Quelle diagram_connectedness.include
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Spracherkennung für: .include vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
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: 0.10 Sekunden, vorverarbeitet 2026-06-17]
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2026-08-25
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