text: In mathematics, it is common to require that the greatest common divisor be a monic polynomial. To get this, it suffices to divide every element of the output by the leading coefficient of  This allows that, if a and b are coprime, one gets 1 in the right-hand side of Bézout's inequality. Otherwise, one may get any non-zero constant. In computer algebra, the polynomials commonly have integer coefficients, and this way of normalizing the greatest common divisor introduces too many fractions to be convenient.
  The second way to normalize the greatest common divisor in the case of polynomials with integer coefficients is to divide every output by the content of  to get a primitive greatest common divisor. If the input polynomials are coprime, this normalisation also provides a greatest common divisor equal to 1. The drawback of this approach is that a lot of fractions should be computed and simplified during the computation.
  A third approach consists in extending the algorithm of subresultant pseudo-remainder sequences in a way that is similar to the extension of the Euclidean algorithm to the extended Euclidean algorithm. This allows that, when starting with polynomials with integer coefficients, all polynomials that are computed have integer coefficients. Moreover, every computed remainder  is a subresultant polynomial. In particular, if the input polynomials are coprime, then the Bézout's identity becomes