Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders. Different ways have been studied to make these as small as possible. The subresultant sequence of two polynomials is a polynomial remainder sequence in which the size of the coefficients is optimal in the generic case, but when taking the input from applications, the coefficients are often larger than necessary. We generalize two improvements of the subresultant sequence to Ore polynomials and derive a new bound for the minimal coefficient size. Our approach also yields a new proof for the results in the commutative case, providing a new point of view on the origin of the extraneous factors of the coefficients.

多项式余数序列包含应用于（非）可交换多项式的欧几里得算法的中间结果。算法的运行时间取决于余数系数的大小。已经研究了不同的方法来使它们尽可能小。两个多项式的子结果序列是多项式余数序列，其中在一般情况下系数的大小是最佳的，但是当从应用程序中获取输入时，系数通常会比所需的大。我们将子结果序列的两个改进推广到Ore多项式，并得出最小系数大小的新界限。我们的方法也为换向情况下的结果提供了新的证明，为系数的无关因素的起源提供了新的观点。