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＜電子ブック＞
Rational Algebraic Curves : A Computer Algebra Approach / by J. Rafael Sendra, Franz Winkler, Sonia Pérez-Diaz
(Algorithms and Computation in Mathematics ; 22)

版	1st ed. 2008.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	X, 270 p. 24 illus : online resource
著者標目	*Sendra, J. Rafael author Winkler, Franz author Pérez-Diaz, Sonia author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Algebra LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Algebraic Geometry FREE:Algebra FREE:Symbolic and Algebraic Manipulation FREE:Mathematical Applications in Computer Science
一般注記	and Motivation -- Plane Algebraic Curves -- The Genus of a Curve -- Rational Parametrization -- Algebraically Optimal Parametrization -- Rational Reparametrization -- Real Curves Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household appliances would be unthinkable without the computational manipulation of algebraic curves and surfaces. Algebraic curves and surfaces combine fas- nating mathematical beauty with challenging computational complexity and wide spread practical applicability. In this book we treat only algebraic curves, although many of the results and methods can be and in fact have been generalized to surfaces. Being the solution loci of algebraic, i. e. , polynomial, equations in two variables, plane algebraiccurvesarewellsuited forbeing investigatedwith symboliccomputer algebra methods. This is exactly the approach we take in our book. We apply algorithms from computer algebra to the analysis, and manipulation of al- braic curves. To a large extent this amounts to being able to represent these algebraic curves in di?erent ways, such as implicitly by de?ning polyno- als, parametrically by rational functions, or locally parametrically by power series expansions around a point HTTP:URL=https://doi.org/10.1007/978-3-540-73725-4

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