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We describe a deterministic algorithm that computes an approximate root of ncomplex polynomial equations in n unknowns in average polynomial time withrespect to the size of the input, in the Blum-Shub-Smale model with squareroot. It rests upon a derandomization of an algorithm of Beltr\'an and Pardoand gives a deterministic affirmative answer to Smale's 17th problem. The mainidea is to make use of the randomness contained in the input itself.

A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time