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This page will survey open source computer algebra systems (OSCAS's).

A computer algebra system (CAS) is a mathematical software package capable of symbolic manipulation. The commercial CAS industry is big business. Few people know more about the CAS industry than Darren McIntyre, VP of Worldwide Sales at Maplesoft. He estimates the worldwide yearly expenditures on computer algebra (buying licenses, employee salaries, and so on) is at least $ 600 million. Clients include not just students and universities, but diverse industries who often find that a CAS is a convenient programming environment to model industrial problems.

The terrain

I have left out CAFE (Computer Algebra and Functional Equations), a group writing a collection of CAS libraries (see [http://www-sop.inria.fr/cafe/main-e.html CAFE]). They appear to be written in Aldor and Maple by (the late) Manuel Bronstein. I cannot determine the license (if any) they are released under. I am also unsure if the "open source" licenses of LiDIA, MAS, and Scilab are compatible with the above-mentioned open source definition. Several of these are under very active development and some of these are essentially dead. Two other sources of information are the Computer algebra handbook [GKW OSCAS#references] and the internet sites [CA].

In any case, we see from this table that there are a lot of open source computer algebra systems out there. Some of these are special purpose (such as Symmetrica) and others are general purpose (such as Axiom). We shall start this series by surveying Maxima, a general purpose CAS.

Maxima

Maxima is perhaps the most popular general purpose open source CAS. It's latest release (as of November 2006) is 5.10.

History

The Maxima homepage and the Maxima FAQ (this information is basically due to Stavros Macrakis) explains some history.

Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. Symbolics licensed Macsyma from M.I.T. and registered Macsyma" as a trademark at some point (presumably with M.I.T.'s permission). When Macsyma source ceased to be freely available, pressure was put on M.I.T. (mostly by Richard Fateman) to transfer the code which had been developed largely with Department of Energy (DOE) funding to the DOE, which then released it to others under certain conditions. That codebase was called DOE Macsyma.

The Maxima branch of Macsyma was maintained by William Schelter from 1982 until he passed away in 2001. In 1998 he obtained permission to release the source code under the GNU General Public License (GPL). Since his passing a group of users and developers has formed to bring Maxima to a wider audience.

Pages 8-9 of the Maxima book \cite{Max} has a more detailed history. More Macsyma history can be found in \cite{GKW}.

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References

• [CA] [http://en.wikipedia.org/wiki/List_of_computer_algebra_systems]

[http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems]

[http://wiki.axiom-developer.org/RosettaStone]

• [GKW] J. Grabmeier, E. Kaltofen, V. Weispfenning, Computer algebra handbook, Springer, 2003.

• [Mc] D. McIntyre, private communication, 11-2006.

• [Max] Paulo Ney de Souza, Richard J. Fateman, Joel Moses, Cliff Yapp, The Maxima Book,

19th September 2004. Available online at: [Maxima book http://maxima.sourceforge.net/docs/maximabook/maximabook-19-Sept-2004.pdf]

[BI-G] A. Ben-Israel, R. Gilbert, Computer-supported calculus, Springer-Verlag, 2002.