A Fast Algorithm for Computing the Truncated Resultant

09/14/2016

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by   Guillaume Moroz, et al.

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Let P and Q be two polynomials in K[x, y] with degree at most d, where K is a field. Denoting by R ∈ K[x] the resultant of P and Q with respect to y, we present an algorithm to compute R mod x^k in O (kd) arithmetic operations in K, where the O notation indicates that we omit polylogarithmic factors. This is an improvement over state-of-the-art algorithms that require to compute R in O (d^3) operations before computing its first k coefficients.