有限环上函数多项式可表示性检验的快速算法
A Faster Algorithm For Testing Polynomial Representability Of Functions Over Finite Integer Rings
摘要：
给定一个从$\mathbb{Z}_n$到其自身的函数，利用Kempner函数可以确定它的多项式可表示性.本文通过构造多项式函数的$\mathbb{Z}_{n}$ -模的生成集，给出了$\mathbb{Z}_n$上多项式函数的另一种刻画.这种特性导致在决定多项式可表示性方面平均更快的算法。我们还扩展到多个变量的功能的特性。
英文摘要：
Given a function from $\mathbb{Z}_n$ to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over $\mathbb{Z}_n$ by constructing a generating set for the $\mathbb{Z}_{n}$-module of polynomial functions. This characterization results in an algorithm that is faster on average in deciding polynomial representability. We also extend the characterization to functions in several variables.
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