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gap> f := GF(3);
GF(3)
gap> id := IdentityMat(2, f);;
gap> clan := List( f, t -> t*id );;
gap> IsqClan( clan, f );
true
gap> clan := qClan(clan, f);
<q-clan over GF(3)>
gap> egq := EGQByqClan( clan );
#I Computed Kantor family. Now computing EGQ...
<EGQ of order [ 9, 3 ] and basepoint 0>
gap> elations := ElationGroup( egq );
<matrix group of size 243 with 8 generators>
gap> points := Points( egq );
<points of <EGQ of order [ 9, 3 ] and basepoint 0>>
gap> p := Random(points);
<a point of class 2 of <EGQ of order [ 9, 3 ] and basepoint 0>>
gap> x := Random(elations);
[ [ Z(3)^0, 0*Z(3), 0*Z(3), Z(3)^0 ], [ 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0 ],
[ 0*Z(3), 0*Z(3), Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ]
gap> OnKantorFamily(p,x);
<a point of class 2 of <EGQ of order [ 9, 3 ] and basepoint 0>>
gap> orbs := Orbits( elations, points, OnKantorFamily);;
gap> Collected(List( orbs, Size ));
[ [ 1, 1 ], [ 9, 4 ], [ 243, 1 ] ]
gap> blt := BLTSetByqClan( clan );
[ <a point in Q(4, 3): -x_1*x_5-x_2*x_4+x_3^2=0>,
<a point in Q(4, 3): -x_1*x_5-x_2*x_4+x_3^2=0>,
<a point in Q(4, 3): -x_1*x_5-x_2*x_4+x_3^2=0>,
<a point in Q(4, 3): -x_1*x_5-x_2*x_4+x_3^2=0> ]
gap> q4q := AmbientGeometry( blt[1] );
Q(4, 3): -x_1*x_5-x_2*x_4+x_3^2=0
gap> span := Span( blt );
<a plane in ProjectiveSpace(4, 3)>
gap> ProjectiveDimension( span );
2
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