Tensor calculus with open-source software: the SageManifolds project
  The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss here some details of the implementation, which relies on Sage's parent/element framework, and present a concrete example of use. 
Eric Gourgoulhon, Michal Bejger, Marco Mancini
gr-qc hep-th math-ph math.MP