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gap> ps := EllipticQuadric(5,7);
Q-(5, 7)
gap> vec := [1,0,0,0,0,0]*Z(7)^0;
[ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7) ]
gap> point := VectorSpaceToElement(ps,vec);
Error, <v> does not generate an element of <geom> called from
<function "unknown">( <arguments> )
called from read-eval loop at line 10 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
gap> EquationForPolarSpace(ps);
x_1^2+x_2^2+x_3*x_4+x_5*x_6
gap> vec := [0,0,1,0,0,0]*Z(7)^0;
[ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ]
gap> point := VectorSpaceToElement(ps,vec);
<a point in Q-(5, 7)>
gap> vec2 := [0,0,0,1,0,0]*Z(7)^0;
[ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ]
gap> point2 := VectorSpaceToElement(ps,vec2);
<a point in Q-(5, 7)>
gap> line := Span(point,point2);
<a line in ProjectiveSpace(5, 7)>
gap> mat := [[0,0,1,0,0,0],[0,0,0,0,1,0]]*Z(7)^0;
[ [ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ],
[ 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ] ]
gap> line2 := VectorSpaceToElement(ps,mat);
<a line in Q-(5, 7)>
gap> meet := Meet(line,line2);
<a point in ProjectiveSpace(5, 7)>
gap> meet in ps;
true
gap> point3 := ElementToElement(ps,meet);
<a point in Q-(5, 7)>
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