Computation of characteristics of the regular finite spectrum of a singular multiparameter polynomial matrix

A modification of a known algorithm for computing the generating eigenvectors of a multiparameter polynomial matrix of full column rank is presented. This modification permits one to compute the characteristic polynomial (or its divisors) for a singular matrix. The algorithm proposed can be extended to the general case and used for computing a minimal basis of the image of a polynomial matrix and also for computing the greatest common divisor of scalar and matrix polynomials. An illustration of implementation of the algorithm is given.