Efficiently and Effectively Recognizing Toricity of Steady State Varieties

Grigoriev, Dima; Iosif, Alexandru; Rahkooy, Hamid; Sturm, Thomas; Weber, Andreas

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1007/s11786-020-00479-9

Link :

https://lilloa.univ-lille.fr/handle/20.500.12210/121527

Title :

Efficiently and Effectively Recognizing Toricity of Steady State Varieties

Author(s) :

Grigoriev, Dima [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Iosif, Alexandru [Auteur]
Rahkooy, Hamid [Auteur]
Sturm, Thomas [Auteur]
Weber, Andreas [Auteur]

Journal title :

Mathematics in Computer Science

Pages :

199-232

Publisher :

Springer

Publication date :

2020-07-21

ISSN :

1661-8270

HAL domain(s) :

Informatique [cs]

English abstract : [en]

Abstract We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, ...
Show more >Abstract We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of shifted toric varieties which generalizes the notion of toric varieties. This requires a geometric view on the varieties rather than an algebraic view on the ideals. We present algorithms and computations on 129 models from the BioModels repository testing for group and coset structures over both the complex numbers and the real numbers. Our methods over the complex numbers are based on Gröbner basis techniques and binomiality tests. Over the real numbers we use first-order characterizations and employ real quantifier elimination. In combination with suitable prime decompositions and restrictions to subspaces it turns out that almost all models show coset structure. Beyond our practical computations, we give upper bounds on the asymptotic worst-case complexity of the corresponding problems by proposing single exponential algorithms that test complex or real varieties for toricity or shifted toricity. In the positive case, these algorithms produce generating binomials. In addition, we propose an asymptotically fast algorithm for testing membership in a binomial variety over the algebraic closure of the rational numbers.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T14:04:44Z

Files

s11786-020-00479-9.pdf
Open access
Access the document

Efficiently and Effectively Recognizing ... BibTeX CSV Excel RIS

Files

Efficiently and Effectively Recognizing ...

BibTeX

CSV

Excel

RIS