[GAP Forum] groups comparison

[Alexander Hulpke]

On Nov 19, 2013, at 6:34 AM, Stefan Kohl <stefan at mcs.st-and.ac.uk> wrote:

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

I would not recommend use of such one-sided methods for infinite groups. If gGens[1] is not in b, but b is infinite (as the space groups are) this will never terminate.

What one could do (but currently is not implemented) is to first test membership in the (finite) point group quotient and then test membership in the translation group by linear algebra.

Best,

    Alexander Hulpke