This last week, I have made progress on my project working on laying the base work for the spin states and in reimplementing logic in the cg_simp method for Clebsch-Gordan coefficients.

First, I have started the work on the implementation of coupled/uncoupled spin states. Currently, this is implemented by adding a coupled property to the spin states. This can be set to True for coupled, False for uncoupled or left as None for other states. As this evolves, I will move to having uncoupled product states be represented by a TensorProduct of two spin states. The next key will be establishing represent and rewrite logic for these spin states. Part of this will be figuring out how exactly these methods will work and what they will return. Namely, the represent method, noting that when representing an uncoupled state as a coupled state, it returns states with multiple j values, which under the current logic, would return matrices of different dimension. Also, we will have to determine what represent will do to uncoupled tensor product spin states. This next week, I will likely rebase this branch against the CG branch so I can start using the Clebsch-Gordan coefficients to implement these functions as the CG pull is finalized.

With the Clebsch-Gordan coefficients, this last week I was able to get the simplification of symbolic Sum objects working. I did this using the pattern matching built into sympy with Wild and .match. The final step with this should be to rework the logic of _cg_simp_add to make it easier to add in additional symmetries.