Spracherkennung für: .include vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
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
