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.
General
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