http://axcas.net is an online computer algebra system I've been working on. I'm working to finish the programming language which is based on C, and I'm adding an ode solver which I plan to use to evaluate special functions.
I release code into the public domain hoping it will be useful. There's some fast code for Groebner basis computations using the F4 algorithm (parallelized - article to follow), and some routines for machine integers e.g. discrete logarithm, factoring, and prime counting.