Tropical Algebraic Geometry in Maple, a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients

TL;DR

This paper introduces a tropical algebraic geometry approach implemented in Maple to efficiently find common factors of multivariate polynomials with approximate coefficients, combining polyhedral and numerical methods.

Contribution

It presents a novel preprocessing algorithm that leverages tropical algebraic geometry to improve factorization of approximate multivariate polynomials.

Findings

Effective preprocessing for polynomial factorization

Integration of polyhedral and numerical techniques

Implementation demonstrated in Maple

Abstract

Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral methods on the exact exponents with numerical techniques on the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.