Skip to Main content Skip to Navigation
Conference papers

Improving Complexity Bounds for the Computation of Puiseux Series over Finite Fields

Adrien Poteaux 1 Marc Rybowicz 2
1 CALFOR - Calcul Formel
LIFL - Laboratoire d'Informatique Fondamentale de Lille
2 XLIM-DMI - DMI
XLIM - XLIM
Abstract : Let L be a field of characteristic p with q elements and F ∈ L[X, Y ] be a polynomial with p > deg Y (F) and total degree d. In [40], we showed that rational Puiseux series of F above X = 0 could be computed with an expected number of O˜d 3 log q) arithmetic operations in L. In this paper, we reduce this bound to O˜og q) using Hensel lifting and changes of variables in the Newton-Puiseux algorithm that give a better control of the number of steps. The only asymptotically fast algorithm required is polynomial multiplication over finite fields. This approach also allows to test the irreducibility of F in L[[X]][Y ] with Oõperations in L. Finally, we describe a method based on structured bivariate multiplication [34] that may speed up computations for some input.
Document type :
Conference papers
Complete list of metadatas

Cited literature [53 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01253216
Contributor : Adrien Poteaux <>
Submitted on : Friday, January 8, 2016 - 6:54:58 PM
Last modification on : Thursday, February 21, 2019 - 10:52:50 AM
Long-term archiving on: : Friday, April 15, 2016 - 7:30:15 PM

File

puiseuxd4.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Adrien Poteaux, Marc Rybowicz. Improving Complexity Bounds for the Computation of Puiseux Series over Finite Fields. ISSAC '15, Jul 2015, Bath, United Kingdom. pp.299--306, ⟨10.1145/2755996.2756650⟩. ⟨hal-01253216⟩

Share

Metrics

Record views

316

Files downloads

358