Implementing real polyhedral homotopy

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; and the third function outputs target solutions from the start system obtained by the second function. This work realizes the theoretical contributions of Ergür and Wolff (2023) as easy-to-use functions, allowing for further investigation into real homotopy algorithms.