Implementation of a Near-Optimal Complex Root Clustering Algorithm

TL;DR

This paper presents Ccluster, a software implementing a near-optimal algorithm for isolating complex roots of polynomials, with performance improvements and comparisons to existing tools.

Contribution

It provides one of the first implementations of a near-optimal complex root clustering algorithm with optimization techniques.

Findings

Ccluster efficiently isolates complex roots of polynomials.

Performance surpasses MPSolve and Maple in benchmark tests.

Low-level optimizations improve algorithm speed.

Abstract

We describe Ccluster, a software for computing natural $\epsilon$-clusters of complex roots in a given box of the complex plane. This algorithm from Becker et al.~(2016) is near-optimal when applied to the benchmark problem of isolating all complex roots of an integer polynomial. It is one of the first implementations of a near-optimal algorithm for complex roots. We describe some low level techniques for speeding up the algorithm. Its performance is compared with the well-known MPSolve library and Maple.