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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/117850
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:21:52Zoai: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:34982025-09-29 10:21:52.431CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.070432 |