On the computation of Bernstein-Sato ideals

Journal of Symbolic Computation

Volumn 37, Issue 5, 2004, Pages 629-639

  Ucha, J M ^a   Castro Jimenez F J ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Bernstein Sato

Indexed keywords

EID: 11144356786     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2003.07.005     Document Type: Article

References (20)

1. Bahloul, R., 2001. Algorithm for computing Bernstein-Sato ideals associated with a polynomial mapping. Effective methods in rings of differential operators. J. Symbolic Comput. 32 (6), 643-662.
2. Bernstein, I.N., 1972. The analytic continuation of generalized functions with respect to a parameter. Funct. Anal. 6, 273-285.
3. Bjork, J.E., 1979. Rings of Differential Operators. North-Holland, Amsterdam.
4. Briançon, J., Maisonobe, Ph., 2002. Remarques sur l'idéal de Bernstein associé à des polynômes (preprint).
5. Briançon, J., Granger, M., Maisonobe, Ph., Miniconi, M., 1989. Algorithme de calcul du polynôme de Bernstein: cas non dégénéré. Ann. Inst. Fourier (Grenoble) 39, 553-610.
6. Bueso, J.L., Castro, F.J., Gómez-Torrecillas, J., Lobillo, F.J., 1998. An introduction to effective calculus in quantum groups. In: Rings, Hopf Algebras and Brauer Groups. Lecture Notes in Pure and Applied Mathematics, vol. 197. Marcel-Dekker, New York, pp. 55-83.
7. Castro-Jiménez, F.J., Narváez-Macarro, L., 1997. Homogenising differential operators, Prepub. n. 36, Dpto. Álgebra de la Universidad de Sevilla. Junio 1997. Available from http://www.us.es/da/prepubli/prepub36.pdf.
8. Greuel, G.-M., Pfister, G., Schönemann, H., 2001. Singular 2.0. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern. Available from http://www.singular.uni-kl.de.
9. Grigoriev, D., 1991. Complexity of solving systems of linear equations over the rings of differential operators. In: Effective Methods in Algebraic Geometry (Castiglioncello, 1990), Progr. Math., vol. 94. Birkhauser, Boston, MA, pp. 195-202.
10. Kandri-Rody, A., Weispfenning, V., 1990. Noncommutative Gröbner bases in algebras of solvable type. J. Symbolic Comput. 9 (1), 1-26.
11. Kashiwara, M., 1976. B-functions and holonomic systems. Rationality of roots of B-functions. Invent. Math. 38 (1), 33-53.
12. Levandovskyy, V., 2002. On Gröbner bases for noncommutative G-algebras. In: Kredel, H., Seiler, W.K. (Eds.), Proceedings of the 8th Rhine Workshop on Computer Algebra. Mannheim, Germany.
13. Malgrange, B., 1975. Le polynôme de Bernstein d'une singularité isolée. In: Fourier Integral Operators and Partial Differential Equations (Colloq. Internat., Univ. Nice, Nice, 1974), Lecture Notes in Mathematics, vol. 459. Springer-Verlag, New York, pp. 98-119.
14. Maynadier, H., 1997. Polynômes de Bernstein-Sato associées à une intersection complète quasi-homogène à singularité isolée. Bull. Soc. Math. France 125, 547-571.
15. Oaku, T., 1997. An algorithm of computing b-functions. Duke Math. J. 87, 115-132.
16. Oaku, T., Takayama, N., 1999. An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation. J. Pure Appl. Algebra 139, 201-233.
17. Reiffen, H.J., 1972. Das Lemma von Poincaré für holomorphe Differential-formen auf komplexen Räumen (German). Math. Z. 101, 269-284.
18. Sabbah, C., 1987. Proximité évanescente II. Equations fonctionelles pour plusieurs fonctions analytiques. Compositio Math. 64, 213-241.
19. Takayama, N., 1991. Kan: a system for computation in algebraic analysis. Source code available for Unix computers from ftp://ftp.math.kobe-u.ac.jp.
20. Walther, U., 2002. Bernstein-Sato polynomial versus cohomology of the Milnor fiber for generic arrangements. Available from arXiv:math.AG/0204080.