Solving Polynomial Equation Systems II: Macaulay's Paradigm and Gröbner Technology

ISBN-13: 9780521811569 / Angielski / Twarda / 2005 / 784 str.

Teo Mora; G. -C Rota; B. Doran

Opis

A complete survey of Grobner bases and their applications, this book will be essential for all workers in commutative algebra, computational algebra and algebraic geometry. The second volume of the treatise focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation is based on the intrinsic linear algebra structure of Grobner bases, making this a state-of-the-art reference on issues of implementation.

Recenzje

'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 für Mathematik

Spis treści

Preface; 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; Bibliography; Index.