Computational Methods in Commutative Algebra and Algebraic Geometry - Algorithms and Computation in Mathematics 2 (Paperback)
  • Computational Methods in Commutative Algebra and Algebraic Geometry - Algorithms and Computation in Mathematics 2 (Paperback)
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Computational Methods in Commutative Algebra and Algebraic Geometry - Algorithms and Computation in Mathematics 2 (Paperback)

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£54.99
Paperback 408 Pages / Published: 18/05/2004
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This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783540213116
Number of pages: 408
Weight: 1320 g
Dimensions: 235 x 155 x 22 mm
Edition: Softcover reprint of the original 1st ed. 199


MEDIA REVIEWS

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)

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