ENGLISH

Groebner Deformations of Hypergeometric Differential Equations

By Bernd Sturmfels , Mutsumi Saito , Nobuki Takayama

Book information

Publisher
Springer
Year
2000
ISBN
3540660658, 9783540660651
Open Library ID
OL16963800M
Language
english
Format
DJVU
Filesize
2 MB (2611964 bytes)
Edition
1
Pages
260\260
Library
Kolxo3
DPI
600
Time added
2009-07-20 03:45:11

Description

In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Groebner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Groebner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The Groebner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and raises many open problems for future research in this area.

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