Algebraic and algorithmic aspects of radical parametrizations

J. Rafael Sendra, David Sevilla, Carlos Villarino

In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We provide algorithms to implicitize radical parametrizations and to check whether a radical parametrization can be reparametrized into a rational parametrization.

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