Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

Topic: How does TensorReduce use assumptions?
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Yi Wang

Posts: 33
Registered: 3/30/12
How does TensorReduce use assumptions?
Posted: Jan 23, 2014 3:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 \[Element] 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 \[Element] Arrays[{d, d}, Antisymmetric[All]] &&
f[DN, DN] \[Element] 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 also tried to modify TensorSymmetry, but without luck either.

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.




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.