Proper real reparametrization of rational ruled surfaces Original Research Article

Let image be a computable field. We present an algorithm to decide whether a proper rational parametrization of a ruled surface, with coefficients in image, can be properly reparametrized over a real (i.e. embedded in image) finite field extension of image. Moreover, in the affirmative case, the algorithm provides a proper parametrization with coefficients in a real extension of image of degree at most 2.