Thanks to GSoC 2012 I am working on a module for differential geometry for SymPy (a CAS written entirely in Python).
- Introductory post
- Objects implemented in the module
- Graph of the Relations between Objects in the diffgeom Module
- Part 1: What is a tensor and how is it implemented in SymPy?
- Tensor vs Tensor Field, Basis vs Coordinate System
- Vector/Form Fields do not form a Vector Space
- Integral Curves
All the posts about it (many of which are just quick status reports of my work for GSoC and thus are not very informative) can be found on the corresponding category page.