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Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra / David A. Cox, John Little and Donal O'Shea.

By: Contributor(s): Series: Undergraduate texts in mathematicsPublication details: Switzerland : Springer, 2015.Edition: 4th edDescription: xvi, 646 p. : diagrams (some color) ; 25 cmISBN:
  • 9783319167206
Subject(s): DDC classification:
  • 516.35 23 C877
Contents:
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.
Summary: This book 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).
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 516.35 C877 (Browse shelf(Opens below)) Available 136482
Total holds: 0

Includes bibliographical references and index.

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.

This book 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).

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