[Date Index]
[Thread Index]
[Author Index]
Re: How does TensorReduce use assumptions?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg132260] Re: How does TensorReduce use assumptions?
*From*: Jose Martin-Garcia <jose at wolfram.com>
*Date*: Fri, 24 Jan 2014 04:21:58 -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
*References*: <20140123083525.A574969EB@smc.vnet.net>
Hi,
The documentation statement on TensorDimensions is correct, but some operations need full information (dimensions, rank and symmetry). For example let us assume that f does not have any symmetry,
In[1]:= TensorDimensions[f[g__]] ^:= d& /@ {g};
TensorRank[f[g__]] ^:= Length[{g}];
TensorSymmetry[f[g__]] ^:= {};
Then you get the expected
In[4]:= Assuming[t \[Element] Arrays[{d, d}, Antisymmetric[All]],
TensorReduce@ TensorContract[t \[TensorProduct] f[DN, DN], {{1, 4}}]]
Out[4]= - TensorContract[t \[TensorProduct] f[DN, DN], {{2, 4}}]
Regards,
Jose.
----- Original Message -----
> From: "Yi Wang" <tririverwangyi at gmail.com>
> To: mathgroup at smc.vnet.net
> Sent: Thursday, January 23, 2014 2:35:25 AM
> Subject: How does TensorReduce use assumptions?
> 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: Part Function**
Next by Date:
**Need Help With Locator in a Manipulate**
Previous by thread:
**Re: How does TensorReduce use assumptions?**
Next by thread:
**Need Help With Locator in a Manipulate**
| |