text: Subresultant pseudo-remainder sequence A subresultant sequence can be also computed with pseudo-remainders. The process consists in choosing  in such a way that every  is a subresultant polynomial. Surprisingly, the computation of  is very easy (see below). On the other hand, the proof of correctness of the algorithm is difficult, because it should take into account all the possibilities for the difference of degrees of two consecutive remainders.
  The coefficients in the subresultant sequence are rarely much larger than those of the primitive pseudo-remainder sequence. As GCD computations in  are not needed, the subresultant sequence with pseudo-remainders gives the most efficient computation.
  With the same input as in the preceding sections, the successive remainders are
  The coefficients have a reasonable size. They are obtained without any GCD computation, only exact divisions. This makes this algorithm more efficient than that of primitive pseudo-remainder sequences.
  The algorithm computing the subresultant  sequence with pseudo-remainders is given below. In this algorithm, the input  is a pair of polynomials in . The  are the successive pseudo remainders in , the variables  and  are non negative integers, and the Greek letters denote elements in . The functions deg() and rem() denote the degree of a polynomial and the remainder of the Euclidean division. In the algorithm, this remainder is always in . Finally the divisions denoted / are always exact and have their result either in  or in .