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gap> mat := IdentityMat(4, GF(9));
[ [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> form := BilinearFormByMatrix(mat,GF(9));
< bilinear form >
gap> Display(form);
Bilinear form
Gram Matrix:
1 . . .
. 1 . .
. . 1 .
. . . 1
gap> mat := [[0*Z(2),Z(16)^12,0*Z(2),Z(4)^2,Z(16)^13],
> [Z(16)^12,0*Z(2),0*Z(2),Z(16)^11,Z(16)],
> [0*Z(2),0*Z(2),0*Z(2),Z(4)^2,Z(16)^3],
> [Z(4)^2,Z(16)^11,Z(4)^2,0*Z(2),Z(16)^3],
> [Z(16)^13,Z(16),Z(16)^3,Z(16)^3,0*Z(2) ]];
[ [ 0*Z(2), Z(2^4)^12, 0*Z(2), Z(2^2)^2, Z(2^4)^13 ],
[ Z(2^4)^12, 0*Z(2), 0*Z(2), Z(2^4)^11, Z(2^4) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2^2)^2, Z(2^4)^3 ],
[ Z(2^2)^2, Z(2^4)^11, Z(2^2)^2, 0*Z(2), Z(2^4)^3 ],
[ Z(2^4)^13, Z(2^4), Z(2^4)^3, Z(2^4)^3, 0*Z(2) ] ]
gap> form := BilinearFormByMatrix(mat,GF(16));
< bilinear form >
gap> Display(form);
Bilinear form
Gram Matrix:
z = Z(16)
. z^12 . z^10 z^13
z^12 . . z^11 z^1
. . . z^10 z^3
z^10 z^11 z^10 . z^3
z^13 z^1 z^3 z^3 .
gap> mat := [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]*Z(7)^0;
[ [ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ], [ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ],
[ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0 ], [ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ] ]
gap> form := BilinearFormByMatrix(mat);
< bilinear form >
gap> WittIndex(form);
1
gap> form := BilinearFormByMatrix(mat,GF(49));
< bilinear form >
gap> WittIndex(form);
2
[ Dauer der Verarbeitung: 0.5 Sekunden
(vorverarbeitet)
]
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