Sage is a free open source computer algebra system written in and based on Python. You can download it free or use it online for free like a Mathematica or Maple worksheet. It can do very many things that Maple and Mathematica can do.
Seriously, you should try it before you knock it! It is a blessing to have something like this free for use.
Yet Another Reason to Learn Python!
Sage is basically just a fancy wrapper around the Python language coupled with the scipy/numpy libraries. So, learn some Python using numpy and scpiy and:
- Chuck Matlab!, Python/Numpy/Scipy can do all this just as fast and easy. (and free.)
- Eventually chuck Maple and Mathematica as Sage matures.
- Read this wonderful book, learn how to mix Python with your Fortran/C/C++ code and become a much more happy and productive programmer.
- Be able to program in all computer areas, GUI, numerical, system, etc... (Something you can't do with Matlab/Mathematica/Fortran.)
Actually, the Sage library contains about half a million lines of code that implements various algorithms on top of its components. NumPy and SciPy are used for various numerical things, but play overall a negligible role for most of the other high level mathematical algorithms implemented.
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