Methods for solving some parameter problems of algebra

Methods for solving the following parameter problems are considered: division of scalar and matrix polynomials and computation of their GCD and LCM; finding bases of the sum, difference, and intersection of the linear span of polynomial vectors; constructing a minimal MFD (matrix fraction description) of a rational matrix; computing a range basis and a minimal basis of the null-space of a rational matrix; solving matrix equations and computing inverse and pseudoinverse matrices (both for polynomial and rational objects); computing generating eigenvectors of a polynomial matrix.