To solving multiparameter problems of algebra. 8. The $RP$-$q$ method and its applications

A new method (the $RP$-$q$ method) for factorizing scalar polynomials in $q$ variables and $q$-parameter polynomial matrices $(q\ge1)$ of full rank is suggested. Applications of the algorithm to solving systems of nonlinear algebraic equations and some spectral problems for a $q$-parameter polynomial matrix $F$ (such as separation of the eigenspectrum and mixed spectrum of $F$, computation of bases with prescribed spectral properties of the null-space of polynomial solutions of $F$, and computation of the hereditary polynomials of $F$) are considered.