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【内容】
本书探讨计算交换代数与凸多胞体理论间的相互作用，内容围绕多项式环的一种特殊理想类(环理想类)展开。环理想类可由单项式差生成的素理想或(不必正规的)环簇的定义理想来描述。书中的特定应用反映出Grobner基的研究的跨学科性质，这些应用属于整数规划和计算统计学的范畴。书中的数学工具涉及交换代数、组合学和多面体几何。
【目录】
Introduction
Chapter 1. Grhbner Basics
Chapter 2. The State Polytope
Chapter 3. Variation of Term Orders
Chapter 4. Toric Ideals
Chapter 5. Enumeration, Sampling and Integer Programming
Chapter 6. Primitive Partition Identities
Chapter 7. Universal Grhbner Bases
Chapter 8. Regular Triangulations
Chapter 9. The Second Hypersimplex
Chapter 10. A-graded Algebras
Chapter 11. Canonical Subalgebra Bases
Chapter 12. Generators, Betti Numbers and Localizations
Chapter 13. Toric Varieties in Algebraic Geometry
Chapter 14. Some Specific Grhbner Bases
Bibliography
Index
Chapter 1. Grhbner Basics
Chapter 2. The State Polytope
Chapter 3. Variation of Term Orders
Chapter 4. Toric Ideals
Chapter 5. Enumeration, Sampling and Integer Programming
Chapter 6. Primitive Partition Identities
Chapter 7. Universal Grhbner Bases
Chapter 8. Regular Triangulations
Chapter 9. The Second Hypersimplex
Chapter 10. A-graded Algebras
Chapter 11. Canonical Subalgebra Bases
Chapter 12. Generators, Betti Numbers and Localizations
Chapter 13. Toric Varieties in Algebraic Geometry
Chapter 14. Some Specific Grhbner Bases
Bibliography
Index
