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2013 | OriginalPaper | Chapter

Local Cohomology Using Macaulay2

Authors : Josep Àlvarez Montaner, Oscar Fernández-Ramos

Published in: Monomial Ideals, Computations and Applications

Publisher: Springer Berlin Heidelberg

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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.

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previous chapter Local Cohomology Modules Supported on Monomial Ideals
Footnotes
1
CoCoA is still working on that.
 
Literature
9.
J. Àlvarez Montaner, A. Leykin, Computing the support of local cohomology modules. J. Symb. Comput. 41, 1328–1344 (2006)MATHCrossRef
15.
F. Barkats, Calcul effectif de groupes de cohomologie locale à support dans des idéaux monomiaux. Ph.D. Thesis, Univ. Nice-Sophia Antipolis, 1995
80.
126.
A. Leykin, D-modules for Macaulay 2, in Mathematical Software: ICMS 2002 (World Scientific, Singapore, 2002), pp. 169–179
127.
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)MathSciNetMATHCrossRef
191.
194.
U. Walther, Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties. J. Pure Appl. Algebra 139, 303–321 (1999)MathSciNetMATHCrossRef
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. 281–323
Metadata
Title
Local Cohomology Using Macaulay2
Authors
Josep Àlvarez Montaner
Oscar Fernández-Ramos
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Monomial Ideals, Computations and Applications

Print ISBN: 978-3-642-38741-8

Electronic ISBN: 978-3-642-38742-5

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-38742-5_6

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