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gap> pg := PG(3,3^5);
ProjectiveSpace(3, 243)
gap> vectors := [ [ Z(3)^0, Z(3^5)^58, Z(3), Z(3^5)^239 ],
> [ Z(3)^0, Z(3^5)^217, Z(3^5)^18, Z(3^5)^65 ],
> [ Z(3)^0, Z(3^5)^202, Z(3^5)^52, Z(3^5)^209 ],
> [ Z(3)^0, Z(3^5)^93, Z(3^5)^123, Z(3^5)^93 ],
> [ Z(3)^0, Z(3^5)^199, Z(3^5)^68, Z(3^5)^13 ] ];
[ [ Z(3)^0, Z(3^5)^58, Z(3), Z(3^5)^239 ],
[ Z(3)^0, Z(3^5)^217, Z(3^5)^18, Z(3^5)^65 ],
[ Z(3)^0, Z(3^5)^202, Z(3^5)^52, Z(3^5)^209 ],
[ Z(3)^0, Z(3^5)^93, Z(3^5)^123, Z(3^5)^93 ],
[ Z(3)^0, Z(3^5)^199, Z(3^5)^68, Z(3^5)^13 ] ]
gap> frame := List(vectors,x->VectorSpaceToElement(pg,x));
[ <a point in ProjectiveSpace(3, 243)>, <a point in ProjectiveSpace(3, 243)>,
<a point in ProjectiveSpace(3, 243)>, <a point in ProjectiveSpace(3, 243)>,
<a point in ProjectiveSpace(3, 243)> ]
gap> sub := SubgeometryOfProjectiveSpaceByFrame(pg,frame,GF(3));
Subgeometry PG(3, 3) of ProjectiveSpace(3, 243)
gap> p := Random(Points(sub));
<a point in Subgeometry PG(3, 3) of ProjectiveSpace(3, 243)>
gap> Coordinates(p);
[ Z(3)^0, Z(3^5)^217, Z(3^5)^18, Z(3^5)^65 ]
gap> plane := Random(Planes(sub));
<a plane in Subgeometry PG(3, 3) of ProjectiveSpace(3, 243)>
gap> DualCoordinatesOfHyperplane(plane);
[ Z(3)^0, Z(3^5)^175, Z(3^5)^160, Z(3^5)^12 ]
gap> dual := [ Z(3)^0, Z(3^5)^78, Z(3^5)^58, Z(3^5)^8 ];
[ Z(3)^0, Z(3^5)^78, Z(3^5)^58, Z(3^5)^8 ]
gap> pi := HyperplaneByDualCoordinates(sub,dual);
<a plane in Subgeometry PG(3, 3) of ProjectiveSpace(3, 243)>
gap> EquationOfHyperplane(pi);
x_1+Z(3^5)^78*x_2+Z(3^5)^58*x_3+Z(3^5)^8*x_4
[ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
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