calculation software

[theytsejam]

Hey all,
I'm in a quantum mechanics class, and my professor seems quick to dole out problem sets with calculations which absolutely require a computer to do. Is there any (preferably free) ubuntu software which can help me with these? I'm looking for something that can evaluate nasty integrals analytically and diagonalize big (6x6 and above) matrices.with variable entries. I've been using mathematica for the matrices and it works quite well, but I don't have access to it directly so I have to bug my friend to log me on to one of his lab computers in order to use it.

So can anyone recommend anything?

Thanks,
Greg

[colo]

I don't know if these applications stand a chance to fulfill your specific requirements, but I used to do quite well with them in my computer science math classes:

There's maxima ( http://maxima.sf.net/ ), a pretty much full-fledged CAS written in Common LISP, and the most advanced free CAS I know of.
Then there's mathomativ, which is rather small and light-weight; you might even get it to run on PDAs and such, once compiled properly. (Check http://www.mathomatic.org/ )

You might also want ot take a look at one of Wikipedia's great lists of just about anything:
http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems