A Fast Algorithm for Computing the Truncated Resultant

Guillaume Moroz 1 Éric Schost 2
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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.
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Guillaume Moroz, Éric Schost. A Fast Algorithm for Computing the Truncated Resultant. ISSAC '16, Sergei A. Abramov; Eugene V. Zima, Jul 2016, Waterloo, Canada. pp.341-348, ⟨10.1145/2930889.2930931⟩. ⟨hal-01366386⟩



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