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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_16153375_v6_n1_p81_Avendano |
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todo:paper_16153375_v6_n1_p81_Avendano2023-10-03T16:28:17Z Newton-Hensel interpolation lifting Avendaño, M. Krick, T. Pacetti, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, M. Krick, T. Pacetti, A. 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. |
| format |
JOUR |
| author |
Avendaño, M. Krick, T. Pacetti, A. |
| author_facet |
Avendaño, M. Krick, T. Pacetti, A. |
| author_sort |
Avendaño, M. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_16153375_v6_n1_p81_Avendano |
| work_keys_str_mv |
AT avendanom newtonhenselinterpolationlifting AT krickt newtonhenselinterpolationlifting AT pacettia newtonhenselinterpolationlifting |
| _version_ |
1782023606604136448 |