  
  [1XD [33X[0;0YDebugging [5Xhomalg[105X[101X[1X[133X[101X
  
  [33X[0;0YBeside  the  [5XGAP[105X builtin debugging facilities (--> [14X'Reference: Debugging and
  Profiling Facilities'[114X) [5Xhomalg[105X provides two ways to debug the computations.[133X
  
  
  [1XD.1 [33X[0;0YIncrease the assertion level[133X[101X
  
  [33X[0;0Y[5Xhomalg[105X  comes  with numerous builtin assertion checks. They are activated if
  the user increases the assertion level using[133X
  [33X[0;0Y[10XSetAssertionLevel[110X( [3Xlevel[103X );[133X
  [33X[0;0Y(--> [14X'Reference: AssertionLevel'[114X), where [3Xlevel[103X is one of the values below:[133X
  
        [3Xlevel[103X │ description                                                                                              
        ──────┼───────────────────────────────────────────────────────────────────────────────────────────────────────  
              │                                                                                                          
        0     │ no assertion checks whatsoever                                                                           
              │                                                                                                          
        3     │ [21Xhigh[121X-level homological assertions are checked                                                          
              │                                                                                                          
        4     │ [21Xmid[121X-level homological assertions are checked                                                           
              │                                                                                                          
        5     │ [21Xlow[121X-level homological assertions are checked                                                           
              │                                                                                                          
        6     │ assertions about basic matrix operations are checked (--> Appendices of the [5XMatricesForHomalg[105X package)   
              │ (these are among the operations often delegated to external systems)                                     
              │                                                                                                          
        ──────┴───────────────────────────────────────────────────────────────────────────────────────────────────────  
  
  [33X[0;0YIn  particular,  if [5Xhomalg[105X delegates matrix operations to an external system
  then  [10XSetAssertionLevel[110X(  4  ); can be used to let [5Xhomalg[105X debug the external
  system.[133X
  
