Grobner Deformations of Hypergeometric Differential Equations - Couverture rigide

Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki

Couverture rigide

ISBN 10 : 3540660658 ISBN 13 : 9783540660651

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1999

Synopsis

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 here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The Gröbner 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.

A propos du livre

Présentation de l'éditeur

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 re-examined 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 focus on the systems of multidimensional hypergeometric partial differential 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 frictions, and it raises many open problems for future research in this rapidly growing area of computational mathematics.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 3540660658
• ISBN 13: 9783540660651
• Reliure: Relié
• Nombre de pages: 262
• Coordonnées du fabricant: non disponible
• Personne responsable: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Allemagne