- Maxima Maxima is a "Symbolic Computation Program" like the commercial ones, Macsyma, Maple and Mathematica. Maxima is a Common Lisp implementation of MIT's Macsyma system, sometimes known as DoE Macsyma. It is now "free software."
- Scilab is a full-featured, interactive computation package, similar to Matlab, but not an exact clone. It has graphics and many applications supported. It comes in binary versions for Linux and MSWindows as well as in source code. There is a book about it available as well. (See the linked site.)
- Octave is a Matlab clone by the free software foundation. It is included in many Linux distributions and the sources are available.
Library functions for programming
- GAMS Guide to Available Mathematical Software, by NIST, is the place to start looking for any needed mathematical subroutine package. It is not all free, but the guide will say which routines are free and which are not.
- FFTW is the "fastest fast Fourier transform in the west"