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...
Guardado en:
Autores principales: | , , |
---|---|
Publicado: |
2006
|
Materias: | |
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: |
id |
paper:paper_16153375_v6_n1_p81_Avendano |
---|---|
record_format |
dspace |
spelling |
paper:paper_16153375_v6_n1_p81_Avendano2023-06-08T16:25:23Z 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 |
_version_ |
1768543439431925760 |