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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);
<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 ]
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