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AXIOM: open source computer algebra system

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William Page
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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 attracked 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. 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. 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].
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Vol. 41, No. 3, September 2007 Conference Abstracts
AXIOM – Open Source Computer Algebra System
William S. Page
Axiom Developer
bill.page@newsynthesis.org
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 attracked 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.
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.
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].
References
[1] Jenks, R.J. and Sutor, R.S. “Axiom – The Scientific Computation System” Springer-Verlag New York (1992) ISBN
0-387-97855-0
[2] Daly, Tim, “Axiom Computer Algebra System”
http://savannah.nongnu.org/projects/axiom
[3] Knuth, Donald E., “Literate Programming” Center for the Study of Language and Information ISBN 0-937073-81-4
Stanford CA (1992)
[4] Page, William, “The Axiom Wiki Website”
http://wiki.axiom-developer.org
[5] Portes, Jose Alfredo, “Doyen”
http://wiki.axiom-developer.org/Doyen
114
A Bibliography of Publications about the AXIOM (formerly, Scratchpad) Symbolic Algebra Language
Article
AAECC-6 [Mor89]. abstract [JSW86]. abstraction [Boe89]. ACM-SIGSAM [ACM89]. Advances [Fat90]. advantages [MR90]. Algebra [Jen84a]. Algebraic [DST88]. algebras [Kos91]. algorithm [GM86]. algorithme [Fou90]. Algorithms [DST88]. Angeles [Pet71]. Annual [Ano95]. Application [And88]. Applications [Pur86]. applied [Mat89, HP89]. April [BC85].
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Algorithmic differentiation in Axiom
Conference Paper
  • Jul 2007
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.
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AXIOM: The Scientific Computation System
Book
  • Jan 1992
Recent advances in hardware performance and software technology have made possible a wholly different approach to computational mathematics. Symbolic computation systems have revolutionized the field, building upon established and recent mathematical theory to open new possibilities in virtually every industry. Formerly dubbed Scratchpad, AXIOM is a powerful new symbolic and numerical system developed at the IBM Thomas J. Watson Research Center. AXIOM's scope, structure, and organization make it outstanding among computer algebra systems. AXIOM: The Scientific Computation System is a companion to the AXIOM system. The text is written in a straightforward style and begins with a spirited foreword by David and Gregory Chudnovsky. The book gives the reader a technical introduction to AXIOM, interacts with the system's tutorial, accesses algorithms newly developed by the symbolic computation community, and presents advanced programming and problem solving techniques. Eighty illustrations and eight pages of color inserts accompany text detailing methods used in the 2D and 3D interactive graphics system, and over 2500 example input lines help the reader solve formerly intractable problems.
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The Axiom Wiki Website
  • William Page
Page, William, " The Axiom Wiki Website " http://wiki.axiom-developer.org
Axiom Computer Algebra System
  • Daly Tim
Daly, Tim, "Axiom Computer Algebra System" http://savannah.nongnu.org/projects/axiom
Center for the Study of Language and Information
  • Donald E Knuth
Knuth, Donald E., "Literate Programming" Center for the Study of Language and Information ISBN 0-937073-81-4