Computational Methods in Commutative Algebra and Algebraic Geometry

Vasconcelos, Wolmer, V.

ISBN 10: 3540605207 / ISBN 13: 9783540605201

Editore: Springer, Berlin, 1998

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Blind stamp and pencil front endpapers.; 8vo; 394 pages.

Codice articolo 28222

Dati bibliografici

• Titolo: Computational Methods in Commutative Algebra and Algebraic Geometry
• Editore: Springer, Berlin
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 3540605207
• ISBN 13: 9783540605201
• Rilegatura: Hardcover
• Condizione: Very Good
• Condizione della sovraccoperta: No Dust Jacket

Descrizione articolo

Riassunto

This ACM volume in computational algebra deals with methods and techniques to tackle 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. It relates discoveries by a growing, interdisciplinary, group of researchers in the past decade. It highlights the use of advanced techniques to bring down the cost of computation. The book includes concrete algorithms written in MACAULAY. It is intended for advanced students and researchers with interests both in algebra and computation. Many parts of it can be read by anyone with a basic abstract algebra course.

Dalla quarta di copertina

This book gives an account of recent developments on the interplay between theoretical aspects of commutative algebra and algebraic geometry and computational issues in algebra. A great deal of emphasis is given to the fact that the non-elementary complexity of the underlying fundamental algorithms and data structures (e.g. factorization, Gröbner bases, matrices with polynomial entries) require that the cost of computation be borne largely by theoretical means. The material is focused on the explicit construction of basic objects of algebrogeometric interest - primary decomposition, integral closure, computation of ideal transforms and cohomology, among others. It looks also at various numerical signatures of rings and modules such as those obtained from their Hilbert functions. Another feature is an analysis of nonlinear systems of polynomial equations with the view as to how best deliver the equations to numerical solvers. There are numerous pointers to the current literature, which together with the exercises and a selected set of challenge questions round the text.

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)