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Lecture Notes in Computer Science
We give a new algorithm, with three versions, for computing the number of real roots of a system of n polynomial equations in n unknowns. The rst version is of Monte Carlo type and, neglecting logarithmic factors, runs in time quadratic in the average number of complex roots of a closely related system. The other two versions run nearly as fast and progressively remove a measure zero locus of failures present in the rst version. Via a slight simpli cation of our algorithm, we can also countdoi:10.1007/3-540-68530-8_11 fatcat:fdw7eef5h5cbjp2uxljgtqlzy4