An important invariant of quadratic forms $(V,q)$ over a field is the Witt index, the dimension of a maximal isotropic subspace of $V$.
Is Sage able to calculate this? I have checked http://doc.sagemath.org/html/en/reference/quadratic_forms/sage/quadratic_forms/quadratic_form.html and there does not seem to be anything there to help me (but I may have overlooked it).