Work

Improved computation of polynomial roots over number fields when using complex embeddings

Year: 2024

Type: article

Abstract: We explore a fairly generic method to compute roots of polynomials over number fields through complex embeddings. Our main contribution is to show how to use a structure of a relative extension to decode in a subfield. Additionally we describe several heuristic options to improve practical efficiency. We provide experimental data from our implementation and compare our methods to the state of the art algorithm implemented in Pari/Gp .

Source: Journal of Computational Algebra

DOI: 10.1016/j.jaca.2024.100026

Authors: Andrea Lesavourey, Thomas Plantard, Willy Susilo

Institutions: XLIM, Université de Limoges, University of Wollongong

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,750

OpenAlex ID: W4403600214

FWCI: 0.27

Cites: 40

Cited by: 1

Related to: 10