Gröbner bases and logarithmic D -modules

Let C [ x ] = C [ x 1 , … , x n ] be the ring of polynomials with complex coefficients and A n the Weyl algebra of order n over C . Elements in A n are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C [ x ] f of rational functions with poles along f...

Full description

Saved in:
Bibliographic Details
Published inJournal of symbolic computation Vol. 41; no. 3; pp. 317 - 335
Main Authors Castro-Jiménez, F.J., Ucha-Enríquez, J.M.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2006
Subjects
[formula omitted]-modules
Free divisors
Gröbner bases
Spencer divisors
Weyl algebra
Gröbner bases
Spencer divisors
D -modules
Weyl algebra
Free divisors
Online AccessGet full text

Cover

Abstract Let C [ x ] = C [ x 1 , … , x n ] be the ring of polynomials with complex coefficients and A n the Weyl algebra of order n over C . Elements in A n are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C [ x ] f of rational functions with poles along f has a natural structure of a left A n -module which is finitely generated by a classical result of I.N. Bernstein. A central problem in this context is how to find a finite presentation of M starting from the input f . In this paper we use Gröbner base theory in the non-commutative frame of the ring A n to compare M to some other A n -modules arising in Singularity Theory as the so-called logarithmic A n -modules. We also show how the analytic case can be treated with computations in the Weyl algebra if the input data f is a polynomial.
AbstractList Let C [ x ] = C [ x 1 , … , x n ] be the ring of polynomials with complex coefficients and A n the Weyl algebra of order n over C . Elements in A n are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C [ x ] f of rational functions with poles along f has a natural structure of a left A n -module which is finitely generated by a classical result of I.N. Bernstein. A central problem in this context is how to find a finite presentation of M starting from the input f . In this paper we use Gröbner base theory in the non-commutative frame of the ring A n to compare M to some other A n -modules arising in Singularity Theory as the so-called logarithmic A n -modules. We also show how the analytic case can be treated with computations in the Weyl algebra if the input data f is a polynomial.
Author Castro-Jiménez, F.J.
Ucha-Enríquez, J.M.
Author_xml – sequence: 1
  givenname: F.J.
  surname: Castro-Jiménez
  fullname: Castro-Jiménez, F.J.
– sequence: 2
  givenname: J.M.
  surname: Ucha-Enríquez
  fullname: Ucha-Enríquez, J.M.
  email: ucha@us.es
BookMark eNp9j81KxDAUhYOM4MzoA7jr1kXrvW3STHElo47CgBsFdyE_t5rSH0mq4Iv5Ar6YLeNaOHBW3-F8K7boh54YO0fIELC8bLIm2iwH4NkcxCO2RKhEuhHiZcGWILlMJUo8YasYGwCoeCGW7GIXfr5NTyExOlJMdO-SdnjVwY9vnbfJTZJ2g_toKZ6y41q3kc7-es2e726ftvfp_nH3sL3epzav5JhaqZEL4wwnXgLnqKlEYacrBDVyNBJtyQtd29xoXgoQeem04WAdbnJRFGuGh10bhhgD1eo9-E6HL4WgZlfVqMlVza5qDuLEXB0Ymo59egoqWk-9JecD2VG5wf9D_wI-Jl0_
CitedBy_id crossref_primary_10_1016_j_jalgebra_2006_12_006
crossref_primary_10_1007_s13160_013_0105_5
Cites_doi 10.1006/aama.1997.0527
10.1016/S0012-9593(01)80004-5
10.1006/jsco.1999.0398
10.1006/jsco.2001.0489
10.1080/10586458.2004.10504553
10.1007/BF01403082
10.1016/S0747-7171(08)80003-X
10.1090/S0002-9939-04-07678-6
10.1016/S0747-7171(03)00063-4
10.1016/S0022-4049(00)00004-9
10.1090/S0002-9947-96-01690-X
10.1007/s00014-002-8330-6
10.1215/S0012-7094-97-08705-6
10.24033/bsmf.2475
10.1007/BF01844169
10.1112/S0010437X04001149
10.1006/jsco.2001.0485
ContentType Journal Article
Copyright 2005 Elsevier Ltd
Copyright_xml – notice: 2005 Elsevier Ltd
DBID 6I.
AAFTH
AAYXX
CITATION
DOI 10.1016/j.jsc.2004.04.011
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1095-855X
EndPage 335
ExternalDocumentID 10_1016_j_jsc_2004_04_011
S0747717105001355
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
29L
4.4
457
4G.
5GY
5VS
6I.
6OB
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFNM
ABJNI
ABMAC
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADFGL
ADMUD
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CAG
COF
CS3
DM4
DU5
EBS
EFBJH
EFLBG
EJD
EO8
EO9
EP2
EP3
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
GBOLZ
HVGLF
HZ~
IHE
IXB
J1W
KOM
LG5
M25
M41
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SPC
SPCBC
SSV
SSW
SSZ
T5K
TN5
UPT
WUQ
XPP
YQT
ZMT
ZU3
~G-
0SF
AAXKI
AAYXX
ADVLN
AFJKZ
AKRWK
CITATION
ID FETCH-LOGICAL-c297t-c7a145bdb4e460441ae615c095e0f141b71c643afc2ba4650526dab40cd182533
IEDL.DBID IXB
ISSN 0747-7171
IngestDate Thu Sep 26 16:19:06 EDT 2024
Fri Feb 23 02:31:32 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 3
Keywords Gröbner bases
Spencer divisors
D -modules
Weyl algebra
Free divisors
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c297t-c7a145bdb4e460441ae615c095e0f141b71c643afc2ba4650526dab40cd182533
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S0747717105001355
PageCount 19
ParticipantIDs crossref_primary_10_1016_j_jsc_2004_04_011
elsevier_sciencedirect_doi_10_1016_j_jsc_2004_04_011
PublicationCentury 2000
PublicationDate 2006-03-01
PublicationDateYYYYMMDD 2006-03-01
PublicationDate_xml – month: 03
  year: 2006
  text: 2006-03-01
  day: 01
PublicationDecade 2000
PublicationTitle Journal of symbolic computation
PublicationYear 2006
Publisher Elsevier Ltd
Publisher_xml – name: Elsevier Ltd
References Calderón-Moreno, Narváez-Macarro (b9) 2002; 238
Calderón-Moreno (b7) 1999; 32
Saito, Sturmfels, Takayama (b29) 2000; vol. 6
Kandri-Rody, Weispfenning (b21) 1990; 9
Buchberger, B., 1965. An algorithm for finding the bases elements of the residue class ring modulo a zero dimensional polynomial ideal (German). Ph.D. Thesis, Univ. of Innsbruck, Austria
module scripts by Leykin A., Tsai H.
Castro-Jiménez, Ucha-Enríquez (b16) 2005; 133
Takayama (b30) 1991
Oaku, Takayama (b26) 2001; 156
Walther (b34) 2005; 141
Castro-Jiménez, F., 1987. Calculs effectifs pour les idéaux d’opérateurs différentiels. In: Actas de la II Conferencia Internacional de Geometría Algebraica. La Rábida, Travaux en Cours 24, Hermann
Cox, Little, O’Shea (b18) 1996
Tsai, Walther (b32) 2001; 32
cycle, Univ. of Paris VII
Castro-Jiménez, Narváez-Macarro, Mond (b13) 1996; 348
Bueso, Gómez Torrecillas, Lobillo, Castro (b6) 1998; vol. 197
Castro-Jiménez, Ucha-Enríquez (b15) 2004; 13
Ucha, J., 1999. Métodos constructivos en álgebras de operadores diferenciales. Ph.D. Thesis, Univ. of Sevilla
Björk (b2) 1979; vol. 21
Calderón Moreno, Mond, Narváez Macarro, Castro Jiménez (b8) 2002; 77
Symbolic Computation in Algebra, Analysis, and Geometry, Berkeley, CA, 1998
Capani, Niesi, Robbiano (b10) 1995
Oaku (b24) 1997; 87
Kashiwara (b22) 1978; 49
Saito (b28) 1980; 27
Oaku (b25) 1997; 19
Buchberger (b5) 1970; 4
.
Briançon, Maisonobe (b3) 1984; 30
Gago-Vargas (b19) 2003; 36
Bernstein (b1) 1972; 6
Mebkhout (b23) 1989; vol. 35
Castro-Jiménez, Ucha (b17) 2002; 238
Castro, F., 1984. Théorème de division pour les opérateurs différentiels et calcul des multiplicités. Thèse de
Torrelli (b31) 2004; 132
Grayson, D., Stillman, M., 1999. Macaulay 2: a computer algebra system for algebraic geometry, version 0.9.2
Castro-Jiménez, Ucha-Enríquez (b14) 2001; 32
Capani (10.1016/j.jsc.2004.04.011_b10) 1995
Bueso (10.1016/j.jsc.2004.04.011_b6) 1998; vol. 197
Gago-Vargas (10.1016/j.jsc.2004.04.011_b19) 2003; 36
10.1016/j.jsc.2004.04.011_b4
10.1016/j.jsc.2004.04.011_b27_2
Castro-Jiménez (10.1016/j.jsc.2004.04.011_b14) 2001; 32
Mebkhout (10.1016/j.jsc.2004.04.011_b23) 1989; vol. 35
Kandri-Rody (10.1016/j.jsc.2004.04.011_b21) 1990; 9
Buchberger (10.1016/j.jsc.2004.04.011_b5) 1970; 4
Calderón-Moreno (10.1016/j.jsc.2004.04.011_b9) 2002; 238
Calderón Moreno (10.1016/j.jsc.2004.04.011_b8) 2002; 77
Cox (10.1016/j.jsc.2004.04.011_b18) 1996
Kashiwara (10.1016/j.jsc.2004.04.011_b22) 1978; 49
Tsai (10.1016/j.jsc.2004.04.011_b32) 2001; 32
Castro-Jiménez (10.1016/j.jsc.2004.04.011_b13) 1996; 348
Saito (10.1016/j.jsc.2004.04.011_b28) 1980; 27
Bernstein (10.1016/j.jsc.2004.04.011_b1) 1972; 6
Castro-Jiménez (10.1016/j.jsc.2004.04.011_b16) 2005; 133
10.1016/j.jsc.2004.04.011_b12
10.1016/j.jsc.2004.04.011_b11
10.1016/j.jsc.2004.04.011_b33
Walther (10.1016/j.jsc.2004.04.011_b34) 2005; 141
Takayama (10.1016/j.jsc.2004.04.011_b30) 1991
Björk (10.1016/j.jsc.2004.04.011_b2) 1979; vol. 21
Calderón-Moreno (10.1016/j.jsc.2004.04.011_b7) 1999; 32
Castro-Jiménez (10.1016/j.jsc.2004.04.011_b17) 2002; 238
Torrelli (10.1016/j.jsc.2004.04.011_b31) 2004; 132
Oaku (10.1016/j.jsc.2004.04.011_b27_1) 2000; 29
Briançon (10.1016/j.jsc.2004.04.011_b3) 1984; 30
Saito (10.1016/j.jsc.2004.04.011_b29) 2000; vol. 6
Oaku (10.1016/j.jsc.2004.04.011_b25) 1997; 19
Castro-Jiménez (10.1016/j.jsc.2004.04.011_b15) 2004; 13
Oaku (10.1016/j.jsc.2004.04.011_b24) 1997; 87
Oaku (10.1016/j.jsc.2004.04.011_b26) 2001; 156
10.1016/j.jsc.2004.04.011_b20
References_xml – volume: vol. 35
  year: 1989
  ident: b23
  publication-title: Le formalisme des six opérations de Grothendieck pour les
  contributor:
    fullname: Mebkhout
– volume: 132
  start-page: 591
  year: 2004
  end-page: 612
  ident: b31
  article-title: On meromorphic functions defined by a differential system of order 1
  publication-title: Bull. Soc. Math. France
  contributor:
    fullname: Torrelli
– volume: 6
  start-page: 26
  year: 1972
  end-page: 40
  ident: b1
  article-title: Analytic continuation of generalized functions with respect to a parameter
  publication-title: Funkcional. Anal. i Priložen.
  contributor:
    fullname: Bernstein
– volume: vol. 197
  start-page: 55
  year: 1998
  end-page: 83
  ident: b6
  article-title: An introduction to effective calculus in quantum groups
  publication-title: Rings, Hopf Algebras, and Brauer Groups (Antwerp/Brussels, 1996)
  contributor:
    fullname: Castro
– volume: 141
  start-page: 121
  year: 2005
  end-page: 145
  ident: b34
  article-title: Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements
  publication-title: Compositio. Math.
  contributor:
    fullname: Walther
– volume: 30
  start-page: 7
  year: 1984
  end-page: 38
  ident: b3
  article-title: Idéaux de germes d’opérateurs différentiels une variable
  publication-title: L’Enseignement Math.
  contributor:
    fullname: Maisonobe
– volume: 77
  start-page: 24
  year: 2002
  end-page: 38
  ident: b8
  article-title: Logarithmic cohomology of the complement of a plane curve
  publication-title: Comment. Math. Helv.
  contributor:
    fullname: Castro Jiménez
– volume: 133
  start-page: 1417
  year: 2005
  end-page: 1422
  ident: b16
  article-title: Logarithmic comparison theorem and some Euler homogeneous free divisors
  publication-title: Proc. Amer. Math. Soc.
  contributor:
    fullname: Ucha-Enríquez
– volume: 156
  start-page: 267
  year: 2001
  end-page: 308
  ident: b26
  article-title: Algorithms for
  publication-title: J. Pure Appl. Algebra
  contributor:
    fullname: Takayama
– volume: 36
  start-page: 845
  year: 2003
  end-page: 853
  ident: b19
  article-title: Bases for projective modules in
  publication-title: J. Symbolic Comput.
  contributor:
    fullname: Gago-Vargas
– volume: 32
  start-page: 597
  year: 2001
  end-page: 617
  ident: b32
  article-title: Computing homomorphisms between holonomic
  publication-title: J. Symbolic Comput.
  contributor:
    fullname: Walther
– volume: 27
  start-page: 265
  year: 1980
  end-page: 291
  ident: b28
  article-title: Theory of logarithmic differential forms and logarithmic vector fields
  publication-title: J. Fac. Sci. Univ. Tokyo Sect. IA Math.
  contributor:
    fullname: Saito
– volume: 32
  start-page: 677
  year: 2001
  end-page: 685
  ident: b14
  article-title: Explicit comparison theorems for D-modules
  publication-title: J. Symbolic Comput.
  contributor:
    fullname: Ucha-Enríquez
– volume: 238
  start-page: 97
  year: 2002
  end-page: 105
  ident: b17
  article-title: Free divisors and duality for D-modules
  publication-title: Proc. Steklov Inst. Math.
  contributor:
    fullname: Ucha
– year: 1995
  ident: b10
  article-title: CoCoa, a system for doing computations in Commutative Algebra
  contributor:
    fullname: Robbiano
– volume: 13
  start-page: 441
  year: 2004
  end-page: 449
  ident: b15
  article-title: Testing the logarithmic comparison theorem for free divisors
  publication-title: Experiment. Math.
  contributor:
    fullname: Ucha-Enríquez
– volume: 19
  start-page: 61
  year: 1997
  end-page: 105
  ident: b25
  article-title: Algorithms for
  publication-title: Adv. in Appl. Math.
  contributor:
    fullname: Oaku
– year: 1996
  ident: b18
  publication-title: Ideals, Varieties and Algorithms
  contributor:
    fullname: O’Shea
– volume: 87
  start-page: 115
  year: 1997
  end-page: 132
  ident: b24
  article-title: An algorithm of computing
  publication-title: Duke Math. J.
  contributor:
    fullname: Oaku
– volume: 4
  start-page: 374
  year: 1970
  end-page: 383
  ident: b5
  article-title: An algorithmical criterion for the solvability of algebraic systems of equations (German)
  publication-title: Aequationes Mathematicae
  contributor:
    fullname: Buchberger
– volume: 238
  start-page: 81
  year: 2002
  end-page: 85
  ident: b9
  article-title: Locally quasi-homogeneous free divisors are Koszul free
  publication-title: Proc. Steklov Inst. Math.
  contributor:
    fullname: Narváez-Macarro
– volume: vol. 6
  year: 2000
  ident: b29
  publication-title: Gröbner deformations of hypergeometric differential equations
  contributor:
    fullname: Takayama
– volume: 9
  start-page: 1
  year: 1990
  end-page: 26
  ident: b21
  article-title: Noncommutative Gröbner bases in algebras of solvable type
  publication-title: J. Symbolic Comput.
  contributor:
    fullname: Weispfenning
– volume: 49
  start-page: 121
  year: 1978
  end-page: 135
  ident: b22
  article-title: On the holonomic systems of linear differential equations. II
  publication-title: Invent. Math.
  contributor:
    fullname: Kashiwara
– year: 1991
  ident: b30
  article-title:
  contributor:
    fullname: Takayama
– volume: 348
  start-page: 3037
  year: 1996
  end-page: 3049
  ident: b13
  article-title: Cohomology of the complement of a free divisor
  publication-title: Trans. Amer. Math. Soc.
  contributor:
    fullname: Mond
– volume: vol. 21
  year: 1979
  ident: b2
  publication-title: Rings of differential operators
  contributor:
    fullname: Björk
– volume: 32
  start-page: 701
  year: 1999
  end-page: 714
  ident: b7
  article-title: Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor
  publication-title: Ann. Sci. École Norm. Sup. (4)
  contributor:
    fullname: Calderón-Moreno
– volume: vol. 197
  start-page: 55
  year: 1998
  ident: 10.1016/j.jsc.2004.04.011_b6
  article-title: An introduction to effective calculus in quantum groups
  contributor:
    fullname: Bueso
– ident: 10.1016/j.jsc.2004.04.011_b11
– volume: 19
  start-page: 61
  issue: 1
  year: 1997
  ident: 10.1016/j.jsc.2004.04.011_b25
  article-title: Algorithms for b-functions, restrictions, and algebraic local cohomology groups of D-modules
  publication-title: Adv. in Appl. Math.
  doi: 10.1006/aama.1997.0527
  contributor:
    fullname: Oaku
– year: 1995
  ident: 10.1016/j.jsc.2004.04.011_b10
  contributor:
    fullname: Capani
– volume: vol. 35
  year: 1989
  ident: 10.1016/j.jsc.2004.04.011_b23
  contributor:
    fullname: Mebkhout
– volume: 32
  start-page: 701
  issue: 5
  year: 1999
  ident: 10.1016/j.jsc.2004.04.011_b7
  article-title: Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor
  publication-title: Ann. Sci. École Norm. Sup. (4)
  doi: 10.1016/S0012-9593(01)80004-5
  contributor:
    fullname: Calderón-Moreno
– volume: vol. 21
  year: 1979
  ident: 10.1016/j.jsc.2004.04.011_b2
  contributor:
    fullname: Björk
– volume: 238
  start-page: 97
  year: 2002
  ident: 10.1016/j.jsc.2004.04.011_b17
  article-title: Free divisors and duality for D-modules
  publication-title: Proc. Steklov Inst. Math.
  contributor:
    fullname: Castro-Jiménez
– volume: 29
  start-page: 721
  issue: 4–5
  year: 2000
  ident: 10.1016/j.jsc.2004.04.011_b27_1
  article-title: A localization algorithm for D-modules
  publication-title: J. Symbolic Comput.
  doi: 10.1006/jsco.1999.0398
  contributor:
    fullname: Oaku
– volume: 32
  start-page: 677
  issue: 6
  year: 2001
  ident: 10.1016/j.jsc.2004.04.011_b14
  article-title: Explicit comparison theorems for D-modules
  publication-title: J. Symbolic Comput.
  doi: 10.1006/jsco.2001.0489
  contributor:
    fullname: Castro-Jiménez
– ident: 10.1016/j.jsc.2004.04.011_b20
– volume: 13
  start-page: 441
  issue: 4
  year: 2004
  ident: 10.1016/j.jsc.2004.04.011_b15
  article-title: Testing the logarithmic comparison theorem for free divisors
  publication-title: Experiment. Math.
  doi: 10.1080/10586458.2004.10504553
  contributor:
    fullname: Castro-Jiménez
– year: 1996
  ident: 10.1016/j.jsc.2004.04.011_b18
  contributor:
    fullname: Cox
– volume: 49
  start-page: 121
  issue: 2
  year: 1978
  ident: 10.1016/j.jsc.2004.04.011_b22
  article-title: On the holonomic systems of linear differential equations. II
  publication-title: Invent. Math.
  doi: 10.1007/BF01403082
  contributor:
    fullname: Kashiwara
– ident: 10.1016/j.jsc.2004.04.011_b4
– volume: 9
  start-page: 1
  issue: 1
  year: 1990
  ident: 10.1016/j.jsc.2004.04.011_b21
  article-title: Noncommutative Gröbner bases in algebras of solvable type
  publication-title: J. Symbolic Comput.
  doi: 10.1016/S0747-7171(08)80003-X
  contributor:
    fullname: Kandri-Rody
– volume: 238
  start-page: 81
  year: 2002
  ident: 10.1016/j.jsc.2004.04.011_b9
  article-title: Locally quasi-homogeneous free divisors are Koszul free
  publication-title: Proc. Steklov Inst. Math.
  contributor:
    fullname: Calderón-Moreno
– volume: 133
  start-page: 1417
  issue: 5
  year: 2005
  ident: 10.1016/j.jsc.2004.04.011_b16
  article-title: Logarithmic comparison theorem and some Euler homogeneous free divisors
  publication-title: Proc. Amer. Math. Soc.
  doi: 10.1090/S0002-9939-04-07678-6
  contributor:
    fullname: Castro-Jiménez
– volume: 36
  start-page: 845
  issue: 6
  year: 2003
  ident: 10.1016/j.jsc.2004.04.011_b19
  article-title: Bases for projective modules in An(k)
  publication-title: J. Symbolic Comput.
  doi: 10.1016/S0747-7171(03)00063-4
  contributor:
    fullname: Gago-Vargas
– ident: 10.1016/j.jsc.2004.04.011_b33
– ident: 10.1016/j.jsc.2004.04.011_b12
– volume: 156
  start-page: 267
  issue: 2–3
  year: 2001
  ident: 10.1016/j.jsc.2004.04.011_b26
  article-title: Algorithms for D-modules—restriction, tensor product, localization, and local cohomology groups
  publication-title: J. Pure Appl. Algebra
  doi: 10.1016/S0022-4049(00)00004-9
  contributor:
    fullname: Oaku
– volume: 348
  start-page: 3037
  issue: 8
  year: 1996
  ident: 10.1016/j.jsc.2004.04.011_b13
  article-title: Cohomology of the complement of a free divisor
  publication-title: Trans. Amer. Math. Soc.
  doi: 10.1090/S0002-9947-96-01690-X
  contributor:
    fullname: Castro-Jiménez
– volume: 27
  start-page: 265
  issue: 2
  year: 1980
  ident: 10.1016/j.jsc.2004.04.011_b28
  article-title: Theory of logarithmic differential forms and logarithmic vector fields
  publication-title: J. Fac. Sci. Univ. Tokyo Sect. IA Math.
  contributor:
    fullname: Saito
– volume: 77
  start-page: 24
  issue: 1
  year: 2002
  ident: 10.1016/j.jsc.2004.04.011_b8
  article-title: Logarithmic cohomology of the complement of a plane curve
  publication-title: Comment. Math. Helv.
  doi: 10.1007/s00014-002-8330-6
  contributor:
    fullname: Calderón Moreno
– year: 1991
  ident: 10.1016/j.jsc.2004.04.011_b30
  contributor:
    fullname: Takayama
– volume: 87
  start-page: 115
  issue: 1
  year: 1997
  ident: 10.1016/j.jsc.2004.04.011_b24
  article-title: An algorithm of computing b-functions
  publication-title: Duke Math. J.
  doi: 10.1215/S0012-7094-97-08705-6
  contributor:
    fullname: Oaku
– volume: 132
  start-page: 591
  year: 2004
  ident: 10.1016/j.jsc.2004.04.011_b31
  article-title: On meromorphic functions defined by a differential system of order 1
  publication-title: Bull. Soc. Math. France
  doi: 10.24033/bsmf.2475
  contributor:
    fullname: Torrelli
– volume: 6
  start-page: 26
  issue: 4
  year: 1972
  ident: 10.1016/j.jsc.2004.04.011_b1
  article-title: Analytic continuation of generalized functions with respect to a parameter
  publication-title: Funkcional. Anal. i Priložen.
  contributor:
    fullname: Bernstein
– ident: 10.1016/j.jsc.2004.04.011_b27_2
– volume: 4
  start-page: 374
  issue: 3
  year: 1970
  ident: 10.1016/j.jsc.2004.04.011_b5
  article-title: An algorithmical criterion for the solvability of algebraic systems of equations (German)
  publication-title: Aequationes Mathematicae
  doi: 10.1007/BF01844169
  contributor:
    fullname: Buchberger
– volume: 141
  start-page: 121
  issue: 1
  year: 2005
  ident: 10.1016/j.jsc.2004.04.011_b34
  article-title: Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements
  publication-title: Compositio. Math.
  doi: 10.1112/S0010437X04001149
  contributor:
    fullname: Walther
– volume: 30
  start-page: 7
  year: 1984
  ident: 10.1016/j.jsc.2004.04.011_b3
  article-title: Idéaux de germes d’opérateurs différentiels une variable
  publication-title: L’Enseignement Math.
  contributor:
    fullname: Briançon
– volume: vol. 6
  year: 2000
  ident: 10.1016/j.jsc.2004.04.011_b29
  contributor:
    fullname: Saito
– volume: 32
  start-page: 597
  issue: 6
  year: 2001
  ident: 10.1016/j.jsc.2004.04.011_b32
  article-title: Computing homomorphisms between holonomic D-modules
  publication-title: J. Symbolic Comput.
  doi: 10.1006/jsco.2001.0485
  contributor:
    fullname: Tsai
SSID ssj0009435
Score 1.7636639
Snippet Let C [ x ] = C [ x 1 , … , x n ] be the ring of polynomials with complex coefficients and A n the Weyl algebra of order n over C . Elements in A n are linear...
SourceID crossref
elsevier
SourceType Aggregation Database
Publisher
StartPage 317
SubjectTerms [formula omitted]-modules
Free divisors
Gröbner bases
Spencer divisors
Weyl algebra
Title Gröbner bases and logarithmic D -modules
URI https://dx.doi.org/10.1016/j.jsc.2004.04.011
Volume 41
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8JAEN4gXrz4NuKD9OBFk5Vu2bbpEVBEqxxUlFuzr0aIFALl6s_yD_jHnOkjaqIXkyabbHabdtrOfDOdmY-QE0cbHchYUN9W4KBoz6FSckFdVwSBUr5pGox33PW93oDfDN1hhXTKWhhMqyx0f67TM21dzDQKaTZmo1HjAVu_gzMCAAFxjIuF5k2wzljEN2x_Nd7lOckmLKa4uvyzmeV4jRdZF0OedTtl7Hfb9M3edDfJegEUrVZ-LVukYpJtslGSMFjFN7lDTq_mH-8ygSk0SAtLJNoCfQYucPoyGSnrwqKTqV6-msUuGXQvHzs9WvAfUOUEfkqVLxh3pZbccM8G3CIM4A8FoMjYMeNM-kwBoBCxcqTgHlLSeVpIbisNXgPguD1STaaJ2ScW-C0CZKRcJRxuAiZNHCPnjITzYsyjRs7KO49meZuLqMz_GkcgJqSr5BEejNUIL2UT_XhWEajhv7cd_G_bIVnLwx6Y93VEqul8aY4BCKSyTlbO31idrLbaT-Etjtdhr49jeP8c1rP34BOdM7TY
link.rule.ids 315,783,787,3515,4511,24130,27583,27938,27939,45599,45677,45693,45888
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV25TsNAEB2FpICGGxFOFzQgreI1u7ZchnAEcjQkKJ21l0Ui4kSJ82v8AD_GrA8BEjRIrlYey56VZ94bj-cBXHja6FDGggSuQoKifY9IyQThXIShUoG5Nrbe0ev77SF7GvFRBVrlvzC2rbKI_XlMz6J1sdIovNmYj8eNZzv6HckIAgSLYzhfgxqigQAZWK1589Lpfs3eZbnOJp5PrEH5cTNr85oss0GGLBt4Sunv6elbyrnfhs0CKzrN_HZ2oGKSXdgqdRic4rXcg8uHxce7THDJ5qSlIxLtYEhDFpy-TsfKuXXIdKZXb2a5D8P7u0GrTQoJBKK8MEiJCgRlXGrJDPNdhC7CIARRiIuMG1NGZUAVYgoRK08K5ltVOl8LyVylkTgglDuAajJLzCE4SF0EuklxJTxmQipNHFvZGYnXtWWPOlyVTx7N80kXUdkCNonQTVaxkkX2oLQOrPRN9GO7IozEf5sd_c_sHNbbg1436j72O8ewkVdBbBvYCVTTxcqcIi5I5Vmx75-JF7Ne
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Gr%C3%B6bner+bases+and+logarithmic+D+-modules&rft.jtitle=Journal+of+symbolic+computation&rft.au=Castro-Jim%C3%A9nez%2C+F.J.&rft.au=Ucha-Enr%C3%ADquez%2C+J.M.&rft.date=2006-03-01&rft.pub=Elsevier+Ltd&rft.issn=0747-7171&rft.eissn=1095-855X&rft.volume=41&rft.issue=3&rft.spage=317&rft.epage=335&rft_id=info:doi/10.1016%2Fj.jsc.2004.04.011&rft.externalDocID=S0747717105001355
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0747-7171&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0747-7171&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0747-7171&client=summon