Newton–Hensel Interpolation Lifting

Autores
Avendaño, Martin; Krick, Teresa Elena Genoveva; Pacetti, Ariel Martín
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power pk for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤp. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].
Fil: Avendaño, Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Pacetti, Ariel Martín. 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
Materia
Newton-Hensel lifting
p-Adic integers
Sparse polynomial interpolation
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:11336/251073
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/251073
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Newton–Hensel Interpolation LiftingAvendaño, MartinKrick, Teresa Elena GenovevaPacetti, Ariel MartínNewton-Hensel liftingp-Adic integersSparse polynomial interpolationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power pk for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤp. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].Fil: Avendaño, Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Pacetti, Ariel Martín. 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; ArgentinaSpringer2006-01info: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/11336/251073Avendaño, Martin; Krick, Teresa Elena Genoveva; Pacetti, Ariel Martín; Newton–Hensel Interpolation Lifting; Springer; Foundations Of Computational Mathematics; 6; 1; 1-2006; 82-1201615-3375CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-005-0172-3info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10208-005-0172-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:30Zoai:ri.conicet.gov.ar:11336/251073instacron: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:34982025-09-03 09:56:31.001CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Newton–Hensel Interpolation Lifting
title Newton–Hensel Interpolation Lifting
spellingShingle Newton–Hensel Interpolation Lifting
Avendaño, Martin
Newton-Hensel lifting
p-Adic integers
Sparse polynomial interpolation
title_short Newton–Hensel Interpolation Lifting
title_full Newton–Hensel Interpolation Lifting
title_fullStr Newton–Hensel Interpolation Lifting
title_full_unstemmed Newton–Hensel Interpolation Lifting
title_sort Newton–Hensel Interpolation Lifting
dc.creator.none.fl_str_mv Avendaño, Martin
Krick, Teresa Elena Genoveva
Pacetti, Ariel Martín
author Avendaño, Martin
author_facet Avendaño, Martin
Krick, Teresa Elena Genoveva
Pacetti, Ariel Martín
author_role author
author2 Krick, Teresa Elena Genoveva
Pacetti, Ariel Martín
author2_role author
author
dc.subject.none.fl_str_mv Newton-Hensel lifting
p-Adic integers
Sparse polynomial interpolation
topic Newton-Hensel lifting
p-Adic integers
Sparse polynomial interpolation
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power pk for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤp. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].
Fil: Avendaño, Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Pacetti, Ariel Martín. 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
description The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power pk for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤp. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].
publishDate 2006
dc.date.none.fl_str_mv 2006-01
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/11336/251073
Avendaño, Martin; Krick, Teresa Elena Genoveva; Pacetti, Ariel Martín; Newton–Hensel Interpolation Lifting; Springer; Foundations Of Computational Mathematics; 6; 1; 1-2006; 82-120
1615-3375
CONICET Digital
CONICET
url http://hdl.handle.net/11336/251073
identifier_str_mv Avendaño, Martin; Krick, Teresa Elena Genoveva; Pacetti, Ariel Martín; Newton–Hensel Interpolation Lifting; Springer; Foundations Of Computational Mathematics; 6; 1; 1-2006; 82-120
1615-3375
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-005-0172-3
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10208-005-0172-3
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 Springer
publisher.none.fl_str_mv Springer
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 13.13397

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