The entire spreadsheet is available, but here are a few things to notice.
First of all, two of our original unkowns have been solved for.
Evidently, F is invertible.
Two other interesting equations appear in the undigested section. The first one involves f and Tp[f].
There is a similar equation involving F and Tp[F].
As it turns out, this is the ``answer''. We can factor these two equations and we can see that f and F correspond to w and w which we described in equations (1) and (2). Thus we have obtained the following theorem.
Theorem: Suppose y and x are invertible and y is in the orbit of x under a linear fractional transformation
|Let m and m be defined as|
|m and m satisfy|
The converse of this theorem remains to be settled. This question is related to the equations which we obtained as output of NCProcess but we did not look at. The next step is to figure out which of these equations we can eliminate.