%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.18",
%%%     date            = "15 August 2014",
%%%     time            = "18:59:18 MDT",
%%%     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             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "32676 4296 20552 200917",
%%%     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 1.18, the year coverage looked
%%%                        like this:
%%%
%%%                             1971 (   3)    1984 (   6)    1997 (   0)
%%%                             1972 (   3)    1985 (   2)    1998 (   1)
%%%                             1973 (   0)    1986 (   4)    1999 (   2)
%%%                             1974 (   1)    1987 (   5)    2000 (   0)
%%%                             1975 (   1)    1988 (   8)    2001 (   1)
%%%                             1976 (   1)    1989 (  18)    2002 (   1)
%%%                             1977 (   1)    1990 (   7)    2003 (   3)
%%%                             1978 (   0)    1991 (  16)    2004 (   1)
%%%                             1979 (   0)    1992 (  16)    2005 (   9)
%%%                             1980 (   0)    1993 (  10)    2006 (   2)
%%%                             1981 (   0)    1994 (  11)    2007 (   6)
%%%                             1982 (   0)    1995 (   7)    2008 (   1)
%%%
%%%                             Article:         34
%%%                             Book:            17
%%%                             InCollection:     1
%%%                             InProceedings:   48
%%%                             Manual:           1
%%%                             MastersThesis:    2
%%%                             Proceedings:     28
%%%                             TechReport:      16
%%%
%%%                             Total entries:  147
%%%
%%%                        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|http://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 =          "http://dx.doi.org/10.1145806266",
  bibdate =      "Thu Jul 26 08:45:53 2001",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/obscure.bib;
                 http://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;
                 http://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;
                 http://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 =          "http://dx.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 =    "http://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 =          "http://dx.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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://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;
                 http://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;
                 http://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;
                 http://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;
                 http://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;
                 http://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;
                 http://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 =          "http://dx.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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://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 =          "http://dx.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 =    "http://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;
                 http://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;
                 http://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 =    "http://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;
                 http://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;
                 http://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;
                 http://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 =    "http://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;
                 http://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;
                 http://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 =    "http://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;
                 http://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;
                 http://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 =    "http://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 =    "http://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;
                 http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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;
                 http://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 =    "http://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;
                 http://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 =          "http://dx.doi.org/10.1145.96895",
  bibdate =      "Thu Jul 26 09:04:25 2001",
  bibsource =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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;
                 http://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 =    "http://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;
                 http://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 =    "http://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 =    "http://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 =    "http://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",
  bibdate =      "Tue Sep 17 06:44:07 MDT 1996",
  bibsource =    "http://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 =    "http://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 =    "http://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;
                 http://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 =    "http://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 =    "http://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 =    "http://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;
                 http://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;
                 http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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;
                 http://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",
  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",
  bibdate =      "Fri Dec 29 18:16:15 1995",
  bibsource =    "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/axiom.bib",
}

@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 =    "http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://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;
                 http://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/;
                 http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 http://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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 http://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 =    "http://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/;
                 http://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 =          "http://dx.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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =          "http://dx.doi.org/10.1023/A:1026553731272",
  ISSN =         "0960-3174",
  ISSN-L =       "0960-3174",
  MRclass =      "Database Expansion Item",
  MRnumber =     "MR1837142",
  bibsource =    "http://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/;
                 http://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 =    "http://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 =    "http://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 =    "http://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/;
                 http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =          "http://dx.doi.org/10.1007/978-3-540-72586-2_35",
  bibdate =      "Tue Aug 12 10:36:21 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 http://www.math.utah.edu/pub/tex/bib/magma.bib;
                 http://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 =    "http://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 =          "http://doi.acm.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/;
                 http://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 =          "http://doi.acm.org/10.1145/1277548.1277595",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://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 =          "http://doi.acm.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/;
                 http://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",
}

%%% ====================================================================
%%% 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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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;
                 http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 http://www.math.utah.edu/pub/tex/bib/issac.bib;
                 http://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 =          "http://dx.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 =    "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib;
                 http://www.math.utah.edu/pub/tex/bib/magma.bib;
                 http://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,
}