Detecting real singularities of a space curve from a real rational parametrization

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 -space without knowing an implicitization. The main idea behind this is a generalization of the -resultant (see [van den Essen, A., Yu, J.-T., 1997. The -resultant, singularities and the degree of unfaithfulness. Proc. Amer. Math. Soc. 25 (3), 689–695]) to 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. [Copyright &y& Elsevier]