Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving
Seiten
2015
Cambridge University Press (Verlag)
978-0-521-81155-2 (ISBN)
Cambridge University Press (Verlag)
978-0-521-81155-2 (ISBN)
This third volume of four describes all the most important techniques, mainly based on Gröbner bases. It covers the 'standard' solutions (Gianni–Kalkbrener, Auzinger–Stetter, Cardinal–Mourrain) as well as the more innovative (Lazard–Rouillier, Giusti–Heintz–Pardo). The author also explores the historical background, from Bézout to Macaulay.
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.
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.
Teo Mora is a Professor of Algebra in the Department of Mathematics at the University of Genoa.
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.
| Erscheint lt. Verlag | 7.8.2015 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Zusatzinfo | Worked examples or Exercises; 7 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 240 mm |
| Gewicht | 620 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-521-81155-4 / 0521811554 |
| ISBN-13 | 978-0-521-81155-2 / 9780521811552 |
| Zustand | Neuware |
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