text: In some contexts, it is essential to control the sign of the leading coefficient of the pseudo-remainder. This is typically the case when computing resultants and subresultants, or for using Sturm's theorem. This control can be done either by replacing  by its absolute value in the definition of the pseudo-remainder, or by controlling the sign of  (if  divides all coefficients of a remainder, the same is true for ).
  Trivial pseudo-remainder sequence
  The simplest (to define) remainder sequence consists in taking always . In practice, it is not interesting, as the size of the coefficients grows exponentially with the degree of the input polynomials. This appears clearly on the example of the preceding section, for which the successive pseudo-remainders are
  The number of digits of the coefficients of the successive remainders is more than doubled at each iteration of the algorithm. This is typical behavior of the trivial pseudo-remainder sequences.
  Primitive pseudo-remainder sequence
  The primitive pseudo-remainder sequence consists in taking for  the content of the numerator. Thus all the  are primitive polynomials.
  The primitive pseudo-remainder sequence is the pseudo-remainder sequence, which generates the smallest coefficients. However it requires to compute a number of GCD's in , and therefore is not sufficiently efficient to be used in practice, especially when Z is itself a polynomial ring.
  With the same input as in the preceding sections, the successive remainders, after division by their content are
  The small size of the coefficients hides the fact that a number of integers GCD and divisions by the GCD have been computed.