Lacunaryx: Computing bounded-degree factors of lacunary polynomials

TL;DR

Lacunaryx is a software library implementing efficient algorithms to compute bounded-degree factors of lacunary polynomials, enabling factorization of sparse polynomials with complexity polynomial in input size and degree.

Contribution

This work introduces Lacunaryx, a library that implements polynomial-time algorithms for bounded-degree factorization of lacunary polynomials in sparse form.

Findings

Algorithms run in polynomial time relative to input size and degree

Lacunaryx successfully factors lacunary polynomials in practice

Provides an open-source tool for sparse polynomial factorization

Abstract

In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as a list of nonzero monomials, and an integer $d$, and compute its irreducible degree-$\le d$ factors. The complexity of these algorithms is polynomial in the sparse size of the input polynomial and $d$.