How can we show that the tensor expression is identically zero?

[Pavel Petrov]

Dear All,

How can I show that the expression in the screenshot is identically zero?

I have attached the screenshot and a file with my attempts.

Thank you very much in advance.  

[Thomas Bäckdahl]

Hi!

First of all. I don't think you need to express F in terms of A for this simplification.

It looks like you need several complicated multi-term symmetries here. Unfortunately, we don't have very good tools to handle this in general in tensor language.
For this reason I usually use spinors instead. I quickly solved your problem in spinor language. Unfortunately, I didn't have time to make it very pedagogical, but at least it simplifies to zero.

Let me know what you think.

Regards
Thomas

--
You received this message because you are subscribed to the Google Groups "xAct Tensor Computer Algebra" group.
To unsubscribe from this group and stop receiving emails from it, send an email to xact+uns...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/xact/231dc465-65c1-4411-8d8f-1e19bcb24dfbn%40googlegroups.com.

[Pavel Petrov]

This  is weird. Seems that in my version of xAct the code works differently. 

I get the xAct package from this webcite, quite recently. xAct: Efficient tensor computer algebra for the Wolfram Language

What could cause the problem ? 

Best regards, 

Pavel

суббота, 5 апреля 2025 г. в 20:34:20 UTC+9, Thomas Bäckdahl:

[Thomas Bäckdahl]

Hi!

It is difficult to see from pictures what is going on.
There could be something that I have fixed on my private versions.

I attach my latest versions of the m-files here. Please let me know if it works. They might also be interesting for other people.
If it makes a difference I think we should make an update to the released files.

If it doesn't work, you can send a private email to me with a notebook.

Regards
Thomas

To view this discussion visit https://groups.google.com/d/msgid/xact/4274da9d-9dac-4263-901d-c8305e8aeb12n%40googlegroups.com.