多項式の方程式の解法 第３巻 Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving (Encyclopedia of Mathematics and its Applications)

Mora, Teo

Cambridge University Press（2015/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 294 p.
• 言語 ENG
• 商品コード 9780521811552
• DDC分類 512.9422

Full Description

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.

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.