Software for physics calculations What is some good free software for doing physics calculations?
I'm mainly interested in symbolic computation (something like Mathematica, but free).
 A: Sage is a Python based system (including Numpy and Scipy) which includes a symbolic computation module.
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. 

A: I'd like to add that GNU Octave is a very good free alternative to Matlab.
Contrary to Scilab which does not aim at being compatible with Matlab, you can practically run your Matlab scripts with Octave with very few modifications (at least with their latest version).
A: 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.
A derivative of GiNaC is Pynac, which forms the backend for symbolic expressions in Sage.
A: Some software I have used or has been recommended to me for physics-related work:


*

*WolframAlpha -- when I don't have Maple around, I use it for simple symbolic calculations

*Maxima -- free open source alternative to Maple/Mathematica 

*DataMelt -- another free and open-source software that runs under the Java platform on all Java-supported OS

*Sage -- quite an interesting open source symbolic/numerical package, you can try it online at sagenb.org

*Scilab/GNU Octave -- alternatives to Matlab, best if you want to any numerical computations

*R -- powerful programming language used for statistical analysis

*OpenOffice Calc -- I'll put it here for completeness as Excel and its variants seem to be the software of choice for most experimental calculations.

A: 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. 
http://www.mhhe.com/engcs/mech/ees/download.html
http://www.fchart.com/ees/
A: 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.
A: I've recently discovered Cadabra. 

A field-theory motivated approach to computer algebra

I'm really impressed.
A: I think DataMelt (Computation and Visualization Environment) is one of the best free software programs for physics.


*

*It was developed for High-Energy Physics at the DESY (Germany) and then ANL physics lab (US)  

*It runs on Linux and Mac, which is the usual  environment in physics 

*It has "physics" Java module for calculations

*It has very detailed manual (but a lot of material is totally free)

