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 coefficients 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.
