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Some years ago I used MuPAD as a free computer algebra system. However since 2005 it's not free anymore. So, are there any good free or even better open-source computer algebra systems for linux coming close to commercial products like mathematica or maple?

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4 Answers

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I would suggest SAGE. It is GPL-licensed software and includes lots of components. SAGE also has a nice tutorial for the first (and second) steps.

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SAGE seems to be promising. Is it necessary to run it in a browser or is there also a "local" graphical interface (which is not a web browser)? – student Sep 11 '11 at 9:37
Is it true that maxima is a part of SAGE, i.e. everything you can do in maxima you can also do in SAGE? – student Sep 11 '11 at 9:57
@user5289 Sage provides two user interfaces, command line (or script) and the web-based notebook. There's no non-web GUI. Maxima is a part of sage and sage uses maxima automatically to solve a number of problems. You can call maxima function directly from within sage if you want to use all of maxima. – Jan Sep 11 '11 at 20:28
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My first suggestion would be Maxima, but it seems I'm out of date. Wikipedia lists several:

Axiom, Cadabra, CoCoA, DoCon, Eigenmath, FriCAS, GAP, GiNaC, Macaulay2, Mathomatic, Maxima, OpenAxiom, PARI/GP, Reduce, Sage, SINGULAR, SymPy, Xcas

It also has a comparison of computer algebra systems.

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In particular the wxmaxima front end, that make it more similar to Mathematica. – enzotib Sep 10 '11 at 15:02
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Many of these are either fairly basic or specialized to a subfield of mathematics. Sage is an ongoing effort to combine many existing computer algebra systems into one huge system. – Gilles Sep 10 '11 at 21:17
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In addition to the already mentioned Maxima, another visible option is Axiom. However, my impression is that Maxima's mindshare and userbase is greater than Axiom. However, I don't think either of these have functionality comparable to Mathematica or Maple. On the other hand, Mathematica at least is quite actively developed, and continues to improve.

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