Gröbner Deformations of Hypergeometric Differential Equations / Algorithms and Computation in Mathematics Bd.6 (PDF)
(Sprache: Englisch)
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...
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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 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 '
Bibliographische Angaben
- Autoren: Mutsumi Saito , Bernd Sturmfels , Nobuki Takayama
- 2013, 2000, 254 Seiten, Englisch
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 366204112X
- ISBN-13: 9783662041123
- Erscheinungsdatum: 09.03.2013
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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- Größe: 23 MB
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Sprache:
Englisch
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