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We apply algorithms from computer algebra to the analysis, and manipulation of algebraic curves. To a large extent this amounts to being able to represent these algebraic curves in different ways, such as implicitly by defining polynomials, parametrically by rational functions, or locally parametrically by power series expansions around a point.
These representations all have their individual advantages; an implicit representation lets us decide easily whether a given point actually lies on a given curve, a parametric representation allows us to generate points of a given curve over the desired coordinate fields, and with the help of a power series expansion we can for instance overcome the numerical problems of tracing a curve through a singularity. The central problem in this book is the determination of rational parametrizability of a curve, and, in case it exists, the computation of a good rational parametrization.
This amounts to determining the genus of a curve, i. Various optimality criteria for rational parametrizations of algebraic curves are discussed. We also point to some applications of these techniques in computer aided geometric design. Many of the symbolic algorithmic methods described in our book are implemented in the program system CASA, which is based on the computer algebra system Maple. Our book is mainly intended for graduate students specializing in constructive algebraic curve geometry. We hope that researchers wanting to get a quick overview of what can be done with algebraic curves in terms of symbolic algebraic computation will also find this book helpful.
CASA is a special-purpose system for computational algebra and constructive algebraic geometry. The system has been developed since , and is the ongoing product of the Computer Algebra Group under the direction of Prof.
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It is built on the CharSet is an Aldor package written by Christian Aistleitner for differential characteristic set computations. Interfaces to the command line, Mathematica and Maple are included. Skip to content. Computer Algebra for Geometry Algebraic varieties are defined by polynomial equations.
Computer algebra methods for solving systems of polynomial equations and similar problems form the basis for a computational theory of Algebraic Geometry. Josef Schicho. Franz Winkler.
Rational Algebraic Curves: A Computer Algebra Approach / Edition 1
Project Lead: Josef Schicho. Software Automatic resolution of singularities Computer Algebra for Geometry. Authors: Gabor Bodnar.
Authors: Franz Winkler. Shop Textbooks. Add to Wishlist. USD Sign in to Purchase Instantly. Temporarily Out of Stock Online Please check back later for updated availability. Overview The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. Product Details Table of Contents. This specific ISBN edition is currently not available.
View all copies of this ISBN edition:. Synopsis About this title The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. Review : From the reviews: "The central problem in the book is the question whether a given algebraic curve is parametrizable and in case to compute a good rational parametrization.
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Roberts, MathDL, May, "The book Rational algebraic curves: a computer algebra approach is a very complete text on rational curves. Bayer, Mathematical Reviews, Issue a "About this title" may belong to another edition of this title. Buy New View Book. Other Popular Editions of the Same Title. Search for all books with this author and title.
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Customers who bought this item also bought. Stock Image. Seller Rating:. New Quantity Available: 8. New Quantity Available: 2. New Quantity Available: 5. Bookshub Karol Bagh, India. Romtrade Corp. Rational Algebraic Curves Sonia P? Rafael Sendra. Published by Springer.
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