Gr Bner Deformations of Hypergeometric Differential Equations

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Saito M.; Sturmfels B.; Takayama N.
ISBN13:9783540660651
ISBN10:3540660658
Publisher:Springer
Language:English
Author:Mutsumi Saito and Bernd Sturmfels and Nobuki Takayama
Binding:Hardback
Pages:254
SUPC: SDL140824187

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Country of Origin or Manufacture or Assembly	India
Common or Generic Name of the commodity	Geometry Books
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In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Grobner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grobner 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 Grobner 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 '"

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Product Type: Mathematics Books Geometry Books
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Binding: Hardback
Language: English

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