This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner 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 Bézout 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.Read more
- Continues the author's survey of the state of the art for solving univariate polynomials
- Covers classical results as well as modern methods
- Third volume of four in the author's comprehensive treatise
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- Date Published: August 2015
- format: Hardback
- isbn: 9780521811552
- length: 294 pages
- dimensions: 240 x 155 x 25 mm
- weight: 0.62kg
- contains: 7 b/w illus.
- availability: Available
Table of Contents
Part VI. Algebraic Solving:
41. Macaulay IV
42. Lazard II
43. Lagrange II
44. Kronecker IV
45. Duval II
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