Detecting Binomiality
arXiv:1502.04893 · doi:10.1016/j.aam.2015.08.004
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, Gröbner-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.
14 pages, v2: Theorem 2.8 replaced by Example 2.8, v3: final version as in Adv.Appl.Math
References in corpus (2)
Cited by in corpus (8)
- Parity binomial edge ideals
- Efficiently and Effectively Recognizing Toricity of Steady State Varieties
- A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks
- Analysis of the Conradi-Kahle Algorithm for Detecting Binomiality on Biological Models
- First-Order Tests for Toricity
- Parametric Toricity of Steady State Varieties of Reaction Networks
- Groebner bases of reaction networks with intermediate species
- Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner Systems