On the numerical condition of algebraic curves and surfaces 1. Implicit equations
Computer Aided Geometric Design
Genus of the intersection curve of two rational surface patches
Computer Aided Geometric Design
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane
Journal of the ACM (JACM)
Symbolic parametrization of curves
Journal of Symbolic Computation
Noether's S-transformation simplifies curve singularities rationally: a local analysis
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Solving genus zero diophantine equations with at most two infinite valuations
Journal of Symbolic Computation
The singular point of an algebraic cubic
Applied Numerical Mathematics - Applied and computational mathematics: Selected papers of the third panamerican workshop Trujillo, Peru, 24-28 April 2000
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
On the complexity of real solving bivariate systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Computation of the singularities of parametric plane curves
Journal of Symbolic Computation
Detecting real singularities of a space curve from a real rational parametrization
Journal of Symbolic Computation
On the asymptotic and practical complexity of solving bivariate systems over the reals
Journal of Symbolic Computation
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Computation of the topology of real algebraic space curves
Journal of Symbolic Computation
Using Smith normal forms and µ-bases to compute all the singularities of rational planar curves
Computer Aided Geometric Design
A geometric strategy for computing intersections of two spatial parametric curves
The Visual Computer: International Journal of Computer Graphics
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Given an irreducible algebraic curve f(x,y)=0 of degree n=3 with rational coefficients,we describe algorithms for determinig whether the curve is singular, and if so, isolating its singular points, computing their multiplicities, and counting the number of distinct tangents at each. The algorithms require only rational arithmetic operations on the coefficients of f(x,y)=0, and avoid the need for more abstract symbolic representations of the singular point coordinates.