Sparse polynomial interpolation. Exploring fast heuristic algorithms over finite fields


Consider a multivariate polynomial over a field , which is given through a black box capable of evaluating at points in , or possibly at points in for any -algebra . The problem of sparse interpolation is to express in its usual form with respect to the monomial basis. We analyze the complexity of various old and new algorithms for this task in terms of bounds and for the total degree of and its number of terms. We mainly focus on the case when is a finite field and explore possible speed-ups under suitable heuristic assumptions.

Authors: Joris van der Hoeven, Grégoire Lecerf

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