Groebner Deformations of Hypergeometric Differential Equations (Hardcover, 2000 ed.)

In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gröbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gröbner 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 Gröbner 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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Algorithms and Computation in Mathematics, 6
Release date:	November 1999
First published:	2000
Authors:	Mutsumi Saito • Bernd Sturmfels • Nobuki Takayama
Dimensions:	235 x 155 x 15mm (L x W x T)
Format:	Hardcover
Pages:	254
Edition:	2000 ed.
ISBN-13:	978-3-540-66065-1
Categories:	Books > Computing & IT > General theory of computing > Mathematical theory of computation Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN:	3-540-66065-8
Barcode:	9783540660651

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