Improperly parametrized rational curves
Computer Aided Geometric Design
Singular points of algebraic curves
Journal of Symbolic Computation
Detecting cusps and inflection points in curves
Computer Aided Geometric Design
Identification of inflection points and cusps on rational curves
Computer Aided Geometric Design
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
On multivariate rational function decomposition
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Plotting missing points and branches of real parametric curves
Applicable Algebra in Engineering, Communication and Computing
Computation of the singularities of parametric plane curves
Journal of Symbolic Computation
Topology of 2D and 3D rational curves
Computer Aided Geometric Design
Computing the singularities of rational space curves
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Computing the shapes arising in a family of space rational curves depending on one parameter
Computer Aided Geometric Design
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Using a bihomogeneous resultant to find the singularities of rational space curves
Journal of Symbolic Computation
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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.