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TitleGood reduction of Puiseux series and applications
Author(s) Adrien Poteaux, Marc Rybowicz
TypeArticle in Journal
AbstractWe have designed a new symbolic–numeric strategy for computing efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field. In essence, computations modulo a well-chosen prime number p are used to obtain the exact information needed to guide floating point computations. In this paper, we detail the symbolic part of our algorithm. First of all, we study modular reduction of Puiseux series and give a good reduction criterion for ensuring that the information required by the numerical part is preserved. To establish our results, we introduce a simple modification of classical Newton polygons, that we call “generic Newton polygons”, which turns out to be very convenient. Finally, we estimate the size of good primes obtained with deterministic and probabilistic strategies. Some of these results were announced without proof at ISSAC’08.
KeywordsPuiseux series, Algebraic functions, Finite fields, Symbolic–numeric algorithm
URL http://www.sciencedirect.com/science/article/pii/S0747717111001209
JournalJournal of Symbolic Computation
Pages32 - 63
Translation No
Refereed No