Symbolic Computation Program/Computer Algebra Systemhttp://maxima.sourceforge.net
Maxima is a full symbolic computation program. It is full featured
doing symbolic manipulation of polynomials, matrices, rational
functions, integration, Todd-coxeter, graphing, bigfloats. It has a
symbolic debugger source level debugger for maxima code. Maxima is
based on the original Macsyma developed at MIT in the 1970's. It is
quite reliable, and has good garbage collection, and no memory leaks.
It comes with hundreds of self tests.