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 \(p\ne 2\) to a power \(p^k\) for any \(k\), and its originality is that it is a mixed version that no...

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Published in:arXiv.org 2005-09
Main Authors: Avendaño, Martin, Krick, Teresa, Pacetti, Ariel
Format: Article
Language:English
Subjects:
Hoisting
Integers
Interpolation
Polynomials
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Krick, Teresa
Pacetti, Ariel
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 \(p\ne 2\) 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 \(\Z_p\). Finally we apply our results to sparse polynomial interpolation in \(\Z[x]\)
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subjects Hoisting
Integers
Interpolation
Polynomials
title Newton-Hensel Interpolation Lifting
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