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Other titles in the Algorithms and Computation in Mathematics series:
Algorithms and Computation in Mathematics, #2: Computational Methods in Commutative Algebra and Algebraic Geometryby Wolmer Vasconcelos
Synopses & Reviews
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
This 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. The book relates discoveries by a growing, interdisciplinary group of researchers in the past decade. It is intended for advanced students and researchers with interests both in algebra and computation.
"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."
Table of Contents
- Principles of Primary Decomposition.
- Computing in Artin Algebras.
- Integral Closure.
- Ideal Transforms and Rings of Invariants.
- Computation of Cohomology (by David Eisenbud).
- Degrees of Complexity of a Graded Module.
- Appendix A. A Primer on Commutative Algebra.
- Appendix B. Hilbert Functions (by Jürgen Herzog).
- Appendix C. Using Macaulay 2 (by David Eisenbud, Daniel Grayson and Michael Stillman.
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