Quelle quadformbybilform.include
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Spracherkennung für: .include vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
gap> mat := [ [ Z(3^2)^7, Z(3)^0, Z(3^2)^2, 0*Z(3), Z(3^2)^5 ],
> [ Z(3)^0, Z(3^2)^7, Z(3^2)^6, Z(3^2)^5, Z(3^2)^2 ],
> [ Z(3^2)^2, Z(3^2)^6, Z(3^2)^7, Z(3^2)^2, Z(3^2)^2 ],
> [ 0*Z(3), Z(3^2)^5, Z(3^2)^2, Z(3^2)^6, Z(3^2)^7 ],
> [ Z(3^2)^5, Z(3^2)^2, Z(3^2)^2, Z(3^2)^7, Z(3) ] ];
[ [ Z(3^2)^7, Z(3)^0, Z(3^2)^2, 0*Z(3), Z(3^2)^5 ],
[ Z(3)^0, Z(3^2)^7, Z(3^2)^6, Z(3^2)^5, Z(3^2)^2 ],
[ Z(3^2)^2, Z(3^2)^6, Z(3^2)^7, Z(3^2)^2, Z(3^2)^2 ],
[ 0*Z(3), Z(3^2)^5, Z(3^2)^2, Z(3^2)^6, Z(3^2)^7 ],
[ Z(3^2)^5, Z(3^2)^2, Z(3^2)^2, Z(3^2)^7, Z(3) ] ]
gap> form := BilinearFormByMatrix(mat,GF(9));
< bilinear form >
gap> Q := QuadraticFormByBilinearForm(form);
< quadratic form >
gap> Display(form);
Bilinear form
Gram Matrix:
z = Z(9)
z^7 1 z^2 . z^5
1 z^7 z^6 z^5 z^2
z^2 z^6 z^7 z^2 z^2
. z^5 z^2 z^6 z^7
z^5 z^2 z^2 z^7 2
gap> Display(Q);
Quadratic form
Gram Matrix:
z = Z(9)
z^7 2 z^6 . z^1
. z^7 z^2 z^1 z^6
. . z^7 z^6 z^6
. . . z^6 z^3
. . . . 2
gap> Set(List(GF(9)^5),x->[x,x]^form=x^Q);
[ true ]
gap> PolynomialOfForm(form);
Z(3^2)^7*x_1^2-x_1*x_2+Z(3^2)^6*x_1*x_3+Z(3^2)*x_1*x_5+Z(3^2)^7*x_2^2+Z(3^2)^2
*x_2*x_3+Z(3^2)*x_2*x_4+Z(3^2)^6*x_2*x_5+Z(3^2)^7*x_3^2+Z(3^2)^6*x_3*x_4+Z(3^2
)^6*x_3*x_5+Z(3^2)^6*x_4^2+Z(3^2)^3*x_4*x_5-x_5^2
gap> PolynomialOfForm(Q);
Z(3^2)^7*x_1^2-x_1*x_2+Z(3^2)^6*x_1*x_3+Z(3^2)*x_1*x_5+Z(3^2)^7*x_2^2+Z(3^2)^2
*x_2*x_3+Z(3^2)*x_2*x_4+Z(3^2)^6*x_2*x_5+Z(3^2)^7*x_3^2+Z(3^2)^6*x_3*x_4+Z(3^2
)^6*x_3*x_5+Z(3^2)^6*x_4^2+Z(3^2)^3*x_4*x_5-x_5^2
[ Dauer der Verarbeitung: 0.87 Sekunden
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2026-03-28
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