Solution of arbitrary systems of nonlinear algebraic equations. Methods and algorithms. IV

This paper considers the solution of a systems of $m$ nonlinear equations in $q\ge2$ variables (SNAEs-$q$). A method for finding all of the finite zero-dimensional roots of a given SNAE-$q$, which extends the method suggested in [2] for $q=2$ and $q=3$ to the case $q\ge2$, is developed and theoretically justified. This method is based on the algorithm of $\Delta W$-$q$ factorization of a polynomial $q$-parameter matrix $[1]$ and on the algorithm of relative factorization of a polynomial in $q$ variables $[3]$.