Bug in BaseChangeOrthogonalBilinear resp. BaseChangeOrthogonalQuadratic or mistake in their source code documentation

[fingolfin]

The comment before BaseChangeOrthogonalBilinear and BaseChangeOrthogonalQuadratic indicate that the second entry of the triple they returns indicates the rank of the (canonical) form. But this does not seem to be true in general.

For BaseChangeOrthogonalBilinear it seems to actually return the rank minus one.

Question is: is the comment wrong, or the code? To decide this, one should look at where this value is used, e.g. to compute the Witt index of a form.

For BaseChangeOrthogonalQuadratic I do not yet quite understand what it is.

[jdebeule]

This code has been used extensively to compute the radical of a form, so I am convinced this is about the documentation. The number could be defined more clearly as follows. If n is the dimension of the vector space, then n-r is the dimension of the radical of the form.