The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite) bit-streams. In other words, coefficients can be approximated to any desired accuracy, but are not known exactly. We show that a variant of the Descartes algorithm can cope with bit-stream coefficients. To isolate the real roots of a square-free real polynomial q(x) = q_nx~n + ... + q_0 with root separation ρ, coefficients |q_n| ≥ 1 and |q_i| ≤ 2~τ, it needs coefficient approximations to O(n(log(1/ρ) + τ)) bits after the binary point and has an expected cost of 0(n~4(log(1/ρ) + τ)~2) bit operations.
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