Abstract
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.
Josep Àlvarez Montaner was partially supported by SGR2009-1284 and MTM2010-20279- C02-01.
Oscar Fernández-Ramos was partially supported by MTM2010-20279-C02-02.
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Notes
- 1.
CoCoA is still working on that.
References
J. Àlvarez Montaner, A. Leykin, Computing the support of local cohomology modules. J. Symb. Comput. 41, 1328–1344 (2006)
F. Barkats, Calcul effectif de groupes de cohomologie locale à support dans des idéaux monomiaux. Ph.D. Thesis, Univ. Nice-Sophia Antipolis, 1995
D. Grayson, M. Stillman, Macaulay2, A software system for research in algebraic geometry (2011). Available at: http://www.math.uiuc.edu/Macaulay2
A. Leykin, D-modules for Macaulay 2, in Mathematical Software: ICMS 2002 (World Scientific, Singapore, 2002), pp. 169–179
A. Leykin, M. Stillman, H. Tsai, D-modules for Macaulay 2 (2011). Available at: http://people.math.gatech.edu/~aleykin3/Dmodules
T. Oaku, N. Takayama, Algorithms for D-modules—restriction, tensor product, localization, and local cohomology groups. J. Pure Appl. Algebra 156, 267–308 (2001)
M. Velasco, Minimal free resolutions that are not supported by a CW-complex. J. Algebra 319, 102–114 (2008)
U. Walther, Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties. J. Pure Appl. Algebra 139, 303–321 (1999)
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. 281–323
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Montaner, J.À., Fernández-Ramos, O. (2013). Local Cohomology Using Macaulay2. In: Bigatti, A., Gimenez, P., Sáenz-de-Cabezón, E. (eds) Monomial Ideals, Computations and Applications. Lecture Notes in Mathematics, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38742-5_6
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