Details:
Title  Detecting real singularities of a space curve from a real rational parametrization  Author(s)  R. Rubio, J.M. Serradilla, M.P. Vélez  Type  Article in Journal  Abstract  In this paper we give an algorithm that detects real singularities, including singularities at infinity, and counts local branches and multiplicities of real rational curves in the affine n space without knowing an implicitization. The main idea behind this is a generalization of the D resultant (see [van den Essen, A., Yu, J.T., 1997. The D resultant, singularities and the degree of unfaithfulness. Proc. Amer. Math. Soc. 25 (3), 689–695]) to n rational functions. This allows us to find all real parameters corresponding to the real singularities between the solutions of a system of polynomials in one variable.  Keywords  Algebraic curves, Rational parametrizations, Singular points, Generalized resultants  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108001405 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  5  Pages  490  498  Year  2009  Note  Spanish National Conference on Computer Algebra  Edition  0  Translation 
No  Refereed 
No 
