Geodesic
To solving multiparameter problems of algebra.~8. The $RP$-$q$ method and its applications
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 149-164

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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. 
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     author = {V. N. Kublanovskaya},
     title = {To solving multiparameter problems of algebra.~8. {The} $RP$-$q$ method and its applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--164},
     publisher = {mathdoc},
     volume = {334},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a10/}
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V. N. Kublanovskaya. To solving multiparameter problems of algebra.~8. The $RP$-$q$ method and its applications. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 149-164. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a10/