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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
[ 0.89Quellennavigators
]
