On Friday, 19 June 2015 09:02:49 UTC+1, Christian Stump wrote: > > GAP4 has 39.5-2 Factorization ( >> http://www.gap-system.org/Manuals/doc/ref/chap39.html) >> >> calling GAP from Sage is not hard... >> > > Thanks for your reply -- but I am still a little puzzled: > > gap has two algorithms to compute a word in generators. This one, and the > one implemented in `word_problem` using the gap commands > `EpimorphismFromFreeGroup` and `PreImagesRepresentative`. > > The first ensures the word to be reduced by iterating through the complete > group, while the second does not necessarily provide a reduced word. > > Is there any reason for not travelling the group along the Cayley graph > with the given set of generators, and returning a word once the element it > found in this graph, without expanding the complete group? >
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. -- 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 sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
