Barnett’s Theorems About the Greatest Common Divisor of Several Univariate Polynomials Through Bezout-like Matrices

AbstractThis article provides a new presentation of Barnett’s theorems giving the degree (resp. coefficients) of the greatest common divisor of several univariate polynomials with coefficients in an integral domain by means of the rank (resp. linear dependencies of the columns) of several Bezout-like matrices. This new presentation uses Bezout or hybrid Bezout matrices instead of polynomials evaluated in a companion matrix as in the original Barnett’s presentation. Moreover, this presentation also allows us to compute the coefficients of the considered greatest common divisor in an easier way than in the original Barnett’s theorems