Quelle cps_evaluateform.include Sprache: unbekannt

gap> f := GF(5);
GF(5)
gap> mat := IdentityMat(4,f);
[ [ Z(5)^0, 0*Z(5), 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5), 0*Z(5) ],
[ 0*Z(5), 0*Z(5), Z(5)^0, 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0 ] ]
gap> form := BilinearFormByMatrix(mat,f);
< bilinear form >
gap> pg := PG(3,5);
ProjectiveSpace(3, 5)
gap> pts := Filtered(Points(pg),x->[x,x]^form = Zero(f));;
gap> ps := PolarSpace(form);
<polar space in ProjectiveSpace(3,GF(5)): x_1^2+x_2^2+x_3^2+x_4^2=0 >
gap> Collected(List(pts,x->x in ps));
[ [ true, 36 ] ]
gap> Size(Points(ps));
36
gap> qform := QuadraticForm(ps);
< quadratic form >
gap> pts2 := Filtered(Points(pg),x->x^qform = Zero(f));;
gap> Collected(List(pts2,x->x in ps));
[ [ true, 36 ] ]

Quelle cps_evaluateform.include Sprache: unbekannt

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