A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks

Stefan Müller, Georg Regensburger, Marcus Aichmayr

Publications: Contribution to bookContribution to proceedingsPeer Reviewed

Abstract

We present our SageMath package elementary_vectors for computing elementary and sign vectors of real subspaces. In this setting, elementary vectors are support-minimal vectors that can be determined from maximal minors of a real matrix representing a subspace. By applying the sign function, we obtain the cocircuits of the corresponding oriented matroid, which in turn allow the computation of all sign vectors of a real subspace. As an application, we discuss sign vector conditions for existence and uniqueness of complex-balanced equilibria of chemical reaction networks with generalized mass-action kinetics. The conditions are formulated in terms of sign vectors of two subspaces arising from the stoichiometric coefficients and the kinetic orders of the reactions. We discuss how these conditions can be checked algorithmically, and we demonstrate the functionality of our package sign_vector_conditions in several examples.

Original languageEnglish
Title of host publicationMathematical Software – ICMS 2024 - 8th International Conference, Proceedings
Subtitle of host publication8th International Conference, Durham, UK, July 22–25, 2024
EditorsKevin Buzzard, Alicia Dickenstein, Bettina Eick, Anton Leykin, Yue Ren
PublisherSpringer Cham
Pages155-164
Number of pages10
Volume14749
ISBN (Electronic)978-3-031-64529-7
ISBN (Print)978-3-031-64528-0
DOIs
Publication statusPublished - 2024

Publication series

SeriesLecture Notes in Computer Science
ISSN0302-9743

Austrian Fields of Science 2012

  • 101005 Computer algebra

Keywords

  • elementary vectors
  • generalized mass-action systems
  • robustness
  • sign vectors
  • deficiency zero theorem
  • oriented matroids

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