Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers. The problem of sparse interpolation is to recover f in its usual sparse representation, as a sum of coefficients times monomials. For the first time we present a quasi-optimal algorithm for this task.

翻译：考虑一个具有整数系数的稀疏多元多项式f。假设f以“模黑箱多项式”的形式表示，例如通过某种算法可在任意整数点上评估f，并以任意正整数为模。稀疏插值问题旨在恢复f的常规稀疏表示，即表示为系数与单项式乘积之和。我们首次提出了一种准最优算法来解决该问题。