An edition of Ideals, varieties, and algorithms (1992)

Ideals, varieties, and algorithms

an introduction to computational algebraic geometry and commutative algebra

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Last edited by MARC Bot
May 19, 2025 | History
An edition of Ideals, varieties, and algorithms (1992)

Ideals, varieties, and algorithms

an introduction to computational algebraic geometry and commutative algebra

  • 4 Want to read

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 1960s. 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 led to some interesting applications - for example, in robotics and in geometric theorem proving.

Publish Date
Publisher
Springer-Verlag
Language
English
Pages
513

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Previews available in: English

Edition Availability
Cover of: Ideals, Varieties, and Algorithms
Cover of: Ideals, Varieties, and Algorithms
Cover of: Ideals, Varieties, and Algorithms
Cover of: Ideals, Varieties, and Algorithms
Cover of: Ideals, Varieties, and Algorithms
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Nov 25, 2010, Springer, Brand: Springer
paperback
Cover of: Ideals, Varieties, and Algorithms
Cover of: Ideals, varieties, and algorithms
Cover of: Ideals, Varieties, and Algorithms
Cover of: Ideals, varieties, and algorithms
Cover of: Ideals, varieties, and algorithms

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Book Details


Edition Notes

Includes bibliographical references (p. [499]-501) and index.

Published in
New York
Series
Undergraduate texts in mathematics

Classifications

Dewey Decimal Class
516.3/5
Library of Congress
QA564 .C688 1992, QA564 .C688 1991

The Physical Object

Pagination
xi, 513 p. :
Number of pages
513

Edition Identifiers

Open Library
OL1711322M
Internet Archive
idealsvarietiesa0000coxd
ISBN 10
038797847X, 354097847X
LCCN
92013290
OCLC/WorldCat
25676395, 223806222
LibraryThing
1203115
Goodreads
4142192

Work Identifiers

Work ID
OL1849157W

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May 19, 2025 Edited by MARC Bot import existing book
April 20, 2025 Edited by MARC Bot import existing book
July 14, 2024 Edited by MARC Bot import existing book
December 19, 2023 Edited by ImportBot import existing book
April 1, 2008 Created by an anonymous user Imported from Scriblio MARC record