[GAP Forum] I need help for programming

[Matan Ziv-Av]

On Wed, 8 Aug 2012, TMU wrote:

> Dear programmers;
> My name is A.Nejati. I want to construct a Coset Graph A=Cos(T,H,HbH)  in
> GAP such that T = <a, b> , H = <a> , a = (3 11 9 7 5)(4 12 10 8 6) , b = (1
> 12)(2 7)(3 10)(4 8)(5 11)(6 9).  How done it is?
> Sincerely yours
>
>
>
> De nition: Let G be a group, H a subgroup of G, and S a subset of G. De
> fine the coset graph of G with respect to H and S to be the directed graph
> with vertex set [G : H] and such that, for any Hx Hy in V ,
> Hx is connected to Hy if and only if yx-1 in HSH,
> and denote the di-graph by Cos(G;H;HSH).

It is natural to translate such a definition to GRAPE:

CosetsGraph:=function(G,H,S)
   local HSH;
   HSH:=Union(List(S,s->DoubleCoset(H,s,H)));;
   return Graph(G,
                RightCosets(G,H),
                OnRightSets,
                function(x,y) return Representative(y)*Representative(x)^-1 in HSH; end
               );
end;


-- 
Matan Ziv-Av.                         matan at svgalib.org