Abstract

By generalizing former considerations, we show that we can modify our FFFG algorithm for computing a Matrix GCD into an algorithm which computes a column-reduced Matrix GCD or more generally a column-reduced form of a Matrix polynomial. When the matrix polynomial has coefficients from an integer domain, the result is a new algorithm for determining a column reduced form using only fraction-free arithmetic while at the same time keeping coefficient growth to a minimum. Such domains are typical when working in computer algebra systems. The algorithm has been implemented and is in the new MatrixPolynomialAlgebra package that will be available in the next release of the Maple computer algebra system.