Grobner Bases and Convex Polytopes
Seiten
1995
American Mathematical Society (Verlag)
978-0-8218-0487-2 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0487-2 (ISBN)
Deals with the interplay of computational commutative algebra and the theory of convex polytopes. This title 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.
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.
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.
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.
| Erscheint lt. Verlag | 1.1.1996 |
|---|---|
| Reihe/Serie | University Lecture Series |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 311 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| ISBN-10 | 0-8218-0487-1 / 0821804871 |
| ISBN-13 | 978-0-8218-0487-2 / 9780821804872 |
| Zustand | Neuware |
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