The connection between Feynman integrals and GKZ A-hypergeometric systems has been a
topic of recent interest with advances in mathematical techniques and computational tools …

A family of polynomial differential systems describing the behavior of a chemical reaction
network with generalized mass action kinetics is investigated. The coefficients and …

This paper presents algorithms for computing the Gröbner fan of an arbitrary polynomial
ideal. The computation involves enumeration of all reduced Gröbner bases of the ideal. Our …

We study algebraic algorithms for expressing the number of non-negative integer solutions
to a unimodular system of linear equations as a function of the right hand side. Our methods …

The polynomial differential system modeling the behavior of a chemical reaction is given by
graph theoretic structures. The concepts from toric geometry are applied to study the steady …

We determine the maximal gap between the optimal values of an integer program and its
linear programming relaxation, where the matrix and cost function are fixed but the right …

The solution and a portable implementation of the inverse kinematics computation of a 3
degree-of-freedom (DOF) robot manipulator using Gröbner bases are presented. The main …

The Gröbner fan of a polynomial ideal I⊆ k [x1,..., xn] is a polyhedral complex in Rn whose
maximal cones are in bijection with the reduced Gröbner bases of I. In tropical algebraic …

The set of all group relaxations of an integer program contains certain special members
called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and …

The Gröbner fan of an ideal in the polynomial ring in n variables is an n-dimensional
polyhedral complex and the tropical variety of the ideal is a certain subcomplex. In this paper …