Quelle polarities_ishermitian.include
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gap> mat := [[0,2,7,1],[2,0,3,0],[7,3,0,1],[1,0,1,0]]*Z(19)^0;
[ [ 0*Z(19), Z(19), Z(19)^6, Z(19)^0 ], [ Z(19), 0*Z(19), Z(19)^13, 0*Z(19) ],
[ Z(19)^6, Z(19)^13, 0*Z(19), Z(19)^0 ],
[ Z(19)^0, 0*Z(19), Z(19)^0, 0*Z(19) ] ]
gap> frob := FrobeniusAutomorphism(GF(19^4));
FrobeniusAutomorphism( GF(19^4) )
gap> phi := PolarityOfProjectiveSpace(mat,frob^2,GF(19^4));
<polarity of PG(3, GF(19^4)) >
gap> IsHermitianPolarityOfProjectiveSpace(phi);
true
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2026-03-28
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