Detecting Binomiality
Carsten Conradi, Thomas Kahle
TL;DR
This paper presents an efficient linear algebra-based algorithm for detecting binomial ideals, especially in chemical reaction network applications, and offers heuristics for simplifying non-binomial ideals.
Contribution
It introduces a Gr"obner-free, linear algebra method for binomiality detection in homogeneous ideals and develops heuristics for inhomogeneous cases.
Findings
Efficient algorithm for homogeneous binomial ideals
Heuristic toolbox for inhomogeneous ideals
Application to chemical reaction network equations
Abstract
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and source of examples is the simplification of steady state equations of chemical reaction networks. For homogeneous ideals we give an efficient, Gr\"obner-free algorithm for binomiality detection, based on linear algebra only. On inhomogeneous input the algorithm can only give a sufficient condition for binomiality. As a remedy we construct a heuristic toolbox that can lead to simplifications even if the given ideal is not binomial.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.