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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Communication dans un congrès
Markus Rosenkranz. ISSAC '16, Jul 2016, Waterloo, Canada. ACM, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, pp.341-348, 2016, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation. <http://www.issac-symposium.org/2016>. <10.1145/2930889.2930931>
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Dernière modification le : jeudi 22 septembre 2016 - 14:31:08
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Guillaume Moroz, Éric Schost. A Fast Algorithm for Computing the Truncated Resultant. Markus Rosenkranz. ISSAC '16, Jul 2016, Waterloo, Canada. ACM, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, pp.341-348, 2016, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation. <http://www.issac-symposium.org/2016>. <10.1145/2930889.2930931>. <hal-01366386>

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