text: and then the subresultant polynomials and the principal subresultant coefficients of  and  are the image by  of those of  and .
  The subresultants have two important properties which make them fundamental for the computation on computers of the GCD of two polynomials with integer coefficients.
  Firstly, their definition through determinants allows bounding, through Hadamard inequality, the size of the coefficients of the GCD.
  Secondly, this bound and the property of good specialization allow computing the GCD of two polynomials with integer coefficients through modular computation and Chinese remainder theorem (see below).
  Technical definition
  Let
  be two univariate polynomials with coefficients in a field K. Let us denote by  the  vector space of dimension  of polynomials of degree less than . For non-negative integer  such that  and , let
  be the linear map such that
  The resultant of  and  is the determinant of the Sylvester matrix, which is the (square) matrix of  on the bases of the powers of . Similarly, the -subresultant polynomial is defined in term of determinants of submatrices of the matrix of
  Let us describe these matrices more precisely;
  Let  for  or , and  for  or . The Sylvester matrix is the -matrix such that the coefficient of the -th row and the -th column is  for  and  for :