Grbner Deformations of Hypergeometric Differential Equations

Authors:
Mutsumi Saito;Bernd Sturmfels;Nobuki Takayama
Affiliations:
-;-;-
Venue:
Grbner Deformations of Hypergeometric Differential Equations
Year:
2011

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Abstract

The theory of Grbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Grbner 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.