gap> T:=[ [  1,  1,  1,  4,  4,  4,  4,  1 ],
>         [  1,  1,  1,  4,  4,  4,  4,  2 ],
>         [  1,  1,  1,  4,  4,  4,  4,  3 ],
>         [  4,  4,  4,  1,  1,  1,  1,  4 ],
>         [  4,  4,  4,  1,  1,  1,  1,  5 ],
>         [  4,  4,  4,  1,  1,  1,  1,  6 ],
>         [  4,  4,  4,  1,  1,  1,  1,  7 ],
>         [  1,  2,  3,  4,  5,  6,  7,  8 ] ];;
gap> M:=MonoidByMultiplicationTable(T);
&lt;monoid of size 8, with 8 generators>
gap> B:=BarComplexOfMonoid(M,8);;
gap> C:=ContractedComplex(B);;
gap> List([0..7],i->Homology(C,i));
[ [ 0 ], [ 2 ], [  ], [ 2 ], [  ], [ 2 ], [  ], [ 2 ] ]


gap> List([0..8],B!.dimension);
[ 1, 7, 49, 343, 2401, 16807, 117649, 823543, 5764801 ]
gap> List([0..8],C!.dimension);
[ 1, 1, 1, 1, 1, 1, 1, 1, 5044201 ]
