GNU Octave is a free/open alternative for Matlab, which is mostly compatible with things built in Matlab. Just make sure your code runs in Octave and you don't

GNU Octave is a free/open alternative for Matlab, which is mostly compatible with things built in Matlab. Just make sure your code runs in Octave and you don't have to do any porting. There's no viable alternative to Mathematica, let alone a compatible one. Even for the basic stuff I've used Mathematica (student license) for, basic symbolic integration, differentiation and simplification, I get inferior results from Sympy and Maxima. I haven't tried XCas yet, some say it is better. And this is only talking about the computer algebra capabilities. Mathematica has all sorts of nice tools for doing plots, interactive UIs and other stuff.