CosetRepresentativesOfScheme

CosetRepresentativesOfScheme(R, L) returns a representatives of coset decomposition of the relations. R is a relation matrix and L must be a closed subset. This function does not check whether L is closed.

We show an example.

gap> R :=
> [ [  0,  1,  2,  3,  4,  4,  4,  4,  5,  5,  5,  5 ],
>   [  1,  0,  3,  2,  4,  4,  4,  4,  5,  5,  5,  5 ],
>   [  2,  3,  0,  1,  5,  5,  5,  5,  4,  4,  4,  4 ],
>   [  3,  2,  1,  0,  5,  5,  5,  5,  4,  4,  4,  4 ],
>   [  4,  4,  5,  5,  0,  1,  4,  4,  2,  3,  5,  5 ],
>   [  4,  4,  5,  5,  1,  0,  4,  4,  3,  2,  5,  5 ],
>   [  4,  4,  5,  5,  4,  4,  0,  1,  5,  5,  2,  3 ],
>   [  4,  4,  5,  5,  4,  4,  1,  0,  5,  5,  3,  2 ],
>   [  5,  5,  4,  4,  2,  3,  5,  5,  0,  1,  4,  4 ],
>   [  5,  5,  4,  4,  3,  2,  5,  5,  1,  0,  4,  4 ],
>   [  5,  5,  4,  4,  5,  5,  2,  3,  4,  4,  0,  1 ],
>   [  5,  5,  4,  4,  5,  5,  3,  2,  4,  4,  1,  0 ] ];;
gap> IsClosedSubset(M, [0, 1]);
true
gap> CosetDecompositionOfScheme(M, [0,1]);
[ [ 0, 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ]
gap> CosetRepresentativesOfScheme(M, [0,1]);
[ 0, 2, 4, 5 ]