Rational Algebraic Curves

J. Rafael Sendra

ISBN 10: 3540737243 / ISBN 13: 9783540737247

Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2007, 2007

Beschreibung

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.

Bestandsnummer des Verkäufers 9783540737247

Bibliografische Details

• Titel: Rational Algebraic Curves
• Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2007
• Erscheinungsjahr: 2007
• Sprache: Englisch
• ISBN-10: 3540737243
• ISBN-13: 9783540737247
• Einband: Buch
• Zustand: Neu
• Abmessungen: 241B x 160 H x 20 T Millimeter Breite: 241 mm, Höhe: 160 mm, Tiefe: 20 mm
• Gewicht: 588 Gramm

Über diesen Titel

Inhaltsangabe

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.