I'm working on a project where we deal with objects very similar to Riemann tensor. In fact they are Christoffel symbols for higher spins. I'm using xTras for modeling problems in wolfram mathematica. I'm struggling to define Christoffel symbols that could hold their form and do not expand during simplification processes.

Here is my code which I'm using

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I've defined 3rd order and 4th order Christoffel symbols like this.

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As you can see they fulfill the following equation

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which is equivalent to:

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Here A vectors are for symmetrization purposes.

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When doing computations with this tensors after simplification they expand by underlying tensor H and it is a big pain to combine them back into their original form.

E.g: Adding two Gammas must give Gamma without printing the expansion. I know that Riemann tensors defined in xTras behave exactly like that, they do not expand the underlying metric structure, instead they hold their form.

How can I define my Cristofel symbols like that?

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