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gap> ps:=HyperbolicQuadric(7,2);
Q+(7, 2)
gap> g:=IsometryGroup(ps);;
gap> reps:=RepresentativesOfElements(ps);
[ <a point in Q+(7, 2)>, <a line in Q+(7, 2)>, <a plane in Q+(7, 2)>,
<a solid in Q+(7, 2)> ]
gap> solids:=Orbit(g,reps[4]);;
gap> ps:=HyperbolicQuadric(7,2);
Q+(7, 2)
gap> g:=IsometryGroup(ps);;
gap> reps:=RepresentativesOfElements(ps);
[ <a point in Q+(7, 2)>, <a line in Q+(7, 2)>, <a plane in Q+(7, 2)>,
<a solid in Q+(7, 2)> ]
gap> h:=DerivedSubgroup(g);; # to get greek and latin solids
gap> orbs:=FiningOrbits(h,Solids(ps));;
50%..100%..gap> List(orbs, Size);
[ 135, 135 ]
gap> Filtered(orbs[2], s -> ProjectiveDimension(Meet(orbs[1][1],s))=2); # to
[ <a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>,
<a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>,
<a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>,
<a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>,
<a solid in Q+(7, 2)>, <a solid in Q+(7, 2)>, <a solid in Q+(7, 2)> ]
gap> #find a latin incident with the greek which is orbs[1][1]
gap> # Now we have a chamber
gap> goodreps:=[reps[1],reps[2],orbs[1][1],last[1]];
[ <a point in Q+(7, 2)>, <a line in Q+(7, 2)>, <a solid in Q+(7, 2)>,
<a solid in Q+(7, 2)> ]
gap> pabs:=List(goodreps, r -> FiningStabiliser(h,r));
[ <projective collineation group of size 1290240 with 2 generators>,
<projective collineation group of size 110592 with 4 generators>,
<projective collineation group of size 1290240 with 2 generators>,
<projective collineation group of size 1290240 with 4 generators> ]
gap> cos:=CosetGeometry(h,pabs);
CosetGeometry( Group(
[ ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,1),8,[
[ Z(2)^0, Z(2)^0, 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), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 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, 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), 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) ],
[ 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), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),8,[[ 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), 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, 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), 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), 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), Z(2)^0, 0*Z(2)
],]),IdentityMapping( GF(2) )), ProjElWithFrob(NewMatrix(IsCMatRep,GF(2,
1),8,[[ 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), 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, 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) ],
[ 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, 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) ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0
],]),IdentityMapping( GF(2) )) ] ) )
gap> IsConnected(cos);
true
gap> IsResiduallyConnected(cos);
true
gap> time;
419960
[ Dauer der Verarbeitung: 0.13 Sekunden
(vorverarbeitet)
]
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