Newton-Hensel插值提升
Newton-Hensel Interpolation Lifting
摘要：
本文的主要结果是一个新版本的牛顿-亨塞尔提升，涉及到插值问题。它允许一个提升多项式在$Z[x]$从信息模一个素数$p\ne 2$的权力$p^k$为任何$k$，其独创性是，它是一个混合的版本，不仅解除系数的多项式，而且其指数。我们表明，这一结果完全对应于一个系统的$2t$广义方程在$2t$未知数的$p$ -进整数$\Z_p$环的牛顿-亨塞尔提升。最后将所得结果应用于$\Z[x]$中的稀疏多项式插值
英文摘要：
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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