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Computational Algebraic Geometry and Commutative Algebra

David Eisenbud, Lorenzo Robbiano (Herausgeber)

Buch | Hardcover

308 Seiten

1993
Cambridge University Press (Verlag)
978-0-521-44218-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	14.10.1993
Reihe/Serie	Symposia Mathematica
Verlagsort	Cambridge
Sprache	englisch
Maße	157 x 235 mm
Gewicht	545 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-521-44218-4 / 0521442184
ISBN-13	978-0-521-44218-3 / 9780521442183
Zustand	Neuware