000			02115nam a22002897a 4500
003			OSt
005			20250228111455.0
008			250224b |||||||| |||| 00| 0 hin d
020			_a9783540660651
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a517.9 _bSAI-G
100			_aSaito, Mutsumi
245			_aGröbner deformations of hypergeometric differential equations
260			_aNew York : _bSpringer, _c2000.
300			_aviii, 254 p. : _bill. ; _c24 cm
490			_aAlgorithms and computation in mathematics, _vv. 6 _x1431-1550 ;
504			_aIncludes bibliographical references (p. [245]-249) and index
520			_aIn 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.
650			_aGröbner bases
650			_aDifferential equations _xAsymptotic theory
650			_aHypergeometric functions
700			_aSturmfels, Bernd
700			_aTakayama, Nobuki
856			_3Table of content _uhttps://link.springer.com/content/pdf/bfm:978-3-662-04112-3/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/5450552-groebner-deformations-of-hypergeometric-differential-equations-algorith#CommunityReviews
942			_2udc _cBK
999			_c35762 _d35762