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Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6 (Algorithms and Computation in Mathematics, 6) Hardback - 1999
by Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki
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- Hardback
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Details
- Title Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6 (Algorithms and Computation in Mathematics, 6)
- Author Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki
- Binding Hardback
- Edition U. S. EDITION
- Condition New
- Pages 254
- Language ENG
- Publisher Springer, Berlin
- Publication date 1999-11-12
- Features Illustrated
- Bookseller's Inventory # Q-3540660658
- ISBN 9783540660651
- Quantity available 1
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From the publisher
First line
This book provides symbolic algorithms for constructing holomorphic solutions to systems of linear partial differential equations with polynomial coefficients.
From the rear cover
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 in this book are particularly useful for studying the systems of multidimensional hypergeometric partial differentiel equations introduced by Gel'fand, Kapranov and Zelevinsky. The Grbner 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 '
