There are a number of free math programs available for Linux.
APL and J
The following examples are taken from Ken Iverson's language J, the latest version of APL, which is available at no charge for Linux and other operating systems under GPL3. Iverson wrote books on Arithmetic, Algebra, and Calculus, all published by APL Press. There are other books in APL on probability, statistics, cryptanalysis, computer graphics, and computer design. Springer-Verlag published APL Programs for the Mathematics Classroom, which came out of the I-APL project to create free math software for schools. In the 1960s IBM loaned a 360 computer to a nearby school system for teaching math, starting in First Grade.
NB. The J comment symbol is NB. NB. The interpreter ignores anything from there to the end of the current line. 1+2 NB. The interpreter indents to wait for input. Results of expressions are displayed with no indent. 3 1-2 NB. Negative result _1 1%2 NB. Division 0.5 2 * 3 + 5 NB. Right to left evaluation; no function priority 16 2 * (3 + 5) 16 (2 * 3) + 5 NB. Parentheses change order of evaluation 25 1 2 3 + 2 NB. Add number to each element of vector 3 4 5 a =. 3 9 7 NB. Assignment +/a NB. Sum 19 #a NB. Number of items 3 (+/a)%(#a) NB. Mean 6.333 (+/ % #) a NB.(f g h) a is evaluated as (f a) g (h a) 6.333 a * a 9 81 49 +/ a * a 139 a +/.* a NB. Vector inner product 139 3 >. 2 3 3 <. 2 2 >. / a 9 <. / a 3 (>. / a) - <. / a 6 range =. (>./) - (<./) NB. Function assignment range a 6
A Free Software version of Macsyma.
Ed Borasky, 25 December 2007: Maxima runs just fine on the XO! In fact, I installed the wxMaxima GUI and that works too. The fonts are a tad big -- I haven't attempted to reconfigure them. Depending on which Maxima run time you pick, the whole thing can get as big as 40 MB of disk space, but I think it's worth it. I haven't found anything smaller that's as comprehensive.
Plus, you get a Lisp interpreter (GCL, CMUCL, Clisp or SBCL). GCL is the default, but I've heard that project is drifting into obscurity, as is CMUCL. So your choices really are between Clisp and SBCL. I picked SBCL, but it is the one that takes up the most disk space.
WIMS (WWW Interactive Multipurpose Server) glues together several math libraries and a quiz engine that reads OEF (Open Exercise Format) files to create a server that's ideal for interactive mathematics and other education.
An article from Free Software Magazine is probably the best introduction to it.