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A new algorithm for sparse multivariate polynomial interpolation is presented. It is a multi-modular extension of the Ben-Or and Tiwari algorithm, and is designed to be a practical method to construct symbolic formulas from numeric data produced by vector or massively-parallel processors. The main idea in our algorithm comes from the wellknown technique for primality test based on Fermat's theorem, and is the application of the generalized Chinese remainder theorem to the monomial exponents. We regard the exponent vector of each multivariate monomial as a mixed-radix representation of the corresponding exponent value obtained after the transformation by Kronecker's technique. It is shown by complexity comparison and experimental results that the step for univariate polynomial factorization is most expensive in our algorithm, and its parallelization is considered. Also reported are some empirical results of the parallelization on KLIC, a portable system of a concurrent logic programming language KL1.

The problem of multipoint polynomial evaluation is revisited znd a new improved algorithm ia presented. The fastness of the algorithm heavily depends on the use of the DFT-based algorithm for polynomial multiplication, and its detailed de scription and analysis are pr-ented in order for an efficient implementation and for efficient task scheduling in parallel processing.