[Date Index]
[Thread Index]
[Author Index]
How does TensorReduce use assumptions?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg132252] How does TensorReduce use assumptions?
*From*: Yi Wang <tririverwangyi at gmail.com>
*Date*: Thu, 23 Jan 2014 03:35:25 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-outx@smc.vnet.net
*Delivered-to*: mathgroup-newsendx@smc.vnet.net
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.
Prev by Date:
**Re: How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?**
Next by Date:
**Re: How to show 1+2+3+ ... = -1/12 using**
Previous by thread:
**Re: Part Function**
Next by thread:
**Re: How does TensorReduce use assumptions?**
| |