|
gap> id := IdentityMat(7, GF(3));;
gap> form := QuadraticFormByMatrix(id, GF(3));
< quadratic form >
gap> ps := PolarSpace( form );
<polar space in ProjectiveSpace(
6,GF(3)): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2=0 >
gap> psl32 := PSL(3,2);
Group([ (4,6)(5,7), (1,2,4)(3,6,5) ])
gap> reps:=[[1,1,1,0,0,0,0], [-1,1,1,0,0,0,0], [1,-1,1,0,0,0,0], [1,1,-1,0,0,0,0]]*Z(3)^0;;
gap> ovoid := Union( List(reps, x-> Orbit(psl32, x, Permuted)) );;
gap> ovoid := List(ovoid, x -> VectorSpaceToElement(ps, x));;
gap> planes := AsList( Planes( ps ) );;
#I Computing collineation group of canonical polar space...
gap> ForAll(planes, p -> Number(ovoid, x -> x in p) = 1);
true
[ Dauer der Verarbeitung: 0.13 Sekunden
(vorverarbeitet)
]
|
