Greatest common divisors from generalized sylvester resultant matrices

Sylvester's classical resultant matrix for determining the degree of the greatest common divisor of two polynomials has recently been generalized to deal with m+1 polynomialsm>1. A slightly stronger version is given in this paper for the case when the polynomials do not all have the same degree. The proof relies .on using an appropriate companion matrix, and thereby provides a link with previous work using this approach. It is then shown how the coefficients in a greatest common divisor can be obtained by reducing this extended resultant matrix to row echelon form, this again being an extension of a previous result for the casem=1. Finally, it is shown how the results can be modified when the polynomials are expressed relative to an arbitrary orthogonal basis.