Eecient Approximation Algorithms for Sparse Polynomials over Finite Fields
نویسندگان
چکیده
We obtain new lower bounds on the number of non zeros of sparse poly-nomials and give a fully polynomial time (;) approximation algorithm for the number of non-zeros of multivariate sparse polynomials over a nite eld of q elements and degree less than q ? 1. This answers partially to an open problem of D. Grigoriev and M. Karpinski. Also, probabilistic and determin-istic algorithms for testing identity to zero of a sparse polynomial given by a "black-box" are given. Finally, we propose an algorithm to estimate the size of the image of a univariate sparse polynomial.
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