Bounds for Polynomials on Algebraic Numbers and Application to Curve Topology

Let P ∈ Z [ X , Y ] be a given square-free polynomial of total degree d with integer coefficients of bitsize less than  τ , and let V R ( P ) : = { ( x , y ) ∈ R 2 ∣ P ( x , y ) = 0 } be the real planar algebraic curve implicitly defined as the vanishing set of  P . We give a deterministic algorithm...

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