ENGLISH

Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6

By Bernd Sturmfels , Mutsumi Saito , Nobuki Takayama

Book information

Publisher
Springer
Year
2000
ISBN
9783540660651, 3540660658
Language
english
Format
DJVU
Filesize
2 MB (1778258 bytes)
Edition
1
Pages
260\260
Time added
2010-10-13 10:14:08

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 Grbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grbner 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 Grbner 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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