Partitioning method for rational and polynomial matrices

We propose an extension of the Grevile's partitioning method for computing the Moore-Penrose inverse, which is applicable to the set of rational matrices. Also, we develop an algorithm for computing the Moore-Penrose inverse of given one-variable polynomial matrix, which is based on the Grevile's method. Major problems arising in the implementation of this method are repetitive recomputations of the same values and simplification of rational and polynomial expressions which contain unknown variable. These algorithms are implemented in the symbolic computational package MATHEMATICA.