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gap> pgsub := PG(2,7);
ProjectiveSpace(2, 7)
gap> pg := PG(2,7^2);
ProjectiveSpace(2, 49)
gap> em := NaturalEmbeddingBySubfield(pgsub,pg);
<geometry morphism from <All elements of ProjectiveSpace(2,
7)> to <All elements of ProjectiveSpace(2, 49)>>
gap> baer := List(Points(pgsub),x->x^em);;
gap> numbers := Collected(List(Lines(pg),x->Number(baer,y->y in x)));
[ [ 1, 2394 ], [ 8, 57 ] ]
gap> mat := [[0,0,0,1],[0,0,-1,0],[0,1,0,0],[-1,0,0,0]]*Z(5)^0;
[ [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0 ], [ 0*Z(5), 0*Z(5), Z(5)^2, 0*Z(5) ],
[ 0*Z(5), Z(5)^0, 0*Z(5), 0*Z(5) ], [ Z(5)^2, 0*Z(5), 0*Z(5), 0*Z(5) ] ]
gap> form := BilinearFormByMatrix(mat,GF(5));
< bilinear form >
gap> symplecticspace := PolarSpace(form);
<polar space in ProjectiveSpace(3,GF(5)): x1*y4-x2*y3+x3*y2-x4*y1=0 >
gap> hermitianspace := HermitianPolarSpace(3,25);
H(3, 5^2)
gap> em := NaturalEmbeddingBySubfield(symplecticspace,hermitianspace);
#I No intertwiner computed. <geom1> must have a collineation group computed
<geometry morphism from <Elements of <polar space in ProjectiveSpace(
3,GF(5)): x1*y4-x2*y3+x3*y2-x4*y1=0 >> to <Elements of H(3, 5^2)>>
gap> l := Random(Lines(symplecticspace));
<a line in W(3, 5): x1*y4-x2*y3+x3*y2-x4*y1=0>
gap> l^em;
<a line in H(3, 5^2)>
[ Dauer der Verarbeitung: 0.12 Sekunden
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