Polynomial and rational solutions of holonomic systems

Journal of Pure and Applied Algebra

Volumn 164, Issue 1-2, 2001, Pages 199-220

  Oaku, Toshinori ^a   Takayama, Nobuki ^b   Tsai, Harrison ^c  

^a Tokyo Woman's Chrstn U ^*  (Japan)

^b KOBE UNIVERSITY   (Japan)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

14Q99; 33F10; 35C05; 35N10

Indexed keywords

EID: 0006806779     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(00)00153-5     Document Type: Article

References (17)

1. Appell P., Kampé de Fériet J. Fonctions Hypergéometrique et Hypersphériques - Polynomes d'Hermite. 1926;Gauthier-Villars, Paris.
2. n -module, J. Pure Appl. Algebra 150 (2000) 27-39.
3. Björk J. Rings of Differential Operators. 1979;North-Holland, Amsterdam.
4. F. Chyzak, An extension of Zeilberger's fast algorithm to general holonomic functions, Formal Power Series and Algebraic Combinatorics, Vienna, 1997, Discrete Math. 217 (2000) 115-134.
5. D. Grayson, M. Stillman, Macaulay 2: a computer algebra system for algebraic geometry, Version 0.8.56, 1999, http://www.math.uiuc.edu/Macaulay2.
6. Kashiwara M. B -functions and holonomic systems Invent. Math. 38:1976;33-53.
7. Kashiwara M. On the holonomic systems of linear partial differential equations II. Invent. Math. 49:1978;121-135.
8. Oaku T. Algorithms for. b -functions, restrictions, and algebraic local cohomology groups of D -modules Adv. Appl. Math. 19:1997;61-105.
9. T. Oaku, N. Takayama, Algorithms for D -modules - Restrictions, tensor product, localization and algebraic local cohomology groups, J. Pure Appl. Algebra 156 (2001) 267-308.
10. T. Oaku, N. Takayama, U. Walther, A localization algorithm for D -modules, J. Symbolic Comput. 29 (2000) 721-728.
11. M. Saito, B. Sturmfels, N. Takayama, Gröbner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Vol. 6, Springer, Berlin, 1999.
12. Singer M. Testing reducibility of linear differential operators: a group theoretic perspective. Appl. Algebra Eng. Comm. Comput. 7:1996;77-104.
13. N. Takayama, Kan: A system for computation in algebraic analysis, 1991, 1994, 1999. ftp.math.kobe-u.ac.jp.
14. H. Tsai, Algorithms for associated primes, Weyl closure, and local cohomology of D -modules, preprint, 2000.
15. H. Tsai, U. Walther, Computing homomorphisms between holonomic D -modules, preprint, 2000.
16. Walther U. Algorithmic computation of local cohomology modules and the local cohomological diension of algebraic varieties. J. Pure Appl. Algebra. 139:1999;303-321.
17. U. Walther, Algorithmic computation of deRham cohomology of complements of complex affine varieties, J. Symbolic Comput. 29 (2000) 795-839.