3) Coming back to specific question of Schreir-Sims algorithm. This algorithm is described in A. Seress book "Permutation group algorithms". IMO this is quite good description. AFAICS think this book is not freely available. Once somebody understands the algorithm tracking code should be relatively easy -- code basicaly is doing what algorithm prescribes. There are few implementation choices, concerning how to efficiently implement some steps. Seress discusses possible alternatives. I have no access to Sims article, but my Univerity have Seress book. So there is good documentation for the permgrps, just it is not freely available.
I don't think it is good enough to say that, in FriCAS, the only documentation for an important topic like group theory is an out-of-print book.
I think that FriCAS (and pan-axiom generally) deserves more users and developers but I don't think it is going to get them with this sort of attitude.
I tried to make a start with some documentation, far from perfect as I said myself, it would be nice if others could contribute and make it better, rather than just reject it.
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