Simple generators of rational function fields

2026/02/11 by Alexander Demin, Gleb Pogudin · 1 citation
Computer Science · Engineering · Mathematics · #Cryptography and Residue Arithmetic #Numerical Methods and Algorithms #Polynomial and algebraic computation #cs.MS #cs.SC #cs.SY #eess.SY #math.AC #math.DS

paper · pdf · doi:10.48550/arxiv.2602.10878

openalex publication_date 2026/02/11 · openalex created_date 2026/02/13 · openalex updated_date 2026/07/28 · arxiv created 2026/08/01 · arxiv updated 2026/08/04

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 Gröbner basis computation via sparse interpolation and efficient search for polynomials of a fixed degree in a subfield of the rational function field.

Citations

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