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gap> pg := PG(3,169);
ProjectiveSpace(3, 169)
gap> l := Random(Lines(pg));
<a line in ProjectiveSpace(3, 169)>
gap> vec := PluckerCoordinates(l);
[ Z(13)^0, Z(13^2)^138, Z(13^2)^93, Z(13^2)^53, Z(13^2)^71, Z(13^2)^106 ]
gap> mat := [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],
> [0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]]*Z(13)^0;
[ [ 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), Z(13)^0 ],
[ 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), Z(13)^0, 0*Z(13) ],
[ 0*Z(13), 0*Z(13), 0*Z(13), Z(13)^0, 0*Z(13), 0*Z(13) ],
[ 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13) ],
[ 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13) ],
[ 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13), 0*Z(13) ] ]
gap> form := QuadraticFormByMatrix(mat,GF(169));
< quadratic form >
gap> klein := PolarSpace(form);
<polar space in ProjectiveSpace(5,GF(13^2)): x_1*x_6+x_2*x_5+x_3*x_4=0 >
gap> VectorSpaceToElement(klein,vec);
<a point in Q+(5, 169): x_1*x_6+x_2*x_5+x_3*x_4=0>
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
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