How do I define nonlinear properties of tensor?

[Nail Khusnutdinov]

Hi colleagues,

In 3D, the Maxwell tensor F has property F.F.F = Inv F, where inv = -F[m,n]F[-m,-n]/2 is an invariant. How about using this relation to simplify the result for xAct? 

In DefTensor, it is possible to say property symmetry or anti-symmetry over indexes. But this is a cubic relation.

Thank you in advance,

Nail  

[Nail Khusnutdinov]

I see, that there is no idea.

воскресенье, 4 августа 2024 г. в 15:34:19 UTC-3, Nail Khusnutdinov:

[Thomas Bäckdahl]

Hi!

One can not specify properties of this kind in DefTensor.
A sensible way to handle relations of this kind is via replacement rules.

See the attached notebook for an example.

Regards
Thomas

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[Nail Khusnutdinov]

Thank you, Thomas.

I understand the way. I already finished my calculation and used this symmetry by hand each time :).

For possible future, I save this file in my library.

Best regards,

Nail

понедельник, 26 августа 2024 г. в 11:12:02 UTC-3, Thomas Bäckdahl: