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Rational Algebraic Curves [electronic resource] :A Computer Algebra Approach / by J. Rafael Sendra, Franz Winkler, Sonia Pérez-Díaz.

by Sendra, J. Rafael [author.]; Winkler, Franz [author.]; Pérez-Díaz, Sonia [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Algorithms and Computation in Mathematics: 22Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: online resource.ISBN: 9783540737254.Subject(s): Mathematics | Computer science | Algebra -- Data processing | Algebra | Geometry, algebraic | Mathematics | Algebraic Geometry | Algebra | Symbolic and Algebraic Manipulation | Math Applications in Computer ScienceDDC classification: 516.35 Online resources: Click here to access online
Contents:
and Motivation -- Plane Algebraic Curves -- The Genus of a Curve -- Rational Parametrization -- Algebraically Optimal Parametrization -- Rational Reparametrization -- Real Curves.
In: Springer eBooksSummary: 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.
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and Motivation -- Plane Algebraic Curves -- The Genus of a Curve -- Rational Parametrization -- Algebraically Optimal Parametrization -- Rational Reparametrization -- Real Curves.

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.

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