Subresultants can be viewed as a generalization of resultants, which are the product of the pairwise differences of the roots of polynomials. Subresultants are the most commonly used tool to compute the resultant or greatest common divisor of two polynomials with coefficients in an integral ring. Subresultants for a few simple pairs of polynomials include S(x - a, x - b) | = | {a - b, 1} S((x - a)(x - b), x - c) | = | {(a - c)(b - c), 1} S((x - a)(x - b), (x - c)(x - d)) | = | {(a - c)(b - c)(a - d)(b - d), a + b - c - d, 1}.
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