Good reduction of Puiseux series and applications
type: Item
instance of: scholarly article
title: Good reduction of Puiseux series and applications
zbMATH Open document ID: 1235.30002
author: Adrien Poteaux
author: Marc Rybowicz
published in: Journal of Symbolic Computation
publication date: 2011-12-21T00:00:00Z
review text: The paper describes in detail a symbolic-numeric strategy to compute floating point Puiseux series defined by a bivariate polynomial. The key idea is to perform modular reduction, that is, working modulo a suitably chosen prime \(p\). The symbolic part of the computation ensures that a later numerical stage has a sufficiently precise input. In Sections 2 and 3, details of Puiseux series expansion are presented such that the paper serves as reference for such computations. In Section 4 the Newton polygon technique is refined to be applicable in the algorithm ``RNPuiseux'', the main result of this paper. To this end the data structure of ``polygon trees'' is defined and examined. Section 5 contains proofs that a good choice of \(p\) is possible, and Section 6 discuss various aspects of the algorithm, such as the size of the chosen prime \(p\).
reviewed by: Thomas Kahle
Mathematics Subject Classification ID: 65D99
Mathematics Subject Classification ID: 11R09
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 5991113
zbMATH Keywords: Puiseux series
zbMATH Keywords: symbolic-numerical computation
zbMATH Keywords: algebraic functions
zbMATH Keywords: modular reduction
zbMATH Keywords: RNPuiseux
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jsc.2011.08.008
OpenAlex ID: W2027088875
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DOI: 10.1016/J.JSC.2011.08.008
description: scientific article; zbMATH DE number 5991113