# Finalizing Arbitrary Spin Coupling

As expected, my work with Sympy slowed drastically once school started, but nevertheless, I have found enough time to polish off the coupling of arbitrary number of spin spaces that I started over the summer. I’ll probably wait until after school is done (and the initial Google Code-In traffic dies down) before opening a pull request, but it has neared the state of conclusion, but I will outline the work done on the branch here.

A notable change from the summer is the coupling and uncoupling code is now much cleaner. The old methods used messy while True loops which would increment some parameters and check if some end condition was reached, which I found very unsatisfactory and open to some weird use case throwing it into complete disarray. The new methods utilize the notion that any coupling or uncoupling will occur such that there is a well defined change in either the j (in the case of coupling) or m (in the case of uncoupling) values from their maximal values, and this change can be applied over the (un)couplings in the same way you can distribute n balls in m boxes, then it is just matching an integer to a given state and check that the given state is physically feasible.

In addition, I have added all necessary documentation for the new functionality and fixed a few other minor issues with other parts of the new code. I may yet change some of the handling of the j_coupling parameter, but I will reevaluate that when I have more time to look at the code after I finish the semester.

The passing of quantum numbers to define the couplings and un-couplings is still quite verbose, but I see no better way of passing the parameters, hopefully in review someone will see a better way of defining states and couplings.