Computational Algebraic Geometry and Commutative Algebra

Out of Print

Part of Symposia Mathematica

Editors:
David Eisenbud
Lorenzo Robbiano

Dave Bayer, David Mumford, David Eisenbud, Th. Dana-Picard, M. Schaps, D. Lazard, Teo Mora, Lorenzo Robbiano, Wolmer V. Vasconcelos, Andre Galligo, Mike Stillman, Marc Giusti, Joos Heintz, Sheldon Katz, Bernd Sturmfels

View all contributors

Date Published: October 1993
availability: Unavailable - out of print July 1997
format: Hardback
isbn: 9780521442183

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Description

Computational methods are an established tool in algebraic geometry and commutative algebra, the key element being the theory of Gröbner bases. This book represents the state of the art in computational algebraic geometry and encapsulates many of the most interesting trends and developments in the field. There are two articles on open problems, orienting the reader to the subject's direction, four surveys describing the most interesting work, and four original research papers. There is also an introduction to the theory of Gröbner bases and their use in computation. Though the perspective of the book is mathematical, it does relate the abstract and the experimental tendencies in the field. Consequently, it will appeal to computer scientists interested in symbolic computation, robotics or Gröbner bases, as well as mathematicians interested in algebraic geometry, commutative algebra, or the classification of algebras.

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Product details
- Date Published: October 1993
- format: Hardback
- isbn: 9780521442183
- length: 308 pages
- dimensions: 235 x 157 x 23 mm
- weight: 0.545kg
- availability: Unavailable - out of print July 1997
Table of Contents
Part I. Open problems and exposition of Gröbner bases:
1. What can be computed in algebraic geometry? Dave Bayer and David Mumford
2. Open problems in computational algebraic geometry David Eisenbud
Part II. Surveys:
3. A computer assisted project: classification of algebras Th. Dana-Picard and M. Schaps
4. Systems of algebraic equations (algorithms and complexity) D. Lazard
5. Points in affine and projective spaces Teo Mora and Lorenzo Robbiano
6. Constructions in commutative algebra Wolmer V. Vasconcelos
Part III. Research papers:
7. Gröbner bases and extensions of scalars Dave Bayer, Andre Galligo and Mike Stillman
8. La determination des point insoles et de la dimension d'une variete algebrique pent se faire en temps polynomial Marc Giusti and Joos Heintz
9. Arithmetically Cohen-Macaulay curves cut out by quadrics Sheldon Katz
10. Sparse elimination theory Bernd Sturmfels.
Editors
David Eisenbud
Lorenzo Robbiano
Contributors
Dave Bayer, David Mumford, David Eisenbud, Th. Dana-Picard, M. Schaps, D. Lazard, Teo Mora, Lorenzo Robbiano, Wolmer V. Vasconcelos, Andre Galligo, Mike Stillman, Marc Giusti, Joos Heintz, Sheldon Katz, Bernd Sturmfels