Best software for tensor manipulation?

AI Thread Summary
The discussion centers on the search for software capable of manipulating tensors, particularly for tasks involving varying Lagrangians and checking gauge and supersymmetry transformations. A key requirement is the ability to handle anti-commuting variables and provide group constants for SU(n) groups. Users express a need for software that can recognize mathematical identities, such as the anti-symmetry in cross products of abstract 3-vectors. While a Wikipedia list of tensor software is mentioned, participants emphasize the desire for user reviews and experiences with specific tools. Mathematica's TensorExpand is noted as a potential option, though further recommendations are sought.
nuclearhead
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Do you know any good software for manipulating tensors: varying Lagrangians, checking gauge and supersymmetry transformations, etc. ? One that could deal with anti-commuting variables would be good too. One that also supplied group constants for SU(n) etc. would also be useful.

I was also looking for some simple software that knew that AxB +BxA = 0 for cross products of abstract 3-vectors but couldn't find any.
 
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Well yeah, but I was hoping for some reviews from people who used them.

I see Mathematica has TensorExpand which is something anyway.
 
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