Embedding polynomial systems into vertically parametrised families: A case study on ODEbase

TL;DR

This paper investigates how to embed polynomial systems into parametrised families, using ODEbase data to understand the algebraic and combinatorial structures involved.

Contribution

It introduces a method to construct vertically parametrised polynomial systems from existing data, specifically applied to the ODEbase collection.

Findings

Empirical analysis of polynomial systems in ODEbase

Methods for constructing parametrised polynomial systems

Insights into algebraic and combinatorial properties

Abstract

Vertically parametrised polynomial systems are a particular nice class of parametrised polynomial systems for which a lot of interesting algebraic information is encoded in its combinatorics. Given a fixed polynomial system, we empirically study what constitutes a good vertically parametrised polynomial system that gives rise to it and how to construct said vertically parametrised polynomial system. For data, we use all polynomial systems in ODEbase, which we have transcribed to an OSCAR readable format, and made available as a Julia package OscarODEbase.