The theory of Grobner bases is a main tool for dealing with rings of
differential operators. This book reexamines the concept of Grobner bases from
the point of view of geometric deformations. The algorithmic methods introduced
in this book are particularly useful for studying the systems of
multidimensional hypergeometric PDE's introduced by Gelfand, Kapranov, and
Zelevinsky. A number of original research results are contained in the book, and
many open problems are raised for future research in this rapidly growing area
of computational mathematics.