Single-factor lifting and factorization of polynomials over local fields

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2012Embargo end date: 01 Jan 2011 English Publisher:Elsevier BVJournal:Journal of Symbolic Computation, volume 47, pages 1,318-1,346 (issn: 0747-7171,

Copyright policy )

Authors: Guàrdia Rubies, Jordi; Nart, Enric; Pauli, S.;

doi: 10.1016/j.jsc.2012.03.001 , 10.48550/arxiv.1104.3181

arXiv: 1104.3181

handle: 2117/16519

Single-factor lifting and factorization of polynomials over local fields

- Summary
- Subjects
- Metrics

Abstract

Let $f(x)$ be a separable polynomial over a local field. Montes algorithm computes certain approximations to the different irreducible factors of $f(x)$, with strong arithmetic properties. In this paper we develop an algorithm to improve any one of these approximations, till a prescribed precision is attained. The most natural application of this "single-factor lifting" routine is to combine it with Montes algorithm to provide a fast polynomial factorization algorithm. Moreover, the single-factor lifting algorithm may be applied as well to accelerate the computational resolution of several global arithmetic problems in which the improvement of an approximation to a single local irreducible factor of a polynomial is required.

9 figures

Related Organizations

Universitat Polit?cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
University of North Carolina at Chapel Hill
United States
University of North Carolina at Greensboro
United States

View all View all

Keywords

Polynomial factorization, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Newton polygon, Algorismes, Polynomials, Ramification and extension theory, FOS: Mathematics, Okutsu approximation, Okutsu invariant, Number Theory (math.NT), Number-theoretic algorithms; complexity, Algebra and Number Theory, Mathematics - Number Theory, Polygons, Algebraic number theory computations, Montes approximation, Computational Mathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, polynomial factorization, Polinomis, Local field, Montes algorithm, Polígons, Algorithms, 11S15, 11S04, 11Y40

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	24
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%