🤖 AI Summary
This work addresses the problem of simplifying generating sets for subfields of multivariate rational function fields, aiming to construct smaller and more efficient generating sets from given complex ones. To this end, the authors propose a novel algorithm that integrates sparse interpolation with partial Gröbner basis computation, enabling efficient search for polynomials of fixed degree within the subfield while avoiding the high computational cost of full basis construction. The method significantly outperforms existing approaches in both efficiency and the quality of the resulting generating sets. Its effectiveness and practical utility are further demonstrated through applications in structural parameter identifiability, where the simplified generating sets yield meaningful and computationally advantageous representations.
📝 Abstract
Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and show that it improves upon the state of the art both in efficiency and the quality of the results. Furthermore, we demonstrate the utility of simplified generators through several case studies from different application domains, such as structural parameter identifiability. The main algorithmic novelties include performing only partial Gr\"obner basis computation via sparse interpolation and efficient search for polynomials of a fixed degree in a subfield of the rational function field.