  
  [1XI Overview of the [5Xhomalg[1X Package Source Code[0X
  
  The  [5Xhomalg[0m  package  reached more than 50.000 lines of [5XGAP4[0m code (excluding
  the documentation) before the first release was made. To keep this amount of
  code tracebale, the package was split in several files.
  
  
  [1XI.1 Rings, Ring Maps, Matrices, Relations, and Generators[0X
  
        Filename [11X.gd[0m/[11X.gi[0m | Content                                  
      -------------------------------------------------------------
        [11Xhomalg[0m           | definitions of the basic [5XGAP4[0m categories 
                         | and some tool functions (e.g. [10XhomalgMode[0m)
                         |                                          
        [11XhomalgTable[0m      | dictionaries between [5Xhomalg[0m              
                         | and the computing engines                
        [11XHomalgRing[0m       | internal and external rings              
                         |                                          
        [11XHomalgRingMap[0m    | ring maps                                
                         |                                          
        [11XHomalgMatrix[0m     | internal and external matrices           
                         |                                          
        [11XHomalgRelations[0m  | a set of relations                       
        [11XSetsOfRelations[0m  | several sets of relations                
        [11XHomalgGenerators[0m | a set of generators                      
        [11XSetsOfGenerators[0m | several sets of generators               
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files[0m
  
  
  
  [1XI.2 The Basic Objects[0X
  
        Filename [11X.gd[0m/[11X.gi[0m       | Content                                      
      -----------------------------------------------------------------------
        [11XHomalgModule[0m           | modules and submodules allowing several      
                               | presentations linked with transition matrices
                               |                                              
        [11XHomalgMap[0m              | maps allowing several presentations          
                               | of their source and target                   
                               |                                              
        [11XHomalgFiltration[0m       | filtration of a module                       
                               |                                              
        [11XHomalgComplex[0m          | (co)complexes of modules or of (co)complexes 
                               |                                              
        [11XHomalgChainMap[0m         | chain maps of (co)complexes                  
                               | consisting of maps or chain maps             
                               |                                              
        [11XHomalgBicomplex[0m        | bicomplexes of modules or of (co)complexes   
                               |                                              
        [11XHomalgBigradedObject[0m   | (differential) bigraded modules              
                               |                                              
        [11XHomalgSpectralSequence[0m | homological and cohomological                
                               | spectral sequences                           
                               |                                              
        [11XHomalgFunctor[0m          | constructors of (multi) functors of          
                               | module categories (yet over the same ring),  
                               | left derivation of covariant functors,       
                               | right derivation of contravariant functors,  
                               | left satellites of covariant functors,       
                               | right satellites of contravariant functors,  
                               | and composition of functors                  
                               |                                              
        [11XHomalgDiagram[0m          | Betti diagrams                               
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files (continued)[0m
  
  
  
  [1XI.3 The Low Level Algorithms[0X
  
  In the following CAS or CASystem mean computer algebra systems.
  
        Filename [11X.gd[0m/[11X.gi[0m | Content                                              
      -------------------------------------------------------------------------
        [11XTools[0m            | the elementary matrix operations that can be         
                         | overwritten using the homalgTable                    
                         | (and hence delegable even to other CASystems)        
                         |                                                      
        [11XService[0m          | the three operations: basis, reduction, and syzygies;
                         | they can also be overwritten using the homalgTable   
                         | (and hence delegable even to other CASystems)        
                         |                                                      
        [11XBasic[0m            | higher level operations for matrices                 
                         | (cannot be overwritten using the homalgTable)        
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files (continued)[0m
  
  
  
  [1XI.4 The High Level Algorithms[0X
  
        Filename [11X.gd[0m/[11X.gi[0m  | Content                                         
      ---------------------------------------------------------------------
        [11XModules[0m           | subfactors, resolutions, syzygy modules,        
                          | parameterizations, intersections, annihilators  
                          |                                                 
        [11XMaps[0m              | resolutions, (co)kernel sequences               
                          |                                                 
        [11XComplexes[0m         | (co)homology, horse shoe lemma, connecting      
                          | homomorphisms, Cartan-Eilenberg resolution      
                          |                                                 
        [11XChainMaps[0m         | (co)homology                                    
                          |                                                 
        [11XSpectralSequences[0m | Grothendieck bicomplexes associated to two      
                          | composable functors, spectral sequences         
                          | of bicomplexes, Grothendieck spectral sequences 
        [11XFiltrations[0m       | spectral filtrations, i.e. filtrations induced  
                          | by spectral sequences of bicomplexes,           
                          | purity filtration                               
                          |                                                 
        [11XToolFunctors[0m      | composition, addition, substraction,            
                          | stacking, augmentation, and post dividing maps  
        [11XBasicFunctors[0m     | cokernel, image, kernel, tensor product, Hom,   
                          | Ext, Tor, RHom, LTensorProduct, HomHom, LHomHom,
                          | BaseChange (preliminary)                        
        [11XOtherFunctors[0m     | torsion submodule, torsion free factor,         
                          | direct sum, pullback, pushout, Auslander dual   
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files (continued)[0m
  
  
  
  [1XI.5 Logical Implications for [5Xhomalg[1X Objects[0X
  
        Filename [11X.gd[0m/[11X.gi[0m | Content                                      
      -----------------------------------------------------------------
        [11XLIRNG[0m            | logical implications for rings               
                         |                                              
        [11XLIMAP[0m            | logical implications for ring maps           
                         |                                              
        [11XLIMAT[0m            | logical implications for matrices            
                         |                                              
        [11XCOLEM[0m            | clever operations for lazy evaluated matrices
                         |                                              
        [11XLIMOD[0m            | logical implications for modules             
                         |                                              
        [11XLIMOR[0m            | logical implications for morphisms           
                         |                                              
        [11XLICPX[0m            | logical implications for complexes           
                         |                                              
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files (continued)[0m
  
  
  
  [1XI.6 The subpackage [5XResidueClassRingForHomalg[1X[0X
  
        Filename [11X.gd[0m/[11X.gi[0m          | Content                                             
      ---------------------------------------------------------------------------------
        [11XResidueClassRingForHomalg[0m | some global variables                               
                                  |                                                     
        [11XResidueClassRing[0m          | residue class rings, their elements, and matrices,  
                                  | together with their constructors and operations     
                                  |                                                     
        [11XResidueClassRingTools[0m     | the elementary matrix operations for matrices       
                                  | over residue class rings                            
                                  |                                                     
        [11XResidueClassRingBasic[0m     | the three operations: basis, reduction, and syzygies
                                  | for matrices over residue class rings               
                                  |                                                     
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files (continued)[0m
  
  
  
  [1XI.7 The homalgTable for [5XGAP4[1X built-in rings[0X
  
  For  the  purposes of [5Xhomalg[0m, the ring of integers is, at least up till now,
  the  only  ring  which  is  properly  supported  in  [5XGAP4[0m. The [5XGAP4[0m built-in
  cababilities  for  polynomial rings (also univariate) and group rings do not
  statisfy  the minimum requirements of [5Xhomalg[0m. The [5XGAP4[0m package [5XGauss[0m enables
  [5XGAP[0m to fullfil the [5Xhomalg[0m requirements for prime fields, and ℤ / p^n.
  
        Filename .gi | Content                                 
      --------------------------------------------------------
        [11XIntegers[0m     | the homalgTable for the ring of integers
  
       [1XTable:[0X [13XThe [5Xhomalg[0m[13X package files (continued)[0m
  
  
