In this paper we present a present a theoretical and algorithmic analysis on the normality of rational parametrizations of algebraic plane curves over arbitrary fields of characteris- tic zero. If the field is algebraically closed we give an algorithm to decide whether a parametrization is proper and, if not, a normal parametrization is computed. If the field is not algebraically closed the problem is more complicated, and a degenerated situa- tion may appear.
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