Deriving w.r.t. Tensor components

[TLa]

Hello everyone,

I'd like to know if there is a way of deriving an expression with respect to tensor

components.

More specifically, lets say I defined a Tensor T on a pre-defined manifold M as:

DefTensor[T[a,b],M]

Then I would like to do e.g.:

d/dT[c,d] (T[a,b]) = delta[a,-c]*delta[b,-d]

where delta indicates the Kronecker-delta. Is there any function in xAct for that matter?

Best,

Armin

[Thomas Bäckdahl]

Hi!

The very short answer is that this is probably not implemented, and I don't see exactly what it would mean in general.

For your particular example, one could try
IndexCoefficient[T[a, b], T[c, d]]
but this is not really computing derivatives.

To actually compute derivatives with respect to a tensor field, one can use VarD.
However, it is only meant for scalar expressions differentiated with respect to tensor fields in the sense of variational derivatives bu
performing integration by parts.

Regards
Thomas

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[TLa]

Hello Thomas

Thank you very much for your answer! 

I will have a look and try around using VarD.

Best,

Armin