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; 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.

13 pages, 1 figure, Version to appear in Journal of Software for Algebra and Geometry