Euclid's algorithm; greatest common divisor; Sylvester matrix
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid's algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using $c$-$s$ transformation and $QR$-factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.