Geodesic
Computing the invariant polynomials of a polinomial matrix.~1
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 123-127

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An algorithm for computing the invariant polynomials and the canonical triangular (trapezoidal) matrix for a polynomial matrix of full column rank is suggested. The algorithm is based on the rank-factorization $(\Delta W-1)$ method for solving algebraic problems for polynomial matrices, previously suggested by the author. 
@article{ZNSL_2002_284_a6,
     author = {V. N. Kublanovskaya},
     title = {Computing the invariant polynomials of a polinomial matrix.~1},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {123--127},
     publisher = {mathdoc},
     volume = {284},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a6/}
}
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V. N. Kublanovskaya. Computing the invariant polynomials of a polinomial matrix.~1. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 123-127. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a6/