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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| Autores principales: | , , |
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2006
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| 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 |
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| Sumario: | 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. |
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