Simple generators of rational function fields
Symbolic Computation
2026-03-06 v2 Mathematical Software
Systems and Control
Systems and Control
Commutative Algebra
Dynamical Systems
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.
Cite
@article{arxiv.2602.10878,
title = {Simple generators of rational function fields},
author = {Alexander Demin and Gleb Pogudin},
journal= {arXiv preprint arXiv:2602.10878},
year = {2026}
}