Quelle polarities_commuting.include
Sprache: unbekannt
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Spracherkennung für: .include vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
gap> mat := [[ 0, 1, 0, 0],[ 1, 0, 0, 0],[ 0, 0, 0, 1],[ 0, 0, 1, 0]]*Z( 5)^ 0;
[ [ 0*Z( 5), Z( 5)^ 0, 0*Z( 5), 0*Z( 5) ], [ Z( 5)^ 0, 0*Z( 5), 0*Z( 5), 0*Z( 5) ],
[ 0*Z( 5), 0*Z( 5), 0*Z( 5), Z( 5)^ 0 ], [ 0*Z( 5), 0*Z( 5), Z( 5)^ 0, 0*Z( 5) ] ]
gap> phi := HermitianPolarityOfProjectiveSpace(mat,GF( 25));
<polarity of PG( 3, GF( 5^ 2)) >
gap> mat2 := IdentityMat( 4,GF( 5));
[ [ Z( 5)^ 0, 0*Z( 5), 0*Z( 5), 0*Z( 5) ], [ 0*Z( 5), Z( 5)^ 0, 0*Z( 5), 0*Z( 5) ],
[ 0*Z( 5), 0*Z( 5), Z( 5)^ 0, 0*Z( 5) ], [ 0*Z( 5), 0*Z( 5), 0*Z( 5), Z( 5)^ 0 ] ]
gap> psi := PolarityOfProjectiveSpace(mat2,GF( 25));
<polarity of PG( 3, GF( 5^ 2)) >
gap> phi*psi = psi*phi;
true
gap> g := CorrelationCollineationGroup(PG( 3, 25));
The FinInG correlation-collineation group PGammaL( 4, 25) : 2
gap> h := CollineationGroup(PG( 3, 25));
The FinInG collineation group PGammaL( 4, 25)
gap> hom := Embedding(h,g);
MappingByFunction( The FinInG collineation group PGammaL( 4, 25), The FinInG cor
relation-collineation group PGammaL( 4, 25) : 2, function( y ) ... end )
gap> coll := PreImagesRepresentative(hom,phi*psi);
< a collineation: <cmat 4x4 over GF( 5, 2)>, F^ 5>
[Dauer der Verarbeitung: 0.12 Sekunden, vorverarbeitet 2026-06-17]
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2026-08-25
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