COMPLEXITY OF BEZOUT THEOREM .4. PROBABILITY OF SUCCESS - EXTENSIONS

We estimate the probability that a given number of projective Newton s teps applied to a linear homotopy of a system of n homogeneous polynom ial equations in n + 1 complex variables of fixed degrees will find al l the roots of the system. We also extend the framework of our analysi s to cover the classical implicit function theorem and revisit the con dition number in this context. Further complexity theory is developed.