Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra

Name: Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra
Availability: InStock
ISBN: 9780387356501

ISBN-10: 0387356509

ISBN-13: 9780387356501

Edition: 3rd 2007 (Revised)

Authors: John Little, David A. Cox, Donal O'Shea

List price: $59.95

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Description:

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? 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,…

Book details

List price: $59.95
Edition: 3rd
Copyright year: 2007
Publisher: Springer
Publication date: 7/31/2008
Binding: Hardcover
Pages: 553
Size: 6.00" wide x 9.50" long x 1.00" tall
Weight: 1.980
Language: English

J.I. Little is a professor in the Department of History at Simon Fraser University, author of Loyalties in Conflict: A Canadian Borderland in War and Rebellion, 1812-1840 , and co-author of An Illustrated History of Quebec: Tradition and Modernity .




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



Some concepts from algebra



Pseudocode



Computer algebra systems



Independent projects