Algorithms for b-functions, induced systems, and algebraic local cohomology of D-modules

Proceedings of the Japan Academy Series A: Mathematical Sciences

Volumn 72, Issue 8, 1996, Pages 173-178

  Oaku, Toshinori ^a  

^a YOKOHAMA CITY UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444439363     PISSN: 03862194     EISSN: None     Source Type: Journal    
DOI: 10.3792/pjaa.72.173     Document Type: Article

References (25)

1. I. N. Bernstein : Modules over a ring of differential operators. Functional Anal. Appl., 5, 89-101 (1971).
2. J. E. Björk: Rings of Differential Operators. North-Holland, Amsterdam (1979).
3. A. Borel et al.: Algebraic D-Modules. Academic Press, Boston (1987).
4. J. Briancon, M. Granger, Ph. Maisonobe, and M. Miniconi: Algorithme de calcul du polynôme de Bernstein: cas non dégénéré. Ann. Inst. Fourier, 39, 533-610 (1989).
5. B. Buchberger: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aequationes Math., 4, 374-383 (1970).
6. F. Castro: Calculs effectifs pour les idéaux d'opérateurs différentiels. Travaux en Cours, vol. 24, Hermann Paris, pp. 1-19 (1987).
7. D. Cox, J. Little, and D. O'Shea, : Ideals, Varieties, and Algorithms. Springer, Berlin (1992).
8. D. Eisenbud, C. Huneke, and W. Vasconcelos: Direct methods for primary decomposition. Invent. Math., 110, 207-235 (1992).
9. A. Galligo: Some algorithmic questions on ideals of differential operators. Lecture Notes in Comput. Sci., vol. 204, Springer, Berlin, pp. 413-421 (1985).
10. M. Kashiwara: B-functions and holonomic systems-Rationality of roots of 6-functions. Invent. Math., 38, 33-53 (1976).
11. M. Kashiwara: On the holonomic systems of linear differential equations. II . Invent. Math., 49, 121-135 (1978).
12. M. Kashiwara: Vanishing cycle sheaves and holonomic systems of differential equations. Lecture Notes in Math., vol. 1016. Springer, Berlin, pp.134-142 (1983).
13. M. Kashiwara and T. Kawai: Second microlocalization and asymptotic expansions. Lecture Notes in Physics, vol. 126, Springer, Berlin, pp. 21-76 (1980).
14. Y. Laurent: Polygône de Newton et b-fonctions pour les modules microdifferentiels. Ann. Sci. Éc. Norm. Sup., 20, 391-441 (1987).
15. Y. Laurent and P. Schapira: Images inverses des modules différentiels. Compositio Math., 61, 229-251 (1987).
16. P. Maisonobe: D-modules: An overview towards effectivity. Computer Algebra and Differential Equations (ed. E. Tournier). Cambridge University Press, pp. 21-55 (1994).
17. B. Malgrange: Le polyôme de Bernstein d'une singularité isolée. Lecture Notes in Math., vol. 459, Springer. Berlin, pp. 98-119 (1975).
18. T. Oaku: Algorithms for finding the structure of solutions of a system of linear partial differential equations. Proceeding of International Symposium on Symbolic and Algebraic Computation (eds, J. Gathen, and M. Giesbrecht). ACM, New York pp. 216-223 (1994).
19. T. Oaku: Algorithmic methods for Fuchsian systems of linear partial differential equations. J. Math. Soc. Japan, 47, 297-328 (1995).
20. T. Oaku: An algorithm of computing b-functions. Duke Math. J. (to appear).
21. M. Sato, M. Kashiwara, T. Kimura, and T. Oshima: Micro-local analysis of prehomogeneous vector spaces. Invent. Math., 62, 117-179 (1980).
22. N. Takayama: Gröbner basis and the problem of contiguous relations. Japan J. Appl. Math., 6, 147-160 (1989).
23. N. Takayama: An algorithm of constructing the integral of a module-an infinite dimensional analog of Gröbner basis. Proceedings of International Symposium on Symbolic and Algebraic Computation (eds, S. Watanabe and M. Nagata). ACM, New York, pp. 206-211 (1990).
24. N. Takayama: Kan: A system for computation in algebraic analysis, http: //www.math. s. kobe-u. ac. jp (1991-).
25. T. Yano: On the theory of b-functions. Publ. RIMS, Kyoto Univ., 14, 111-202 (1978).