عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9781475726930
(Number (ISBN
9781475726954
NATIONAL BIBLIOGRAPHY NUMBER
Number
b403789
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Ideals, Varieties, and Algorithms
General Material Designation
[Book]
Other Title Information
An Introduction to Computational Algebraic Geometry and Commutative Algebra /
First Statement of Responsibility
by David Cox, John Little, Donal O'Shea.
EDITION STATEMENT
Edition Statement
Second Edition.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York, NY :
Name of Publisher, Distributor, etc.
Imprint: Springer,
Date of Publication, Distribution, etc.
1997.
SERIES
Series Title
Undergraduate Texts in Mathematics,
ISSN of Series
0172-6056
CONTENTS NOTE
Text of Note
1. Geometry, Algebra, and Algorithms -- 2. Groebner Bases -- 3. Elimination Theory -- 4. The Algebra-Geometry Dictionary -- 5. Polynomial and Rational Functions on a Variety -- 6. Robotics and Automatic Geometric Theorem Proving -- 7. Invariant Theory of Finite Groups -- 8. Projective Algebraic Geometry -- 9. The Dimension of a Variety -- Appendix A. Some Concepts from Algebra -- {sect}1 Fields and Rings -- {sect}2. Groups -- {sect}3. Determinants -- Appendix B. Pseudocode -- {sect}1. Inputs, Outputs, Variables, and Constants -- {sect}2. Assignment Statements -- {sect}3. Looping Structures -- {sect}4. Branching Structures -- Appendix C. Computer Algebra Systems -- {sect}1. AXIOM -- {sect}2. Maple -- {sect}3. Mathematica -- {sect}4. REDUCE -- {sect}5. Other Systems -- Appendix D. Independent Projects -- {sect}1. General Comments -- {sect}2. Suggested Projects -- References.
0
SUMMARY OR ABSTRACT
Text of Note
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.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9781475726954
PIECE
Title
Springer eBooks
TOPICAL NAME USED AS SUBJECT
Logic, Symbolic and mathematical.
Mathematics.
PERSONAL NAME - PRIMARY RESPONSIBILITY
Cox, David.
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Little, John.
O'Shea, Donal.
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Date of Transaction
20190301083400.0
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
