Computing

Most of the code of the numerical computations for our research is written in Python (employing efficient libraries in the back with some parts using embedded C++ or cython).
Why Python? Python is a high-level, dynamic, object-oriented programming language. In addition to scripts/programs python can be used interactively.

Together with NumPy, SciPy and matplotlib it is an excellent free alternative to commercial tools. In addition one has the advantage of a complete programming language.

For a simple example, see Quantum maps providing code to compute the eigenvalues of quantum maps and the level spacing distribution.

Python packages for scientific computing

Python itself is already installed on most Unix systems during the standard installation. For Windows see, e.g., Python(x,y).

Additionally needed/recommended packages are

Numpy (Base array package)
Scipy (Library for scientific computing )
Matplotlib (Interactive plotting and more)
Ipython (Enhanced interactive shell)

Highly recommended are

Mayavi (excellent 3D visualization)
PyX (publication-ready .eps/.pdf graphics)

A good explanation and an overview of further packages can be found at Scipy - getting starting.