Algorithms and Computation in Mathematics

1 primary work

Groebner Deformations of Hypergeometric Differential Equations

by Mutsumi Saito, Bernd Sturmfels, and Nobuki Takayama

Published 12 November 1999

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