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
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_0885064X_v23_n2_p193_Avendano
Ver los metadatos del registro completo
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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/ar2025-09-29T13:43:06Zpaperaa: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:18962025-09-29 13:43:07.53Biblioteca 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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13.070432 |