Reparametrizing swung surfaces over the reals
Let \(\mathbb {K}\subseteq \mathbb {R}\) be a computable subfield of the real numbers (for instance, \(\mathbb {Q}\)). We present an algorithm to decide whether a given parametrization of a rational swung surface, with coefficients in \(\mathbb {K}(\mathtt {i})\), can be reparametrized over a real (i.e., embedded in \(\mathbb {R}\)) finite field extension of \(\mathbb {K}\). Swung surfaces include, in particular, surfaces of revolution.
swung surfaces revolution surfaces real and complex surfaces rational parametrization ultraquadrics