replacement rules

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olse barn

Mar 11, 2023, 8:51:34 AMMar 11
to xAct Tensor Computer Algebra
Hey everyone, 

I have again a very specific question: I have a couple of Tensors, let's call them A[i] and B[i], that satisfy certain relations e.g. for A[i]:


I would now like to use these relations in a very long expression that includes for example 


such that, the two given terms vanish. 
More specifically, I face the problem that the index names are potentially different, i.e. they could occur in a form like:


Is there an easy way to obtain such a replacement rule?

All the best.


Mar 11, 2023, 9:27:14 AMMar 11
to xAct Tensor Computer Algebra

In general it is not a great idea to make rules that tries to replace several terms with something else. It is better to make a rule that replaces one term with something with more symmetries.

For instance split PD[i]A[j] into its symmetric and antisymmetric part like in the following discussion:
After that you could set the symmetric part to zero. This gives a systematic way of doing it which does not depend on the names of the indices.

Se also the following discussions regarding similar problems:

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