Duke Mathematical Journal

An algorithm of computing $b$-functions

Toshinori Oaku
Source: Duke Math. J. Volume 87, Number 1 (1997), 115-132.
First Page: Show Hide
Primary Subjects: 16S32
Secondary Subjects: 35A20, 35A27
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077241952
Mathematical Reviews number (MathSciNet): MR1440065
Zentralblatt MATH identifier: 0893.32009
Digital Object Identifier: doi:10.1215/S0012-7094-97-08705-6

References

[BW] T. Becker and V. Weispfenning, Gröbner bases, Graduate Texts in Mathematics, vol. 141, Springer-Verlag, New York, 1993.
Mathematical Reviews (MathSciNet): MR95e:13018
Zentralblatt MATH: 0772.13010
[Be1] I. N. Bernstein, Modules over a ring of differential operators, Functional Anal. Appl. 5 (1971), 89–101.
Zentralblatt MATH: 0233.47031
Mathematical Reviews (MathSciNet): MR290097
[Be2] I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl. 6 (1972), 273–285.
Zentralblatt MATH: 0282.46038
Mathematical Reviews (MathSciNet): MR320735
[Bj] J.-E. Björk, Rings of differential operators, North-Holland Mathematical Library, vol. 21, North-Holland Publishing Co., Amsterdam, 1979.
Mathematical Reviews (MathSciNet): MR82g:32013
Zentralblatt MATH: 0499.13009
[BGMM] J. Briançon, M. Granger, Ph. Maisonobe, and M. Miniconi, Algorithme de calcul du polynôme de Bernstein: cas non dégénéré, Ann. Inst. Fourier (Grenoble) 39 (1989), no. 3, 553–610.
Mathematical Reviews (MathSciNet): MR91k:32040
Zentralblatt MATH: 0675.32008
[Bu] B. Buchberger, Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems, Aequationes Math. 4 (1970), 374–383.
Mathematical Reviews (MathSciNet): MR42:3077
Zentralblatt MATH: 0212.06401
Digital Object Identifier: doi:10.1007/BF01844169
[C] F. Castro, Calculs effectifs pour les idéaux d'opérateurs différentiels, Géométrie algébrique et applications, III (La Rábida, 1984), Travaux en Cours, vol. 24, Hermann, Paris, 1987, pp. 1–19.
Mathematical Reviews (MathSciNet): MR89a:32010
Zentralblatt MATH: 0633.13009
[CLO] D. Cox, J. Little, and D. O'Shea, Ideals, varieties, and algorithms, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1992.
Mathematical Reviews (MathSciNet): MR93j:13031
Zentralblatt MATH: 0756.13017
[E] D. Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995.
Mathematical Reviews (MathSciNet): MR97a:13001
Zentralblatt MATH: 0819.13001
[G] A. Galligo, Some algorithmic questions on ideals of differential operators, EUROCAL '85, Vol. 2 (Linz, 1985), Lecture Notes in Comput. Sci., vol. 204, Springer, Berlin, 1985, pp. 413–421.
Mathematical Reviews (MathSciNet): MR87g:32012
Zentralblatt MATH: 0634.16001
[KW] A. Kandri-Rody and V. Weispfenning, Noncommutative Gröbner bases in algebras of solvable type, J. Symbolic Comput. 9 (1990), no. 1, 1–26.
Mathematical Reviews (MathSciNet): MR91e:13025
Zentralblatt MATH: 0715.16010
Digital Object Identifier: doi:10.1016/S0747-7171(08)80003-X
[K1] M. Kashiwara, $B$-functions and holonomic systems. Rationality of roots of $B$-functions, Invent. Math. 38 (1976/77), no. 1, 33–53.
Mathematical Reviews (MathSciNet): MR55:3309
Zentralblatt MATH: 0354.35082
Digital Object Identifier: doi:10.1007/BF01390168
[K2] M. Kashiwara, On the holonomic systems of linear differential equations. II, Invent. Math. 49 (1978), no. 2, 121–135.
Mathematical Reviews (MathSciNet): MR80a:58035
Zentralblatt MATH: 0401.32005
Digital Object Identifier: doi:10.1007/BF01403082
[K3] M. Kashiwara, Vanishing cycle sheaves and holonomic systems of differential equations, Algebraic geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., vol. 1016, Springer, Berlin, 1983, pp. 134–142.
Mathematical Reviews (MathSciNet): MR85e:58137
Zentralblatt MATH: 0566.32022
[KK] M. Kashiwara and T. Kawai, Second-microlocalization and asymptotic expansions, Complex analysis, microlocal calculus and relativistic quantum theory (Proc. Internat. Colloq., Centre Phys., Les Houches, 1979), Lecture Notes in Phys., vol. 126, Springer, Berlin, 1980, pp. 21–76.
Mathematical Reviews (MathSciNet): MR81i:58038
Zentralblatt MATH: 0458.46027
Digital Object Identifier: doi:10.1007/3-540-09996-4_29
[L] Y. Laurent, Polygône de Newton et $b$-fonctions pour les modules microdifférentiels, Ann. Sci. École Norm. Sup. (4) 20 (1987), no. 3, 391–441.
Mathematical Reviews (MathSciNet): MR89k:58282
Zentralblatt MATH: 0646.58021
[LS] Y. Laurent and P. Schapira, Images inverses des modules différentiels, Compositio Math. 61 (1987), no. 2, 229–251.
Mathematical Reviews (MathSciNet): MR88f:32044
Zentralblatt MATH: 0617.32014
[La] D. Lazard, Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations, Computer algebra (London, 1983), Lecture Notes in Comput. Sci., vol. 162, Springer, Berlin, 1983, pp. 146–156.
Mathematical Reviews (MathSciNet): MR86m:13002
Zentralblatt MATH: 0539.13002
[Mai] P. Maisonobe, $\scr D$-modules: an overview towards effectivity, Computer algebra and differential equations (1992), London Math. Soc. Lecture Note Ser., vol. 193, Cambridge Univ. Press, Cambridge, 1994, pp. 21–55.
Mathematical Reviews (MathSciNet): MR95g:32019
Zentralblatt MATH: 0804.35009
[M1] B. Malgrange, Le polynôme de Bernstein d'une singularité isolée, Fourier integral operators and partial differential equations (Colloq. Internat., Univ. Nice, Nice, 1974), Springer, Berlin, 1975, 98–119. Lecture Notes in Math., Vol. 459.
Mathematical Reviews (MathSciNet): MR54:7845
Zentralblatt MATH: 0308.32007
Digital Object Identifier: doi:10.1007/BFb0074194
[M2] B. Malgrange, Polynômes de Bernstein-Sato et cohomologie évanescente, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 243–267.
Mathematical Reviews (MathSciNet): MR86f:58148
Zentralblatt MATH: 0528.32007
[Mo] F. Mora, An algorithm to compute the equations of tangent cones, Computer algebra (Marseille, 1982), Lecture Notes in Comput. Sci., vol. 144, Springer, Berlin, 1982, pp. 158–165.
Mathematical Reviews (MathSciNet): MR84c:13012
Zentralblatt MATH: 0568.68029
[O1] T. Oaku, Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients, Japan J. Indust. Appl. Math. 11 (1994), no. 3, 485–497.
Mathematical Reviews (MathSciNet): MR95g:35012
Zentralblatt MATH: 0811.35006
Digital Object Identifier: doi:10.1007/BF03167233
[O2] T. Oaku, Algorithms for finding the structure of solutions of a system of linear partial differential equations, ISSAC '94: Proceeedings of the 1994 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, 1994, pp. 216–223.
Zentralblatt MATH: 0964.35505
[O3] T. Oaku, Algorithmic methods for Fuchsian systems of linear partial differential equations, J. Math. Soc. Japan 47 (1995), no. 2, 297–328.
Mathematical Reviews (MathSciNet): MR96f:35012a
Zentralblatt MATH: 0847.35032
Digital Object Identifier: doi:10.2969/jmsj/04720297
Project Euclid: euclid.jmsj/1227104381
[SKKO] M. Sato, M. Kashiwara, T. Kimura, and T. Oshima, Microlocal analysis of prehomogeneous vector spaces, Invent. Math. 62 (1980/81), no. 1, 117–179.
Mathematical Reviews (MathSciNet): MR83g:32016
Zentralblatt MATH: 0456.58034
Digital Object Identifier: doi:10.1007/BF01391666
[T1] N. Takayama, Gröbner basis and the problem of contiguous relations, Japan J. Appl. Math. 6 (1989), no. 1, 147–160.
Mathematical Reviews (MathSciNet): MR90d:12005
Zentralblatt MATH: 0691.68032
Digital Object Identifier: doi:10.1007/BF03167920
[T2] N. Takayama, An approach to the zero recognition problem by Buchberger algorithm, J. Symbolic Comput. 14 (1992), no. 2-3, 265–282.
Mathematical Reviews (MathSciNet): MR93j:68090
Zentralblatt MATH: 0763.65007
Digital Object Identifier: doi:10.1016/0747-7171(92)90039-7
[T3] N. Takayama, A system for computation in algebraic analysis, 1991, ftp://ftp.math.s.kobe-u.ac.jp/pub/kan/kan96.tgz.
[Y] T. Yano, On the theory of $b$-functions, Publ. Res. Inst. Math. Sci. 14 (1978), no. 1, 111–202.
Mathematical Reviews (MathSciNet): MR80h:32026
Zentralblatt MATH: 0389.32005
Digital Object Identifier: doi:10.2977/prims/1195189282

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?