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 $q(x) = q_nx^n+ldots+q_0$ with root

separation $

ho$, coefficients $abs{q_n}ge1$ and $abs{q_i} le 2^ au$,

it needs coefficient approximations to $O(n(log(1/

ho) + au))$

bits after the binary point and has an expected cost of

$O(n^4 (log(1/

ho) + au)^2)$ bit operations.