Improperly parametrized rational curves
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Singular points of algebraic curves
Journal of Symbolic Computation
CASA: A computer algebra package for constructive algebraic geometry
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic 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
Computing parameterizations of rational algebraic curves
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
An algorithm for computing the Weierstrass normal form
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
A relatively optimal rational space curve reparametrization algorithm through canonical divisors
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Symbolic parametrization of pipe and canal surfaces
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Solving genus zero diophantine equations with at most two infinite valuations
Journal of Symbolic Computation
Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Distributed maple: parallel computer algebra in networked environments
Journal of Symbolic Computation
Implicitization of differential rational parametric equations
Journal of Symbolic Computation
Computing all parametric solutions for blending parametric surfaces
Journal of Symbolic Computation
Numerical parameterization of affine varieties using
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Inversion of parameterized hypersurfaces by means of subresultants
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Parametrization of approximate algebraic curves by lines
Theoretical Computer Science - Algebraic and numerical algorithm
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
Computation of the singularities of parametric plane curves
Journal of Symbolic Computation
The moving curve ideal and the Rees algebra
Theoretical Computer Science
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
On convolutions of algebraic curves
Journal of Symbolic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Reparameterization of curves and surfaces with respect to their convolution
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Using polynomial interpolation for implicitizing algebraic curves
Computer Aided Geometric Design
Algorithms for Rational Real Algebraic Curves
Fundamenta Informaticae
Journal of Computational and Applied Mathematics
Journal of Symbolic Computation
A partial solution to the problem of proper reparametrization for rational surfaces
Computer Aided Geometric Design
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If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to the other are of utmost importance. We investigate the transformation of an implicit representation of a plane algebraic curve into a parametric representation. Various methods for computing a rational parametrization, if one exists, are described. As a new idea we introduce the concept of working with classes of conjugate (singular or simple) points on curves. All the necessary operations, like determining the multiplicity and the character of the singular points or passing a linear system of curves through these points, can be applied to such classes of conjugate points. Using this idea one can parametrize a curve if one knows only one simple point on it. We do not propose any new method for finding such a simple point. By classical methods a rational point on a rational curve can be computed, if such a point exists. Otherwise, one can express the coordinates of such a point in an algebraic extension of degree 2 over the ground field.