Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra (eBook, 2007) [WorldCat.org]
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Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra

Author: David A Cox; John B Little; Donal O'Shea
Publisher: New York : Springer, ©2007.
Series: Undergraduate texts in mathematics.
Edition/Format:   eBook : Document : English : 3rd edView all editions and formats
Summary:
"The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory,  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Cox, David A.
Ideals, varieties, and algorithms.
New York : Springer, ©2007
(DLC) 2006930875
(OCoLC)78203220
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David A Cox; John B Little; Donal O'Shea
ISBN: 9780387356518 0387356517 9780387356501 0387356509 1441922571 9781441922571
OCLC Number: 186509567
Language Note: English.
Description: 1 online resource (xv, 551 pages) : illustrations
Contents: Preface to the First Edition --
Preface to the Second Edition --
Preface to the Third Edition --
Geometry, Algebra, and Algorithms --
Groebner Bases --
Elimination Theory --
The Algebra-Geometry Dictionary --
Polynomial and Rational Functions on a Variety --
Robotics and Automatic Geometric Theorem Proving --
Invariant Theory of Finite Groups --
Projective Algebraic Geometry --
The Dimension of a Variety --
Appendix A. Some Concepts from Algebra --
Appendix B. Pseudocode --
Appendix C. Computer Algebra Systems --
Appendix D. Independent Projects --
References --
Index.
Series Title: Undergraduate texts in mathematics.
Responsibility: David A. Cox, John Little, Donal O'Shea.
More information:

Abstract:

This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and  Read more...

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From the reviews of the third edition: "The book gives an introduction to Buchberger's algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction Read more...

 
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