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. An algorithm is presented to compute µ-basis from algebraic ruled surfaces.An alternatively simpler method is given to determine and parameterize algebraic ruled surfaces.An interchange graph is built for the different representations of a rational ruled surface.

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