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Computational Methods in Commutative Algebra and Algebraic Geometry : Algorithms and Computation in Mathematics - Wolmer Vasconcelos

Computational Methods in Commutative Algebra and Algebraic Geometry

Algorithms and Computation in Mathematics

By: Wolmer Vasconcelos, David Eisenbud (Contribution by), Daniel R. Grayson (Contribution by), J. Herzog (Contribution by), M. Stillman (Contribution by)

Paperback

Published: 18th May 2004
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From the reviews:

..". Many parts of the book can be read by anyone with a basic abstract algebra course... it was one of the author's intentions to equip students who are interested in computational problems with the necessary algebraic background in pure mathematics and to encourage them to do further research in commutative algebra and algebraic geometry. But researchers will also benefit from this exposition. They will find an up-to-date description of the related research ... The reviewer recommends the book to anybody who is interested in commutative algebra and algebraic geometry and its computational aspects."

Math. Reviews 2002

..". a sophisticated notebook, with plenty of suggestions, examples and cross references ... It is a welcome new and deep exploration into commutative algebra and its relations with algebraic geometry. It is full of results, from simple tricks to more elaborate constructions, all having in common a computational and constructive nature..."

Jahresberichte der DMV 1999

From the reviews of the hardcover edition:

"... Many parts of the book can be read by anyone with a basic abstract algebra course. It seems to the reviewer that it was one of the author's intentions to equip students who are interested in computational problems with the necessary algebraic background in pure mathematics and to encourage them to do further research in commutative algebra and algebraic geometry. But researchers will also benefit from this exposition. They will find an up-to-date description of the related research. ... The reviewer recommends the book to anybody who is interested in commutative algebra and algebraic geometry and its computational aspects." (P.Schenzel, Mathematical Reviews 2002)

"... I would describe this book as a sophisticated notebook, with plenty of suggestions, examples and cross references, reporting on the work of Vasconcelos himself and of many others. ... It is a welcome new and deep exploration into commutative algebra and its relations with algebraic geometry. It is full of results, from simple tricks to more elaborate constructions, all having in common a computational and constructive nature. It will be a gold mine especially for those commutative algebraists who share with Vasconcelos the tast for a homological point of view. ..." (E.Sernesi, Jahresberichte der DMV 1999, Vol. 101, Issue 4)

"... Das Buch ist ... kein Lehrbuch im herkoemmlichen Verstandnis, obwohl fur Graduiertenseminare bei entsprechenden Vorkenntnissen durchaus geeignet (und vom Autor auf verschiedenen Sommerschulen auch bereits eingesetzt). Es beginnt im wesentlichen dort, wo in den oben genannten grundlegenderen Monographien insbesondere konstruktive Aspekte nicht weiter vertieft werden und ist damit ein Mosaikstein im wirklichen Sinne.

Es ist zugleich keine Monographie im herkoemmlichen Verstandnis, die sich an einem engen Thema erschoepfend abarbeitet, sondern mehr eine Fundgrube von Ideen und Ansatzen, in denen die verschiedensten Techniken der kommutativen Algebra bis hin zu tiefliegenden homologischen Methoden zusammenspielen. Sie sind, wie vom Autor gewohnt, oft unterschiedlich detailliert ausgearbeitet, beleuchten aber an vielen Stellen Querverbindungen, die man in dieser Konstellation in anderen Arbeiten selten findet.

Fur ein detailliertes Studium insbesondere von Fragestellungen, die in den spateren Kapiteln aufgegriffen werden, wird der Leser deshalb kaum um die Konsultation der entsprechenden Zeitschriftenaufsatze herumkommen, sofern er sie nicht sowieso schon kennt. Als guter Leitfaden fur ein solches Unterfangen ist das vorliegnede Buch allerdings bestens geeignet und deshalb jedem, der sich ernsthaft mit konstruktiven Methoden in der kommutativen Algebra beschaftigen moechte, zu empfehlen. ..." (H.-G. Grabe, Computeralgebra Rundbrief GI-DMV-GAMM, Nr. 22, Marz 1998)

Fundamental Algorithms
Toolkit
Principles of Primary Decomposition
Computing in Artin Algebras
NullstellensStze
Integral Closure
Ideal Transforms and Rings of Invariants
Computation of Cohomology
Degrees of Complexity of a Graded Module
A Primer on Commutative Algebra
Hilbert Functions
Using Macaulay 2
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540213116
ISBN-10: 3540213112
Series: Algorithms and Computation in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 408
Published: 18th May 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 2.49
Weight (kg): 1.32
Edition Number: 3