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Newton–Hensel Interpolation Lifting

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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 pk 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].

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Correspondence to Martin Avendano, Teresa Krick or Ariel Pacetti.

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Avendano, M., Krick, T. & Pacetti, A. Newton–Hensel Interpolation Lifting. Found Comput Math 6, 82–120 (2006). https://doi.org/10.1007/s10208-005-0172-3

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  • DOI: https://doi.org/10.1007/s10208-005-0172-3