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gap> q := 16;
16
gap> mat := [[0,1,0,0,0],[0,0,0,0,0],[0,0,1,0,0],[0,0,0,0,0],[0,0,0,1,0]]*Z(q)^0;
[ [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ] ]
gap> form := QuadraticFormByMatrix(mat,GF(q));
< quadratic form >
gap> q4q := PolarSpace(form);
<polar space in ProjectiveSpace(4,GF(2^4)): x_1*x_2+x_3^2+x_4*x_5=0 >
gap> em := SelfDuality(q4q);
#I No intertwiner computed. The polar space must have a collineation group computed
<geometry morphism from <Elements of Q(4,
16): x_1*x_2+x_3^2+x_4*x_5=0> to <Elements of Q(4,
16): x_1*x_2+x_3^2+x_4*x_5=0>>
gap> CollineationGroup(q4q);
#I Computing collineation group of canonical polar space...
<projective collineation group of size 4380799795200 with 3 generators>
gap> em := SelfDuality(q4q);
<geometry morphism from <Elements of Q(4,
16): x_1*x_2+x_3^2+x_4*x_5=0> to <Elements of Q(4,
16): x_1*x_2+x_3^2+x_4*x_5=0>>
gap> hom := Intertwiner(em);
MappingByFunction( <projective collineation group of size 4380799795200 with
3 generators>, <projective collineation group of size 4380799795200 with
3 generators>, function( el ) ... end, function( el ) ... end )
gap> q := 16;
16
gap> w := SymplecticSpace(3,q);
W(3, 16)
gap> em := SelfDuality(w);
<geometry morphism from <Elements of W(3, 16)> to <Elements of W(3, 16)>>
[ Dauer der Verarbeitung: 0.20 Sekunden
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