Factoring bivariate sparse (lacunary) polynomials

Autores
Avendaño, Martín; Krick, Teresa Elena Genoveva; Sombra, Martín
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, Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Krick, Teresa Elena Genoveva. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina
Fil: Sombra, Martín. Universidad de Barcelona; España
Materia
HEIGHT OF POINTS
LACUNARY (SPARSE) POLYNOMIALS
LEHMER'S PROBLEM
POLYNOMIAL FACTORIZATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/117850
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Factoring bivariate sparse (lacunary) polynomialsAvendaño, MartínKrick, Teresa Elena GenovevaSombra, MartínHEIGHT OF POINTSLACUNARY (SPARSE) POLYNOMIALSLEHMER'S PROBLEMPOLYNOMIAL FACTORIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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, Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Krick, Teresa Elena Genoveva. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Sombra, Martín. Universidad de Barcelona; EspañaAcademic Press Inc Elsevier Science2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/117850Avendaño, Martín; Krick, Teresa Elena Genoveva; Sombra, Martín; Factoring bivariate sparse (lacunary) polynomials; Academic Press Inc Elsevier Science; Journal Of Complexity; 23; 2; 12-2007; 193-2160885-064XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0885064X06000471info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2006.06.002info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:40Zoai:ri.conicet.gov.ar:11336/117850instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:54:40.62CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Factoring bivariate sparse (lacunary) polynomials
title Factoring bivariate sparse (lacunary) polynomials
spellingShingle Factoring bivariate sparse (lacunary) polynomials
Avendaño, Martín
HEIGHT OF POINTS
LACUNARY (SPARSE) POLYNOMIALS
LEHMER'S PROBLEM
POLYNOMIAL FACTORIZATION
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, Martín
Krick, Teresa Elena Genoveva
Sombra, Martín
author Avendaño, Martín
author_facet Avendaño, Martín
Krick, Teresa Elena Genoveva
Sombra, Martín
author_role author
author2 Krick, Teresa Elena Genoveva
Sombra, Martín
author2_role author
author
dc.subject.none.fl_str_mv HEIGHT OF POINTS
LACUNARY (SPARSE) POLYNOMIALS
LEHMER'S PROBLEM
POLYNOMIAL FACTORIZATION
topic HEIGHT OF POINTS
LACUNARY (SPARSE) POLYNOMIALS
LEHMER'S PROBLEM
POLYNOMIAL FACTORIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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, Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Krick, Teresa Elena Genoveva. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina
Fil: Sombra, Martín. Universidad de Barcelona; España
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 2007-12
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/11336/117850
Avendaño, Martín; Krick, Teresa Elena Genoveva; Sombra, Martín; Factoring bivariate sparse (lacunary) polynomials; Academic Press Inc Elsevier Science; Journal Of Complexity; 23; 2; 12-2007; 193-216
0885-064X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/117850
identifier_str_mv Avendaño, Martín; Krick, Teresa Elena Genoveva; Sombra, Martín; Factoring bivariate sparse (lacunary) polynomials; Academic Press Inc Elsevier Science; Journal Of Complexity; 23; 2; 12-2007; 193-216
0885-064X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0885064X06000471
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2006.06.002
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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