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Synopsis
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. It provides a nice and easy introduction to the topic for students.
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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.
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Rational Algebraic Curves
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Springer Berlin Heidelberg, 2010
ISBN 10 : 3642092918
ISBN 13 : 9783642092916
Neuf
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Nice and easy introduction to topic for studentsThe 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 ra. N° de réf. du vendeur 5048308
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Rational Algebraic Curves : A Computer Algebra Approach
Edité par
Springer Berlin Heidelberg, 2010
ISBN 10 : 3642092918
ISBN 13 : 9783642092916
Neuf
Taschenbuch
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783642092916
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Rational Algebraic Curves
Edité par
Springer Berlin Heidelberg Nov 2010, 2010
ISBN 10 : 3642092918
ISBN 13 : 9783642092916
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves. 280 pp. Englisch. N° de réf. du vendeur 9783642092916
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Rational Algebraic Curves
Edité par
Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2010, 2010
ISBN 10 : 3642092918
ISBN 13 : 9783642092916
Neuf
Taschenbuch
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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 280 pp. Englisch. N° de réf. du vendeur 9783642092916
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Rational Algebraic Curves: A Computer Algebra Approach (Algorithms and Computation in Mathematics, 22)
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Rational Algebraic Curves: A Computer Algebra Approach (Algorithms and Computation in Mathematics, 22)
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Rational Algebraic Curves : A Computer Algebra Approach
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Rational Algebraic Curves: A Computer Algebra Approach (Algorithms and Computation in Mathematics)
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Rational Algebraic Curves: A Computer Algebra Approach (Algorithms and Computation in Mathematics, 22)
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Rational Algebraic Curves: A Computer Algebra Approach (Algorithms and Computation in Mathematics (22))
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