— This is interesting question.
Answer by Harris B. Daniels:
In my opinion, the best free/open source math software today is SAGE. It isn't as well developed as MATLAB, but most free software isn't.
SAGE is avalable for free at http://www.sagemath.org and there is a nice online reference manual here http://www.sagemath.org/doc/reference/ The reference manual is filled with examples which I have found o be very helpful.
The reason I love sage is that it is built on python. So it is essentially python with a bunch of advanced math commands built added. This makes it very easy to write small programs to do fairly complex computations. Thus if there isn't a function already built in, it isn't very hard to add yourself.
If you are skeptical, you can go to http://www.sagenb.org and use their free online calculator. It has been acting up recently, so it may not be the best way to try out the software.