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An analysis of the subresultant algorithm over an algebraic number field

We show that we can compute the Subresultant Polynomial Remainder Sequence over an algebraic number field in 0((n5m3 + n4m5) log2(nDEm)) binary operations, where the generator of the field is given by a monic irreducible polynomial of degree m with integer coefficients bounded by E in absolute value, and where the two input polynomials are of degree at most n and with integer coefficients bounded by D in absolute value.