Solving Polynomial Equation Systems II
Macaulay's Paradigm and Groebner Technology
Published on 24. October 2014
978-1-107-26655-1 (ISBN)
Description
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.
Reviews / Votes
'The author treats all relevant steps and results in great detail also including advanced and most recent developments respectively, both of the theoretical and the algorithmic side ... an abundance of worked out examples shows the effectivity of the various algorithms.' Monatshefte fuer MathematikMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
File size
4,42 MB
ISBN-13
978-1-107-26655-1 (9781107266551)
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Schweitzer Classification
Other editions
Additional editions
Book
05/2005
Cambridge University Press
€293.40
Shipment within 15-20 days
Person
Content
Preface; Part III. Gauss, Euclid, Buchberger - Elementary Groebner Bases: 20. Hilbert; 21. Gauss; 22. Buchberger; 23. Macaulay I; 24. Groebner I; 25. Gebauer and Traverso; 26. Spear; Part IV. Duality: 27. Noether; 28. Moeller I; 29. Lazard; 30. Macaulay II; 31. Groebner II; 32. Groebner III; 33. Moeller II; Part IV. Beyond Dimension Zero: 34. Groebner IV; 35. Gianni Trager Zacharias; 36. Macaulay III; 37. Galligo; 38. Giusti; Bibliography; Index.
