Solution of systems of general-form nonilinear algebraic equations. Methods and algorithms. IV

This paper considers the solution of a system of m nonlinear equations in q>02 variables (SNAE-q). A method for finding all of the finite zero-dimensional roots of a given SNAE-q, which extends the method suggested previously for q=2 and q=3 to the case q≥2, is developed and theoretically justified. This method is based on the algorithm of the ΔW-q factorization of a polynomial q-parameter matrix and on the algorithm of relative factorization of a scalar polynomial in q variables. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 124–146. Translated by V. N. Kublanovskaya.