Fast interpolation of multivariate polynomials with sparse exponents

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 fat arbitrary integer points, modulo arbitrary positive integers. The problem of sparse interpolation is to recover fin its usual sparse representation, as a sum of coefficients times monomials. For the first time we present a quasi-optimal algorithm for this task in term of the product of the number of terms of f by the maximum of the bit-size of the terms of f. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.