Simplifying Expressions

[olse barn]

Hello everyone, 

I am completely new to xAct and was wondering if it is possible to tell xAct how to simplify expressions.

Is there, for example, a way (e.g. in form of a supplied rule) to automatically simplify Maxwell equations given as

CD[-b][CD[-a][A[b]]] - CD[-b][CD[b][A[-a]]]

to 

CD[-a]@F[a, b]

where 

F[a_, b_] := CD[a][A[b]] - CD[b][A[a]] ?

Any help is appreciated.

[Thomas Bäckdahl]

Hi!

I would work with equations and do it like this.

Regards
Thomas

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[Jose]

Hi,

I'd like to stress the fact that Thomas used equations and rules, but not assignments like F[a_, b_] := ... because then trying to insert F[a, b] in the computations would immediately use that assignment.

Thomas' idea is to replace CD[a][A[b]] by a sum of its antisymmetric part (i.e. F[a, b]) and its symmetric part. Another possibility is to define a rule of the form:

   rule = CD[a_][A[b_]] :> F[a, b] + CD[b][A[a]] /; IndexOrderedQ[{a, b}]

Then you also have

In[ ]:= CD[-b][CD[-a][A[b]]] - CD[-b][CD[b][A[-a]]] /. rule
Out[ ]= CD[-b][F[-a, b]]

Cheers,

Jose.

[olse barn]

Thank you both for the fast and informative reply!

best