Implementing real polyhedral homotopy

TL;DR

This paper presents an implementation of a real polyhedral homotopy method with three functions that certify applicability, generate binomial start systems, and compute solutions, making the theoretical approach more accessible for practical use.

Contribution

The work translates theoretical real polyhedral homotopy concepts into practical, easy-to-use functions for solving polynomial systems.

Findings

Provides a certification function for applicability

Generates binomial start systems efficiently

Outputs solutions from start systems

Abstract

We implement a real polyhedral homotopy method using three functions. The first function provides a certificate that our real polyhedral homotopy is applicable to a given system; the second function generates binomial systems for a start system; the third function outputs target solutions from the start system obtained by the second function. This work realizes the theoretical contributions in \cite{ergur2019polyhedral} as easy to use functions, allowing for further investigation into real homotopy algorithms.