In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gr�bner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gr�bner 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 ...
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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 Gr�bner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gr�bner 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 Gr�bner 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.
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Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2011
Language:
English
Alibris ID:
17383584701
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New. 254 p. Algorithms and Computation in Mathematics , 6. 5 Illustrations, black and white; VIII, 254 p. 5 illus. Intended for professional and scholarly audience.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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2011
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English
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17988261407
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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2011
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English
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New. Print on demand Contains: Illustrations, black & white. Algorithms and Computation in Mathematics . VIII, 254 p. 5 illus. Intended for professional and scholarly audience.
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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2011
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17988119656
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New. Contains: Illustrations, black & white. Algorithms and Computation in Mathematics . VIII, 254 p. 5 illus. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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2011
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English
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