Grobner Bases and Convex Polytopes. Bernd Sturmfels. This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties not necessarily normal. The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book.
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Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. This book is about the interplay of computational commutative algebra and the theory of convex polytopes.
It centers around a special class of ideals in a polynomial ring: the class of toric ideals. 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. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry. Graduate students and mathematicians interested in computer science and theoretical operations research.
It is an essential introduction for those who wish to perform research in this fast-developing, interdisciplinary field. It underlines the powerful techniques of commutative algebra in the interplay with combinatorics and polyhedral geometry. The exposition is clear and very well motivated. There is an abundance of illustrative examples; often, the same example is carried through a number of chapters to give coherence to the discussion … The reader will be amply rewarded, as this is an elegantly written work of wide scholarship.
This monograph represents a well written introduction to a rapidly developing field of algebra. The exercises and bibliographical remarks included will make it easy for the reader keen on understanding the interplay between commutative algebra and the subjects quoted above to gain deeper insight. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase.
AMS Homepage. Join our email list. Sign up. Ordering on the AMS Bookstore is limited to individuals for personal use only. Advanced search. Author s Product display : Bernd Sturmfels. Abstract: This book is about the interplay of computational commutative algebra and the theory of convex polytopes. Volume: 8. Publication Month and Year: Copyright Year: Page Count: Cover Type: Softcover.
Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: 13 ; Secondary MSC: 52 ; Applied Math? MAA Book? Electronic Media? Apparel or Gift: false. Online Price 1 Label: List. Online Price 1: Print Price 1 Label: List. Print Price 1: Online Price 2: Print Price 2: Online Price 3: Print Price 3: Dual Price 1 Label: List. Dual Price 1: Dual Price 2: Print Available to Order: true. Readership: Graduate students and mathematicians interested in computer science and theoretical operations research.
Convex Polytopes and Gröbner Bases
Among them, one of the most important topics is the correspondence to triangulations of convex polytopes. The purpose of this chapter is to explain these topics in detail. First, we will explain convex polytopes, weight vectors, and monomial orders, all of which play a basic role in the rest of this chapter. Third, we will discuss the correspondence between the initial ideals of toric ideals and triangulations of convex polytopes, and the related ring-theoretic properties. Finally, we will consider the examples of configuration matrices that arise from finite graphs or contingency tables, and we will use them to verify the theory stated above. If you would like to pursue this topic beyond what is included in this chapter, we suggest the books [ 2 , 7 ]. Skip to main content.
Gröbner Bases and Convex Polytopes
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