[GAP Forum] [group-pub-forum] Homomorphisms of finitely presented groups

[Gabe Cunningham]

>
> What you could do is to install your own,  method for \= (equality) for
> elements of fp group (the standard method is in line 164 of lib/grpfp.gi,
> you could just start from this method and modify it. If you read it in
> later it will rank higher than the library method) that would not only test
> for equality of the word expressions, but also checks --  if
> HasFpElementEquatityMethod(FamilyObj(left))-=false, i.e. no good equality
> test exists yet --
> whether the word is  equal to any of the relators (or products, inverses,
> conjugates, etc.) This quickly will get more complicated than you might
> have hoped for, and you need to decide for a good heuristic how far you
> consider a consequence from relators as "obvious" (e.g. in your example,
> what if G has the relator (xy^4y^5x^4y^-5(xy)^2 instead while H is the
> same?)
>

Okay -- this is what I expected the answer to be, but I wanted to be sure
before I hand-coded something. I have a heuristic in mind that would cover
many of the cases that come up for me in practice -- namely, that G has
relators [w_1^a_1, ..., w_k^a_k], and H has at least the relators [w_1^b_1,
..., w_k^b_k] with each b_i dividing a_i. In this case, I can tell at a
glance that G covers H, and I just want for GAP to be as fast as I am :)

Thanks! (And thanks for moving the message to the right place -- I was a
little fuzzy on where a question like this should go.)
Gabe