GAP (Modules) - Appendix C: Overview of the Modules Package Source Code

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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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