Journal of Symbolic Computation
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Symbolic parametrization of curves
Journal of Symbolic Computation
Algorithmic algebra
Parametrization of algebraic curves over optimal field extensions
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrizations of algebraic curves using a canonical divisor
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Real reparametrizations of real curves
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
A relatively optimal rational space curve reparametrization algorithm through canonical divisors
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
CASA - A System for Computer Aided Constructive Algebraic Geometry
DISCO '96 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Points on Algebraic Curves and the Parametrization Problem
Selected Papers from the International Workshop on Automated Deduction in Geometry
Real Parametrization of Algebraic Curves
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
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In this paper, we study fundamental properties of real curves, especially of rational real curves, and we derive several algorithms to decide the reality and rationality of curves in the complex plane. Furthermore, if the curve is real and rational, we determine a real parametrization. More precisely, we present a reality test algorithm for plane curves, and three different types of real parametrization algorithms that we call: direct parametrization algorithms (they compute a rational real parametrization, if it exists), algebraically optimal parametrization algorithms (they compute a rational real parametrization over the smallest possible real field extension, if the curve is rational and real), and hybrid parametrization algorithms (they combine parametrization and reparametrization techniques to derive algebraically optimal rational real parametrizations).