Real Algebraic and Analytic Geometry
Submission: 2007, March 2.
In this paper we give an algorithm that detects real singularities and counts local branches of real rational curves without knowing an implicitization. The main idea behind this is a generalization of the D-resultant (see van den Essen and Yu (1997)) to n rational functions. This allows us to describe all the singularities as solutions of a system of polynomials in one variable.
Mathematics Subject Classification (2000): 14Q05, 14H20, 14P05.
Keywords and Phrases: Algebraic curves, rational parametrizations, singular points, generalized resultants.
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