The sage project (sagemath.org) has explicitly stated that its goal is to become a viable open source alternative to Mathematica, Matlab, and Maple. To a reaso

The sage project (sagemath.org) has explicitly stated that its goal is to become a viable open source alternative to Mathematica, Matlab, and Maple. To a reasonable extent, it has already reached that goal and it is progressing and changing rapidly. And it plays well with other mathematical systems (R, Octave, Mathematica, Matlab, Maple, Maxima, Magma, etc.). sage is built as an extension to Python with both a terminal interface (extended version of ipython) and a web-based interface. It builds on Scipy and many other tools. Anyway, it's a strong enough system that I've used it to replace both Mathematica and Matlab in my daily activities. It's FFT is similar in speed to that of Matlab (both based on the same open source software). Check it out.