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FriCAS

From Wikipedia, the free encyclopedia
Computer algebra system
FriCAS
DeveloperWaldek Hebisch + independentgroup of people
Stable release
1.3.12 / 3 June 2025; 5 months ago (2025-06-03)
Implementation languageSPAD,Aldor, Boot,Common Lisp
OSCross-platform
LicenseModified BSD License
Filename extensions.spad,.input,.as
Websitefricas.github.io

FriCAS is a general purposecomputer algebra system with a strong focus on mathematical research and development of newalgorithms. It comprises aninterpreter, acompiler and a still-growinglibrary[1]of more than 1,000 domains and categories.

FriCAS provides astrongly typedhigh-level programming language called SPAD and a similar interactive languagethat usestype-inferencing for convenience.Aldor was intentionally developed being the next generation compile preparation for the Axiom CAS and itsforks. FriCAS optionally allows running Aldor programs (aldor is not required for compiling or running fricas). Both languagesshare a similar syntax and a sophisticated (dependent)type system.[2][3][4]

FriCAS is comprehensively documented and available assource code and as a binarydistribution for the most commonplatforms. Compiling the Axiom lisp resources requires besides other prerequisites aCommon Lisp environment and freely available asopen source). A list of (incompatible) CL implementations are supported by fricas lisp code.

FriCAS runs on manyPOSIX platforms such asLinux,macOS,Unix,BSD as well as underCygwin andMicrosoft Windows (WSL).

History

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Two computer algebra systems namedScratchpad were developed byIBM. The first one was started in 1965 by James Griesmer[5] at the request ofRalph Gomory, and written inFortran.[6] The development of this software was stopped before any public release. The second Scratchpad, originally namedScratchpad II, was developed from 1977 on, atThomas J. Watson Research Center, under the direction of Richard Dimick Jenks.[7]

The design is principally due to Richard D. Jenks (IBM Research),James H. Davenport (University of Bath), Barry M. Trager (IBM Research), David Y.Y. Yun (Southern Methodist University) andVictor S. Miller (IBM Research). Early consultants on the project were David Barton (University of California, Berkeley) andJames W. Thatcher (IBM Research). Implementation included Robert Sutor (IBM Research), Scott C. Morrison (University of California, Berkeley), Christine J. Sundaresan (IBM Research), Timothy Daly (IBM Research),Patrizia Gianni (University of Pisa), Albrecht Fortenbacher (Universitaet Karlsruhe),Stephen M. Watt (IBM Research and University of Waterloo), Josh Cohen (Yale University), Michael Rothstein (Kent State University), Manuel Bronstein (IBM Research), Michael Monagan (Simon Fraser University), Jonathan Steinbach (IBM Research), William Burge (IBM Research), Jim Wen (IBM Research), William Sit (City College of New York), and Clifton Williamson (IBM Research).[8]

Scratchpad II was renamedAxiom when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold toNAG. In 2001, it was withdrawn from the market and re-released to Tim Daly under theModified BSD License. In 2007, Axiom wasforked asFriCAS by Waldek Hebisch following encouragement from Tim Daly[9] to resolve disagreements about project goals.[10]

Examples

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FriCAS has a largely complete implementation of theRisch–Bronstein–Trager algorithm.[11]

Another useful feature isstream:

)set stream calculate 5exp_series := series(exp x, x=0)

    1+x+12 x2+16 x3+124 x4+1120 x5+O(x6){\displaystyle \ \ \ \ 1+x+{{\frac {1}{2}}\ {{x}^{2}}}+{{\frac {1}{6}}\ {{x}^{3}}}+{{\frac {1}{24}}\ {{x}^{4}}}+{{\frac {1}{120}}\ {{x}^{5}}}+{O\left({{x}^{6}}\right)}}

Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)

So any coefficient may be retrieved, for instancen=40{\displaystyle n=40}:

coefficient(exp_series,40)

    1815915283247897734345611269596115894272000000000{\displaystyle \ \ \ \ {\frac {1}{815915283247897734345611269596115894272000000000}}}

Type: Expression(Integer)


See also

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References

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  1. ^FriCAS API
  2. ^Poll, Erik; Thompson, Simon (May 1998)."Adding the axioms to Axiom: Towards a system of automated reasoning in Aldor"(Monograph). Retrieved2017-01-27.
  3. ^Poll, Erik; Thompson, Simon."The Type System of Aldor"(Monograph). Retrieved2017-01-27.
  4. ^Poll, Erik; Thompson, Simon."Integrating Computer Algebra and Reasoning through the Type System of Aldor". In Hélène Kirchner; Christophe Ringeissen (eds.).Frontiers of Combining Systems. 3rd International Workshop on Frontiers of Combining Systems (FroCoS 2000). Vol. 1794. Nancy, France: Springer-Verlag Berlin. pp. 136–150.ISBN 978-3-540-67281-4. Retrieved2017-01-27.
  5. ^Fitch, John (July 23, 2012)."James Griesmer 1929--2011".ACM Communications in Computer Algebra.46 (1/2):10–11.doi:10.1145/2338496.2338499.S2CID 36788754.
  6. ^"Axiom Computer Algebra System".axiom-developer.org.
  7. ^"Richard D. Jenks Biographical Information".www.eecis.udel.edu.
  8. ^"EUROCAL '85 | SpringerLink".www.springer.com.
  9. ^"[Axiom-developer] A modest proposal".lists.nongnu.org.
  10. ^"History — FriCAS".fricas.github.io.
  11. ^"MathAction RischImplementationStatus".wiki.fricas.org. Retrieved2021-10-03.

External links

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Related:

Open-source
Proprietary
Discontinued
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