  
  [1XF Overview of the [5XMatricesForHomalg[1X Package Source Code[0X
  
  
  [1XF.1 Rings, Ring Maps, Matrices, Ring Relations[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 [5XMatricesForHomalg[0m   
                            | and the computing engines                
        [11XHomalgRing[0m          | internal and external rings              
                            |                                          
        [11XHomalgRingMap[0m       | ring maps                                
                            |                                          
        [11XHomalgMatrix[0m        | internal and external matrices           
                            |                                          
        [11XHomalgRingRelations[0m | a set of ring relations                  
  
       [1XTable:[0X [13XThe [5XMatricesForHomalg[0m[13X package files[0m
  
  
  
  [1XF.2 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 [5XMatricesForHomalg[0m[13X package files (continued)[0m
  
  
  
  [1XF.3 Logical Implications for [5XMatricesForHomalg[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
                         |                                              
  
       [1XTable:[0X [13XThe [5XMatricesForHomalg[0m[13X package files (continued)[0m
  
  
  
  [1XF.4 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 [5XMatricesForHomalg[0m[13X package files (continued)[0m
  
  
  
  [1XF.5 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 [5XMatricesForHomalg[0m[13X package files (continued)[0m
  
  
