MathematicaMathematica is a scientific calculation package, which contains a Computer Algebra System, developed by Wolfram Research.
Mathematica is an impressive piece of software, because contrary to other technical symbolic calculation software, it is based on a real, well-designed programming language, hence can be extended in ways both clean and advanced, allowing for incremental enhancements. Thus, even if a given version of Mathematica does a few things not as well as a rival software, Mathematica will win on its overall capabilities, and can easily be made to further scale up on the long run, whereas the rival software just can't adapt.
Unhappily, it is expensive proprietary software only, thus cannot benefit from open development in a free world. This is a very sad situation, as the world really needs some reliable, free (for in the software world, freedom is the way to optimize reliability), symbolic calculation software.
Mathematica is available for Linux as well as for lesser platforms.
On the other hand, I've been told that I was overly generous towards Mathematica (partly because I didn't use it deeply enough to see its shortcomings, whereas Maple disgusted me).
Wolfram Research's WWW sites: