MARC details
| 000 -LEADER |
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| fixed length control field |
04228nmm a22003255i 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20230705150645.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
150430s2015 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319167213 |
| -- |
978-3-319-16721-3 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.35 |
| Edition number |
23 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Cox, David A. |
| 9 (RLIN) |
20905 |
| 245 ## - TITLE STATEMENT |
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| Title |
Ideals, Varieties, and Algorithms |
| Medium |
[electronic resource] : |
| Remainder of title |
An Introduction to Computational Algebraic Geometry and Commutative Algebra / |
| Statement of responsibility, etc. |
by David A. Cox, John Little, Donal O'Shea. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
4th ed. 2015. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Cham : |
| Name of publisher, distributor, etc. |
Springer International Publishing : |
| -- |
Imprint: Springer, |
| Date of publication, distribution, etc. |
2015. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XVI, 646 p. 95 illus., 7 illus. in color. |
| Other physical details |
online resource. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Preface -- Notation for Sets and Functions -- 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 -- 10. Additional Groebner Basis Algorithms -- Appendix A. Some Concepts from Algebra -- Appendix B. Pseudocode -- Appendix C. Computer Algebra Systems -- Appendix D. Independent Projects -- References -- Index. . |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry-the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz-this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of Maple™, Mathematica®, and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. From the reviews of previous editions: "...The book gives an introduction to Buchberger's algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations, and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry." -Peter Schenzel, zbMATH, 2007 "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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Algebraic geometry. |
| 9 (RLIN) |
20906 |
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| Topical term or geographic name entry element |
Commutative algebra. |
| 9 (RLIN) |
20907 |
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| Topical term or geographic name entry element |
Commutative rings. |
| 9 (RLIN) |
20908 |
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| Topical term or geographic name entry element |
Mathematical logic. |
| 9 (RLIN) |
20909 |
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| Topical term or geographic name entry element |
Computer software. |
| 9 (RLIN) |
20910 |
|
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| Topical term or geographic name entry element |
Algebraic Geometry. |
| 9 (RLIN) |
20911 |
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| Topical term or geographic name entry element |
Commutative Rings and Algebras. |
| 9 (RLIN) |
20912 |
|
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| Topical term or geographic name entry element |
Mathematical Logic and Foundations. |
| 9 (RLIN) |
20913 |
|
|---|
| Topical term or geographic name entry element |
Mathematical Software. |
| 9 (RLIN) |
20914 |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Little, John. |
| Relator term |
author. |
| Relationship |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) |
20915 |
|
|---|
| Personal name |
O'Shea, Donal. |
| Relator term |
author. |
| Relationship |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) |
20916 |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-3-319-16721-3">https://doi.org/10.1007/978-3-319-16721-3</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Koha item type |
e-Book |
