gap> M:=RegularCWComplex(ClosedSurface(2));;
gap> W:=DirectProduct(M,M);
Regular CW-complex of dimension 4
gap> Size(W);
5776
gap> W:=SimplifiedComplex(W);;
gap> Size(W);
1024
gap> Homology(W,2);
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
gap> Homology(W,4);
[ 0 ]
gap> cup:=CupProduct(W);;
gap> SecondCohomologtGens:=IdentityMat(18);;
gap> A:=NullMat(18,18);;
gap> for i in [1..18] do
> for j in [1..18] do
> A[i][j]:=cup(2,2,SecondCohomologtGens[i],SecondCohomologtGens[j])[1];
> od;od;
gap> Display(A);
[ [ 0, -1, 0, 0, 0, 0, 3, -2, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0 ],
[ -1, -10, 1, 2, -2, 1, 6, -1, 0, -3, 4, -1, -1, -1, 4, -2, -2, 0 ],
[ 0, 1, -2, 1, 0, -1, 0, 0, 1, 0, -1, 1, 0, 0, 1, -1, 0, 0 ],
[ 0, 2, 1, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 2, 0, 0 ],
[ 0, -2, 0, 1, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0 ],
[ 0, 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 1, -1, 0, 0 ],
[ 3, 6, 0, 0, 1, 0, -4, 0, -1, 2, 4, -5, 2, -1, 1, 0, 3, 0 ],
[ -2, -1, 0, -1, -1, 1, 0, 4, -2, 0, 0, 3, -1, 1, -1, 0, -2, 0 ],
[ 0, 0, 1, 0, 0, -1, -1, -2, 4, -3, -10, 1, 0, 0, -3, 3, 0, 0 ],
[ 0, -3, 0, 1, 0, 1, 2, 0, -3, 2, 3, 0, 0, 0, 1, -3, 0, 0 ],
[ 0, 4, -1, 0, -1, 0, 4, 0, -10, 3, 18, 1, 0, 0, 0, 4, 0, 1 ],
[ 1, -1, 1, 0, 0, 0, -5, 3, 1, 0, 1, 0, 0, 0, -2, -1, -1, 0 ],
[ -1, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0 ],
[ 0, 4, 1, -1, 0, 1, 1, -1, -3, 1, 0, -2, 1, 0, 0, 2, 2, 0 ],
[ 1, -2, -1, 2, -1, -1, 0, 0, 3, -3, 4, -1, 0, -1, 2, 0, 0, 0 ],
[ 0, -2, 0, 0, 0, 0, 3, -2, 0, 0, 0, -1, 0, -1, 2, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ] ]
gap> SignatureOfSymmetricMatrix(A);
rec( determinant := -1, negative_eigenvalues := 9, positive_eigenvalues := 9,
zero_eigenvalues := 0 )
¤ Dauer der Verarbeitung: 0.11 Sekunden
(vorverarbeitet)
¤
*© Formatika GbR, Deutschland
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