GAP4 has 39.5-2 Factorization 
(http://www.gap-system.org/Manuals/doc/ref/chap39.html)

calling GAP from Sage is not hard...


On Tuesday, 16 June 2015 17:02:35 UTC+1, Christian Stump wrote:
>
> Hi there, 
>
> I wasn't able to find the following functionality: Let W = 
> PermutationGroup(gens) be a permutation group and let w in W. Find a 
> *shortest* expression as a group of w as a word in gens and their 
> inverses. 
>
> w.word_problem() finds a word, but this has not necessarily the 
> shortest possible length. In GAP3 there was such a functionality which 
> I currently use. 
>
> * Is there already such functionality in Sage (and I was simply ignorant)? 
>
> * Does anyone know how to achieve this using Sage and GAP4? 
>
> * Should I open a ticket and provide GAP3 code for this functionality 
> for permutation groups? 
>
> Thanks! 
>
>     Christian 
>

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