[GAP Forum] groups comparison

[Stefan Kohl]

On Tue, November 19, 2013 12:56 pm, ÷ÌÁÄÉÍÉÒ ûÉÒÏËÉÊ wrote:
> I'm using cryst and crystcat packages and i want to compare two groups
> g:=SpaceGroupIT(3,75);
> gGens:=GeneratorsOfGroup(g);
> gGens2:=[gGens[2], gGens[3], gGens[4], gGens[5]]
> a:=Group(gGens);
> b:=Group(gGens2);
>
> I know, that they are the same groups, because gGens[2]*gGens[2]=gGens[1]
>
> how can i check it OR how can i find all relations between generators (in
> this case there is another one: gGens[2]^-1*gGens[3]*gGens[2]=gGens[4] )

Unfortunately, at present the checks "a = b;" and "gGens[1] in b;"
fail due to a lack of available methods for your group:

gap> a = b;
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 3rd choice method found for `Enumerator' on 1 arguments called from
Enumerator( D ) called from
[ ... ]
gap> gGens[1] in b;
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 3rd choice method found for `Enumerator' on 1 arguments called from
Enumerator( D ) called from
[ ... ]

However what you can do is the following:

gap> First(b,g->g=gGens[1]);
[ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]

Since the result is not "fail", this tells you that gGens[1] is an
element of b.

Note that this may require some package --
try RCWA if it otherwise doesn't work for you.

Hope this helps,

    Stefan Kohl