Real Algebraic Geometry, Michel Coste; Louis Mahe; Marie-Francoise Roy

Автор: Wolfram Decker; Christoph Lossen
Название: Computing in Algebraic Geometry
ISBN: 3642067018 ISBN-13(EAN): 9783642067013
Издательство: Springer
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Описание: This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations.

Автор: Aldo Conca; Sandra Di Rocco; Jan Draisma; June Huh
Название: Combinatorial Algebraic Geometry
ISBN: 3319048694 ISBN-13(EAN): 9783319048697
Издательство: Springer
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Описание: Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics.

Автор: Vladimir I. Arnold; Ilia Itenberg; Viatcheslav Kha
Название: Real Algebraic Geometry
ISBN: 3642362427 ISBN-13(EAN): 9783642362422
Издательство: Springer
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Описание: This book addresses the relationship between algebraic formulas and geometric images. In spite of the simplicity and importance of this problem, it remains unsolved to this day although, as the book shows, many remarkable results have been discovered.

Автор: Jacek Bochnak; Michel Coste; Marie-Francoise Roy
Название: Real Algebraic Geometry
ISBN: 364208429X ISBN-13(EAN): 9783642084294
Издательство: Springer
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Описание: The present volume is a translation, revision and updating of our book (pub- lished in French) with the title "Geometrie Algebrique Reelle." Since its pub- lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. We wish to thank Michael Buchner for his careful reading of the text and for his linguistic corrections and stylistic improvements. The initial Jb. TEiX file was prepared by Thierry van Effelterre. The three authors participate in the European research network "Real Algebraic and Analytic Geometry." The first author was partially supported by NATO Collaborative Research Grant 960011. Jacek Bochnak April 1998 Michel Coste Marie-Pranroise Roy Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Ordered Fields, Real Closed Fields . . . . . . . . . . . . . . . . . . . . . . . 7 1. 1 Ordered Fields, Real Fields . . . . . " . . . . . . . . . . . . . . . . . . . . . . . 7 1. 2 Real Closed Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1. 3 Real Closure of an Ordered Field. . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 4 The Tarski-Seidenberg Principle. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. Semi-algebraic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1 Algebraic and Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . . . . 23 2. 2 Projection of Semi-algebraic Sets. Semi-algebraic Mappings. . 26 2. 3 Decomposition of Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . 30 2. 4 Connectedness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2. 5 Closed and Bounded Semi-algebraic Sets. Curve-selection Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2. 6 Continuous Semi-algebraic Functions. Lojasiewicz's Inequality 42 2. 7 Separation of Closed Semi-algebraic Sets. . . . . . . . . . . . . . . . . .

Автор: Jacek Bochnak; Michel Coste; Marie-Francoise Roy
Название: Real Algebraic Geometry
ISBN: 3540646639 ISBN-13(EAN): 9783540646631
Издательство: Springer
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Описание: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordered Fields, Real Closed Fields . . . . . . 1 Ordered Fields, Real Fields . " . Semi-algebraic Sets . Curve-selection Lemma .

Автор: Bert J?ttler; Ragni Piene
Название: Geometric Modeling and Algebraic Geometry
ISBN: 3642445519 ISBN-13(EAN): 9783642445514
Издательство: Springer
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Описание: Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways.

Автор: Eisenbud
Название: Commutative Algebra and Noncommutative Algebraic Geometry
ISBN: 1107065623 ISBN-13(EAN): 9781107065628
Издательство: Cambridge Academ
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Описание: This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Автор: Ciro Ciliberto; Friedrich Hirzebruch; Rick Miranda
Название: Applications of Algebraic Geometry to Coding Theory, Physics and Computation
ISBN: 1402000049 ISBN-13(EAN): 9781402000041
Издательство: Springer
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Описание: Proceedings of the NATO Advanced Research Workshop, held in Eilat, Israel, from 25th February to 1st March 2001

Автор: Fox Ralph Hartzler, Fox R. H.
Название: Algebraic Geometry and Topology: A Symposium in Honor of Solomon Lefschetz
ISBN: 0691626804 ISBN-13(EAN): 9780691626802
Издательство: Wiley
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Описание: Many of the developments of modern algebraic geometry and topology stem from the ideas of S. Lefschetz. These are featured in this volume of contemporary research papers contributed by mathematical colleagues to celebrate his seventieth birthday. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology

Автор: Fabrizio Catanese; Jean-Pierre Demailly; Ciro Cili
Название: Transcendental Methods in Algebraic Geometry
ISBN: 3540620389 ISBN-13(EAN): 9783540620389
Издательство: Springer
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Описание: Presents lectures given at the 3rd session of the Centro Internazionale Matematico Estivo, held in Cetraro, Italy, in July 1994. The topics covered include four manifolds, line bundles and manifolds of semi-positive curvature.

Автор: Caporaso
Название: Current Developments in Algebraic Geometry
ISBN: 110745946X ISBN-13(EAN): 9781107459465
Издательство: Cambridge Academ
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Описание: This volume, based on a workshop by the MSRI and addressed to both beginners and experts, offers an expository overview of the state of the art in many areas of algebraic geometry. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research.