Buch, Englisch, Band 6, 254 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 576 g
Buch, Englisch, Band 6, 254 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 576 g
Reihe: Algorithms and Computation in Mathematics
ISBN: 978-3-540-66065-1
Verlag: Springer
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.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
Weitere Infos & Material
1. Basic Notions.- 2. Solving Regular Holonomic Systems.- 3. Hypergeometric Series.- 4. Rank versus Volume.- 5. Integration of D-modules.- References.
