SageMath ("System for Algebra and Geometry Experimentation") is an open source computer algebra system based on Python. It uses various libraries written in R, Fortran, Maxima etc. to realize an extensive application of numerical and abstract mathematics. In 2013, a new extension called "SageManifolds", fully implemented into SageMath, was created. SageManifolds comes with tensor algebra on manifolds, like computations on vector fields, curvatures and differential forms .
For my master thesis, I participated in the development process and implemented vector bundles, mixed differential forms and characteristic classes, along with bugfixes and various minor improvements.
In this talk, I will give a short look behind the scenes and reveal some implementation concepts. Furthermore, I will present some live computations.