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products/sources/formale Sprachen/GAP/pkg/fining/examples/include/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 27.6.2023 mit Größe 2 kB

Quelle incgeom_underlyingobject.include Sprache: unbekannt

gap> pg := PG(2,2);
ProjectiveSpace(2, 2)
gap> p := Random(Points(pg));
<a point in ProjectiveSpace(2, 2)>
gap> UnderlyingObject(p);
<cvec over GF(2,1) of length 3>
gap> l := Random(Lines(pg));
<a line in ProjectiveSpace(2, 2)>
gap> UnderlyingObject(l);
<cmat 2x3 over GF(2,1)>
gap> mat := [ [ 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
>   [ 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
>   [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
>   [ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
>   [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 ],
>   [ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ],
>   [ 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
>   [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
>   [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
>   [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
>   [ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 ],
>   [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1 ],
>   [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1 ],
>   [ 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 ],
>   [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1 ] ];
[ [ 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
  [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
  [ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
  [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ],
  [ 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
  [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
  [ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1 ],
  [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1 ],
  [ 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1 ] ]
gap> gp := GeneralisedPolygonByIncidenceMatrix(mat);
<generalised quadrangle of order [ 2, 2 ]>
gap> p := Random(Points(gp));
<a point in <generalised quadrangle of order [ 2, 2 ]>>
gap> UnderlyingObject(p);
15
gap> l := Random(Lines(gp));
<a line in <generalised quadrangle of order [ 2, 2 ]>>
gap> UnderlyingObject(l);
[ 7, 13, 15 ]
gap> egq := EGQByBLTSet(BLTSetByqClan(LinearqClan(3)));
#I  Now embedding dual BLT-set into W(5,q)...
#I  Computing elation group...
<EGQ of order [ 9, 3 ] and basepoint in W(5, 3 ) >
gap> p := Random(Points(egq));
<a point in <EGQ of order [ 9, 3 ] and basepoint in W(5, 3 ) >>
gap> UnderlyingObject(p);
<a point in W(5, 3)>