You should check out SAGE: http://www.sagemath.org/
It is based on Python. It is a free open source alternative to Magma, Maple, Mathematica and Matlab, created at the University of Washington. It has a CAS that is on par with Mathematica, but it has a lot of capabilities that no other package has (especially in Algebra).
SAGE is the most scientific package I know of, since everything is open source, so you can actually prove how accurate its results are by analyzing the code. You don't just enter a formula and get a magical result.
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You should check out SAGE: http://www.sagemath.org/ It is based on Python. It is a free open source alternative to Magma, Maple, Mathematica and Matlab, created at the University of Washington. It has a CAS that is on par with Mathematica, but it has a lot of capabilities that no other package has (especially in Algebra). SAGE is the most scientific package I know of, since everything is open source, so you can actually prove how accurate its results are by analyzing the code. You don't just enter a formula and get a magical result.