Newton-Hensel interpolation lifting

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 p k for any k, and its originality is that it is a mixed version that not only lifts the...

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Detalles Bibliográficos
Autores principales:	Avendaño, Martín, Krick, Teresa Elena Genoveva, Pacetti, Ariel Martin
Publicado:	2006
Materias:	Newton-Hensel lifting p-Adic integers Sparse polynomial interpolation Generalized Equations Hensel lifting Prime number Sparse polynomial interpolations Computational methods Interpolation
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v6_n1_p81_Avendano http://hdl.handle.net/20.500.12110/paper_16153375_v6_n1_p81_Avendano
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_16153375_v6_n1_p81_Avendano
record_format	dspace
spelling	paper:paper_16153375_v6_n1_p81_Avendano2025-07-30T19:01:02Z Newton-Hensel interpolation lifting Avendaño, Martín Krick, Teresa Elena Genoveva Pacetti, Ariel Martin Newton-Hensel lifting p-Adic integers Sparse polynomial interpolation Generalized Equations Hensel lifting Newton-Hensel lifting p-Adic integers Prime number Sparse polynomial interpolations Computational methods Interpolation 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 p k 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]. © 2005 SFoCM. 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:Pacetti, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v6_n1_p81_Avendano http://hdl.handle.net/20.500.12110/paper_16153375_v6_n1_p81_Avendano
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Newton-Hensel lifting p-Adic integers Sparse polynomial interpolation Generalized Equations Hensel lifting Newton-Hensel lifting p-Adic integers Prime number Sparse polynomial interpolations Computational methods Interpolation
spellingShingle	Newton-Hensel lifting p-Adic integers Sparse polynomial interpolation Generalized Equations Hensel lifting Newton-Hensel lifting p-Adic integers Prime number Sparse polynomial interpolations Computational methods Interpolation Avendaño, Martín Krick, Teresa Elena Genoveva Pacetti, Ariel Martin Newton-Hensel interpolation lifting
topic_facet	Newton-Hensel lifting p-Adic integers Sparse polynomial interpolation Generalized Equations Hensel lifting Newton-Hensel lifting p-Adic integers Prime number Sparse polynomial interpolations Computational methods Interpolation
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 p k 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]. © 2005 SFoCM.
author	Avendaño, Martín Krick, Teresa Elena Genoveva Pacetti, Ariel Martin
author_facet	Avendaño, Martín Krick, Teresa Elena Genoveva Pacetti, Ariel Martin
author_sort	Avendaño, Martín
title	Newton-Hensel interpolation lifting
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
publishDate	2006
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16153375_v6_n1_p81_Avendano http://hdl.handle.net/20.500.12110/paper_16153375_v6_n1_p81_Avendano
work_keys_str_mv	AT avendanomartin newtonhenselinterpolationlifting AT krickteresaelenagenoveva newtonhenselinterpolationlifting AT pacettiarielmartin newtonhenselinterpolationlifting
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Newton-Hensel interpolation lifting

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