Newton-Okounkov Bodies of Chemical Reaction Networks
Newton-Okounkov Bodies of Chemical Reaction Networks
joint work with Nida Obatake
joint work with Nida Obatake
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.