On Friday, 19 June 2015 11:35:36 UTC+1, Christian Stump wrote: > > the reason must be efficiency. E.g. for permutation groups one would work >> with a strong generating set S, rather than the original generators; >> expressing an element in terms of S is very quick, and then you hold >> expressions for each element of S in terms of the original generators >> (which need not be the shortest one); so you get some kind of expression >> quite quickly. >> > > I agree, but I still wonder why gap is not providing also an algorithm > along the Cayley graph. Or would you expect that to be slower than the > algorithm used in `Factorization` ? > yes, sure, this would be slow. What sizes of groups are you talking about? GAP has functions to investigate the group grows: GrowthFunctionOfGroup( G, radius ) which are fast; e.g. gap> GrowthFunctionOfGroup(PSL(3,101),5); is kind of instant... So it would be natural to extend GAP here.
> But even if it were, it wouldn't need to ruin through the complete group > for elements that are close to the identity in the Cayley graph (i.e., > which have short reduced factorizations). > > Since this means that there is no algorithm available for big groups, it > might be nice to have that in sage by adding the naive algorithm to the > perm_grp element class, don't you think so? > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
