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Section: Software

AbelianSystems

Participants : Alban Quadrat [correspondent] , Mohamed Barakat [Univ. Kaiserslautern] .

The AbelianSystems package is an implementation of the algorithm developed in [63] , [72] for the computation of the purity filtration [77] , [78] in the powerful homalg package of GAP4 dedicated to constructive homological algebra methods, developed by Barakat (University of Kaiserslautern) and his collaborators (http://homalg.math.rwth-aachen.de/ ). This package supersedes the existing homalg procedure which computes purity filtrations based on the computation of spectral sequences and the PurityFiltration package which is based on the rather slow Maple Gröbner basis computation (see Section  5.6 ). Using the design of the homalg package, where the different layers such as the computational engine (which can the computer algebra systems Singular , Macaulay2 , OreModules , MAGMA , SAGE ), the module-theoretic results, and the homological ones are separated, the AbelianSystems package can be used for the computation of purity filtration of different objects in abelian categories (e.g., purity filtration of sheaf cohomology of projective varieties). This package will be soon available on the homalg website and at http://www-sop.inria.fr/members/Alban.Quadrat/AbelianSystems.html .


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