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On the computation of singularities of parametrized ruled surfaces. (English) Zbl 1470.14054

Summary: Given a ruled surface \(\mathcal{V}\) defined in the standard parametric form \(\mathcal{P}(t_1, t_2)\), we present an algorithm that determines the singularities (and their multiplicities) of \(\mathcal{V}\) from the parametrization \(\mathcal{P}\). More precisely, from \(\mathcal{P}\) we construct an auxiliary parametric curve and we show how the problem can be simplified to determine the singularities of this auxiliary curve. Only one univariate resultant has to be computed and no elimination theory techniques are necessary. These results improve some previous algorithms for detecting singularities for the special case of parametric ruled surfaces.

MSC:

14H20 Singularities of curves, local rings
14J17 Singularities of surfaces or higher-dimensional varieties
68W30 Symbolic computation and algebraic computation
14J26 Rational and ruled surfaces
14Q10 Computational aspects of algebraic surfaces

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References:

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