Solving polynomial systems (Q1098563)

The paper presents a short but very essential review of the main ideas on the homotopy continuation method of solving polynomial systems by means of reducing them to some Cauchy problem for a corresponding system of ordinary differential equations. Starting from a simple example the author discusses all the possible difficulties in the application of the method, especially so-called deficient polynomial systems. One of the more general results on the subject - the theorem on `random product homotopy' is formulated and its application to finding of equilibrium points of the four-dimensional Lorenz attractor is presented.