How to express all group elements in terms of generators in GAP

Question

I have a permutation group given in terms of its generators, such as

G := Group((2, 3), (1, 4), (1, 3)(2, 4));

I can iterate through the group and get all elements in cycle form. How can I get each element in terms of the generators? I imagine GAP has these expressions once it generates each element or not?

Answer 1

Section 39.5 of the GAP manual, "Expressing Elements as Words in Generators":

http://www.gap-system.org/Manuals/doc/ref/chap39.html#X7E19F92284F6684E

describes the two ways how this can be done: Factorization guarantees a word of minimum length (but is more memory/time intensive). PreImagesRepresentative, when applied to EpimorphismFromFreeGroup, is faster but does not attempt to obtain minimum length.