Algebraic solving
著者
書誌事項
Algebraic solving
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 157 . Solving polynomial equation systems ; v. 3）
Cambridge University Press, 2015
- : hardback
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注記
Includes bibliographical references (p. [267]-272) and index
内容説明・目次
内容説明
This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Groebner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni-Kalkbrener Theorem, Stetter Algorithm, Cardinal-Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bezout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
目次
- Preface
- Setting
- Part VI. Algebraic Solving: 39. Trinks
- 40. Stetter
- 41. Macaulay IV
- 42. Lazard II
- 43. Lagrange II
- 44. Kronecker IV
- 45. Duval II
- Bibliography
- Index.
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