Algebraic solving
Author(s)
Bibliographic Information
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
Available at / 37 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackS||EMA||157200033968031
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hardback/M 792080385656
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Note
Includes bibliographical references (p. [267]-272) and index
Description and Table of Contents
Description
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.
Table of Contents
- 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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