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It depends which parts of Mathematica you need.

Python is an alternative, especially within the Sage package [0].

Then there is also Maxima [1].

[0] http://www.sagemath.org/ [1] http://maxima.sourceforge.net/




I use Octave daily (in the last hour, will return to it when I finish my soup), but have never seen anything that matched Mathematica's symbolic/pure math functionality.

Will check out Sage, haven't used Maxima since 2004. Thanks!

Edit: Sage looks nifty, Maxima looks unchanged, at least at screenshot-level.

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SymPy (sympy.org) is a well-developed Python package that works with symbolic/analytical mathematics on a level comparable to Mathematica's.

Octave is more of an open source Matlab equivalent. That is, mostly linear algebra.

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Indeed, there are plenty of open source solutions that can solve your particular problem, and many problems don't need any sort of symbolic tools. There's also Octave with a nice collection of packages on Octave-Forge, there's PARI (included in Sage), and there's LAPACK, and I'm sure there are others I'm either forgetting or haven't heard of.

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I too can attest to the extensive abilities of the Sage package. It's extremely powerful and easy to use given that it's based in Python. Even if you don't want to download it, give the notebook a try: http://www.sagenb.org/.

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