A partial solution to the problem of proper reparametrization for rational surfaces Original Research Article

Given an algebraically closed field image, and a rational parametrization image of an algebraic surface image, we consider the problem of computing a proper rational parametrization image from image (reparametrization problem). More precisely, we present an algorithm that computes a rational parametrization image of image such that the degree of the rational map induced by image is less than the degree induced by image. The properness of the output parametrization image is analyzed. In particular, if the degree of the map induced by image is one, then image is proper and the reparametrization problem is solved. The algorithm works if at least one of two auxiliary parametrizations defined from image is not proper.