Open Source Mathematical Software

The label open source is normally associated with software. Open source mathematics is mathematics done with the help of open source mathematical software.

David Joyner and William Stein argued in a American Mathematical Society publication, that mathematical proofs, like the proof of the Four Color problem, are sometimes very lengthy and involve use of mathematical software. Whereas ordinary mathematical proofs can readily be inspected by others using only paper and pencil, computer aided proofs can only be verified if the verifier has the same mathematical software (usually commercial products such as Wolfram's Mathematica and MathLab).
But who can guarantee that the mathematical software is correct and bug-free? If the mathematical software is open source then in principle anyone can also verify the correctness of the software.

William Stein created Sage (www.sagemath.org) with this in mind. It is not the first open source mathematical software, but probably the most extensive. It "can do anything from mapping a 12-dimensional object to calculating rainfall patterns under global warming."
Indeed it can be used for algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.

Sage is written in Python, confirming yet again the versatility of the Python. It is browser based. It makes use of many other open source software including GAP, GNU Multi-Precision Library, GNU Scientific Library, Matplotlib, Maxima, Mwrank, NetworkX, NTL, Numerical Python, PARI, and Singular.

This is the strength and the weakness at the same time. To install Sage, you can choose to install Sage with all the dependencies, or you can have everything bundled as one package (VMWare on Windows). The VMWare package is 642M.

Here is an example of building a car using Sage:
Related:

• SageMath main site
  
• Sage blog by William Stein
• Google Videos of Sage
• Python declared as the 2007 programming language of the year