Details:
Title  Good reduction of Puiseux series and applications  Author(s)  Adrien Poteaux, Marc Rybowicz  Type  Article in Journal  Abstract  We 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 wellchosen 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.  Keywords  Puiseux series, Algebraic functions, Finite fields, Symbolic–numeric algorithm  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111001209 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  1  Pages  32  63  Year  2012  Edition  0  Translation 
No  Refereed 
No 
