Gröbner bases and convex polytopes
Author(s)
Bibliographic Information
Gröbner bases and convex polytopes
（University lecture series, 8）
American Mathematical Society, c1996
Available at / 73 libraries
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Etchujima library, Tokyo University of Marine Science and Technology工流通情報システム
411.8/St9201152025
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Note
Bibliography: p. 155-159
Includes index
Description and Table of Contents
Description
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. 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.
Table of Contents
Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The second hypersimplex $\mathcal A$-graded algebras Canonical subalgebra bases Generators, Betti numbers and localizations Toric varieties in algebraic geometry Some specific Grobner bases Bibliography Index.
by "Nielsen BookData"
