1gap> #constructing the same form over different fields
2gap> mat :=
3> [[Z(2)^0,Z(2)^0,0*Z(2),0*Z(2)],[0*Z(2),Z(2)^0,0*Z(2),0*Z(2)],
4>  [0*Z(2),0*Z(2),0*Z(2),Z(2)^0],[0*Z(2),0*Z(2),0*Z(2),0*Z(2)]];
5[ [ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ],
6  [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ], [ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ] ]
7gap> form := QuadraticFormByMatrix(mat);
8< quadratic form >
9gap> WittIndex(form);
101
11gap> form := QuadraticFormByMatrix(mat,GF(4));
12< quadratic form >
13gap> WittIndex(form);
142
15gap> quit;
16