  We prove that double Schubert polynomials have the Saturated Newton Polytope
property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are
motivated by the theory of multidegrees. We introduce a notion of
standardization of ideals that enables us to study non-standard multigradings.
This allows us to show that the support of the multidegree polynomial of each
Cohen-Macaulay prime ideal, and in particular, that of each Schubert
determinantal ideal is a discrete polymatroid.
