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?
>

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