Local Cohomology Using Macaulay2

  • Josep Àlvarez MontanerEmail author
  • Oscar Fernández-Ramos
Part of the Lecture Notes in Mathematics book series (LNM, volume 2083)


Over the last 20 years there were many advances made in the computational theory of D-modules. Nowadays, the most common computer algebra systems such as Macaulay2 or Singular have important available packages for working with D-modules. In particular, the package D-modules [127] for Macaulay 2 [80] developed by A. Leykin and H. Tsai contains an implementation of the algorithms given by U. Walther [194] and T. Oaku and N.


Simplicial Complex Polynomial Ring Betti Number Computational Theory Monomial Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 9.
    J. Àlvarez Montaner, A. Leykin, Computing the support of local cohomology modules. J. Symb. Comput. 41, 1328–1344 (2006)zbMATHCrossRefGoogle Scholar
  2. 15.
    F. Barkats, Calcul effectif de groupes de cohomologie locale à support dans des idéaux monomiaux. Ph.D. Thesis, Univ. Nice-Sophia Antipolis, 1995Google Scholar
  3. 80.
    D. Grayson, M. Stillman, Macaulay2, A software system for research in algebraic geometry (2011). Available at:
  4. 126.
    A. Leykin, D-modules for Macaulay 2, in Mathematical Software: ICMS 2002 (World Scientific, Singapore, 2002), pp. 169–179Google Scholar
  5. 127.
    A. Leykin, M. Stillman, H. Tsai, D-modules for Macaulay 2 (2011). Available at:
  6. 153.
    T. Oaku, N. Takayama, Algorithms for D-modules—restriction, tensor product, localization, and local cohomology groups. J. Pure Appl. Algebra 156, 267–308 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 191.
    M. Velasco, Minimal free resolutions that are not supported by a CW-complex. J. Algebra 319, 102–114 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 194.
    U. Walther, Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties. J. Pure Appl. Algebra 139, 303–321 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 195.
    U. Walther, D-modules and cohomology of varieties, in Computations in Algebraic Geometry with Macaulay 2. Algorithms and Computations in Mathematics, vol. 8 (Springer, Berlin, 2002), pp. 281–323Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Josep Àlvarez Montaner
    • 1
    Email author
  • Oscar Fernández-Ramos
    • 2
  1. 1.Departamento de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Dipartimento di MatematicaUniversità degli Studi di GenovaGenovaItaly

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