Derivation of isolated solutions of a complex variable polynomial system

The problem of solving systems of polynomial equations is faced daily by scientists and engineers. For solving polynomial systems, in this work, a new homotopy continuation method is presented, based on integrating a regular differential system of a complex variable, and on finding all zeros of an analytic function. The new method differs from classical techniques in that it is global and exhaustive, it does not require a choice of initial solutions, and it finds all solutions.