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gap> pg:=SymplecticSpace(5,2);
W(5, 2)
gap> pi:=Random(Planes(pg));
<a plane in W(5, 2)>
gap> l:=Random(Lines(pi));
<a line in W(5, 2)>
gap> p:=Random(Points(l));
<a point in W(5, 2)>
gap> g:=CollineationGroup(pg);
PGammaSp(6,2)
gap> g1:=Stabilizer(g,p);
<projective collineation group of size 23040 with 3 generators>
gap> g2:=Stabilizer(g,l);
<projective collineation group of size 4608 with 4 generators>
gap> g3:=Stabilizer(g,pi);
<projective collineation group of size 10752 with 3 generators>
gap> cg:=CosetGeometry(g, [g1,g2,g3]);
CosetGeometry( PGammaSp(6,2) )
gap> RandomFlag(cg); # Time of last command: 10745 ms
<Flag of coset geometry < CosetGeometry( PGammaSp(6,2) ,
[
Group(
[ ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ],
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2)
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ],
[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ],
[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )) ] ),
Group(
[ ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0 ],
[ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )) ] ),
Group(
[ ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0 ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0
],]),IdentityMapping( GF(2) )),
ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ],
[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2)
],]),IdentityMapping( GF(2) )) ] ) ] ) >>
gap> Type(last);
[ ]
gap> ResidueOfFlag(last2);
CosetGeometry( PGammaSp(6,2) )
gap> Rank(last);
3
gap> NrElementsOfIncidenceStructure(last2,1);
63
gap> flg:=RandomFlag(cg);;
gap> can:=CanonicalResidueOfFlag(cg,flg);
CosetGeometry( Group( ... ) )
gap> Type(flg);
[ 1, 2 ]
gap> Rank(can);
1
gap> res:=ResidueOfFlag(flg);
CosetGeometry( Group(
[ ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),6,[
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),6,[[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),6,[[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),6,[[ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),6,[[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),6,[[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0 ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )) ] ) )
gap> IsIsomorphicIncidenceStructureWithNauty(res,can);
#I Using NiceMonomorphism...
#I Using NiceMonomorphism...
true
[ Dauer der Verarbeitung: 0.12 Sekunden
(vorverarbeitet)
]
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