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gap> r := PolynomialRing(GF(9),4);
GF(3^2)[x_1,x_2,x_3,x_4]
gap> poly := -r.1*r.2+Z(3^2)*r.3^2+r.4^2;
-x_1*x_2+Z(3^2)*x_3^2+x_4^2
gap> qform := QuadraticFormByPolynomial(poly,r);
< quadratic form >
gap> Display( qform );
Quadratic form
Gram Matrix:
z = Z(9)
. 2 . .
. . . .
. . z^1 .
. . . 1
Polynomial: -x_1*x_2+Z(3^2)*x_3^2+x_4^2
gap> form := BilinearFormByQuadraticForm( qform );
< bilinear form >
gap> Display(form);
Bilinear form
Gram Matrix:
z = Z(9)
. 1 . .
1 . . .
. . z^1 .
. . . 1
gap> Set(GF(9)^4, x -> [x,x]^form = x^qform);
[ true ]
[ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
]
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