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I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce:

If TensorDimensions[ten] does not return a list of dimensions, then the expression ten is returned unchanged.

I would have inferred from above that if I modify TensorDimensions[ten], TensorReduce should work. Thus I did

Unprotect[TensorDimensions];
TensorDimensions[f_[g__]] := d & /@ {g};
Protect[TensorDimensions];

Assuming[ t ∈ Arrays[{d, d}, Antisymmetric[All]] ,
 TensorReduce @ TensorContract[ t\[TensorProduct]f[DN, DN], {1, 4}]]

However, this doesn't work. i.e. TensorReduce does nothing, and the result is

TensorContract[ t\[TensorProduct]f[DN, DN], {{1, 4}}]

To compare, having defined

Assuming[ t ∈ Arrays[{d, d}, Antisymmetric[All]] && 
          f[DN, DN] ∈ Arrays[{d, d}],
 TensorReduce @ TensorContract[ t\[TensorProduct]f[DN, DN], {1, 4}]]
- TensorContract[ t\[TensorProduct]f[DN, DN], {{2, 4}}]

the result is indeed simplified as desired:

I'd like to understand what are the assumptions that TensorReduce really uses. Is there a way that I can work with TensorReduce as above, with pattern like declaration of tensors?

PS: Currently I generate a list of assumptions of f_[g__] using Cases, and put those assumptions together in Assuming. This makes the code slow and ugly.

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This question is answered perfactly by Jose at groups.google.com/forum/?hl=zh-cn#!topic/… –  Yi Wang Jan 24 at 21:16

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