Detecting When an Implicit Equation or a Rational Parametrization Defines a Conical or Cylindrical Surface, or a Surface of Revolution.

Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e., the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a surface of revolution.