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gap> ps := PG(6,27);
ProjectiveSpace(6, 27)
gap> frame := RandomFrameOfProjectiveSpace(ps);
[ <a point in ProjectiveSpace(6, 27)>, <a point in ProjectiveSpace(6, 27)>,
<a point in ProjectiveSpace(6, 27)>, <a point in ProjectiveSpace(6, 27)>,
<a point in ProjectiveSpace(6, 27)>, <a point in ProjectiveSpace(6, 27)>,
<a point in ProjectiveSpace(6, 27)>, <a point in ProjectiveSpace(6, 27)> ]
gap> sub := SubgeometryOfProjectiveSpaceByFrame(ps,frame,GF(3));
Subgeometry PG(6, 3) of ProjectiveSpace(6, 27)
gap> Points(sub);
<points of Subgeometry PG(6, 3) of ProjectiveSpace(6, 27)>
gap> Lines(sub);
<lines of Subgeometry PG(6, 3) of ProjectiveSpace(6, 27)>
gap> Planes(sub);
<planes of Subgeometry PG(6, 3) of ProjectiveSpace(6, 27)>
gap> Solids(sub);
<solids of Subgeometry PG(6, 3) of ProjectiveSpace(6, 27)>
gap> Hyperplanes(sub);
<proj. 5-subspaces of Subgeometry PG(6, 3) of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,1);
<points of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,2);
<lines of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,3);
<planes of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,4);
<solids of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,5);
<proj. 4-subspaces of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,6);
<proj. 5-subspaces of ProjectiveSpace(6, 27)>
gap> ElementsOfIncidenceStructure(ps,7);
Error, <ps> has no elements of type <j> at ./pkg/fining/lib/projectivespace.gi:274 called from
<function "ElementsOfIncidenceStructure for a projective space and an integer"
>( <arguments> )
called from read-eval loop at *stdin*:22
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
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