All polynomials $f\!\! can be solved over $K$ within deterministic time$\log^{7+o(1)(dH)$ (resp. $2$) in the classical Turing model . For each such root generates an approximation in $\mathbb{Q}$ withlogarithmic height $O(\log^3(d H)$ that converges at a rate of $O\!(1/p)^{2^i) after $i$ steps of Newton iteration . We alsoprove significant speed-ups in certain settings, a minimal spacing bound of $p^{-O(p\log^2_p)

Author(s) : J. Maurice Rojas, Yuyu Zhu

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Keywords : log - polynomials - root - alsoprove - significant -

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