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gap> #test_forms1.g
gap> f := GF(3);;
gap> gram := [[0,0,0,0,0,2],[0,0,0,0,2,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,2,0,0,0,0],[2,0,0,0,0,0]]*Z(3)^0;
[ [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ],
[ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3), 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*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ] ]
gap> form := BilinearFormByMatrix(gram,f);
< bilinear form >
gap> Display(BaseChangeToCanonical(form));
1 . 1 1 . 1
1 . 2 2 . 1
1 2 2 1 . 2
2 . 1 2 2 1
2 . 1 2 . 1
. 1 2 1 2 .
gap> Display(form);
Hyperbolic bilinear form
Gram Matrix:
. . . . . 2
. . . . 2 .
. . . 1 . .
. . 1 . . .
. 2 . . . .
2 . . . . .
Witt Index: 3
gap> TypeOfForm(form);
1
gap> quit;
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
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