@inproceedings{8a2a90e743a14e4c89c975f87457552f,
title = "A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks",
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.",
keywords = "elementary vectors, generalized mass-action systems, robustness, sign vectors, deficiency zero theorem, oriented matroids",
author = "Stefan M{\"u}ller and Georg Regensburger and Marcus Aichmayr",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",
year = "2024",
doi = "10.1007/978-3-031-64529-7_17",
language = "English",
isbn = "978-3-031-64528-0",
volume = "14749",
series = "Lecture Notes in Computer Science",
publisher = "Springer Cham",
pages = "155--164",
editor = "Kevin Buzzard and Alicia Dickenstein and Bettina Eick and Anton Leykin and Yue Ren",
booktitle = "Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings",
}