simplifying total derivatives

[apt45]

Hello,

I want to try simplifying an expression involving a linear combination of operators which involves three insertions of rank-three tensors. I want to find the coefficients of the linear combination such that I can recover total derivatives.

This is how I thought to solve the problem. I interpret the operators as interactions of some lagrangian and compute the 3-point amplitude. If the result is proportional to (p1+p2-p3) in momentum space (p1,p2 are incoming momenta and p3 outgoing), then it is a total derivative.

You find attached a notebook with some check for spin-1, spin-2 and spin-3 case. While all the example that I made are solvable, the last expression that you find at the end of the notebook is hard to simplify. Do you think I can make this method sharper?

The notebook is commented. Let me know if something is unclear.

Thanks,