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

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 obtai...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Aichmayr, Marcus S, Müller, Stefan, Regensburger, Georg
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 17.07.2024
Subjects:
Chemical reactions
Subspaces
ISSN:2331-8422
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.2407.12660