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gap> #Background theory: example 4
gap> mat := [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],
> [0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]*Z(16)^0;
[ [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ] ]
gap> form := BilinearFormByMatrix(mat,GF(16));
< bilinear form >
gap> Display(form);
Bilinear form
Gram Matrix:
. 1 . . . .
1 . . . . .
. . . . . 1
. . . . 1 .
. . . 1 . .
. . 1 . . .
gap> IsSymmetricForm(form);
true
gap> IsAlternatingForm(form);
true
gap> IsDegenerateForm(form);
false
gap> WittIndex(form);
3
gap> quit;
[ Dauer der Verarbeitung: 0.5 Sekunden
(vorverarbeitet)
]
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