Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra / David A. Cox, John Little, Donal O'Shea
Tipo de material: TextoIdioma: Inglés Series Undergraduate texts in mathematicsFecha de copyright: New York : Springer, 2015Edición: Fourth editionDescripción: xvi, 646 pages : illustrations ; 25 cmISBN:- 9783319167206 (hbk)
- 9783319167213 (ebook)
- 23 516.35
- QA564 .C688 2007
Tipo de ítem | Biblioteca actual | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems | |
---|---|---|---|---|---|---|---|---|
Colección general | Biblioteca Yachay Tech | 516.35 C8773i 2015 (Navegar estantería(Abre debajo)) | Ej. 1 | Disponible | 005845 |
Includes bibliographical references (p. 535-539) and index.
Preface -- Notation for Sets and Functions -- 1. Geometry, Algebra, and Algorithms -- 2. Gröbner 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 Gröbner Basis Algorithms -- Appendix A. Some Concepts from Algebra -- Appendix B. Pseudocode -- Appendix C. Computer Algebra Systems -- Appendix D. Independent Projects.
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).
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