Yesterday, on the train, I met another young scientist, and he introduced me to the mathematical software package SAGE. It is comparable to Mathematica, Maple and MATLAB in terms of performance, ease of use and portability but, in sharp contrast to the former products, freely available on the internet (via http://www.sagemath.org/). SAGE also understands commands known from several other similar packages (including Mathematica and Maple), so migration from there should be very easy.

I had a closer look today and will definitely give it some detailed trials but if any of you already have experience with this tool, please share it here. Thanks!

See also
http://en.wikipedia.org/wiki/SAGE_%28computer_algebra_system%29 and
http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_syst... .