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Original Essays | June 20, 2014

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    Lauren Owen 9780812993271

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25 Remote Warehouse Mathematics- Differential Equations

This title in other editions

Algorithms and Computation in Mathematics #6: Gr Bner Deformations of Hypergeometric Differential Equations

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Algorithms and Computation in Mathematics #6: Gr Bner Deformations of Hypergeometric Differential Equations Cover

 

Synopses & Reviews

Publisher Comments:

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 '

Synopsis:

The theory of Gröbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Gröbner bases from the point of view of geometric deformations. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric PDE's introduced by Gelfand, Kapranov, and Zelevinsky. A number of original research results are contained in the book, and many open problems are raised for future research in this rapidly growing area of computational mathematics.

Table of Contents

Chapter 1. Basic Notions.- Chapter 2. Gröbner Deformations of Regular Holonomic Systems.- Chapter 3. Hypergeometric Series.- Chapter 4. Rank versus volume.- Chapter 5. Integration of D-modules

Product Details

ISBN:
9783642085345
Author:
Saito, Mutsumi
Publisher:
Springer
Author:
Takayama, Nobuki
Author:
Sturmfels, Bernd
Location:
Berlin, Heidelberg
Subject:
Mathematical Analysis
Subject:
Grbner Basen
Subject:
Grbner bases
Subject:
Hypergeometrische Funktionen
Subject:
Weyl algebra
Subject:
combinatorial commutative algebra
Subject:
holonome Systeme
Subject:
holonomic systems
Subject:
Hypergeometric functions.
Subject:
kombinatorische kommutative Algebra
Subject:
Analysis
Subject:
Algorithms
Subject:
Algebraic Geometry
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Combinatorics
Subject:
Combinatorics Es handelt sich um das erste Buch zu diesem Thema. Es ist sowohl eine Forschungsmonographie als auch ein Buch, welches in einem Kurs zu symbolischem Rechnen, algebraischer Geometrie oder algebraischer Analysis Verwendung finden kann.
Subject:
Mathematics-Differential Equations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Subject:
Geometry - Algebraic
Copyright:
Edition Description:
1st Edition. Softcover version of original hardcover edition 2000
Series:
Algorithms and Computation in Mathematics
Series Volume:
6
Publication Date:
20110403
Binding:
TRADE PAPER
Language:
English
Pages:
262
Dimensions:
235 x 155 mm

Related Subjects

Science and Mathematics » Environmental Studies » Environment
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry

Algorithms and Computation in Mathematics #6: Gr Bner Deformations of Hypergeometric Differential Equations New Trade Paper
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$99.25 In Stock
Product details 262 pages Springer - English 9783642085345 Reviews:
"Synopsis" by , The theory of Gröbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Gröbner bases from the point of view of geometric deformations. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric PDE's introduced by Gelfand, Kapranov, and Zelevinsky. A number of original research results are contained in the book, and many open problems are raised for future research in this rapidly growing area of computational mathematics.
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