Factoring bivariate sparse (lacunary) polynomials

Autores
Avendaño, M.; Krick, T.; Sombra, M.
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved.
Fil:Avendaño, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Sombra, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Complexity 2007;23(2):193-216
Materia
Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Algebra
Degrees of freedom (mechanics)
Factorization
Problem solving
Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Polynomials
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0885064X_v23_n2_p193_Avendano
Acceder
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oai_identifier_str paperaa:paper_0885064X_v23_n2_p193_Avendano
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Factoring bivariate sparse (lacunary) polynomialsAvendaño, M.Krick, T.Sombra, M.Height of pointsLacunary (sparse) polynomialsLehmer's problemPolynomial factorizationAlgebraDegrees of freedom (mechanics)FactorizationProblem solvingHeight of pointsLacunary (sparse) polynomialsLehmer's problemPolynomial factorizationPolynomialsWe present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved.Fil:Avendaño, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Sombra, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0885064X_v23_n2_p193_AvendanoJ. Complexity 2007;23(2):193-216reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-23T11:18:32Zpaperaa:paper_0885064X_v23_n2_p193_AvendanoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-23 11:18:33.315Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Factoring bivariate sparse (lacunary) polynomials
title Factoring bivariate sparse (lacunary) polynomials
spellingShingle Factoring bivariate sparse (lacunary) polynomials
Avendaño, M.
Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Algebra
Degrees of freedom (mechanics)
Factorization
Problem solving
Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Polynomials
title_short Factoring bivariate sparse (lacunary) polynomials
title_full Factoring bivariate sparse (lacunary) polynomials
title_fullStr Factoring bivariate sparse (lacunary) polynomials
title_full_unstemmed Factoring bivariate sparse (lacunary) polynomials
title_sort Factoring bivariate sparse (lacunary) polynomials
dc.creator.none.fl_str_mv Avendaño, M.
Krick, T.
Sombra, M.
author Avendaño, M.
author_facet Avendaño, M.
Krick, T.
Sombra, M.
author_role author
author2 Krick, T.
Sombra, M.
author2_role author
author
dc.subject.none.fl_str_mv Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Algebra
Degrees of freedom (mechanics)
Factorization
Problem solving
Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Polynomials
topic Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Algebra
Degrees of freedom (mechanics)
Factorization
Problem solving
Height of points
Lacunary (sparse) polynomials
Lehmer's problem
Polynomial factorization
Polynomials
dc.description.none.fl_txt_mv We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved.
Fil:Avendaño, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Sombra, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n2_p193_Avendano
url http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n2_p193_Avendano
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Complexity 2007;23(2):193-216
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.982451

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