abstract = "We describe a rational algorithm that computes the
full partial fraction expansion of a rational function
over the algebraic closure of its field of definition.
The algorithm uses only gcd operations over the initial
field but the resulting decomposition is expressed with
linear denominators. We give examples from its Axiom
and Maple implementations.",
acknowledgement = ack-nhfb,
affiliation = "Wissenschaftliches Rechnen, Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "B0290D (Functional analysis); B0290H (Linear
algebra); B0290M (Numerical integration and
differentiation); C4120 (Functional analysis); C4140
(Linear algebra); C4160 (Numerical integration and
differentiation); C7310 (Mathematics computing)",
keywords = "ACM; Algebraic closure; algebraic computation; Axiom;
Decomposition; Full partial fraction decomposition; Gcd
operations; Maple; Polynomial; Rational functions;
SIGSAM; symbolic computation; Symbolic integration,
ISSAC; theory; verification",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General.
{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms.",
thesaurus = "Function evaluation; Integration; Matrix
decomposition; Polynomial matrices; Symbol
manipulation",
}
@TechReport{Davenport:1993:PTR,
author = "J. H. Davenport",
title = "Primality Testing Revisited",
number = "TR2/93 (ATR/6) (NP2556)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
month = aug,
year = "1993",
bibdate = "Fri Dec 29 16:31:49 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
abstract = "Rabin's algorithm is commonly used in computer algebra
systems and elsewhere for primality testing. This paper
presents an experience with this in the Axiom computer
algebra system. As a result of this experience, we
suggest certain strengthenings of the algorithm.",
acknowledgement = ack-nhfb,
}
@InProceedings{Goodloe:1993:ADT,
author = "A. Goodloe and P. Loustaunau",
title = "An abstract data type development of graded rings",
crossref = "Fitch:1993:DIS",
pages = "193--202",
month = "",
year = "1993",
bibdate = "Tue Sep 17 06:37:45 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Novel computer algebra systems such as Scratchpad and
Weyl have been developed with built in mechanisms for
expressing abstract data types. These systems are
object oriented in that they incorporate multiple
inheritance and polymorphic types. The authors are
taking a similar approach to the development of
algorithms for computing in graded rings. They develop
the tools required to compute with polynomials with
coefficients in a graded ring R. They focus on graded
rings R which are polynomial rings graded by a monoid,
and allow partial orders on the monomials. The ideas
presented can be applied to more general graded rings
R, such as associated graded rings to filtered rings,
as long as certain computational `requirements' are
satisfied.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., George Mason Univ., Fairfax, VA, USA",
classification = "C4130 (Interpolation and function approximation);
C6120 (File organisation); C7310 (Mathematics)",
keywords = "Abstract data types; Computer algebra systems;
Filtered rings; Graded rings; Monoid; Multiple
inheritance; Object oriented; Partial orders;
Polymorphic types; Polynomial rings; Scratchpad; Weyl",
language = "English",
thesaurus = "Abstract data types; Polynomials; Symbol
manipulation",
}
@InProceedings{Monagan:1993:GPD,
author = "M. B. Monagan",
title = "{Gauss}: a parameterized domain of computation system
with support for signature functions",
crossref = "Miola:1993:DIS",
pages = "81--94",
month = "",
year = "1993",
bibdate = "Fri Dec 29 12:46:02 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The fastest known algorithms in classical algebra make
use of signature functions. That is, reducing
computation with formulae to computing with the
integers modulo p, by substituting random numbers for
variables, and mapping constants modulo p. This idea is
exploited in specific algorithms in computer algebra
systems, e.g. algorithms for polynomial greatest common
divisors. It is also used as a heuristic to speed up
other calculations. But none exploit it in a systematic
manner. The author designs an AXIOM like system in
which these signature functions can be constructed
automatically, hence better exploited. He exploits them
in new ways. He reports on the design of such a system,
Gauss.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, ETH, Zurich,
Switzerland",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "AXIOM like system; Classical algebra; Computation
system; Computer algebra systems; Gauss; Heuristic;
Integers modulo; Mapping constants modulo;
Parameterized domain; Polynomial greatest common
divisors; Random numbers; Signature functions",
language = "English",
thesaurus = "Polynomials; Symbol manipulation",
}
@InProceedings{Petitot:1993:EA,
author = "M. Petitot",
title = "Experience with {Axiom}",
crossref = "Jacob:1993:PSI",
pages = "240",
month = "",
year = "1993",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The computer algebra system Axiom (formerly
Scratchpad) allows a strict typing of the manipulated
data. Using examples from noncommutative algebra
(polynomials in noncommutative variables, Lie
polynomials, Poincar{\'e}--Birkoff--Witt basis) the
authors show the interest and the limits of some
essential notions in Axiom: the genericity, the
inheritance, the distinction domain/category and the
type inference.",
acknowledgement = ack-nhfb,
affiliation = "LIFL, Lille I Univ., Villeneuve d'Ascq, France",
classification = "C1230 (Artificial intelligence); C4130
(Interpolation and function approximation); C7310
(Mathematics)",
keywords = "Category; Computer algebra system Axiom; Distinction
domain; Genericity; Inheritance; Lie polynomials;
Manipulated data; Noncommutative algebra;
Poincar{\'e}--Birkoff--Witt basis; Polynomials;
Scratchpad; Type inference",
language = "English",
thesaurus = "Inference mechanisms; Lie algebras; Mathematics
computing; Polynomials",
}
@InProceedings{Weber:1993:CCA,
author = "A. Weber",
title = "On coherence in computer algebra",
crossref = "Miola:1993:DIS",
pages = "95--106",
month = "",
year = "1993",
bibdate = "Fri Dec 29 12:46:02 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Modern computer algebra systems (e.g. AXIOM) support a
rich type system including parameterized data types and
the possibility of implicit coercions between types. In
such a type system it will be frequently the case that
there are different ways of building coercions between
types. An important requirement is that all coercions
between two types coincide, a property which is called
coherence. The author proves a coherence theorem for a
formal type system having several possibilities of
coercions covering many important examples. Moreover,
he gives some informal reasoning why the formally
defined restrictions can be satisfied by an actual
system.",
acknowledgement = ack-nhfb,
affiliation = "Wilhelm-Schickard-Inst. fur Inf., Tubingen Univ.,
Germany",
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory); C7310 (Mathematics)",
keywords = "AXIOM; Coherence; Coherence theorem; Computer algebra;
Formal type system; Informal reasoning; Parameterized
data types; Type system",
language = "English",
thesaurus = "Symbol manipulation; Theorem proving; Type theory",
}
@Article{Beneke:1994:DFM,
author = "T. Beneke and W. Schwippert",
title = "Double-track into the future: {MathCAD} will gain new
users with {Standard} and {Plus} versions",
journal = j-ELECTRONIK,
volume = "43",
number = "15",
pages = "107--110",
month = jul,
year = "1994",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "MathCAD software is a type of `intelligent scratchpad
with a pocket calculator function'. Hitherto it has
been suitable only to a limited extent for engineering
mathematics. The new Version 5.0 is now offered in two
implementations: as an inexpensive basic package and in
a considerably more costly Plus version. The authors
question whether MathCAD can catch up with the
classical Maple and Mathematica products.",
acknowledgement = ack-nhfb,
classification = "C7310 (Mathematics computing)",
fjournal = "Elektronik",
keywords = "Engineering mathematics; Intelligent scratchpad;
MathCAD software",
language = "German",
pubcountry = "Germany",
thesaurus = "CAD; Mathematics computing; Software packages",
}
@Article{Brown:1994:CSC,
author = "R. Brown and A. Tonks",
title = "Calculations with simplicial and cubical groups in
{AXIOM}",
journal = j-J-SYMBOLIC-COMP,
volume = "17",
number = "2",
pages = "159--179",
month = feb,
year = "1994",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Work on calculations with simplicial and cubical
groups in AXIOM was carried out using loan equipment
and software from IBM UK and guidance from L. A. Lambe.
We report on the results of this work, and present the
AXIOM code written by the second author during this
period. This includes an implementation of the monoids
which model cubes and simplices, together with a new
AXIOM category of near-rings with which to carry out
non-abelian calculations. Examples of the use of this
code in interactive AXIOM sessions are also given.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Math., Univ. of Wales, Bangor, UK",
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "AXIOM; Cubical groups; Monoids; Nonabelian
calculations; Simplicial groups; Software",
language = "English",
pubcountry = "UK",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@Article{Gruntz:1994:IG,
author = "D. Gruntz and M. Monagan",
title = "Introduction to {Gauss}",
journal = j-SIGSAM,
volume = "28",
number = "2",
pages = "3--19",
month = aug,
year = "1994",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Dec 12 09:33:35 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "The Gauss package offers Maple users a new approach to
programming based on the idea of parameterized types
(domains) which is central to the AXIOM system. This
approach to programming is now regarded by many as the
right way to go in computer algebra systems design. We
describe how Gauss is designed and show examples of
usage. We end with some comments about how Gauss is
being used in Maple.",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Sci. Comput., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
classification = "C6110 (Systems analysis and programming); C6130
(Data handling techniques); C7310 (Mathematics
computing)",
fjournal = "SIGSAM Bulletin",
keywords = "AXIOM system; Computer algebra systems design; Gauss
package; Maple users; Parameterized types;
Programming",
language = "English",
pubcountry = "USA",
thesaurus = "Programming environments; Software packages; Symbol
manipulation; Systems analysis; Type theory",
}
@InProceedings{Jenks:1994:HMA,
author = "Richard D. Jenks and Barry M. Trager",
title = "How to make {AXIOM} into a {Scratchpad}",
crossref = "ACM:1994:IPI",
pages = "32--40",
year = "1994",
MRclass = "68W30 (Symbolic computation and algebraic
computation)",
bibdate = "Tue Sep 17 06:29:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
ZMnumber = "0945.68543",
abstract = "Scratchpad (Griesmer and Jenks, 1971) was a computer
algebra system that had one principal representation
for mathematical formulae based on expression trees.
Its user interface design was based on a
pattern-matching paradigm with infinite rewrite rule
semantics, providing what we believe to be the most
natural paradigm for interactive symbolic problem
solving. Like M and M, however, user programs were
interpreted, often resulting in poor performance
relative to similar facilities coded in standard
programming languages such as FORTRAN and C. Scratchpad
development stopped in 1976 giving way to a new system
design that evolved into AXIOM. AXIOM has a
strongly-typed programming language for building a
library of parameterized types and algorithms, and a
type-inferencing interpreter that accesses the library
and can build any of an infinite number of types for
interactive use. We suggest that the addition of an
expression tree type to AXIOM can allow users to
operate with the same freedom and convenience of
untyped systems without giving up the expressive power
and run-time efficiency provided by the type system. We
also present a design that supports a multiplicity of
programming styles, from the Scratchpad
pattern-matching paradigm to functional programming to
more conventional procedural programming.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "C6180 (User interfaces); C7310 (Mathematics
computing)",
keywords = "AXIOM; C; Computer algebra system; Expression trees;
FORTRAN; Functional programming; Infinite rewrite rule
semantics; Library; Mathematical formulae;
Pattern-matching; Procedural programming; Run-time
efficiency; Scratchpad; Strongly-typed programming
language; Symbolic problem solving; Type-inferencing
interpreter; Untyped systems; User interface design;
User programs",
language = "English",
thesaurus = "Mathematics computing; Pattern matching; Program
interpreters; Programming; Symbol manipulation; User
interfaces",
}
@TechReport{Keady:1994:PAS,
author = "G. Keady and G. Nolan",
title = "Production of {Argument SubPrograms} in the {AXIOM}
--- {NAG} link: examples involving nonlinear systems",
number = "TR1/94 ATR/7 (NP2680)",
institution = inst-NAG,
address = inst-NAG:adr,
pages = "??",
year = "1994",
bibdate = "Thu Jan 04 18:40:00 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Seiler:1994:CIA,
author = "W. M. Seiler",
title = "Completion to involution in {AXIOM}",
crossref = "Calmet:1994:RWC",
pages = "103--104",
month = "",
year = "1994",
bibdate = "Tue Sep 17 06:32:41 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "We have implemented an algorithm to complete a given
system of partial differential equations to an
involutive one in the computer algebra system AXIOM. An
earlier version of this program has been described in
Schu, Seiler, and Calmet (1992). The new version is
much more efficient due to better simplification and
many new features. It also provides procedures for the
analysis of the arbitrariness of the general solution.
The goal of the implementation was not to transform
simply an algorithm into a program but to start with
the construction of an environment for symbolic
computations within the geometric theory of
differential equations. The modular structure allows an
easy extension e.g. by a package for the symmetry
analysis.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "C4170 (Differential equations); C7310 (Mathematics
computing)",
keywords = "AXIOM; Computer algebra system; Involution; Partial
differential equations; Symbolic computations; Symmetry
analysis",
language = "English",
thesaurus = "Mathematics computing; Partial differential equations;
Symbol manipulation",
}
@Article{Seiler:1994:PDO,
author = "Werner M. Seiler",
title = "Pseudo differential operators and integrable systems
in {AXIOM}",
journal = j-COMP-PHYS-COMM,
volume = "79",
number = "2",
pages = "329--340",
month = apr,
year = "1994",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(94)90076-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 21:29:43 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465594900760",
abstract = "An implementation of the algebra of pseudo
differential operators in the computer algebra system
AXIOM is described. In several examples the application
of the package to typical computations in the theory of
integrable systems is demonstrated.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
Univ., Germany",
classification = "C4170 (Differential equations); C7310
(Mathematics)",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "AXIOM; Computer algebra; PDO; Pseudo differential
operators",
language = "English",
pubcountry = "Netherlands",
thesaurus = "Mathematics computing; Partial differential equations;
Symbol manipulation",
}
@Article{vanHoeij:1994:ACI,
author = "M. van Hoeij",
title = "An algorithm for computing an integral basis in an
algebraic function field",
journal = j-J-SYMBOLIC-COMP,
volume = "18",
number = "4",
pages = "353--363",
month = oct,
year = "1994",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Fri Dec 29 12:46:02 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Algorithms for computing integral bases of an
algebraic function field are implemented in some
computer algebra systems. They are used e.g. for the
integration of algebraic functions. The method used by
Maple 5.2 and AXIOM is given by B. M. Trager (1984). He
adapted an algorithm of Ford and Zassenhaus (1978),
that computes the ring of integers in an algebraic
number field, to the case of a function field. It turns
out that using algebraic geometry one can write a
faster algorithm. The method we give is based on
Puiseux expansions. One can see this as a variant on
the Coates' algorithm as it is described by Davenport
(1981). Some difficulties in computing with Puiseux
expansions can be avoided using a sharp bound for the
number of terms required which are given. We derive
which denominator is needed in the integral basis.
Using this result `intermediate expression swell' can
be avoided. The Puiseux expansions generally introduce
algebraic extensions.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Nijmegen Univ., Netherlands",
classification = "C6130 (Data handling techniques); C7310 (Mathematics
computing)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Algebraic function field; Algebraic number field;
AXIOM; Computer algebra systems; Integral basis;
Intermediate expression swell; Maple 5.2; Puiseux
expansions",
language = "English",
pubcountry = "UK",
thesaurus = "Mathematics computing; Symbol manipulation",
}
@Article{Anonymous:1995:GAM,
author = "Anonymous",
title = "{GAMM} 94 Annual Meeting",
journal = j-ZEIT-ANGE-MATH-PHYS,
volume = "75",
number = "suppl. 2",
pages = "",
year = "1995",
CODEN = "ZAMMAX",
ISSN = "0044-2267",
bibdate = "Fri Dec 29 12:46:02 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "4--8 April 1994",
conflocation = "Braunschweig, Germany",
pubcountry = "Germany",
}
@Article{Arnault:1995:CCN,
author = "Fran{\c{c}}ois Arnault",
title = "Constructing {Carmichael} Numbers Which are Strong
Pseudoprimes to Several Bases",
journal = j-J-SYMBOLIC-COMP,
volume = "20",
number = "2",
pages = "151--162 (or 151--161??)",
month = aug,
year = "1995",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "11Y11 (11A51)",
MRnumber = "96k:11153",
MRreviewer = "Andrew Granville",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics computing); C1160 (Combinatorial
mathematics)",
corpsource = "Fac. des Sci., Limoges Univ., France",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Axiom; Carmichael numbers; composite numbers; Lucas;
Maple; number theory; pseudoprimes; Rabin-Miller test;
symbol manipulation",
treatment = "T Theoretical or Mathematical",
}
@Article{Boulanger:1995:OOM,
author = "J.-L. Boulanger",
title = "Object oriented method for {Axiom}",
journal = j-SIGPLAN,
volume = "30",
number = "2",
pages = "33--41",
month = feb,
year = "1995",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Sep 17 06:32:41 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Axiom is a very powerful computer algebra system which
combines two language paradigms (functional and OOP).
The mathematical world is complex and mathematicians
use abstraction to design it. The paper presents some
aspects of object oriented development in Axiom. Axiom
programming is based on several new tools for object
oriented development, it uses two levels of class and
some operations such as coerce, retract or convert
which permit the type evolution. These notions
introduce the concept of multi-view.",
acknowledgement = ack-nhfb,
affiliation = "Lab. d'Inf. Fondamentale de Lille, Lille I Univ.,
Villeneuve d'Ascq, France",
classification = "C4240 (Programming and algorithm theory); C6110J
(Object-oriented programming); C6120 (File
organisation); C6130 (Data handling techniques); C6140D
(High level languages); C7310 (Mathematics computing)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Abstraction; Axiom; Axiom programming; Class; Coerce;
Computer algebra system; Convert; Functional language;
Multiview concept; Object oriented development; Object
oriented method; Object-oriented language; Retract;
Tools; Type evolution",
language = "English",
pubcountry = "USA",
thesaurus = "Abstract data types; Functional languages; Functional
programming; Mathematics computing; Object-oriented
languages; Object-oriented programming; Symbol
manipulation; Type theory",
}
@InProceedings{Broadbery:1995:IDE,
author = "P. A. Broadbery and T. G{\'o}mez-D{\'\i}az and S. M.
Watt",
title = "On the Implementation of Dynamic Evaluation",
crossref = "Levelt:1995:IPI",
pages = "77--84",
year = "1995",
bibdate = "Thu Mar 12 08:42:30 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p77-broadbery/",
abstract = "Dynamic evaluation is a technique for producing
multiple results according to a decision tree which
evolves with program execution. Sometimes we need to
produce results for all possible branches in the
decision tree, while on other occasions it may be
sufficient to compute a single result which satisfies
certain properties. This technique finds use in
computer algebra where computing the correct result
depends on recognising and properly handling special
cases of parameters. In previous work, programs using
dynamic evaluation have explored all branches of
decision trees by repeating the computations prior to
decision points. The paper presents two new
implementations of dynamic evaluation which avoid
recomputing intermediate results. The first approach
uses Scheme `continuations' to record the state for
resuming program execution. The second implementation
uses the Unix `fork' operation to form new processes to
explore alternative branches in parallel. These
implementations are based on modifications to Lisp- and
C-based run-time systems for the Axiom Version 2
extension language (previously known as $ A^{\mbox
{Hash}} $ ). This allows the same high-level source
code to be compared using the `re-evaluation', the
`continuation', and the `fork' implementations.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Algorithms Group Ltd., Oxford, UK",
classification = "C1140E (Game theory); C1160 (Combinatorial
mathematics); C6130 (Data handling techniques); C6150G
(Diagnostic, testing, debugging and evaluating
systems); C6150J (Operating systems)",
keywords = "algebraic computation, Dynamic evaluation; algorithms;
Axiom Version 2 extension language; C-based run-time
systems; Computer algebra; Decision points; Decision
tree; High-level source code; ISSAC; languages;
Lisp-based run-time systems; Multiple results; Program
execution; Re-evaluation; Scheme continuations; State
recording; symbolic computation; Unix fork operation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf D.3.2} Software, PROGRAMMING
LANGUAGES, Language Classifications, SCHEME. {\bf
F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on polynomials. {\bf D.3.2}
Software, PROGRAMMING LANGUAGES, Language
Classifications, C.",
thesaurus = "Decision theory; Symbol manipulation; System
monitoring; Trees [mathematics]; Unix",
}
@Article{Duval:1995:DEA,
author = "Dominique Duval",
title = "{{\'E}}valuation dynamique et cl{\^o}ture
alg{\'e}brique en {Axiom}. (French) {Dynamic evaluation
and algebraic closure in Axiom}",
journal = "J. Pure Appl. Algebra",
volume = "99",
number = "3",
pages = "267--295",
year = "1995",
DOI = "https://doi.org/10.1016/0022-4049(94)00053-L",
ISSN = "0022-4049",
MRclass = "11Y40 (Algebraic number theory computations) 68W30
(Symbolic computation and algebraic computation) 68Q65
(Abstract data types; algebraic specification) 18C10
(Algebraic theories, etc.)",
bibdate = "Tue Mar 30 18:47:12 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
ZMnumber = "0851.1107",
abstract = "Dynamic evaluation is a method of computing that
permits the computation to be refined into different
cases that are considered separately. A precise
description and mathematical foundation was given in
terms of sketch theory by {\it D. Duval} and {\it J.-C.
Reynaud} [Math. Structures Comput. Sci. 4, 239-271
(1994; Zbl 0822.68063)]. In the present paper, the
mechanism of dynamic evaluation is explained without
reference to sketch theory in order to make it
accessible to a wider audience. Next, it is shown how
dynamic evaluation can be employed to compute with
algebraic numbers without having to do explicit
factorization of polynomials. The essential step here
is to define the dynamic algebraic closure of a field.
Finally, a program for the Axiom system implementing
dynamic algebraic closure is presented.",
acknowledgement = ack-nhfb,
keywords = "algebraic numbers; Axiom; dynamic algebraic closure of
a field; dynamic evaluation; sketches",
language = "French",
reviewer = "A. Bijlsma (Eindhoven)",
}
@Article{Roesner:1995:VSP,
author = "K. G. Roesner",
title = "Verified solutions for parameters of an exact solution
for {non-Newtonian} liquids using computer algebra",
journal = j-ZEIT-ANGE-MATH-PHYS,
volume = "75",
number = "suppl. 2",
pages = "S435--S438",
month = "",
year = "1995",
ISSN = "0044-2267",
bibdate = "Fri Dec 29 12:46:02 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "An exact solution of the time independent velocity
field for the Taylor--Couette flow of a polymer
solution is derived solving the resulting first order
ordinary differential equation of fifth degree
analytically. Intensive use is made of computer algebra
systems AXIOM and MACSYMA to find the exact solution.
The coaxial cylinders in the Taylor--Couette flow
problem are assumed to rotate at different angular
velocities. The geometrical and kinematic parameters
can be chosen arbitrarily. The model equation for the
material law of the viscoelastic liquid is based on the
thermodynamic model for dilute solutions due to
Lhuillier and Ouibrahim (1980) which is an analogy to
the earlier paper of Frankel and Acrivos (1970). In the
present investigation the influence of the parameters
of the viscoelastic model on the velocity profile in
the cylindrical gap is studied and the range of
validity of the constitutive equation is
investigated.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Mech., Tech. Hochschule Darmstadt, Germany",
classification = "A0210 (Algebra, set theory, and graph theory); A0230
(Function theory, analysis); A0270 (Computational
techniques); A4710 (General fluid dynamics theory,
simulation and other computational methods); A4715
(Laminar flows); A4730 (Rotational flow, vortices,
buoyancy and other flows involving body forces); A4750
(Non-Newtonian dynamics)",
keywords = "AXIOM; Coaxial cylinders; Computer algebra;
Constitutive equation; Cylindrical gap; Dilute
solutions; Exact solution; First order ordinary
differential equation; Geometrical parameters;
Kinematic parameters; MACSYMA; Material law;
NonNewtonian liquids; Polymer solution; Taylor--Couette
flow; Thermodynamic model; Time independent velocity
field; Velocity profile; Viscoelastic liquid;
Viscoelastic model",
language = "English",
thesaurus = "Algebra; Couette flow; Differential equations; Flow
simulation; Non-Newtonian fluids; Physics computing;
Polymer solutions; Rotational flow; Thermodynamics",
}
@Book{Benker:1998:ICS,
author = "Hans Benker",
title = "{Ingenieurmathematik mit Computeralgebra-Systemen.
AXIOM, DERIVE, MACSYMA, MAPLE, MATHCAD, MATHEMATICA,
MATLAB und MuPAD in der Anwendung}. (German)
{Engineering mathematics with computer algebra systems.
The applications: AXIOM, DERIVE, MACSYMA, MAPLE,
MATHCAD, MATHEMATICA, MATLAB UND MuPAD.}",
publisher = pub-VIEWEG,
address = pub-VIEWEG:adr,
pages = "xiii + 439",
year = "1998",
MRclass = "68W30 (Symbolic computation and algebraic computation)
68-01 (Textbooks (computer science)) 00A06 (Mathematics
for non-mathematicians) 68-04 (Machine computation,
programs (computer science)) 65D18 (Computer graphics
and computational geometry)",
bibdate = "Tue Mar 30 18:49:35 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
ZMnumber = "0909.68109",
acknowledgement = ack-nhfb,
keywords = "calculus; differential equations; Fourier transform;
Laplace transform; linear algebra; optimization;
probability theory; statistics; textbook",
language = "German",
reviewer = "Helmut K{\"o}cher (Dresden)",
}
@InProceedings{Doye:1999:ACA,
author = "Nicolas J. Doye",
title = "Automated coercion for {Axiom}",
crossref = "Dooley:1999:IJS",
pages = "229--235",
year = "1999",
bibdate = "Sat Mar 11 16:39:42 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
acknowledgement = ack-nhfb,
}
@Article{Kendall:2001:SIC,
author = "Wilfrid S. Kendall",
title = "Symbolic {It{\^o}} calculus in {AXIOM}: an ongoing
story",
journal = j-STAT-COMP,
volume = "11",
number = "1",
pages = "25--35",
year = "2001",
CODEN = "STACE3",
DOI = "https://doi.org/10.1023/A:1026553731272",
ISSN = "0960-3174",
ISSN-L = "0960-3174",
MRclass = "Database Expansion Item",
MRnumber = "MR1837142",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
fjournal = "Statistics and Computing",
keywords = "computer algebra; coupling of random processes; Dryden
density Mathematica; financial mathematics; Itovsn3;
It{\^o} calculus; It{\^o} formula; Macsyma; Maple;
Mardia; REDUCE; semimartingale; statistics of shape;
stochastic calculus; stochastic integral; symbolic
It{\^o} calculus; XIOM",
}
@Article{Daly:2002:AOS,
author = "T. Daly",
title = "{Axiom} as Open Source",
journal = j-SIGSAM,
volume = "36",
number = "1",
pages = "28--??",
month = mar,
year = "2002",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Mon Apr 29 07:16:09 MDT 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "139",
}
@Book{Daly:2003:AVA,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 5: {Axiom} Interpreter",
pages = "xlvi + 1387",
year = "2003",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol5.pdf",
acknowledgement = ack-nhfb,
}
@Book{Grabmeier:2003:CAH,
editor = "Johannes Grabmeier and Erich Kaltofen and Volker
Weispfenning",
title = "Computer algebra handbook: foundations, applications,
systems",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xx + 637",
year = "2003",
ISBN = "3-540-65466-6",
ISBN-13 = "978-3-540-65466-7",
LCCN = "QA155.7.E4 C64954 2003",
MRclass = "68W30, 00B15, 68-06",
bibdate = "Tue Nov 22 06:00:25 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
z3950.loc.gov:7090/Voyager",
note = "Includes CD-ROM.",
URL = "http://www.springer.com/sgw/cda/frontpage/0,11855,1-102-22-1477871-0,00.html",
acknowledgement = ack-nhfb,
keywords = "Aldor; AXIOM; Derive; exact arithmetic; Macsyma;
Magma; Maple Mathematica; MuPAD; REDUCE; TI-92",
subject = "Algebra; Data processing",
}
@Book{Jenks:2003:AVS,
author = "Richard D. Jenks and Robert S. Sutor and Tim Daly",
title = "{Axiom} Volume 0: The Scientific Computation System",
pages = "xviii + 1187",
year = "2003",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol0.pdf",
acknowledgement = ack-nhfb,
}
@Article{Caviness:2004:MRD,
author = "Bob Caviness and Barbara Gatje and James H. Griesmer
and Tony Hearn and Manual Bronstein and Erich
Kaltofen",
title = "In Memoriam: {Richard Dimick Jenks}: {Axiom} Developer
and Computer Algebra Pioneer",
journal = j-SIGSAM,
volume = "38",
number = "1",
pages = "30--30",
month = mar,
year = "2004",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Sat Apr 17 11:49:58 MDT 2004",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://savannah.nongnu.org/projects/axiom/",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "147",
}
@Book{Daly:2005:AVAb,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 2: {Axiom} Users Guide",
pages = "iv + 7",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol2.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAc,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 3: {Axiom} Programmers Guide",
pages = "iv + 3",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol3.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAd,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 4: {Axiom} Developers Guide",
pages = "v + 91",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol4.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAe,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 6: {Axiom} Command",
pages = "vi + 187",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol6.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAf,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 8: {Axiom} Graphics",
pages = "xi + 538",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol8.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAg,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 9: {Axiom} Compiler",
pages = "iv + 30",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol9.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAh,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 10: {Axiom} Algebra: Implementation",
pages = "iv + 5",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol10.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAi,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 12: {Axiom} Crystal",
pages = "iv + 9",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol12.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2005:AVAj,
author = "Tim Daly and Martin Dunstan",
title = "{Axiom} Volume 7: {Axiom} Hyperdoc",
pages = "xvi + 632",
year = "2005",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol7.pdf",
acknowledgement = ack-nhfb,
}
@Book{Daly:2006:AVA,
author = "Timothy Daly",
title = "{Axiom} Volume 1: {Axiom} Tutorial",
publisher = "Lulu, Inc.",
address = "860 Aviation Parkway, Suite 300, Morrisville, NC
27560, USA",
pages = "iv + 285",
year = "2006",
ISBN = "1-4116-6597-X",
ISBN-13 = "978-1-4116-6597-2",
LCCN = "????",
bibdate = "Thu Mar 23 05:24:19 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
price = "US\$15.00",
URL = "http://www.axiom-developer.org/axiom-website/bookvol1.pdf;
http://www.lulu.com/content/190827",
acknowledgement = ack-nhfb,
}
@Article{Li:2006:EIP,
author = "Xin Li and Moreno Maza",
title = "Efficient Implementation of Polynomial Arithmetic in a
Multiple-Level Programming Environment",
journal = j-LECT-NOTES-COMP-SCI,
volume = "4151",
pages = "12--23",
year = "2006",
CODEN = "LNCSD9",
ISBN = "3-540-38084-1",
ISBN-13 = "978-3-540-38084-9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Apr 19 08:40:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "Proceedings of the International Congress of
Mathematical Software (ICMS 2006).",
URL = "http://www.csd.uwo.ca/~moreno//Publications/Li-MorenoMaza-ICMS-06.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
keywords = "Axiom symbolic-algebra system",
}
@InProceedings{Li:2007:VGP,
author = "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
title = "On the Virtues of Generic Programming for Symbolic
Computation",
crossref = "Shi:2007:CSIb",
pages = "251--258",
year = "2007",
DOI = "https://doi.org/10.1007/978-3-540-72586-2_35",
bibdate = "Tue Aug 12 10:36:21 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
acknowledgement = ack-nhfb,
keywords = "Axiom; Magma; Maple",
}
@Book{Portes:2007:AVA,
author = "Alfredo Portes and Arthur Ralfs and Timothy Daly and
Martin Dunstan",
title = "{Axiom} Volume 11: {Axiom} Browser",
pages = "xix + 1193",
year = "2007",
LCCN = "????",
bibdate = "Tue Mar 30 08:43:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
URL = "http://www.axiom-developer.org/axiom-website/bookvol11.pdf",
acknowledgement = ack-nhfb,
}
@Article{Page:2007:AOS,
author = "William S. Page",
title = "{Axiom}: open source computer algebra system",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "41",
number = "3",
pages = "114--114",
month = sep,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1145/1358190.1358206",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Jun 18 09:23:01 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "Axiom has been in development since 1971. Originally
called Scratchpad II, it was developed by IBM under the
direction of Richard Jenks[1]. The project evolved over
a period of 20 years as a research platform for
developing new ideas in computational mathematics.
ScratchPad also attracted the interest and
contributions of a large number of mathematicians and
computer scientists outside of IBM. In the 1990s, the
Scratchpad project was renamed to Axiom, and sold to
the Numerical Algorithms Group (NAG) in England who
marketed it as a commercial system. NAG withdrew Axiom
from the market in October 2001 and agreed to release
Axiom as free software, under an open source
license.\par
Tim Daly (a former ScratchPad developer at IBM) setup a
pubic open source Axiom project[2] in October 2002 with
a primary goal to improve the documentation of Axiom
through the extensive use of literate programming[3].
The first free open source version of Axiom was
released in 2003. Since that time the project has
attracted a small but very active group of developers
and a growing number of users.\par
This exhibit includes a laptop computer running a
recent version of Axiom, Internet access (if available)
to the Axiom Wiki website[4], and CDs containing Axiom
software for free distribution[5].",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "161",
}
@InProceedings{Smith:2007:ADA,
author = "Jacob Smith and Gabriel {Dos Reis} and Jaakko
J{\"a}rvi",
title = "Algorithmic differentiation in {Axiom}",
crossref = "Brown:2007:PIS",
pages = "347--354",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277595",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "This paper describes the design and implementation of
an algorithmic differentiation framework in the Axiom
computer algebra system. Our implementation works by
transformations on Spad programs at the level of the
typed abstract syntax tree -- Spad is the language for
extending Axiom with libraries. The framework
illustrates an algebraic theory of algorithmic
differentiation, here only for Spad programs, but we
suggest that the theory is general. In particular, if
it is possible to define a compositional semantics for
programs, we define the exact requirements for when a
program can be algorithmically differentiated. This
leads to a general algorithmic differentiation system,
and is not confined to functions which compute with
basic data types, such as floating point numbers.",
acknowledgement = ack-nhfb,
keywords = "algorithmic differentiation; axiom; program
transformation; symbolic-numeric computation",
}
@Article{Joyner:2008:OSC,
author = "David Joyner",
title = "Open source computer algebra systems: {Axiom}",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "42",
number = "1--2",
pages = "39--47",
month = mar # "/" # jun,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1145/1394042.1394046",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Tue Aug 12 17:30:40 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
abstract = "This survey will look at Axiom, a free and very
powerful computer algebra system available. It is a
general purpose CAS useful for symbolic computation,
research, and the development of new mathematical
algorithms. Axiom is similar in some ways to Maxima,
covered in the survey [J1], but different in many ways
as well. Axiom, Maxima, and SAGE [S], are the largest
of the general-purpose open-source CAS's. If you want
to 'take a test drive,' Axiom can be tested without
installation via the web interface [AS] or the SAGE
online interface [S].",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
}
@Book{Beebe:2017:MFC,
author = "Nelson H. F. Beebe",
title = "The Mathematical-Function Computation Handbook:
Programming Using the {MathCW} Portable Software
Library",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxvi + 1114",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-64110-2",
ISBN = "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
ISBN-13 = "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
(e-book)",
LCCN = "QA75.5-76.95",
bibdate = "Sat Jul 15 19:34:43 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/mupad.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
URL = "http://www.springer.com/us/book/9783319641096",
acknowledgement = ack-nhfb,
ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
tableofcontents = "List of figures / xxv \\
List of tables / xxxi \\
Quick start / xxxv \\
1: Introduction / 1 \\
1.1: Programming conventions / 2 \\
1.2: Naming conventions / 4 \\
1.3: Library contributions and coverage / 5 \\
1.4: Summary / 6 \\
2: Iterative solutions and other tools / 7 \\
2.1: Polynomials and Taylor series / 7 \\
2.2: First-order Taylor series approximation / 8 \\
2.3: Second-order Taylor series approximation / 9 \\
2.4: Another second-order Taylor series approximation /
9 \\
2.5: Convergence of second-order methods / 10 \\
2.6: Taylor series for elementary functions / 10 \\
2.7: Continued fractions / 12 \\
2.8: Summation of continued fractions / 17 \\
2.9: Asymptotic expansions / 19 \\
2.10: Series inversion / 20 \\
2.11: Summary / 22 \\
3: Polynomial approximations / 23 \\
3.1: Computation of odd series / 23 \\
3.2: Computation of even series / 25 \\
3.3: Computation of general series / 25 \\
3.4: Limitations of Cody\slash Waite polynomials / 28
\\
3.5: Polynomial fits with Maple / 32 \\
3.6: Polynomial fits with Mathematica / 33 \\
3.7: Exact polynomial coefficients / 42 \\
3.8: Cody\slash Waite rational polynomials / 43 \\
3.9: Chebyshev polynomial economization / 43 \\
3.10: Evaluating Chebyshev polynomials / 48 \\
3.11: Error compensation in Chebyshev fits / 50 \\
3.12: Improving Chebyshev fits / 51 \\
3.13: Chebyshev fits in rational form / 52 \\
3.14: Chebyshev fits with Mathematica / 56 \\
3.15: Chebyshev fits for function representation / 57
\\
3.16: Extending the library / 57 \\
3.17: Summary and further reading / 58 \\
4: Implementation issues / 61 \\
4.1: Error magnification / 61 \\
4.2: Machine representation and machine epsilon / 62
\\
4.3: IEEE 754 arithmetic / 63 \\
4.4: Evaluation order in C / 64 \\
4.5: The {\tt volatile} type qualifier / 65 \\
4.6: Rounding in floating-point arithmetic / 66 \\
4.7: Signed zero / 69 \\
4.8: Floating-point zero divide / 70 \\
4.9: Floating-point overflow / 71 \\
4.10: Integer overflow / 72 \\
4.11: Floating-point underflow / 77 \\
4.12: Subnormal numbers / 78 \\
4.13: Floating-point inexact operation / 79 \\
4.14: Floating-point invalid operation / 79 \\
4.15: Remarks on NaN tests / 80 \\
4.16: Ulps --- units in the last place / 81 \\
4.17: Fused multiply-add / 85 \\
4.18: Fused multiply-add and polynomials / 88 \\
4.19: Significance loss / 89 \\
4.20: Error handling and reporting / 89 \\
4.21: Interpreting error codes / 93 \\
4.22: C99 changes to error reporting / 94 \\
4.23: Error reporting with threads / 95 \\
4.24: Comments on error reporting / 95 \\
4.25: Testing function implementations / 96 \\
4.26: Extended data types on Hewlett--Packard HP-UX
IA-64 / 100 \\
4.27: Extensions for decimal arithmetic / 101 \\
4.28: Further reading / 103 \\
4.29: Summary / 104 \\
5: The floating-point environment / 105 \\
5.1: IEEE 754 and programming languages / 105 \\
5.2: IEEE 754 and the mathcw library / 106 \\
5.3: Exceptions and traps / 106 \\
5.4: Access to exception flags and rounding control /
107 \\
5.5: The environment access pragma / 110 \\
5.6: Implementation of exception-flag and
rounding-control access / 110 \\
5.7: Using exception flags: simple cases / 112 \\
5.8: Using rounding control / 115 \\
5.9: Additional exception flag access / 116 \\
5.10: Using exception flags: complex case / 120 \\
5.11: Access to precision control / 123 \\
5.12: Using precision control / 126 \\
5.13: Summary / 127 \\
6: Converting floating-point values to integers / 129
\\
6.1: Integer conversion in programming languages / 129
\\
6.2: Programming issues for conversions to integers /
130 \\
6.3: Hardware out-of-range conversions / 131 \\
6.4: Rounding modes and integer conversions / 132 \\
6.5: Extracting integral and fractional parts / 132 \\
6.6: Truncation functions / 135 \\
6.7: Ceiling and floor functions / 136 \\
6.8: Floating-point rounding functions with fixed
rounding / 137 \\
6.9: Floating-point rounding functions: current
rounding / 138 \\
6.10: Floating-point rounding functions without {\em
inexact\/} exception / 139 \\
6.11: Integer rounding functions with fixed rounding /
140 \\
6.12: Integer rounding functions with current rounding
/ 142 \\
6.13: Remainder / 143 \\
6.14: Why the remainder functions are hard / 144 \\
6.15: Computing {\tt fmod} / 146 \\
6.16: Computing {\tt remainder} / 148 \\
6.17: Computing {\tt remquo} / 150 \\
6.18: Computing one remainder from the other / 152 \\
6.19: Computing the remainder in nonbinary bases / 155
\\
6.20: Summary / 156 \\
7: Random numbers / 157 \\
7.1: Guidelines for random-number software / 157 \\
7.2: Creating generator seeds / 158 \\
7.3: Random floating-point values / 160 \\
7.4: Random integers from floating-point generator /
165 \\
7.5: Random integers from an integer generator / 166
\\
7.6: Random integers in ascending order / 168 \\
7.7: How random numbers are generated / 169 \\
7.8: Removing generator bias / 178 \\
7.9: Improving a poor random number generator / 178 \\
7.10: Why long periods matter / 179 \\
7.11: Inversive congruential generators / 180 \\
7.12: Inversive congruential generators, revisited /
189 \\
7.13: Distributions of random numbers / 189 \\
7.14: Other distributions / 195 \\
7.15: Testing random-number generators / 196 \\
7.16: Applications of random numbers / 202 \\
7.17: The \textsf {mathcw} random number routines / 208
\\
7.18: Summary, advice, and further reading / 214 \\
8: Roots / 215 \\
8.1: Square root / 215 \\
8.2: Hypotenuse and vector norms / 222 \\
8.3: Hypotenuse by iteration / 227 \\
8.4: Reciprocal square root / 233 \\
8.5: Cube root / 237 \\
8.6: Roots in hardware / 240 \\
8.7: Summary / 242 \\
9: Argument reduction / 243 \\
9.1: Simple argument reduction / 243 \\
9.2: Exact argument reduction / 250 \\
9.3: Implementing exact argument reduction / 253 \\
9.4: Testing argument reduction / 265 \\
9.5: Retrospective on argument reduction / 265 \\
10: Exponential and logarithm / 267 \\
10.1: Exponential functions / 267 \\
10.2: Exponential near zero / 273 \\
10.3: Logarithm functions / 282 \\
10.4: Logarithm near one / 290 \\
10.5: Exponential and logarithm in hardware / 292 \\
10.6: Compound interest and annuities / 294 \\
10.7: Summary / 298 \\
11: Trigonometric functions / 299 \\
11.1: Sine and cosine properties / 299 \\
11.2: Tangent properties / 302 \\
11.3: Argument conventions and units / 304 \\
11.4: Computing the cosine and sine / 306 \\
11.5: Computing the tangent / 310 \\
11.6: Trigonometric functions in degrees / 313 \\
11.7: Trigonometric functions in units of $ \pi $ / 315
\\
11.8: Computing the cosine and sine together / 320 \\
11.9: Inverse sine and cosine / 323 \\
11.10: Inverse tangent / 331 \\
11.11: Inverse tangent, take two / 336 \\
11.12: Trigonometric functions in hardware / 338 \\
11.13: Testing trigonometric functions / 339 \\
11.14: Retrospective on trigonometric functions / 340
\\
12: Hyperbolic functions / 341 \\
12.1: Hyperbolic functions / 341 \\
12.2: Improving the hyperbolic functions / 345 \\
12.3: Computing the hyperbolic functions together / 348
\\
12.4: Inverse hyperbolic functions / 348 \\
12.5: Hyperbolic functions in hardware / 350 \\
12.6: Summary / 352 \\
13: Pair-precision arithmetic / 353 \\
13.1: Limitations of pair-precision arithmetic / 354
\\
13.2: Design of the pair-precision software interface /
355 \\
13.3: Pair-precision initialization / 356 \\
13.4: Pair-precision evaluation / 357 \\
13.5: Pair-precision high part / 357 \\
13.6: Pair-precision low part / 357 \\
13.7: Pair-precision copy / 357 \\
13.8: Pair-precision negation / 358 \\
13.9: Pair-precision absolute value / 358 \\
13.10: Pair-precision sum / 358 \\
13.11: Splitting numbers into pair sums / 359 \\
13.12: Premature overflow in splitting / 362 \\
13.13: Pair-precision addition / 365 \\
13.14: Pair-precision subtraction / 367 \\
13.15: Pair-precision comparison / 368 \\
13.16: Pair-precision multiplication / 368 \\
13.17: Pair-precision division / 371 \\
13.18: Pair-precision square root / 373 \\
13.19: Pair-precision cube root / 377 \\
13.20: Accuracy of pair-precision arithmetic / 379 \\
13.21: Pair-precision vector sum / 384 \\
13.22: Exact vector sums / 385 \\
13.23: Pair-precision dot product / 385 \\
13.24: Pair-precision product sum / 386 \\
13.25: Pair-precision decimal arithmetic / 387 \\
13.26: Fused multiply-add with pair precision / 388 \\
13.27: Higher intermediate precision and the FMA / 393
\\
13.28: Fused multiply-add without pair precision / 395
\\
13.29: Fused multiply-add with multiple precision / 401
\\
13.30: Fused multiply-add, Boldo/\penalty
\exhyphenpenalty Melquiond style / 403 \\
13.31: Error correction in fused multiply-add / 406 \\
13.32: Retrospective on pair-precision arithmetic / 407
\\
14: Power function / 411 \\
14.1: Why the power function is hard to compute / 411
\\
14.2: Special cases for the power function / 412 \\
14.3: Integer powers / 414 \\
14.4: Integer powers, revisited / 420 \\
14.5: Outline of the power-function algorithm / 421 \\
14.6: Finding $a$ and $p$ / 423 \\
14.7: Table searching / 424 \\
14.8: Computing $\log_n(g/a)$ / 426 \\
14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
14.10: Exact products / 430 \\
14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
14.12: Computing $n^{w_2}$ / 437 \\
14.13: The choice of $q$ / 438 \\
14.14: Testing the power function / 438 \\
14.15: Retrospective on the power function / 440 \\
15: Complex arithmetic primitives / 441 \\
15.1: Support macros and type definitions / 442 \\
15.2: Complex absolute value / 443 \\
15.3: Complex addition / 445 \\
15.4: Complex argument / 445 \\
15.5: Complex conjugate / 446 \\
15.6: Complex conjugation symmetry / 446 \\
15.7: Complex conversion / 448 \\
15.8: Complex copy / 448 \\
15.9: Complex division: C99 style / 449 \\
15.10: Complex division: Smith style / 451 \\
15.11: Complex division: Stewart style / 452 \\
15.12: Complex division: Priest style / 453 \\
15.13: Complex division: avoiding subtraction loss /
455 \\
15.14: Complex imaginary part / 456 \\
15.15: Complex multiplication / 456 \\
15.16: Complex multiplication: error analysis / 458 \\
15.17: Complex negation / 459 \\
15.18: Complex projection / 460 \\
15.19: Complex real part / 460 \\
15.20: Complex subtraction / 461 \\
15.21: Complex infinity test / 462 \\
15.22: Complex NaN test / 462 \\
15.23: Summary / 463 \\
16: Quadratic equations / 465 \\
16.1: Solving quadratic equations / 465 \\
16.2: Root sensitivity / 471 \\
16.3: Testing a quadratic-equation solver / 472 \\
16.4: Summary / 474 \\
17: Elementary functions in complex arithmetic / 475
\\
17.1: Research on complex elementary functions / 475
\\
17.2: Principal values / 476 \\
17.3: Branch cuts / 476 \\
17.4: Software problems with negative zeros / 478 \\
17.5: Complex elementary function tree / 479 \\
17.6: Series for complex functions / 479 \\
17.7: Complex square root / 480 \\
17.8: Complex cube root / 485 \\
17.9: Complex exponential / 487 \\
17.10: Complex exponential near zero / 492 \\
17.11: Complex logarithm / 495 \\
17.12: Complex logarithm near one / 497 \\
17.13: Complex power / 500 \\
17.14: Complex trigonometric functions / 502 \\
17.15: Complex inverse trigonometric functions / 504
\\
17.16: Complex hyperbolic functions / 509 \\
17.17: Complex inverse hyperbolic functions / 514 \\
17.18: Summary / 520 \\
18: The Greek functions: gamma, psi, and zeta / 521 \\
18.1: Gamma and log-gamma functions / 521 \\
18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
18.3: Polygamma functions / 547 \\
18.4: Incomplete gamma functions / 560 \\
18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
18.6: An Italian excursion: Fibonacci numbers / 575 \\
18.7: A German gem: the Riemann zeta function / 579 \\
18.8: Further reading / 590 \\
18.9: Summary / 591 \\
19: Error and probability functions / 593 \\
19.1: Error functions / 593 \\
19.2: Scaled complementary error function / 598 \\
19.3: Inverse error functions / 600 \\
19.4: Normal distribution functions and inverses / 610
\\
19.5: Summary / 617 \\
20: Elliptic integral functions / 619 \\
20.1: The arithmetic-geometric mean / 619 \\
20.2: Elliptic integral functions of the first kind /
624 \\
20.3: Elliptic integral functions of the second kind /
627 \\
20.4: Elliptic integral functions of the third kind /
630 \\
20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
20.7: Historical algorithms for elliptic integrals /
643 \\
20.8: Auxiliary functions for elliptic integrals / 645
\\
20.9: Computing the elliptic auxiliary functions / 648
\\
20.10: Historical elliptic functions / 650 \\
20.11: Elliptic functions in software / 652 \\
20.12: Applications of elliptic auxiliary functions /
653 \\
20.13: Elementary functions from elliptic auxiliary
functions / 654 \\
20.14: Computing elementary functions via $R_C(x,y)$ /
655 \\
20.15: Jacobian elliptic functions / 657 \\
20.16: Inverses of Jacobian elliptic functions / 664
\\
20.17: The modulus and the nome / 668 \\
20.18: Jacobian theta functions / 673 \\
20.19: Logarithmic derivatives of the Jacobian theta
functions / 675 \\
20.20: Neville theta functions / 678 \\
20.21: Jacobian Eta, Theta, and Zeta functions / 679
\\
20.22: Weierstrass elliptic functions / 682 \\
20.23: Weierstrass functions by duplication / 689 \\
20.24: Complete elliptic functions, revisited / 690 \\
20.25: Summary / 691 \\
21: Bessel functions / 693 \\
21.1: Cylindrical Bessel functions / 694 \\
21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
21.4: Experiments with recurrences for $J_0(x)$ / 705
\\
21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
21.6: Computing $J_n(x)$ / 710 \\
21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
21.8: Computing $Y_n(x)$ / 715 \\
21.9: Improving Bessel code near zeros / 716 \\
21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
21.14: Properties of spherical Bessel functions / 731
\\
21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
21.17: Modified spherical Bessel functions / 743 \\
21.18: Software for Bessel-function sequences / 755 \\
21.19: Retrospective on Bessel functions / 761 \\
22: Testing the library / 763 \\
22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
22.4: Testing cylindrical Bessel functions / 769 \\
22.5: Testing exponent/\penalty \exhyphenpenalty
significand manipulation / 769 \\
22.6: Testing inline assembly code / 769 \\
22.7: Testing with Maple / 770 \\
22.8: Testing floating-point arithmetic / 773 \\
22.9: The Berkeley Elementary Functions Test Suite /
774 \\
22.10: The AT\&T floating-point test package / 775 \\
22.11: The Antwerp test suite / 776 \\
22.12: Summary / 776 \\
23: Pair-precision elementary functions / 777 \\
23.1: Pair-precision integer power / 777 \\
23.2: Pair-precision machine epsilon / 779 \\
23.3: Pair-precision exponential / 780 \\
23.4: Pair-precision logarithm / 787 \\
23.5: Pair-precision logarithm near one / 793 \\
23.6: Pair-precision exponential near zero / 793 \\
23.7: Pair-precision base-$n$ exponentials / 795 \\
23.8: Pair-precision trigonometric functions / 796 \\
23.9: Pair-precision inverse trigonometric functions /
801 \\
23.10: Pair-precision hyperbolic functions / 804 \\
23.11: Pair-precision inverse hyperbolic functions /
808 \\
23.12: Summary / 808 \\
24: Accuracy of the Cody\slash Waite algorithms / 811
\\
25: Improving upon the Cody\slash Waite algorithms /
823 \\
25.1: The Bell Labs libraries / 823 \\
25.2: The {Cephes} library / 823 \\
25.3: The {Sun} libraries / 824 \\
25.4: Mathematical functions on EPIC / 824 \\
25.5: The GNU libraries / 825 \\
25.6: The French libraries / 825 \\
25.7: The NIST effort / 826 \\
25.8: Commercial mathematical libraries / 826 \\
25.9: Mathematical libraries for decimal arithmetic /
826 \\
25.10: Mathematical library research publications / 826
\\
25.11: Books on computing mathematical functions / 827
\\
25.12: Summary / 828 \\
26: Floating-point output / 829 \\
26.1: Output character string design issues / 830 \\
26.2: Exact output conversion / 831 \\
26.3: Hexadecimal floating-point output / 832 \\
26.4: Octal floating-point output / 850 \\
26.5: Binary floating-point output / 851 \\
26.6: Decimal floating-point output / 851 \\
26.7: Accuracy of output conversion / 865 \\
26.8: Output conversion to a general base / 865 \\
26.9: Output conversion of Infinity / 866 \\
26.10: Output conversion of NaN / 866 \\
26.11: Number-to-string conversion / 867 \\
26.12: The {\tt printf} family / 867 \\
26.13: Summary / 878 \\
27: Floating-point input / 879 \\
27.1: Binary floating-point input / 879 \\
27.2: Octal floating-point input / 894 \\
27.3: Hexadecimal floating-point input / 895 \\
27.4: Decimal floating-point input / 895 \\
27.5: Based-number input / 899 \\
27.6: General floating-point input / 900 \\
27.7: The {\tt scanf} family / 901 \\
27.8: Summary / 910 \\
A: Ada interface / 911 \\
A.1: Building the Ada interface / 911 \\
A.2: Programming the Ada interface / 912 \\
A.3: Using the Ada interface / 915 \\
B: C\# interface / 917 \\
B.1: C\# on the CLI virtual machine / 917 \\
B.2: Building the C\# interface / 918 \\
B.3: Programming the C\# interface / 920 \\
B.4: Using the C\# interface / 922 \\
C: C++ interface / 923 \\
C.1: Building the C++ interface / 923 \\
C.2: Programming the C++ interface / 924 \\
C.3: Using the C++ interface / 925 \\
D: Decimal arithmetic / 927 \\
D.1: Why we need decimal floating-point arithmetic /
927 \\
D.2: Decimal floating-point arithmetic design issues /
928 \\
D.3: How decimal and binary arithmetic differ / 931 \\
D.4: Initialization of decimal floating-point storage /
935 \\
D.5: The {\tt } header file / 936 \\
D.6: Rounding in decimal arithmetic / 936 \\
D.7: Exact scaling in decimal arithmetic / 937 \\
E: Errata in the Cody\slash Waite book / 939 \\
F: Fortran interface / 941 \\
F.1: Building the Fortran interface / 943 \\
F.2: Programming the Fortran interface / 944 \\
F.3: Using the Fortran interface / 945 \\
H: Historical floating-point architectures / 947 \\
H.1: CDC family / 949 \\
H.2: Cray family / 952 \\
H.3: DEC PDP-10 / 953 \\
H.4: DEC PDP-11 and VAX / 956 \\
H.5: General Electric 600 series / 958 \\
H.6: IBM family / 959 \\
H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
H.8: Unusual floating-point systems / 966 \\
H.9: Historical retrospective / 967 \\
I: Integer arithmetic / 969 \\
I.1: Memory addressing and integers / 971 \\
I.2: Representations of signed integers / 971 \\
I.3: Parity testing / 975 \\
I.4: Sign testing / 975 \\
I.5: Arithmetic exceptions / 975 \\
I.6: Notations for binary numbers / 977 \\
I.7: Summary / 978 \\
J: Java interface / 979 \\
J.1: Building the Java interface / 979 \\
J.2: Programming the Java MathCW class / 980 \\
J.3: Programming the Java C interface / 982 \\
J.4: Using the Java interface / 985 \\
L: Letter notation / 987 \\
P: Pascal interface / 989 \\
P.1: Building the Pascal interface / 989 \\
P.2: Programming the Pascal MathCW module / 990 \\
P.3: Using the Pascal module interface / 993 \\
P.4: Pascal and numeric programming / 994 \\
Bibliography / 995 \\
Author/editor index / 1039 \\
Function and macro index / 1049 \\
Subject index / 1065 \\
Colophon / 1115",
}
%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Petrick:1971:PSS,
editor = "S. R. Petrick",
booktitle = "{Proceedings of the second symposium on Symbolic and
Algebraic Manipulation, March 23--25, 1971, Los
Angeles, California}",
title = "{Proceedings of the second symposium on Symbolic and
Algebraic Manipulation, March 23--25, 1971, Los
Angeles, California}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 464",
year = "1971",
LCCN = "QA76.5 .S94 1971",
bibdate = "Sat Dec 30 08:56:27 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{Online:1972:OCP,
key = "Online'72",
booktitle = "{Online 72: conference proceedings \ldots{}
international conference on online interactive
computing, Brunel University, Uxbridge, England, 4--7
September 1972}",
title = "{Online 72: conference proceedings \ldots{}
international conference on online interactive
computing, Brunel University, Uxbridge, England, 4--7
September 1972}",
publisher = "Online Computer Systems Ltd",
address = "Uxbridge, England",
pages = "various",
month = sep,
year = "1972",
ISBN = "0-903796-02-3",
ISBN-13 = "978-0-903796-02-6",
LCCN = "QA76.55 .O54 1972",
bibdate = "Fri Dec 29 18:31:29 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Golden:1984:PMU,
editor = "V. Ellen Golden and M. A. Hussain",
booktitle = "{Proceedings of the 1984 MACSYMA Users' Conference:
Schenectady, New York, July 23--25, 1984}",
title = "{Proceedings of the 1984 MACSYMA Users' Conference:
Schenectady, New York, July 23--25, 1984}",
publisher = "General Electric",
address = "Schenectady, NY, USA",
pages = "xv + 567",
year = "1984",
bibdate = "Sat Dec 30 09:01:01 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Fitch:1984:E,
editor = "J. P. Fitch",
booktitle = "{EUROSAM '84: International Symposium on Symbolic and
Algebraic Computation, Cambridge, England, July 9--11,
1984}",
title = "{EUROSAM '84: International Symposium on Symbolic and
Algebraic Computation, Cambridge, England, July 9--11,
1984}",
volume = "174",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 396",
year = "1984",
ISBN = "0-387-13350-X",
ISBN-13 = "978-0-387-13350-8",
LCCN = "QA155.7.E4 I57 1984",
bibdate = "Fri Dec 29 18:17:16 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
series = "Lecture Notes In Computer Science",
acknowledgement = ack-nhfb,
}
@Proceedings{Buchberger:1985:EEC,
editor = "Bruno Buchberger and Bob F. Caviness",
booktitle = "{EUROCAL '85: European Conference on Computer Algebra,
Linz, Austria, April 1--3, 1985: proceedings}",
title = "{EUROCAL '85: European Conference on Computer Algebra,
Linz, Austria, April 1--3, 1985: proceedings}",
volume = "204",
publisher = pub-SV,
address = pub-SV:adr,
pages = "various",
year = "1985",
ISBN = "0-387-15983-5 (vol. 1), 0-387-15984-3 (vol. 2)",
ISBN-13 = "978-0-387-15983-6 (vol. 1), 978-0-387-15984-3 (vol.
2)",
LCCN = "QA155.7.E4 E86 1985",
bibdate = "Fri Dec 29 18:07:46 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "Two volumes.",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
}
@Proceedings{Wexelblat:1987:IIT,
editor = "Richard L. Wexelblat",
booktitle = "{Proceedings of the SIGPLAN '87 Symposium on
Interpreters and Interpretive Techniques, St. Paul,
Minnesota, June 24--26, 1987}",
title = "{Proceedings of the SIGPLAN '87 Symposium on
Interpreters and Interpretive Techniques, St. Paul,
Minnesota, June 24--26, 1987}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "vii + 291",
year = "1987",
ISBN = "0-89791-235-7",
ISBN-13 = "978-0-89791-235-8",
LCCN = "QA76.7 .S54 v.22:7",
bibdate = "Thu Jan 04 18:40:07 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "SIGPLAN Notices, vol. 22, no. 7 (July 1987).",
price = "US\$23.00",
acknowledgement = ack-nhfb,
keywords = "design; interpreters (computer programs) ---
congresses; languages",
subject = "D.0 Software, GENERAL",
}
@Proceedings{Janssen:1988:TCA,
editor = "R. Jan{\ss}en",
booktitle = "{Trends in Computer Algebra, International Symposium
Bad Neuenahr, May 19--21, 1987, Proceedings}",
title = "{Trends in Computer Algebra, International Symposium
Bad Neuenahr, May 19--21, 1987, Proceedings}",
volume = "296",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??",
year = "1988",
ISBN = "3-540-18928-9, 0-387-18928-9",
ISBN-13 = "978-3-540-18928-2, 978-0-387-18928-4",
LCCN = "QA155.7.E4T74 1988",
bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib",
series = "Lecture Notes in Computer Science",
notes = "{\footnotesize Die Beitr{\"a}ge in diesem Band geben
einen guten {\"U}berblick {\"u}ber den aktuellen Stand
der Forschung in verschiedenen f{\"u}r die \CA\
wichtigen Teilgebieten, so z.B. Faktorisierung von
Polynomen, konstruktive Galois Theory,
Termersetzungssysteme und das System Scratchpad II.
\hfill F. Schwarz}",
}
@Proceedings{ACM:1989:PAI,
editor = "{ACM}",
booktitle = "{Proceedings of the ACM-SIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation, ISSAC
'89}",
title = "{Proceedings of the ACM-SIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation, ISSAC
'89}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "399",
year = "1989",
ISBN = "0-89791-325-6",
ISBN-13 = "978-0-89791-325-6",
LCCN = "QA76.95.I59 1989",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "17--19 July 1989",
conflocation = "Portland, OR, USA",
confsponsor = "ACM",
pubcountry = "USA",
}
@Proceedings{Huguet:1989:AAA,
editor = "L. Huguet and A. Poli",
booktitle = "{Applied Algebra, Algebraic Algorithms and
Error-Correcting Codes. 5th International Conference,
AAECC-5 Proceedings}",
title = "{Applied Algebra, Algebraic Algorithms and
Error-Correcting Codes. 5th International Conference,
AAECC-5 Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "417",
year = "1989",
ISBN = "3-540-51082-6",
ISBN-13 = "978-3-540-51082-6",
LCCN = "QA268.A35 1987",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "15--19 June 1987",
conflocation = "Menorca, Spain",
pubcountry = "West Germany",
}
@Proceedings{Davenport:1989:EEC,
editor = "J. H. Davenport",
booktitle = "{EUROCAL '87. European Conference on Computer Algebra
Proceedings}",
title = "{EUROCAL '87. European Conference on Computer Algebra
Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 499",
year = "1989",
ISBN = "3-540-51517-8",
ISBN-13 = "978-3-540-51517-3",
LCCN = "QA155.7.E4E86 1987",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "2--5 June 1987",
conflocation = "Leipzig, East Germany",
confsponsor = "Robotron; Rank Xerox",
pubcountry = "West Germany",
}
@Proceedings{Gianni:1989:SAC,
editor = "P. (Patrizia) Gianni",
booktitle = "{Symbolic and Algebraic Computation. International
Symposium ISSAC '88, Rome, Italy, July 4--8, 1988.
Proceedings}",
title = "{Symbolic and Algebraic Computation. International
Symposium ISSAC '88, Rome, Italy, July 4--8, 1988.
Proceedings}",
volume = "358",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 543",
year = "1989",
ISBN = "3-540-51084-2",
ISBN-13 = "978-3-540-51084-0",
LCCN = "QA76.95 .I57 1988",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "Conference held jointly with AAECC-6.",
series = "Lecture Notes In Computer Science",
acknowledgement = ack-nhfb,
confdate = "4--8 July 1988",
conflocation = "Rome, Italy",
pubcountry = "West Germany",
}
@Proceedings{Mora:1989:AAA,
editor = "T. Mora",
booktitle = "{Applied Algebra, Algebraic Algorithms and
Error-Correcting Codes. 6th International Conference,
AAECC-6, Rome, Italy, July 4--8, 1988. Proceedings}",
title = "{Applied Algebra, Algebraic Algorithms and
Error-Correcting Codes. 6th International Conference,
AAECC-6, Rome, Italy, July 4--8, 1988. Proceedings}",
volume = "357",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 480",
year = "1989",
ISBN = "3-540-51083-4",
ISBN-13 = "978-3-540-51083-3",
LCCN = "QA268 .A35 1988",
bibdate = "Tue Sep 17 06:46:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "Conference held jointly with ISSAC '88.",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
confdate = "4--8 July 1988",
conflocation = "Rome, Italy",
pubcountry = "West Germany",
}
@Proceedings{Watanabe:1990:IPI,
editor = "Shunro Watanabe and Morio Nagata",
booktitle = "{ISSAC '90. Proceedings of the International Symposium
on Symbolic and Algebraic Computation}",
title = "{ISSAC '90. Proceedings of the International Symposium
on Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 307",
year = "1990",
ISBN = "0-89791-401-5",
ISBN-13 = "978-0-89791-401-7",
LCCN = "QA76.95 .I57 1990",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "20--24 Aug. 1990",
conflocation = "Tokyo, Japan",
confsponsor = "Inf. Processing Soc. Japan; Japan Soc. Software Sci.
Technol.; ACM",
pubcountry = "USA",
}
@Proceedings{Miola:1990:DIS,
editor = "A. Miola",
booktitle = "{Design and Implementation of Symbolic Computation
Systems, International Symposium DISCO '90, Capri,
Italy, April 10--12, 1990, Proceedings}",
title = "{Design and Implementation of Symbolic Computation
Systems, International Symposium DISCO '90, Capri,
Italy, April 10--12, 1990, Proceedings}",
volume = "429",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 283",
year = "1990",
ISBN = "0-387-52531-9 (New York), 3-540-52531-9 (Berlin)",
ISBN-13 = "978-0-387-52531-0 (New York), 978-3-540-52531-8
(Berlin)",
LCCN = "QA76.9.S88I576 1990",
bibdate = "Tue Sep 17 06:44:07 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
confdate = "10--12 April 1990",
conflocation = "Capri, Italy",
pubcountry = "West Germany",
}
@Proceedings{Cohen:1991:EIS,
editor = "G. Cohen and P. Charpin",
booktitle = "{EUROCODE '90. International Symposium on Coding
Theory and Applications Proceedings}",
title = "{EUROCODE '90. International Symposium on Coding
Theory and Applications Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 392",
year = "1991",
ISBN = "0-387-54303-1 (New York), 3-540-54303-1 (Berlin)",
ISBN-13 = "978-0-387-54303-1 (New York), 978-3-540-54303-9
(Berlin)",
LCCN = "QA268.E95 1990",
bibdate = "Tue Sep 17 06:41:20 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "5--9 Nov. 1990",
conflocation = "Udine, Italy",
pubcountry = "Germany",
}
@Proceedings{Watt:1991:PIS,
editor = "Stephen M. Watt",
booktitle = "{Proceedings of the 1991 International Symposium on
Symbolic and Algebraic Computation, ISSAC'91, July
15--17, 1991, Bonn, Germany}",
title = "{Proceedings of the 1991 International Symposium on
Symbolic and Algebraic Computation, ISSAC'91, July
15--17, 1991, Bonn, Germany}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiii + 468",
year = "1991",
ISBN = "0-89791-437-6",
ISBN-13 = "978-0-89791-437-6",
LCCN = "QA76.95.I59 1991",
bibdate = "Fri Dec 29 18:17:57 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1991:PAC,
editor = "Anonymous",
booktitle = "{Proceedings 1991 Annual Conference, American Society
for Engineering Education. Challenges of a Changing
World}",
title = "{Proceedings 1991 Annual Conference, American Society
for Engineering Education. Challenges of a Changing
World}",
publisher = "ASEE",
address = "Washington, DC, USA",
pages = "xxi + 2026",
year = "1991",
bibdate = "Tue Sep 17 06:37:45 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "2 vol.",
acknowledgement = ack-nhfb,
confdate = "16--19 June 1991",
conflocation = "New Orleans, LA, USA",
pubcountry = "USA",
}
@Proceedings{Wang:1992:ISS,
editor = "Paul S. Wang",
booktitle = "{International System Symposium on Symbolic and
Algebraic Computation 92}",
title = "{International System Symposium on Symbolic and
Algebraic Computation 92}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 406",
year = "1992",
ISBN = "0-89791-489-9 (soft cover), 0-89791-490-2 (hard
cover)",
ISBN-13 = "978-0-89791-489-5 (soft cover), 978-0-89791-490-1
(hard cover)",
LCCN = "QA76.95.I59 1992",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "27--29 July 1992",
conflocation = "Berkeley, CA, USA",
confsponsor = "ACM",
pubcountry = "USA",
}
@Proceedings{Bronstein:1993:IPI,
editor = "Manuel Bronstein",
booktitle = "{ISSAC'93: proceedings of the 1993 International
Symposium on Symbolic and Algebraic Computation, July
6--8, 1993, Kiev, Ukraine}",
title = "{ISSAC'93: proceedings of the 1993 International
Symposium on Symbolic and Algebraic Computation, July
6--8, 1993, Kiev, Ukraine}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 321",
year = "1993",
ISBN = "0-89791-604-2",
ISBN-13 = "978-0-89791-604-2",
LCCN = "QA 76.95 I59 1993",
bibdate = "Thu Sep 26 05:45:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "ACM order number: 505930.",
abstract = "The following topics were dealt with: algebraic
solutions of equations; computer algebra systems;
algorithm theory and complexity; automated theorem
proving; polynomials; and matrix algebra.",
acknowledgement = ack-nhfb,
classification = "C4210 (Formal logic); C4240 (Programming and
algorithm theory); C7310 (Mathematics computing)",
confdate = "6--8 July 1993",
conflocation = "Kiev, Ukraine",
confsponsor = "ACM",
keywords = "algebra --- data processing --- congresses; Algorithm
theory; Automated theorem proving; Complexity; Computer
algebra; mathematics --- data processing ---
congresses; Matrix algebra; Polynomials",
pubcountry = "USA",
source = "ISSAC '93",
sponsor = "Association for Computing Machinery.",
thesaurus = "Computational complexity; Mathematics computing;
Matrix algebra; Polynomials; Symbol manipulation;
Theorem proving",
}
@Proceedings{Fitch:1993:DIS,
editor = "J. Fitch",
booktitle = "{Design and Implementation of Symbolic Computation
Systems International Symposium, DISCO '92
Proceedings}",
title = "{Design and Implementation of Symbolic Computation
Systems International Symposium, DISCO '92
Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "214",
year = "1993",
ISBN = "0-387-57272-4 (New York), 3-540-57272-4 (Berlin)",
ISBN-13 = "978-0-387-57272-7 (New York), 978-3-540-57272-5
(Berlin)",
LCCN = "QA76.9.S88I576 1992",
bibdate = "Tue Sep 17 06:37:45 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "13--15 April 1992",
conflocation = "Bath, UK",
pubcountry = "Germany",
}
@Proceedings{Jacob:1993:PSI,
editor = "G. Jacob and N. E. Oussous and S. Steinberg",
booktitle = "{Proceedings SC 93. International IMACS Symposium on
Symbolic Computation. New Trends and Developments}",
title = "{Proceedings SC 93. International IMACS Symposium on
Symbolic Computation. New Trends and Developments}",
publisher = "LIFL Univ. Lille",
address = "Lille, France",
pages = "vii + 239",
year = "1993",
bibdate = "Tue Sep 17 06:35:39 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "14--17 June 1993",
conflocation = "Lille, France",
confsponsor = "IMACS-AICA",
pubcountry = "France",
}
@Proceedings{Miola:1993:DIS,
editor = "A. Miola",
booktitle = "{Design and Implementation of Symbolic Computation
Systems International Symposium. DISCO '93 Gmunden,
Austria, September 15--17, 1993: Proceedings}",
title = "{Design and Implementation of Symbolic Computation
Systems International Symposium. DISCO '93 Gmunden,
Austria, September 15--17, 1993: Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 383",
year = "1993",
ISBN = "3-540-57235-X",
ISBN-13 = "978-3-540-57235-0",
LCCN = "QA76.9.S88I576 1993",
bibdate = "Fri Dec 29 12:46:02 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "15--17 Sept. 1993",
conflocation = "Gmunden, Austria",
pubcountry = "Germany",
}
@Proceedings{ACM:1994:IPI,
editor = "{ACM}",
booktitle = "{ISSAC'94. Proceedings of the International Symposium
on Symbolic and Algebraic Computation}",
title = "{ISSAC'94. Proceedings of the International Symposium
on Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 359",
year = "1994",
ISBN = "0-89791-638-7",
ISBN-13 = "978-0-89791-638-7",
LCCN = "QA76.95.I59 1994",
bibdate = "Tue Sep 17 06:29:18 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "20--22 July 1994",
conflocation = "Oxford, UK",
confsponsor = "ACM",
pubcountry = "USA",
}
@Proceedings{Calmet:1994:RWC,
editor = "J. Calmet",
booktitle = "{Rhine Workshop on Computer Algebra. Proceedings}",
title = "{Rhine Workshop on Computer Algebra. Proceedings}",
publisher = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "v + 224",
year = "1994",
bibdate = "Tue Sep 17 06:32:41 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
confdate = "22--24 March 1994",
conflocation = "Karlsruhe, Germany",
confsponsor = "Universit{\"a}t Karlsruhe",
pubcountry = "Germany",
}
@Proceedings{Levelt:1995:IPI,
editor = "A. H. M. Levelt",
booktitle = "{ISSAC '95: Proceedings of the 1995 International
Symposium on Symbolic and Algebraic Computation: July
10--12, 1995, Montr{\'e}al, Canada}",
title = "{ISSAC '95: Proceedings of the 1995 International
Symposium on Symbolic and Algebraic Computation: July
10--12, 1995, Montr{\'e}al, Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xviii + 314",
year = "1995",
ISBN = "0-89791-699-9",
ISBN-13 = "978-0-89791-699-8",
LCCN = "QA 76.95 I59 1995",
bibdate = "Thu Sep 26 05:34:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
note = "ACM order number: 505950",
series = "ISSAC -PROCEEDINGS- 1995",
abstract = "The following topics were dealt with: differential
equations; visualisation; algebraic numbers;
algorithms; systems; polynomial and differential
algebra; seminumerical methods; greatest common
divisors; and.",
acknowledgement = ack-nhfb,
classification = "C4100 (Numerical analysis); C4170 (Differential
equations); C7310 (Mathematics computing)",
confdate = "10--12 July 1995",
conflocation = "Montr{\'e}al, Que., Canada",
confsponsor = "ACM",
keywords = "algebra --- data processing --- congresses; Algebraic
numbers; Algorithms; Differential algebra; Differential
equations; Greatest common divisors; mathematics ---
data processing --- congresses; Polynomial;
Seminumerical methods; Systems; Visualisation",
pubcountry = "USA",
source = "ISSAC '95",
thesaurus = "Data visualisation; Differential equations; Group
theory; Numerical analysis; Symbol manipulation",
}
@Proceedings{Dooley:1999:IJS,
editor = "Sam Dooley",
booktitle = "{ISSAC 99: July 29--31, 1999, Simon Fraser University,
Vancouver, BC, Canada: proceedings of the 1999
International Symposium on Symbolic and Algebraic
Computation}",
title = "{ISSAC 99: July 29--31, 1999, Simon Fraser University,
Vancouver, BC, Canada: proceedings of the 1999
International Symposium on Symbolic and Algebraic
Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxii + 311",
year = "1999",
ISBN = "1-58113-073-2",
ISBN-13 = "978-1-58113-073-7",
LCCN = "QA76.95 .I57 1999",
bibdate = "Sat Mar 11 16:51:59 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Brown:2007:PIS,
editor = "C. W. Brown",
booktitle = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
title = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2007",
ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
ISBN-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1
(CD-ROM)",
LCCN = "QA76.5 S98 2007",
bibdate = "Fri Jun 20 08:53:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
note = "ACM order number 505070.",
acknowledgement = ack-nhfb,
}
@Proceedings{Shi:2007:CSIb,
editor = "Yong Shi and Geert Dick van Albada and Jack Dongarra
and Peter M. A. Sloot",
booktitle = "{Computational Science --- ICCS 2007: 7th
International Conference, Beijing, China, May 27 ---
30, 2007, Proceedings, Part II}",
title = "{Computational Science --- ICCS 2007: 7th
International Conference, Beijing, China, May 27 ---
30, 2007, Proceedings, Part II}",
volume = "4488",
publisher = pub-SV,
address = pub-SV:adr,
pages = "153 (est.)",
year = "2007",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-540-72586-2",
ISBN = "3-540-72585-7 (print), 3-540-72586-5 (e-book)",
ISBN-13 = "978-3-540-72585-5 (print), 978-3-540-72586-2
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "????",
bibdate = "Wed Dec 19 15:19:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
series = ser-LNCS,
URL = "http://www.springerlink.com/content/978-3-540-72586-2",
acknowledgement = ack-nhfb,
}