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Implementing real polyhedral homotopy

Kisun Lee, Julia Lindberg and Jose Israel Rodriguez

Vol. 14 (2024), 59–71
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.

Keywords
homotopy continuation, numerical algebraic geometry, real algebraic geometry, amoeba, discriminant, polyhedral homotopy
Mathematical Subject Classification
Primary: 65H14
Secondary: 14P99
Supplementary material

A package for finding real roots of systems of polynomial equations using polyhedral homotopy.

Milestones
Received: 11 July 2022
Revised: 9 January 2024
Accepted: 24 January 2024
Published: 30 April 2024
Authors
Kisun Lee
School of Mathematical and Statistical Science
Clemson University
Clemson, SC
United States
Julia Lindberg
Department of Mathematics
University of Texas-Austin
Austin, TX
United States
Jose Israel Rodriguez
Department of Mathematics
University of Wisconsin
Madison, WI
United States