Spracherkennung für: .include vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
gap> pg1 := PG(
2,
3);
ProjectiveSpace(
2,
3)
gap> pg2 := PG(
2,
9);
ProjectiveSpace(
2,
9)
gap> em := NaturalEmbeddingBySubfield(pg1,pg2);
<geometry morphism from <All elements of ProjectiveSpace(
2,
3)> to <All elements of ProjectiveSpace(
2,
9)>>
gap> points := AsList(Points( pg1 ));
[ <a point in ProjectiveSpace(
2,
3)>, <a point in ProjectiveSpace(
2,
3)>,
<a point in ProjectiveSpace(
2,
3)>, <a point in ProjectiveSpace(
2,
3)>,
<a point in ProjectiveSpace(
2,
3)>, <a point in ProjectiveSpace(
2,
3)>,
<a point in ProjectiveSpace(
2,
3)>, <a point in ProjectiveSpace(
2,
3)>,
<a point in ProjectiveSpace(
2,
3)>, <a point in ProjectiveSpace(
2,
3)>,
<a point in ProjectiveSpace(
2,
3)>, <a point in ProjectiveSpace(
2,
3)>,
<a point in ProjectiveSpace(
2,
3)> ]
gap> image := ImagesSet(em, points);
[ <a point in ProjectiveSpace(
2,
9)>, <a point in ProjectiveSpace(
2,
9)>,
<a point in ProjectiveSpace(
2,
9)>, <a point in ProjectiveSpace(
2,
9)>,
<a point in ProjectiveSpace(
2,
9)>, <a point in ProjectiveSpace(
2,
9)>,
<a point in ProjectiveSpace(
2,
9)>, <a point in ProjectiveSpace(
2,
9)>,
<a point in ProjectiveSpace(
2,
9)>, <a point in ProjectiveSpace(
2,
9)>,
<a point in ProjectiveSpace(
2,
9)>, <a point in ProjectiveSpace(
2,
9)>,
<a point in ProjectiveSpace(
2,
9)> ]
gap> hom := Intertwiner(em);
MappingByFunction( The FinInG projectivity group PGL(
3,
3), <projective colline
ation group of size
5616 with
2 generators>, function( x ) ... end, function( y ) ... end )
gap> group1 := ProjectivityGroup(pg1);
The FinInG projectivity group PGL(
3,
3)
gap> gens := GeneratorsOfGroup(group1);
[ < a collineation: <cmat
3x3 over GF(
3,
1)>, F^
0>,
< a collineation: <cmat
3x3 over GF(
3,
1)>, F^
0> ]
gap> group1_image := Group(List(gens,x->x^hom));
<projective collineation group with
2 generators>
gap> Order(group1_image);
5616
gap> group2 := ProjectivityGroup(pg2);
The FinInG projectivity group PGL(
3,
9)
gap> Order(group2);
42456960
gap> g := Random(group2);
< a collineation: <cmat
3x3 over GF(
3,
2)>, F^
0>
gap> PreImageElm(hom,g);
#I <el> is not in the range of the intertwiner
fail
