Sparse multivariate factorization by mean of a few bivariate factorizations

TL;DR

This paper presents an algorithm that efficiently factors sparse multivariate polynomials by leveraging a small number of bivariate factorizations proportional to the number of variables, improving computational efficiency.

Contribution

The paper introduces a novel algorithm that reduces multivariate polynomial factorization to a linear number of bivariate factorizations, implemented in Giac/Xcas.

Findings

Algorithm requires O(d) bivariate factorizations for d variables

Implementation available in Giac/Xcas system

Demonstrates efficiency in sparse polynomial factorization

Abstract

We describe an algorithm to factor sparse multivariate polynomials using O(d) bivariate factorizations where d is the number of variables. This algorithm is implemented in the Giac/Xcas computer algebra system.