In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity results for the power series multiplication in many variables. Our algorithms are implemented and freely available within the Mathemagix software. We show that their theoretical costs are well-reflected in practice.

Keywords: sparse multiplication, power series, multi-point evaluation, algorithm

A.M.S. subject classification: 68W30, 12-04, 30B10, 42-04, 11Y05

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