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gap> mat := [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,-1]]*Z(9)^0;
[ [ 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) ] ]
gap> form := BilinearFormByMatrix(mat,GF(9));
< bilinear form >
gap> Display(form);
Bilinear form
Gram Matrix:
1 . . .
. 1 . .
. . 1 .
. . . 2
gap> IsReflexiveForm(form);
true
gap> IsSymmetricForm(form);
true
gap> IsAlternatingForm(form);
false
gap> r := RadicalOfForm(form);
<vector space of dimension 0 over GF(3^2)>
gap> Dimension(r);
0
[ Dauer der Verarbeitung: 0.11 Sekunden
(vorverarbeitet)
]
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