Newton-Okounkov Bodies of Chemical Reaction Networks

joint work with Nida Obatake

Abstract

We provide an algorithm to estimate the number of solutions to a polynomial system using Newton-Okounkov bodies.

The Newton-Okounkov body of a general system of equations on a variety can be used to bound the number of solutions to that system. This bound is not necessarily straight forward to apply to a system of polynomials when the underlying variety is not a toric variety. We give an algorithm on how to apply the Newton-Okounkov body bound to a system of polynomials and demonstrate the computations through examples. We furthermore apply the Newton-Okounkov body bound to chemical reaction networks and demonstrate its effectiveness in providing tighter bounds than similar methods, such as mixed volume.

Algorithm Implementation

We demonstrate our homotopy algorithms in Macaulay2 on various examples. Code for all of the examples in the paper can be found on my GitHub. 

Publication

Preprint