TY  - BOOK
AU  - Saito, Mutsumi
AU  - Sturmfels, Bernd
AU  - Takayama, Nobuki
TI  - Gröbner deformations of hypergeometric differential equations
T2  - Algorithms and computation in mathematics,
SN  - 9783540660651
U1  - 517.9 
PY  - 2000///
CY  - New York
PB  - Springer
KW  - Gröbner bases
KW  - Differential equations
KW  - Asymptotic theory
KW  - Hypergeometric functions
N1  - Includes bibliographical references (p. [245]-249) and index
N2  - 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
UR  - https://link.springer.com/content/pdf/bfm:978-3-662-04112-3/1
UR  - https://www.goodreads.com/book/show/5450552-groebner-deformations-of-hypergeometric-differential-equations-algorith#CommunityReviews
ER  -