A Singular Introduction to Commutative Algebra - Couverture souple

Greuel, Gert-Martin

Couverture souple

ISBN 10 : 3540428976 ISBN 13 : 9783540428978

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2002

Synopsis

This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, it is shown how to handle it by computer. The computations are exemplified with the computer algebra system Singular developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD with a version of Singular for various platforms (Unix/Linux, Windows, Macintosh), including all examples and procedures explained in the book. The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.

A propos du livre

Présentation de l'éditeur

From the reviews of the first edition: "It is certainly no exaggeration to say that … A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra … . Among the great strengths and most distinctive features … is a new, completely unified treatment of the global and local theories. … making it one of the most flexible and most efficient systems of its type....another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic....Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike." J.B. Little, MAA, March 2004 The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative rings, a chapter on characteristic and triangular sets with applications to primary decomposition and polynomial solving and an appendix on polynomial factorization including factorization over algebraic field extensions and absolute factorization, in the uni- and multivariate case.

Revue de presse

"The book under review is the second, extended edition of the first ... published in 2002. ... A new CD is included containing all the examples of the book and most of the SINGULAR-libraries. ... It provides the theory in a clear way as well as all the requirements for practical experiments conceived for SINGULAR ... . It is highly recommended for all students and researchers who are interested in practical computations of their algebraic interests as well as for introductory research projects for students." --Peter Schenzel, Zentralblatt MATH, Vol. 1133 (11), 2008

"It is certainly no exaggeration to say that ... A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra ... . Among the great strengths and most distinctive features ... is a new, completely unified treatment of the global and local theories. ... Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike." --John B. Little, MAA, March 2004

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 2002
• Langue: anglais
• ISBN 10: 3540428976
• ISBN 13: 9783540428978
• Reliure: Broché
• Nombre de pages: 606
• Coordonnées du fabricant: non disponible