Computing μ-bases from algebraic ruled surfaces

We find a μ-basis for a rational ruled surface, starting from its implicit representation. A parametrization for this ruled surface is then deduced form this μ-basis. This parametrization does not have any non-generic base points and its directrix has the lowest possible degree. A complete interchange graph is built for the algebraic equation, the μ-basis and the parametric equation of a rational ruled surface.