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gap> q := 8;
8
gap> pg := PG(3,q);
ProjectiveSpace(3, 8)
gap> f := GF(q);
GF(2^3)
gap> vecs := Union(List(f,x->List(f,y->[One(f),x*y+x^6+y^4,x,y])));;
gap> Add(vecs,[0,1,0,0]*Z(q)^0);
gap> ovoid := List(vecs,x->VectorSpaceToElement(pg,x));;
gap> numbers := List(Planes(pg),x->Number(ovoid,y->y in x));
[ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9,
9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1,
9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1,
9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 1, 9, 9,
1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 1, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 1, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 1, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9,
9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 1, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 1,
9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 1, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 1, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9,
9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9,
9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9,
9, 1, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1,
9, 1, 9, 9, 9, 9, 9, 9, 9, 1 ]
gap> Collected(numbers);
[ [ 1, 65 ], [ 9, 520 ] ]
gap> group := HomographyGroup(pg);
The FinInG projectivity group PGL(4,8)
gap> stab := FiningSetwiseStabiliser(group,ovoid);
#I Computing adjusted stabilizer chain...
<projective collineation group with 5 generators>
gap> time;
55290
gap> IsSimple(stab);
true
gap> Order(stab);
29120
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
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