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＜電子ブック＞
Gröbner Deformations of Hypergeometric Differential Equations / by Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama
(Algorithms and Computation in Mathematics ; 6)

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	VIII, 254 p. 5 illus : online resource
著者標目	*Saito, Mutsumi author Sturmfels, Bernd author Takayama, Nobuki author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Algorithms LCSH:Algebraic geometry LCSH:Mathematical physics LCSH:Discrete mathematics FREE:Analysis FREE:Computational Mathematics and Numerical Analysis FREE:Algorithms FREE:Algebraic Geometry FREE:Theoretical, Mathematical and Computational Physics FREE:Discrete Mathematics
一般注記	1. Basic Notions -- 2. Solving Regular Holonomic Systems -- 3. Hypergeometric Series -- 4. Rank versus Volume -- 5. Integration of D-modules -- References 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 in this book are particularly useful for studying the systems of multidimensional hypergeometric partial differentiel equations introduced by Gel'fand, Kapranov and Zelevinsky. The Gröbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and thus 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 it raises many open problems for future research in this rapidly growing area of computational mathematics ' HTTP:URL=https://doi.org/10.1007/978-3-662-04112-3

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