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gap> ps := HyperbolicQuadric(5,7);
Q+(5, 7)
gap> em := KleinCorrespondenceExtended(ps);
<geometry morphism from <All elements of ProjectiveSpace(3,
7)> to <Elements of Q+(5, 7)>>
gap> hom := Intertwiner(em);
MappingByFunction( The FinInG collineation group PGL(4,7), <projective colline
ation group with 2 generators>, function( g ) ... end, function( g ) ... end )
gap> mat := [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],
> [0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]]*Z(7)^0;
[ [ 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0 ],
[ 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ],
[ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ],
[ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ],
[ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7) ],
[ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7) ] ]
gap> g := Projectivity(mat,GF(7));
< a collineation: <cmat 6x6 over GF(7,1)>, F^0>
gap> g in CollineationGroup(ps);
true
gap> PreImageElm(hom,g);
#I <el> is not inducing a collineation of PG(3,q)
fail
[ Dauer der Verarbeitung: 0.7 Sekunden
(vorverarbeitet)
]
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