Grobner Bases and Convex Polytopes (University Lecture Series, No. 8)
| Author | : | |
| Rating | : | 4.91 (533 Votes) |
| Asin | : | 0821804871 |
| Format Type | : | paperback |
| Number of Pages | : | 162 Pages |
| Publish Date | : | 2015-03-24 |
| Language | : | English |
DESCRIPTION:
"This book is a state-of-the-art account of the rich interplay between combinatorics and geometry of convex polytopes and computational commutative algebra via the tool of Gröbner bases. For the math programmer, this book could be viewed as an exposition of the interactions between integer programming and Gröbner bases." ---- Optima"Material is presented in a concise way lots of motivating examples not only of interest for mathematicians studying Gröbner bases, but also for researchers work
A dense, but excellent, text Davis C. Doherty I cannot recommend this text highly enough to anyone who is working with Grobner bases, especially in computational commutative algebra. Toric ideals, the state polytope, several algorithms for computing Grobner bases -- Sturmfels brings all this together, as well as showing how it can all be applied to problems such as that of integer programming.Thanks to his excellent taste in the theorems he presents, Sturmfels has managed to put all this together in a relatively small, well-written package. However, his brevity h
This book is about the interplay of computational commutative algebra and the theory of convex polytopes. The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). These applications lie in the domains of integer programming and computational statistics. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. The mathematical