Finding more and more solutions of a system of nonlinear equations (Q919747)

The author considers the problem of finding possibly all solutions to a nonlinear equation. Starting from the idea of deflation for polynomials in one dimension, he develops a method for general functions of one variable with the aid of so-called locally affective functions. He then tries to extend this to the multi-dimensional case. It is here where the paper is obviously seriously flawed. Apparently it does not occur to the author that a vector may be non-zero and still have some zero component. Therefore the author's proposal for a multi- dimensional locally affective function does not satisfy the general criteria set forth by himself in the last section.