To solving multiparameter problems of algebra. 10. Computing zeros of a scalar polynomial

The paper considers the problem of computing zeros of scalar polynomials in several variables. The zeros of a polynomial are subdivided into the regular (eigen-and mixed) zeros and the singular ones. An algorithm for computing regular zeros, based on a decomposition of a given polynomial into a product of primitive polynomials, is suggested. The algorithm is applied to solving systems of nonlinear algebraic equations. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 119–130.