gap> ps := HyperbolicQuadric(5,3);
Q+(5, 3)
gap> x := Random(Points(ps));;
gap> planes_on_x := AsList( Planes(x) );
[ <a plane in Q+(5, 3)>, <a plane in Q+(5, 3)>, <a plane in Q+(5, 3)>,
<a plane in Q+(5, 3)>, <a plane in Q+(5, 3)>, <a plane in Q+(5, 3)>,
<a plane in Q+(5, 3)>, <a plane in Q+(5, 3)> ]
gap> proj := NaturalProjectionBySubspace(ps, x);
<geometry morphism from <Elements of Q+(5,
3)> to <Elements of <polar space in ProjectiveSpace(
3,GF(3)): x_1*x_2+x_3*x_4=0 >>>
gap> image := ImagesSet(proj, planes_on_x);
[ <a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0>,
<a line in Q+(3, 3): x_1*x_2+x_3*x_4=0> ]
