rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Gröbner Deformations of Hypergeometric Differential Equations
  name:
    name part: Saito, Mutsumi.
    role:
      role term: creator
  name:
    name part: Sturmfels, Bernd.
  name:
    name part: Takayama, Nobuki.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 2000
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (viii, 254 pages)
  abstract: 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 '
  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.
  note: by Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Algorithms
  subject:
    topic: Combinatorial analysis
  subject:
    topic: Algorithms
  subject:
    topic: Combinatorial analysis
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Mathematics
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Algorithms and computation in mathematics ; 6
  identifier: 9783662041123 (electronic bk.)
  identifier: 366204112X (electronic bk.)
  identifier: 9783642085345
  identifier: 3642085342
  identifier: 366204112X
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130217
    record change date: 20260422164758.8
    record identifier: in00003557650
    language of cataloging:
      language term: eng