good reduction of puiseux series and complexity of the newton-puiseux algorithm over finite fields
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.
puiseux series complexity finite fields algebraic functions modular methods symbolic-numeric algorithms