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.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [28 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01366386
Contributor : Guillaume Moroz <>
Submitted on : Wednesday, September 14, 2016 - 3:09:28 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:26 PM
Document(s) archivé(s) le : Thursday, December 15, 2016 - 3:19:13 PM

Files

resultant_series_draft.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

376

Files downloads

152