(I am the lead developer of SymPy)

The important thing to note about SymPy Gamma is that it does only the mathematics part of WolframAlpha. It's also relatively new. There is no natural language input. There are no non-mathematical capabilities. The syntax should match Python syntax for the most part, though there are extensions to allow things like "sin x" or "x^2" or "2 x". All this will hopefully improve in the future (and pull requests are welcome!).

Most of the code was written by David Li (who is actually a high school student). You can watch a presentation about it here: http://conference.scipy.org/scipy2013/presentation_detail.ph.... It started out as a "because we can" toy, and it's gotten much better.

The real benefit of SymPy Gamma over WolframAlpha is that there are no barriers around it, since it's entirely (BSD) open source. For example, if you start computing something interesting and want to try more, you can move to SymPy Live (http://live.sympy.org/) and compute in a more session like environment. Or you can use SymPy locally on your own computer.

Regarding the comments that wolfram is mostly used for play, I'm not so sure about it. Wolfram is invaluable to students as a calculator. Sure Google can compute 100 * pi, but it falls apart when you try to compute integrate(sin(x) * x, x). When I was in college (which was last year), I saw people use it all the time. It's been very successful in making computer algebra accessible to virtually everyone.

By the way, probably the best feature of SymPy Gamma right now is the integration steps. See for instance the "integral steps" section of http://www.sympygamma.com/input/?i=integrate%28sin%28x%29*x%.... This is a feature that used to be free at WolframAlpha, and it's extremely useful if you are learning integration in calculus. It doesn't work for all integrals, because not all integrals are computed the way you would by hand.