Mathematica is expensive and several kinds of weird (it gets better once you figure out that it's trying to camouflage the fact that it's a Lisp), but especiall

Mathematica is expensive and several kinds of weird (it gets better once you figure out that it's trying to camouflage the fact that it's a Lisp), but especially the newer version seem to have very nice visualization tools as well as a large collection of mathematical-ish functions. (It's not "C++ fast", of course.)