Contents Introduction i x Chapter 1 . Grobner Basic s 1 Chapter 2 . The Stat e Pol y tope 9 Chapter 3 . Variation o f Term Order s 1 9 Chapter 4 . Toric Ideal s 3 1 Chapter 5 . Enumeration, Samplin g an d Intege r Programmin g 3 9 Chapter 6 . Primitiv e Partitio n Identitie s 4 7 Chapter 7 . Universal Grobne r Base s 5 5 Chapter 8 . Regular Triangulation s 6 3 Chapter 9 . The Secon d Hypersimple x 7 5 Chapter 10 . ^4-graded Algebra s 8 5 Chapter 11 . Canonical Subalgebr a Base s 9 9 Chapter 12 . Generators, Bett i Number s an d Localization s 11 3 Chapter 13 . Toric Varietie s i n Algebrai c Geometr y 12 7 Chapter 14 . Some Specifi c Grobne r Base s 14 1 Bibliography 15 5 Index 16 1
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