An efficient method for analyzing the topology of plane real algebraic curve

A practically efficient algorithm for analyzing the topology of plane real algebraic curves is given. Given a bivariate polynomial, the algorithm produces a planar graph which is topologically equivalent to the real variety of the polynomial on the Euclidean plane. The method does not require the expensive computations of g.c.d., divisions, and root bounds of polynomials with real algebraic number coefficients. Further, it utilizes floating point arithmetic and interval arithmetic whenever possible. Experiments show that most benchmark curves found in the literature can be analyzed within a few seconds on a workstation. Timings on randomly generated polynomials also indicate that the algorithm is efficient to be useful in practice.