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Catalogue Information
Field name	Details
Dewey Class	515
Title	Gröbner Deformations of Hypergeometric Differential Equations ([EBook] /) / by Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama.
Author	Saito, Mutsumi
Added Personal Name	Sturmfels, Bernd author.
Added Personal Name	Takayama, Nobuki author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2000.
Physical Details	VIII, 254 p. 5 illus. : online resource.
Series	Algorithms and computation in mathematics 1431-1550 ; ; 6
ISBN	9783662041123
Summary Note	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 '.:
Contents note	1. Basic Notions -- 2. Solving Regular Holonomic Systems -- 3. Hypergeometric Series -- 4. Rank versus Volume -- 5. Integration of D-modules -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-04112-3
Links to Related Works	Subject References: Algebraic Geometry . Algorithms . Analysis . Analysis (Mathematics) . Combinatorics . Computational Mathematics and Numerical Analysis . Computer mathematics . Mathematical analysis . Mathematics . Physics . Theoretical, Mathematical and Computational Physics . Authors: Saito, Mutsumi . Sturmfels, Bernd . Takayama, Nobuki . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and computation in mathematics . Classification: 515 .

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Gröbner Deformations of Hypergeometric Differential Equations

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