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C Overview of the Modules Package Source Code
 C.1 Relations and Generators
 C.2 The Basic Objects
 C.3 The High Level Homological Algorithms
 C.4 Logical Implications for homalg Objects

C Overview of the Modules Package Source Code

C.1 Relations and Generators

Table: The homalg package files
Filename .gd/.gi Content
HomalgRingMap operations and methods ring maps
HomalgRelations a set of relations
SetsOfRelations several sets of relations
HomalgGenerators a set of generators
SetsOfGenerators several sets of generators

 


C.2 The Basic Objects

Table: The homalg package files (continued)
Filename .gd/.gi Content
HomalgModule modules allowing several presentations
linked with transition matrices
HomalgSubmodule submodules allowing several sets of generators
HomalgMap maps allowing several presentations
of their source and target
HomalgFiltration filtration of a module
HomalgComplex (co)complexes of modules or of (co)complexes
HomalgChainMap chain maps of (co)complexes
consisting of maps or chain maps
HomalgBicomplex bicomplexes of modules or of (co)complexes
HomalgBigradedObject (differential) bigraded modules
HomalgSpectralSequence homological and cohomological
spectral sequences
HomalgDiagram Betti diagrams

 


C.3 The High Level Homological Algorithms

Table: The homalg package files (continued)
Filename .gd/.gi Content
Modules subfactors, resolutions,
parameterizations, intersections, annihilators
ToolFunctors zero map, composition, addition, substraction,
stacking, augmentation, and post dividing maps
BasicFunctors cokernel, image, kernel, tensor product, Hom,
Ext, Tor, RHom, LTensorProduct, HomHom, LHomHom,
BaseChange (preliminary)
OtherFunctors direct sum

 


C.4 Logical Implications for homalg Objects

Table: The homalg package files (continued)
Filename .gd/.gi Content
LIMOD logical implications for modules
LIHOM logical implications for module homomorphisms

 


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