Finding Simple Generators of Rational Function Fields

Consider a subfield of the field of rational functions in several indeterminates represented explicitly by a list of rational functions, its generators. In this paper, we present methods for computing simpler sets of generators for such subfields when working over the rational numbers. Our method uses a reduction to ideals of polynomial rings and is based on probabilistic sparse rational function interpolation. We implement our method in Julia with a focus on computational efficiency, and use the implementation to tackle problems in structural identifiability analysis of dynamical models.