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Grobner Deformations of Hypergeometric Differential Equations
Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki
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Description for Grobner Deformations of Hypergeometric Differential Equations
Paperback. Series: Algorithms and Computation in Mathematics. Num Pages: 262 pages, 5 black & white illustrations, biography. BIC Classification: PBKJ; PBMW; UYA. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 14. Weight in Grams: 409.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2011
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Germany
Number of pages
262
Condition
New
Series
Algorithms and Computation in Mathematics
Number of Pages
254
Place of Publication
Berlin, Germany
ISBN
9783642085345
SKU
V9783642085345
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
Reviews for Grobner Deformations of Hypergeometric Differential Equations
".. The book is very well written and, despite the deep results it contains, it is easy to read. Each chapter provides good and nice examples illustrating all main notions. In the reviewer's opinion this book can be addressed not only to researchers but also to beginners in D-module theory and expecially in algorithmic D-module theory." Francisco Jesus ... Read more