Section: Software

AbelianSystems

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

The AbelianSystems package is an implementation of an algorithm developed in [97] , [77] , [76] for the computation of the purity/grade filtration [102] , [103] in the powerful homalg package of GAP 4 dedicated to constructive homological algebra methods, and developed by Barakat (University of Kaiserslautern) and his collaborators (http://homalg.math.rwth-aachen.de/ ). This package both supersedes the existing PurityFiltration package which uses the non-efficient Maple Gröbner basis computation (see Section  5.7 ), and the original homalg procedure which computes purity filtration by means of time-consuming spectral sequences. Using the homalg package philosophy, the AbelianSystems package can be used for the computation of the purity filtration of objects in different constructive abelian categories such as sheaves over projective varieties as demonstrated in the homag package called Sheaves (see http://homalg.math.rwth-aachen.de/ ).