| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/fining/examples/include/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 27.6.2023 mit Größe 3 kB |
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Quelle diagram_connectedness.include Sprache: unbekannt |
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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: 0.14 Sekunden (vorverarbeitet) ] |
2026-03-28