Good reduction of puiseux series and complexity of the Newton-Puiseux algorithm over finite fields

Authors:
Adrien Poteaux;Marc Rybowicz
Affiliations:
XLIM-DMI (UMR CNRS 6172), Limoges, France;XLIM-DMI (UMR CNRS 6172), Limoges, France
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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Abstract

In [12], we sketched a numeric-symbolic method to compute Puiseux series with floating point coefficients. In this paper, we address the symbolic part of our algorithm. We study the reduction of Puiseux series coefficients modulo a prime ideal and prove a good reduction criterion sufficient to preserve the required information, namely Newton polygon trees. We introduce a convenient modification of Newton polygons that greatly simplifies proofs and statements of our results. Finally, we improve complexity bounds for Puiseux series calculations over finite fields, and estimate the bit-complexity of polygon tree computation.