Abstract

Duval defined and studied rational Puiseux expansions. In this paper we first prove that the existence of rational Puiseux expansions follows from the structure of algebraic extensions of a completion of the rational function field. We then describe a canonical system of rational Puiseux expansions, which are constructed in terms of the coeficients of classical Puiseux expansions. Using recent effective results on algebraic functions, we use this construction to prove that a system of rational Puiseux expansions exists whose height can be bounded in terms of the degrees and height of the polynomial determining the rational Puiseux expansions.

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