Solving Polynomial Equation Systems II

Macaulay's Paradigm and Gröbner Technology

Teo Mora - Collection Encyclopedia of Mathematics and its Applications

785 pages, parution le 19/05/2005

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Résumé

The second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation here is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in issues of implementation. The same language describes the applications of Groebner technology to the central problems of commutative algebra.

The book can be also used as a reference on elementary ideal theory and a source for the state-of-the-art in its algorithmization. Aiming to provide a complete survey on Groebner bases and their applications, the author also includes advanced aspects of Buchberger theory, such as the complexity of the algorithm, Galligo's theorem, the optimality of degrevlex, the Gianni-Kalkbrener theorem, the FGLM algorithm, and so on. Thus it will be essential for all workers in commutative algebra, computational algebra and algebraic geometry.

Elementary introduction to Groebner bases and Buchberger's Algorithm which also discusses the
state-of-the-art of the best implementations
Survey of last twenty years work on applying Groebner technology to commutative algebra
Unique in stressing modern framework for computational work and solution methods

Sommaire

Part III. Gauss, Euclid, Buchberger - Elementary Gröbner Bases: 20. Hilbert
- 21. Gauss
- 22. Buchberger
- 23. Macaulay I
- 24. Gröbner I
- 25. Gebauer and Traverso
- 26. Spear
Part IV. Duality: 27. Noether
- 28. Möller I
- 29. Lazard
- 30. Macaulay II
- 31. Gröbner II
- 32. Gröbner III
- 33. Möller II
Part IV. Beyond Dimension Zero: 34. Gröbner IV
- 35. Gianni Trager Zacharias
- 36. Macaulay III
- 37. Galligo
- 38. Giusti

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Teo Mora
Collection	Encyclopedia of Mathematics and its Applications
Parution	19/05/2005
Nb. de pages	785
Format	16 x 24
Couverture	Relié
Poids	1250g
Intérieur	Noir et Blanc
EAN13	9780521811569
ISBN13	978-0-521-81156-9