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Abstract

In order to approximate the solution of an analytic function by homotopy continuation method, one follows a curve starting from a trivial system and numerically moves along this curve to find the solution of the given function.
In this paper a new technique is developed to determine the orientation of the movement along the path by computing of the vector field of the corresponding differential equation. Namely as a main result we show that the orientation is derived from computation of the corresponding vector field. -