More problems with orthogonal groups ...

[ThomasBreuer]

I am trying to get a solution for the problem from issue #500, in the direction of what @frankluebeck, @fingolfin, and @stevelinton had suggested.
The problem seems to be that the quadratic forms stored in the groups Omega( -1, 2m, 2^n ) are wrong.
Or do I misunderstand something?

gap> m:= 4;; q:= 2;;
gap> g:= Omega( -1, m, q );;
gap> gens:= GeneratorsOfGroup( g );;
gap> Q:= InvariantQuadraticForm( g ).matrix;;   # the stored form
gap> ForAll( GF(q)^m, v -> ForAll( gens, g -> v*Q*v = (v*g)*Q*(v*g) ) );
false
gap> Q:= [[0,0,0,1],[0,1,1,0],[0,0,1,0],[0,0,0,0]] * Z(2);;  # the correct form
gap> ForAll( GF(q)^m, v -> ForAll( gens, g -> v*Q*v = (v*g)*Q*(v*g) ) );
true
gap> m:= 6;; q:= 2;;
gap> g:= Omega( -1, m, q );;
gap> gens:= GeneratorsOfGroup( g );;
gap> Q:= InvariantQuadraticForm( g ).matrix;;   # the stored form
gap> ForAll( GF(q)^m, v -> ForAll( gens, g -> v*Q*v = (v*g)*Q*(v*g) ) );
false
gap> Q:= [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]] * Z(2);;  # the correct form
gap> ForAll( GF(q)^m, v -> ForAll( gens, g -> v*Q*v = (v*g)*Q*(v*g) ) );
true