Hi,

> I would be interested in seeing a project on GR.  I suspect that
> there are equivalent packages in Mathematica.  It might be helpful to
> investigate how they approach the problem.

Just two Links:

"xAct is a suite of free packages for tensor computer algebra in Mathematica. 
xAct implements state-of-the-art algorithms for fast manipulations of indices 
and has been modelled on the current geometric approach to General Relativity. 
It is highly programmable and configurable. Since its first public release in 
March 2004, xAct has been intensively tested and has solved a number of hard 
problems in GR."

xAct: http://www.xact.es/


And for Tensors: https://en.wikipedia.org/wiki/Tensor_software

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