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Add HallSubgroup fallback method #3080
Add HallSubgroup fallback method #3080
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This allows computing Hall subgroups for arbitrary finite groups via an isomorphism into a permutation group.
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As it is a fallback method, wouldn't it make sense to rank it with a value of -1, so that any other method for finite groups will automatically rank higher?
Similar issues are likely to hold for for other non-basic routines: Conjugacy classes, subgroups, automorphisms and so on. They work for permutation groups, if handled through nice monomorphism, or if FittingFreeLiftSetup is available, but there is no translation for other basic cases.
I don't quite see why adjusting the rank by -1 would be useful, it seems rather arbitrary to me. After all, why would any future "generic" method for finite groups necessarily be better than this one? Instead, I'd think that any such method would need to be evaluated against the one added in this PR; and then the two should either be merged, using a heuristic to choose which approach to use; or if the new one is strictly superior to this method here, then the new should simply replace this one. And if a package wants to add a better method, they can adjust the rank by +1 instead. (That said, I won't resist if people really think it's necessary to adjust the rank by -1, it just seems pointless from my vantage point). As to other operations being affected: sure, you are of course absolutely right. See also issues #1580 and #596. As discussed on PR #1580, instead of adding this method, we could certainly also try to give the user a more helpful method other than "method not found", something like "... perhaps try converting your group to another representation first". It just is note quite clear where to add that. |
@fingolfin |
This allows computing Hall subgroups for arbitrary finite groups
via an isomorphism into a permutation group.