# Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

## David Cox; John Little; Donal O'Shea

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( 29 valoraciones por Goodreads )

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, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing a new edition of Ideals, Varieties and Algorithms the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple , Mathematica and REDUCE.

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"I consider the book to be wonderful...The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging...offers the heart and soul of modern commutative and algebraic geometry." -The American Mathematical Monthly

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## 1.Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Editorial: Springer, U.S.A. (2006)
ISBN 10: 0387946802 ISBN 13: 9780387946801
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(Raleigh, NC, Estados Unidos de America)
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Descripción Springer, U.S.A., 2006. Hard Cover. Estado de conservación: New. Estado de la sobrecubierta: No DJ. Second Edition, Corrected 5th Printing. This is a new hardcover second edition, 5th corrected printing copy in slick yellow binding, no DJ, Size: 8vo - over 7¾" - 9¾" tall. Nº de ref. de la librería 078425

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## 2.Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Editorial: Springer (2006)
ISBN 10: 0387946802 ISBN 13: 9780387946801
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Irish Booksellers
(Rumford, ME, Estados Unidos de America)
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Descripción Springer, 2006. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M0387946802

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## 3.Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra [Undergraduate Texts in Mathematics]

Editorial: Springer, New York (1997)
ISBN 10: 0387946802 ISBN 13: 9780387946801
Librería
Tiber Books
(Cockeysville, MD, Estados Unidos de America)
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Descripción Springer, New York, 1997. Hardcover. Estado de conservación: New. . . . . 2nd edition. 8vo, hardcover. No dj, as issued. NEW. Bright, crisp & clean, unread; covers glossy. xiii, 536 p., illus. Nº de ref. de la librería 1150605.20

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## 4.Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutati

Editorial: Springer (2006)
ISBN 10: 0387946802 ISBN 13: 9780387946801
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Murray Media
(North Miami Beach, FL, Estados Unidos de America)
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Descripción Springer, 2006. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P110387946802

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## 5.Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Editorial: Springer
ISBN 10: 0387946802 ISBN 13: 9780387946801
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Cloud 9 Books
(Wellington, FL, Estados Unidos de America)
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Descripción Springer. Hardcover. Estado de conservación: New. 0387946802 New Condition. Nº de ref. de la librería NEW7.1062589

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## 6.Ideals, Varieties, and Algorithms

Editorial: Springer
ISBN 10: 0387946802 ISBN 13: 9780387946801
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Majestic Books
(London, ,, Reino Unido)
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Descripción Springer. Estado de conservación: New. pp. 556. Nº de ref. de la librería 5770258

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## 7.Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Editorial: Springer (2006)
ISBN 10: 0387946802 ISBN 13: 9780387946801
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Ergodebooks
(RICHMOND, TX, Estados Unidos de America)
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Descripción Springer, 2006. Hardcover. Estado de conservación: New. 2nd. This item is printed on demand. Nº de ref. de la librería DADAX0387946802

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