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gap> q := 9;
9
gap> f := GF(q);
GF(3^2)
gap> squares := AsList(Group(Z(q)^2));
[ Z(3)^0, Z(3^2)^6, Z(3), Z(3^2)^2 ]
gap> n := First(GF(q), x -> not IsZero(x) and not x in squares);
Z(3^2)
gap> sigma := FrobeniusAutomorphism( f );
FrobeniusAutomorphism( GF(3^2) )
gap> zero := Zero(f);
0*Z(3)
gap> qclan := List(GF(q), t -> [[t, zero], [zero,-n * t^sigma]] );
[ [ [ 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3) ] ],
[ [ Z(3^2), 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ],
[ [ Z(3^2)^5, 0*Z(3) ], [ 0*Z(3), Z(3) ] ],
[ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3^2)^5 ] ],
[ [ Z(3^2)^2, 0*Z(3) ], [ 0*Z(3), Z(3^2)^3 ] ],
[ [ Z(3^2)^3, 0*Z(3) ], [ 0*Z(3), Z(3^2)^6 ] ],
[ [ Z(3), 0*Z(3) ], [ 0*Z(3), Z(3^2) ] ],
[ [ Z(3^2)^7, 0*Z(3) ], [ 0*Z(3), Z(3^2)^2 ] ],
[ [ Z(3^2)^6, 0*Z(3) ], [ 0*Z(3), Z(3^2)^7 ] ] ]
gap> IsqClan( qclan, f );
true
gap> qclan := qClan(qclan , f);
<q-clan over GF(3^2)>
gap> egq1 := EGQByqClan( qclan);
#I Computed Kantor family. Now computing EGQ...
<EGQ of order [ 81, 9 ] and basepoint 0>
gap> blt := BLTSetByqClan( qclan );
[ <a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0>,
<a point in Q(4, 9): -x_1*x_5-x_2*x_4+Z(3^2)^5*x_3^2=0> ]
gap> egq2 := EGQByBLTSet( blt );
#I Now embedding dual BLT-set into W(5,q)...
#I Computing elation group...
<EGQ of order [ 81, 9 ] and basepoint in W(5, 9 ) >
[ Dauer der Verarbeitung: 0.4 Sekunden
(vorverarbeitet)
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