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gap> pg := PG(3,8);
ProjectiveSpace(3, 8)
gap> vec := [0,1,0,1]*Z(8)^0;
[ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0 ]
gap> point := VectorSpaceToElement(pg,vec);
<a point in ProjectiveSpace(3, 8)>
gap> mat := [[0,0,1,1],[0,1,0,0]]*Z(8)^0;
[ [ 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ] ]
gap> line := VectorSpaceToElement(pg,mat);
<a line in ProjectiveSpace(3, 8)>
gap> mat2 := [[1,0,0,1],[1,0,1,0],[1,1,0,0]]*Z(8)^0;
[ [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ], [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ],
[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ] ]
gap> plane := VectorSpaceToElement(pg,mat2);
<a plane in ProjectiveSpace(3, 8)>
gap> IsIncident(point,line);
false
gap> IsIncident(line,point);
false
gap> point * line;
false
gap> line * point
> point in line;
Syntax error: ; expected
point in line;
^
gap> line in point;
false
gap> IsIncident(point,plane);
true
gap> IsIncident(line,plane);
false
gap> line in plane;
false
gap> plane2 := Span(point,line);
<a plane in ProjectiveSpace(3, 8)>
gap> Meet(plane,plane2);
<a line in ProjectiveSpace(3, 8)>
gap> mat3 := [[1,0,0,0],[0,0,0,1]]*Z(8)^0;
[ [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ] ]
gap> line2 := VectorSpaceToElement(pg,mat3);
<a line in ProjectiveSpace(3, 8)>
gap> Meet(line,line2);
< empty subspace >
gap> Span(plane,plane2);
ProjectiveSpace(3, 8)
[ Dauer der Verarbeitung: 0.3 Sekunden
(vorverarbeitet)
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