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gap> mat := IdentityMat(4,GF(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, 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> phi := PolarityOfProjectiveSpace(mat,GF(3));
<polarity of PG(3, GF(3)) >
gap> points := AbsolutePoints(phi);
<points of Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>
gap> List(points);
[ <a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0>,
<a point in Q+(3, 3): x_1^2+x_2^2+x_3^2+x_4^2=0> ]
[ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
]
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