Computer Algebra Programs

In some cases I have written programs to help with evaluating and illustrating mathematical topics (see this page) but writing a general purpose abstract algebra program is not really sensible when there already exist such programs so I have also used Axiom/FriCAS:

Axiom

Axiom is a free general purpose computer algebra system. It has been in development since 1971 originally as Scratchpad by researchers at IBM under the direction of Richard Dimick Jenks. In the 1990s it was sold to NAG and given its current name. In 2001 it was withdrawn from the market and released to Tim Daly, the project lead developer, under the Modified BSD License. In 2007, Axiom was forked into two different open source projects: OpenAxiom, and FriCAS.

It is a pity that the developer effort and user resources are fragmented by these forks in this way but sometimes it can help to have several varients because if one fork does not work very well with your operating system then there is a chance that another fork will work better.

So I suggest you try one or more of the versions availible and see which works best with your computer and operating system etc. For more information see:

• My page about Axiom.
• My page about FriCAS.

No slight to OpenAxiom intended, Once I found a setup that worked then I just havent got round to trying anything else yet.

Just to explain the issues involved I will go through some of my experiences in using these programs with the openSUSE operating system, you may have different expeiences so I'm not suggesting you make the same choices as me, if you have any problems both forks have very helpful email groups.

My Expieriences using openSUSE 11.1

Just by chance I first tried Axiom (see this page for details). At first this went very well except that anything involving the draw function failed with:

>> System error:
Unknown bfd format

This was a bit annoying, but since I did not need to use the draw function it did not hold be back, however when I first compiled an SPAD program and tried to use it I got the exact same error:

>> System error:
Unknown bfd format

This was a big problem so I asked on the email group and altough they are helpful and friendly there were no answers to this particular problem.

So at this stage I thought I would try another fork: FriCAS (see this page for details). At first this was worse, I could not even get the program to start, every time I ran the script to run FriCAS, the cursor steped down about 3 lines and then, after a short delay, returned to the command line prompt without any error messages on the system at all.

So I asked about this on the FriCAS email group and they also are are helpful and friendly there, in the end Bill Page found the answer, it seems that on SuSE the virtual memory limit is set rather low by default. The command:

ulimit -v unlimited

added to the startup script removed this limit and now the FriCAS program works perfectly, including draw function and user compiled programs.

Other Computer Algebra Programs

There is a wider list on this page:
http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems
Here are my own comments on some of them:

Program	Comments
Axiom/FriCAS/OpenAxiom http://www.axiom-developer.org/ http://fricas.sourceforge.net/ http://www.open-axiom.org/	pro's Covers a wide range of algebras, includes equation solvers. con's Steep learning curve, need to learn SPAD language, very poor error messages, no IDE environment, no direct access to class library. Language SPAD/Aldor - written in mixture of lisp and C.
DoCon http://www.haskell.org/docon/	pro's Can program in Haskell environment. con's Non-standard open source licence. Does not cover such a wide range of algebras as Axiom. Language Haskell.
UACalc http://www.uacalc.org/	Universal Algebra Calculator - a more specialised program just for universal algebra. Language Java.
Scalala http://code.google.com/p/scalala/	pro's This is an internal DSL (Domain Specific Language) for Scala and so users have full access to Java environment. con's Only supports numeric programming. Language Scala.
kiama http://code.google.com/p/kiama/wiki/Lambda2	Includes a library for parsing lambda calculus, but not a general mathematics language program. Language Scala
Java Algebra System http://krum.rz.uni-mannheim.de/jas/	Language Java and Java Python
SymJA http://code.google.com/p/symja/	Language Java.
Gap http://www.gap-system.org/	discrete algebra no longer supported
Macaulay2 http://www.math.uiuc.edu/Macaulay2/	Own Language
Maxima http://maxima.sourceforge.net/	Lisp
Octave http://www.gnu.org/software/octave/	numerical

SPAD Language

Although the Axiom/FriCAS computer algebra system is written in Lisp, users of the program don't need to know Lisp. The SPAD (a contraction of Scratchpad) language is used to impement particular algebras and so on.

For more information about the SPAD language see this page.

Set Symbols

Installing Linux SUSE 11.2