Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra
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 o...
Bewaard in:
| Hoofdauteurs: | , , |
|---|---|
| Formaat: | Livre numérique |
| Taal: | Anglais |
| Gepubliceerd in: |
New York, NY :
Springer New York : Imprint: Springer
[20..].
Cham : Springer Nature |
| Editie: | 3rd ed. 2007. |
| Reeks: | Undergraduate Texts in Mathematics
|
| Onderwerpen: | |
| Online toegang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Opmerking: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Ideals, varieties, and algorithms, an introduction to computational algebraic geometry and commutative algebra, David Cox, John Little, Donal O'Shea, 3rd edition, 2007, New-York, Springer, 1 vol. (XV-551 p.), Undergraduate texts in mathematics, 978-0-387-35650-1 |
| LEADER | 05170nam a22004937a 4500 | ||
|---|---|---|---|
| 001 | 938795 | ||
| 008 | 080410q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN123145244 | ||
| 020 | |a 9780387356518 (En ligne) | ||
| 041 | 0 | |a eng | |
| 082 | |a 516.35 | ||
| 084 | |a 14-01. 2010 | ||
| 084 | |a 13-01. 2010 | ||
| 084 | |a 13Pxx. 2010 | ||
| 084 | |a 13P10. 2010 | ||
| 084 | |a 14Qxx. 2010 | ||
| 084 | |a I.1 | ||
| 100 | 1 | |a Cox, David A., |d 1948-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Ideals, varieties, and algorithms : |b an introduction to computational algebraic geometry and commutative algebra |c David Cox, John Little, Donal O Shea. |
| 250 | |a 3rd ed. 2007. | ||
| 260 | |a New York, NY : |b Springer New York : |b Imprint: Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Undergraduate Texts in Mathematics |x 2197-5604 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 535-539 de l'édition imprimée. Index | ||
| 505 | 0 | |a Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- Geometry, Algebra, and Algorithms -- Groebner Bases -- Elimination Theory -- The Algebra-Geometry Dictionary -- Polynomial and Rational Functions on a Variety -- Robotics and Automatic Geometric Theorem Proving -- Invariant Theory of Finite Groups -- Projective Algebraic Geometry -- The Dimension of a Variety -- Appendix A. Some Concepts from Algebra -- Appendix B. Pseudocode -- Appendix C. Computer Algebra Systems -- Appendix D. Independent Projects -- References -- Index | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: A significantly updated section on Maple in Appendix C Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3 From the 2nd Edition: "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 | |a Complexité de calcul (informatique) | ||
| 650 | |a Algèbres commutatives |x Informatique | ||
| 650 | |a Variétés algébriques | ||
| 650 | |a Idéaux (algèbre) | ||
| 650 | |a Géométrie algébrique |x Informatique | ||
| 700 | 1 | |a Little, John B., |d 1956- |4 aut | |
| 700 | 1 | |a O'Shea, Donal, |d 1952- |4 aut | |
| 776 | 0 | |0 11397986X |t Ideals, varieties, and algorithms |o an introduction to computational algebraic geometry and commutative algebra |f David Cox, John Little, Donal O'Shea |e 3rd edition |d 2007 |c New-York |n Springer |p 1 vol. (XV-551 p.) |s Undergraduate texts in mathematics |z 978-0-387-35650-1 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-0-387-35651-8 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-ZV5678TJ-4 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747889554 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-0-387-35651-8 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750902655 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-0-387-35651-8 |z Accès INSA CVL | |
| 997 | |0 938795 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||