Probabilistic absolute irreducibility test for polynomials
type: Item
instance of: scholarly article
title: Probabilistic absolute irreducibility test for polynomials
zbMATH Open document ID: 1011.12011
DOI: 10.1016/S0022-4049(01)00165-7
author: Jean-François Ragot
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: The paper gives a fast deterministic algorithm to do the following: given a multivariate polynomial over the integers, return ``yes'' if it is proven to be absolutely irreducible. It is shown that most absolutely irreducible polynomials are recognized as such by this algorithm, assuming a certain probability distribution. The algorithm is used by the computer algebra system Maple in order to avoid the more costly decision algorithm for absolute irreducibility in most cases.
reviewed by: Josef Schicho
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 68W40
zbMATH DE Number: 1787463
zbMATH Keywords: irreducibility test
zbMATH Keywords: maple
zbMATH Keywords: multivariate polynomials
describes a project that uses: Maple
MaRDI profile type: Publication
cites work: Factoring Rational Polynomials over the Complex Numbers
cites work: Q4083660
cites work: Q4470456
cites work: Q5521594
cites work: The distribution of irreducible polynomials in several indeterminates
cites work: The Distribution of Irreducible Polynomials in Several Indeterminates II
cites work: Q5184990
cites work: The distribution of irreducible polynomials in several indeterminates over a finite field
cites work: Absolute Factorization of Polynomials: A Geometric Approach
cites work: Q3031075
cites work: The Distribution of Absolutely Irreducible Polynomials in Several Indeterminates
cites work: Q3027108
cites work: Q4226966
cites work: Q5184991
cites work: Q3912021
cites work: Fast parallel absolute irreducibility testing
cites work: Effective Noether irreducibility forms and applications
cites work: Q5588717
cites work: Counting polynomials with zeros of given multiplicities in finite fields
cites work: Equations over finite fields. An elementary approach
cites work: On the parallel Risch Algorithm (II)
cites work: Q3784166
description: scientific article; zbMATH DE number 1787463