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gap> gl:=GL(3,3);
GL(3,3)
gap> go:=GO(3,3);
GO(0,3,3)
gap> form := PreservedSesquilinearForms(go)[1];
< bilinear form >
gap> gram := GramMatrix( form );
[ [ 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3) ] ]
gap> b := BaseChangeToCanonical(form);;
gap> hom := BaseChangeHomomorphism(b, GF(3));
^[ [ 0*Z(3), 0*Z(3), Z(3) ], [ Z(3), Z(3), Z(3)^0 ], [ Z(3), 0*Z(3), Z(3) ] ]
gap> newgo := Image(hom, go);
Group(
[
[ [ Z(3)^0, 0*Z(3), Z(3) ], [ Z(3)^0, Z(3), Z(3)^0 ],
[ 0*Z(3), 0*Z(3), Z(3) ] ],
[ [ Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3) ],
[ Z(3)^0, Z(3)^0, Z(3) ] ] ])
gap> gens := GeneratorsOfGroup(newgo);;
gap> canonical := b * gram * TransposedMat(b);
[ [ Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0 ],
[ 0*Z(3), Z(3)^0, 0*Z(3) ] ]
gap> ForAll(gens, y -> y * canonical * TransposedMat(y) = canonical);
true
[ Dauer der Verarbeitung: 0.13 Sekunden
(vorverarbeitet)
]
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