TITLE: Software for differential geometry
QUESTION [6 upvotes]: What is the software for computations with tensor fields? I'm interested in computations with vector-valued differential forms on Riemannien manifolds. Wedge product, exterior derivative, likely Hodge dual, tensor product, contractions of all kinds.
Basically just rewriting and then possibly casting equations into a given base.
I know EXCALC for REDUCE, but apparently it misses vector-valued differential forms and working with metrics in it is rather obscured.

REPLY [4 votes]: You may find Maxima to be the best fit for your purposes.
Here's an article by Viktor Toth that describes Maxima's facilities.  Viktor wrote the tensor packages for Maxima.  He describes his interest in general relativity, what motivated the need for software extensions, and how he has solved these needs with general packages.
His solutions may well cover all that you need.