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gap> #A form for W(5,3)
gap> f := GF(3);
GF(3)
gap> gram := [
> [0,0,0,1,0,0],
> [0,0,0,0,1,0],
> [0,0,0,0,0,1],
> [-1,0,0,0,0,0],
> [0,-1,0,0,0,0],
> [0,0,-1,0,0,0]] * One(f);;
gap> form := BilinearFormByMatrix( gram, f );
< bilinear form >
gap> IsSymplecticForm( form );
true
gap> Display( form );
Symplectic form
Gram Matrix:
. . . 1 . .
. . . . 1 .
. . . . . 1
2 . . . . .
. 2 . . . .
. . 2 . . .
gap> b := BaseChangeToCanonical( form );
< immutable compressed matrix 6x6 over GF(3) >
gap> Display( b );
1 . . . . .
. . . 1 . .
. . 1 . . .
. . . . . 1
. . . . 1 .
. 2 . . . .
gap> Display( b * gram * TransposedMat(b) );
. 1 . . . .
2 . . . . .
. . . 1 . .
. . 2 . . .
. . . . . 1
. . . . 2 .
gap> quit;
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