The central problem considered in this book is the determination of rational parametrizability of an algebraic curve, and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve, i.e. its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. Various optimality criteria for rational parametrizations of algebraic curves are discussed. This book is mainly intended for graduate students and researchers in constructive algebraic curve geometry.
Author(s): J. Rafael Sendra, Franz Winkler, Sonia Pérez-Diaz
Series: Algorithms and Computation in Mathematics
Year: 2007
Language: English
Pages: 272
Preface......Page 4
Contents......Page 6
Introduction and Motivation......Page 9
Plane Algebraic Curves......Page 22
The Genus of a Curve......Page 73
Rational Parametrization......Page 93
Algebraically Optimal Parametrization......Page 154
Rational Reparametrization......Page 192
Real Curves......Page 214
The System CASA......Page 243
Algebraic Preliminaries......Page 251
References......Page 261
Index......Page 269
