Mass-action chemical reaction systems are frequently used in computational biology. The
corresponding polynomial dynamical systems are often large (consisting of tens or even …

Tropical geometry is used to develop a new approach to the theory of discriminants and
resultants in the sense of Gel $’$ fand, Kapranov and Zelevinsky. The tropical $ A $-discriminant …

Toric dynamical systems are known as complex balancing mass action systems in the
mathematical chemistry literature, where many of their remarkable properties have been …

This article is a survey of the recent use of some techniques from computational algebraic
geometry to address mathematical challenges in systems biology.(Bio) chemical reaction …

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of
families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our …

Deciding membership for polynomial ideals represents a classical problem of computational
commutative algebra which is exponential space hard. This means that the usual …

The subject of this book is the solution of polynomial equations, that is, systems of (generally)
non-linear algebraic equations. This study is at the heart of several areas of mathematics …

Many dynamical systems arising in biology and other areas exhibit multistationarity (two or
more positive steady states with the same conserved quantities). Although deciding …

Resultants, Jacobians and residues are basic invariants of multivariate polynomial systems.
We examine their interrelations in the context of toric geometry. The global residue in the …

We introduce a general framework for biological systems, called MESSI systems, that
describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove …