Systems of equations with a single solution

TL;DR

This paper classifies polynomial systems with exactly one solution, linking them to lattice polytopes of minimal positive mixed volume, and offers an algorithm to find that unique solution.

Contribution

It provides a comprehensive classification of systems with a single solution and introduces an algorithm for solving them.

Findings

Classification of systems with a single solution

Connection to lattice polytopes of minimal positive mixed volume

Algorithm for evaluating the unique solution

Abstract

We classify general systems of polynomial equations with a single solution, or, equivalently, collections of lattice polytopes of minimal positive mixed volume. As a byproduct, this classification provides an algorithm to evaluate the single solution of such a system.