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

Source: [A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks](<https://www.sota2.com/research/paper/68fa5c181e209131ce9ce139>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:10.245Z

Authors: Marcus S. Aichmayr, Stefan M\\"uller, Georg Regensburger

Published: 2024-07-17T15:44:53.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2407.12660>)

[PDF](<https://arxiv.org/pdf/2407.12660.pdf>)