Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving

This third volume of four describes all the most important techniques, mainly based on Gröbner bases.

Teo Mora (Author)

9780521811552, Cambridge University Press

Hardback, published 7 August 2015

294 pages, 7 b/w illus.
24 x 15.5 x 2.5 cm, 0.62 kg

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.

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.

Subject Areas: Mathematical theory of computation [UYA], Algebraic geometry [PBMW], Algebra [PBF]