  Diophantine approximation is the problem of approximating a real number by
rational numbers. We propose a version of this in which the numerators are
approximately related to the denominators by a Laurent polynomial. Our
definition is motivated by the problem of constructing strict deformation
quantizations of symplectic manifolds. We show that this type of approximation
exists for any real number and also investigate what happens if the number is
rational or a quadratic irrational.
