Quelle  varieties_hermitian.include  Sprache: unbekannt

gap>; F:=GF(25);
GF(5^2)
gap>; r:=PolynomialRing(F,3);
GF(5^2)[x_1,x_2,x_3]
gap>; x:=IndeterminatesOfPolynomialRing(r);
[ x_1, x_2, x_3 ]
gap>; pg:=PG(2,F);
ProjectiveSpace(2, 25)
gap>; f:=x[1]^6+x[2]^6+x[3]^6;
x_1^6+x_2^6+x_3^6
gap>; hv:=HermitianVariety(pg,f);
Hermitian Variety in ProjectiveSpace(2, 25)
gap>; AsSet(List(Lines(pg),l->Size(Filtered(Points(l),x->x in hv))));
[ 1, 6 ]
gap>; hv:=HermitianVariety(5,4);
Hermitian Variety in ProjectiveSpace(5, 4)
gap>; hps:=PolarSpace(hv);
<;polar space in ProjectiveSpace(
5,GF(2^2)): x_1^3+x_2^3+x_3^3+x_4^3+x_5^3+x_6^3=0 >;
gap>; hf:=SesquilinearForm(hv);
<; hermitian form >
gap>; PolynomialOfForm(hf);
x_1^3+x_2^3+x_3^3+x_4^3+x_5^3+x_6^3