Algorithm REAL-NORMAL-PARAMETRIZATION Given a proper rational parametrization P(t) = χ1 1(t) χ1 2(t) , χ2 1(t) χ2 2(t)  ∈ L(t) 2, in reduced form, where L is a computable subfield of R, of an affine rational real curve C, the algorithm decides whether C can be R-normally parametrized, and in the affirmative case computes an Rnormal parametrization of C.

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