Computational Algebraic Geometry and Commutative Algebra : Cortona 1991
著者
書誌事項
Computational Algebraic Geometry and Commutative Algebra : Cortona 1991
（Symposia mathematica, v. 34）
Cambridge University Press, 1993
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注記
"The Cortona Conference on Computional Algebraic Geometry and Commutative Algebra, sponserd by INDAM (Istituto Nazionale di Alta Matematica) and supported by C.N.R. (Consiglio Mazionale delle Ricerche) took place June 17 to June 21, 1991"--Pref
Includes bibliographical references
内容説明・目次
内容説明
Computational methods are an established tool in algebraic geometry and commutative algebra, the key element being the theory of Groebner 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 Groebner 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 Groebner bases, as well as mathematicians interested in algebraic geometry, commutative algebra, or the classification of algebras.
目次
- Part I. Open problems and exposition of Groebner 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. Groebner 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.
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