You know, I fear to suggest anything but Perl on a Perl board, but what about Maple? It's great for solving all sorts of math problems, and it can double as a programming language (albeit not your normal programming language).

I used to loathe Maple because all of your stupid low level math classes would make you use it, when you could do the problem directly in your head. Then I used it in my System State Modelling class (I know, it sounds like it wouldn't be the best of ideas for that), we were forced to, and while I thought there was better things we could've used, it did force me to learn Maple.

As I learned it, I realized I should've been using it in my higher level math classes, like Linear Algebra, Differential Equations, etc. I'm certain it has what you're looking for.

Just a suggestion... feel free to flame.