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gap> pg := PG(2,25);
ProjectiveSpace(2, 25)
gap> pts := Set(Points(pg));;
gap> lns := Set(Lines(pg));;
gap> inc := \*;
<Operation "*">
gap> gp := GeneralisedPolygonByElements(pts,lns,inc);
<projective plane order 25>
gap> time;
26427
gap> grp := CollineationGroup(pg);
The FinInG collineation group PGammaL(3,25)
gap> act := OnProjSubspaces;
function( var, el ) ... end
gap> gp := GeneralisedPolygonByElements(pts,lns,inc,grp,act);
<projective plane order 25>
gap> time;
127
gap> q := 4;
4
gap> conic := Set(Points(ParabolicQuadric(2,q)));
[ <a point in Q(2, 4)>, <a point in Q(2, 4)>, <a point in Q(2, 4)>,
<a point in Q(2, 4)>, <a point in Q(2, 4)> ]
gap> pg := PG(3,q);
ProjectiveSpace(3, 4)
gap> hyp := HyperplaneByDualCoordinates(pg,[1,0,0,0]*Z(q)^0);
<a plane in ProjectiveSpace(3, 4)>
gap> em := NaturalEmbeddingBySubspace(PG(2,q),pg,hyp);
<geometry morphism from <All elements of ProjectiveSpace(2,
4)> to <All elements of ProjectiveSpace(3, 4)>>
gap> O := List(conic,x->x^em);;
gap> group := CollineationGroup(pg);
The FinInG collineation group PGammaL(4,4)
gap> stab := FiningSetwiseStabiliser(group,O);
#I Computing adjusted stabilizer chain...
<projective collineation group with 6 generators>
gap> points1 := Set(Filtered(Points(pg),x->not x in hyp));;
gap> tangents := List(conic,x->TangentSpace(x)^em);
[ <a line in ProjectiveSpace(3, 4)>, <a line in ProjectiveSpace(3, 4)>,
<a line in ProjectiveSpace(3, 4)>, <a line in ProjectiveSpace(3, 4)>,
<a line in ProjectiveSpace(3, 4)> ]
gap> planes := List(tangents,x->Filtered(Planes(x),y->not y in hyp));;
gap> points2 := Union(planes);;
gap> points3 := [hyp];
[ <a plane in ProjectiveSpace(3, 4)> ]
gap> linesa := Union(List(O,x->Filtered(Lines(x),y->not y in hyp)));;
gap> linesb := Set(O);;
gap> pts := Union(points1,points2,points3);;
gap> lns := Union(linesa,linesb);;
gap> inc := \*;
<Operation "*">
gap> gp := GeneralisedPolygonByElements(pts,lns,inc,stab,\^);
<generalised quadrangle of order [ 4, 4 ]>
gap> time;
50
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
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