Dear Max and Alexander, Thank you for useful information and insights. It is good to know that it is not an error and how to deal with it if I need a different effect.
Best, Ignat https://www.math.lsu.edu/~ignatsoroko/ On Fri, Jul 24, 2020 at 10:34 AM Hulpke,Alexander <alexander.hul...@colostate.edu> wrote: > > Dear Forum, Dear Ignat Soroko, > > It is intended behavior, because (pseudo-)random elements are used. If you > need reproducable results you would have to store the random seed, as Max > Horn described. > > Currently, the default method for `IsomorphismPermGroup` for finitely > presented groups (that is, if such a homomorphism has not yet been stored) is > as follows: > > If the group does not yet know its `Size`, GAP takes subgroups generated by > random elements and tries to have a coset enumeration complete. If this works > (within the set parameters), it rewrites the presentation to the subgroup > (easy, since cyclic, and will give subgroup order) and calculates the group > order as product of subgroup index and subgroup order. It also has (from the > coset table) a permutation representation on the cosets, and can check > whether it is faithful. > > If the size is already known, or the permutation representation obtained this > way is not faithful or of too large degree, it tries coset representations on > subgroups generated b a few random elements, until it finds a faithful > permutation rep (which might be regular). > > Finally `SmnallerDegreePermutationRepresentation` (with option `cheap`) is > called to reduce the degree. > > The result thsu is heavily dependent on the random seed.For larger groups > this whole process also might be more memory intensive. > > What you can do to speed things up is to use `SetSize(Q, 2359296);` if Q does > not yet know its size. > > I have used other strategies in the past for finding permutation > representations. A good one is calling: > > l:=LowIndexSubgroups(Q,20); # or whatever index works well > k:=Intersection(l); > q:=DefiningQuotientHomomorphism(k); > > and to check whether `Size(Image(q))` is correct -- then q is faithful, and > you could store it with `SetIsomorphismPermGroup`. > > Even if q is not faithful, you could try to take a subgroup u of Image(q) of > moderate index (using permutation group tools) and then try whether > > sub:=LargerQuotientBySubgroupAbelianization(q,u); > > returns a subgroup (not fail) and if so set > > k:=Intersection(k,sub); > q:=DefiningQuotientHomomorphism(k); > > and repeat. > > The problem with implementing this approach for a generic method is that it > can perform horribly badly for some particular cases, e.g. certain solvable > groups or Schur Covers, and I can't think of a good heuristic to decide a > priory if this alternate method is worth trying. > > Best, > > Alexander Hulpke > > -- Colorado State University, Department of Mathematics, > Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA > email: hul...@colostate.edu, > http://www.math.colostate.edu/~hulpke > _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
