Factorization( G, g )
Let G be a group with generators g_1, ..., g_n and let g be an
element of G. Factorization
returns a representation of g as word
in the generators of G.
The group record of G must have a component G.abstractGenerators
which contains a list of n abstract words h_1, ..., h_n. Otherwise a
list of n abstract generators is bound to G.abstractGenerators
. The
function returns an abstract word h = h_{i_1}^{e_1} * ... *
h_{i_m}^{e_m} such that g_{i_1}^{e_1} * ... * g_{i_m}^{e_m} = <g>.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> Factorization( s4, (1,2,3) ); x1^3*x2*x1*x2 gap> (1,2,3,4)^3 * (1,2) * (1,2,3,4) * (1,2); (1,2,3)
The default group function GroupOps.Factorization
needs a finite group
G. It computes the set of elements of G using a Dimino algorithm,
together with a representation of these elements as words in the
generators of G.
GAP 3.4.4