What is some good free software for doing physics calculations?
I'm mainly interested in symbolic computation (something like Mathematica, but free).
Some software I have used or has been recommended to me for physics-related work:
It is probably worth your while to buy Mathematica, Maple, or Matlab, depending on your needs. I wish it weren't so, but this is one area in which the commercial tools are still vastly better than their free counterparts.
If you are a student, you can buy these at fairly afforable prices. Maple 14 Student Edition is only $99. Mathematica for Students is \$140, and Matlab/Simulink is \$99 for students. It is also possible that your school or department already has a site license, allowing you to obtain and use this software for no additional cost.
For symbolic calculations, you want either Mathematica or Maple, with Maple being more user-friendly, and Mathematica being more prevalent (in my experience) in actual research environments. Matlab's focus is on numerical calculations.
I've recently discovered Cadabra.
A field-theory motivated approach to computer algebra
I'm really impressed.
From the Sage homepage:
Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
GiNaC is a c++ symbolic manipulation framework oriented to high-energy physics computations. It has a couple of interactive frontends, although its main usage is as part of the Root framework at CERN.
I used this software in my energy transfer courses, I never used it for symbolic, so I don't know if you can do symbolic computation, however it is very good at solving equations. As well as for conversions. It is not free, however you can download a student version, which I used the whole semester without problems. It is called ees. The company I think is called f chart. I know it is not exactly what you asked for, however it's a useful software to have around, especially when working with a lot of equations, since the software actually warns you about any inconsistency in the units.
It is also useful if you want to calculate say for example entropy, the software can do it for you if you have the pressure or temperature.
I think DataMelt (Computation and Visualization Environment) is one of the best free software programs for physics.