|
gap> mat := IdentityMat(5,GF(9));
[ [ Z(3)^0, 0*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), 0*Z(3), Z(3)^0, 0*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), 0*Z(3), Z(3)^0 ] ]
gap> form := BilinearFormByMatrix(mat,GF(9));
< bilinear form >
gap> ps := PolarSpace(form);
<polar space in ProjectiveSpace(4,GF(3^2)): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2=0 >
gap> IsParabolicQuadric(ps);
true
gap> mat := [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,0],[0,0,0,0,1],[0,0,0,0,0]]*Z(2)^0;
[ [ Z(2)^0, 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), 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), 0*Z(2) ] ]
gap> form := QuadraticFormByMatrix(mat,GF(8));
< quadratic form >
gap> ps := PolarSpace(form);
<polar space in ProjectiveSpace(4,GF(2^3)): x_1^2+x_2*x_3+x_4*x_5=0 >
gap> IsParabolicQuadric(ps);
true
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
|