Using algebraic geometry. 2nd ed. (English) Zbl 1079.13017
Graduate Texts in Mathematics 185. New York, NY: Springer (ISBN 0-387-20706-6/hbk; 0-387-20733-3/pbk). xii, 575 p. (2005).
This is the second edition of the book under review. The first one appeared 1998; see the review in Zbl 0920.13026.
The book has been very successful. It succeeded in establishing a bridge between modern computer science and classical algebraic geometry.
This second edition contains several improvements and some new topics which have been developed recently. Chapter 1 contains a unified discussion of how matrices can be used to define monomial orderings. The presentation of the Mora normal form algorithm in chapter 4 is rewritten. Chapter 8 contains two new sections about the Gröbner fan and the Gröbner walk. The last section of chapter 9 is extended to a new chapter 10 including the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. Finally the Maple code has been updated and Macaulay 2 is used instead of Macaulay.
The book has been very successful. It succeeded in establishing a bridge between modern computer science and classical algebraic geometry.
This second edition contains several improvements and some new topics which have been developed recently. Chapter 1 contains a unified discussion of how matrices can be used to define monomial orderings. The presentation of the Mora normal form algorithm in chapter 4 is rewritten. Chapter 8 contains two new sections about the Gröbner fan and the Gröbner walk. The last section of chapter 9 is extended to a new chapter 10 including the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. Finally the Maple code has been updated and Macaulay 2 is used instead of Macaulay.
Reviewer: Gerhard Pfister (Kaiserslautern)
MSC:
| 13Pxx | Computational aspects and applications of commutative rings |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 14-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry |
| 13-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra |
| 14Q20 | Effectivity, complexity and computational aspects of algebraic geometry |
| 13-02 | Research exposition (monographs, survey articles) pertaining to commutative algebra |
