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

2024/12/30 by Oliver Daisey, Yue Ren, Daisey, Oliver +2
Computer Science · Decision Sciences · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical methods for differential equations #Polynomial and algebraic computation #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2501.00156

openalex publication_date 2024/12/30 · openalex created_date 2025/01/04 · openalex updated_date 2026/07/28

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.

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