Programs for Algebra (Topic)

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Empirical and statistical analyses aren't the only use for computers in social sciences any more -- a number of programs now exist designed to handle algebraic manipulations, which can be helpful for solving things like game theory models. Moreover, theses tools can also be helpful for numerically simulating results to help you get a feel for expressions you are working with.

Wolfram Alpha

The easiest tool for algebraic manipulation is Wolfram Alpha, which does a good job of parsing algebra written intuitively. There is both a free version and a Pro version that offers slightly more feedback.

Mathematica

Wolfram Alpha is actually just a stripped down version of a more powerful program called Mathematica, which can do everything Wolfram Alpha can do and much, much more. Probably the biggest advantage over Wolfram Alpha is that you can store results in a "notebook" (kind of like a Stata do-file or a .R file), which is very helpful for project management and development.

Matlab

Matlab includes a library for symbolic manipulation the symbolic math toolbox. It's not what Matlab was built to do, but if you already have Matlab, you don't have to buy or learn a new program!

SymPy (Python)

A free but very powerful tool is SymPy, which is essentially an open source version of Mathematica.