Exact Bivariate Polynomial Factorization in Q by Approximation of Roots

TL;DR

This paper introduces an algorithm that uses numerical methods to exactly factorize bivariate polynomials with rational coefficients, enabling implementation in common programming languages and facilitating applications in engineering and sciences.

Contribution

The paper presents a novel numerical approach for exact bivariate polynomial factorization in Q, compatible with efficient programming languages like C++ and supporting parallel computation.

Findings

Algorithm successfully factors bivariate polynomials with rational coefficients.

Implementation in C++ with GNU MP library is feasible and efficient.

Numerical computation requires only double precision and is parallelizable.

Abstract

Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, we present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. Our method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library. In addition, the numerical computation part often only requires double precision and is easily parallelizable.