  
  
                                [1X ToolsForHomalg [101X
  
  
               [1X Special methods and knowledge propagation tools [101X
  
  
                                   2025.05-01
  
  
                                   2 May 2025
  
  
                                Mohamed Barakat
  
                               Sebastian Gutsche
  
                             Markus Lange-Hegermann
  
  
  
  Mohamed Barakat
      Email:    [7Xmailto:mohamed.barakat@uni-siegen.de[107X
      Homepage: [7Xhttps://mohamed-barakat.github.io[107X
      Address:  [33X[0;14YWalter-Flex-Str. 3[133X
                [33X[0;14Y57072 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttps://sebasguts.github.io[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57072 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Markus Lange-Hegermann
      Email:    [7Xmailto:markus.lange.hegermann@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/~markus/[107X
      Address:  [33X[0;14YMarkus Lange-Hegermann[133X
                [33X[0;14YLehrstuhl B fuer Mathematik, RWTH Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (ToolsForHomalg)[101X
  
  1 [33X[0;0YCaches[133X
    1.1 [33X[0;0YObject constructors[133X
      1.1-1 CachingObject
      1.1-2 CachingObject
    1.2 [33X[0;0YSetters, getters[133X
      1.2-1 CacheValue
      1.2-2 SetCacheValue
      1.2-3 IsEqualForCache
    1.3 [33X[0;0YManaging functions[133X
      1.3-1 SetCachingObjectCrisp
      1.3-2 SetCachingObjectWeak
      1.3-3 DeactivateCachingObject
    1.4 [33X[0;0YInstall functions[133X
      1.4-1 InstallMethodWithCache
      1.4-2 InstallMethodWithCrispCache
      1.4-3 InstallMethodWithCacheFromObject
      1.4-4 FunctionWithCache
  2 [33X[0;0YLazy arrays[133X
    2.1 [33X[0;0YGAP categories[133X
      2.1-1 IsLazyArray
    2.2 [33X[0;0YConstructors[133X
      2.2-1 LazyArrayWithValues
  3 [33X[0;0YLazy homogeneous lists[133X
    3.1 [33X[0;0YGAP categories[133X
      3.1-1 IsLazyHList
    3.2 [33X[0;0YConstructors[133X
      3.2-1 LazyHList
  4 [33X[0;0YLists with attributes[133X
    4.1 [33X[0;0YGAP categories[133X
      4.1-1 IsListWithAttributes
    4.2 [33X[0;0YConstructors[133X
      4.2-1 TypedListWithAttributes
      4.2-2 ListWithAttributes
  5 [33X[0;0YToDo-list[133X
    5.1 [33X[0;0YBlueprints[133X
      5.1-1 ToDoListEntryToMaintainEqualAttributes
      5.1-2 ToDoListEntryToMaintainFollowingAttributes
      5.1-3 ToDoListEntry
      5.1-4 ToDoList_this_object
      5.1-5 ToDoListEntryToMaintainEqualAttributesBlueprint
      5.1-6 ToDoListEntryToMaintainFollowingAttributesBlueprint
      5.1-7 ToDoListEntryBlueprint
    5.2 [33X[0;0YToDo-list entries[133X
      5.2-1 AddToToDoList
      5.2-2 SourcePart
      5.2-3 TargetPart
      5.2-4 ProcessAToDoListEntry
      5.2-5 ToDoListEntry
      5.2-6 ToDoListEntry
      5.2-7 SetTargetValueObject
      5.2-8 SetTargetObject
      5.2-9 ToDoListEntryWithContraposition
      5.2-10 DescriptionOfImplication
      5.2-11 ToDoListEntryForEqualAttributes
      5.2-12 ToDoListEntryForEquivalentAttributes
    5.3 [33X[0;0YCategory[133X
      5.3-1 IsToDoList
    5.4 [33X[0;0YConstructor[133X
      5.4-1 NewToDoList
    5.5 [33X[0;0YThis is the magic[133X
      5.5-1 Process_A_ToDo_List_Entry
      5.5-2 ProcessToDoList
    5.6 [33X[0;0YMethods for all objects[133X
      5.6-1 ToDoList
    5.7 [33X[0;0YProof tracking[133X
      5.7-1 TraceProof
    5.8 [33X[0;0YMaintainance[133X
      5.8-1 ActivateToDoList
      5.8-2 ActivateToDoList
      5.8-3 DeactivateToDoList
      5.8-4 DeactivateToDoList
      5.8-5 ActivateWhereInfosInEntries
      5.8-6 DeactivateWhereInfosInEntries
  6 [33X[0;0YBasics[133X
    6.1 [33X[0;0YGlobal variables[133X
      6.1-1 HOMALG_TOOLS
    6.2 [33X[0;0YGAP Categories[133X
      6.2-1 IsStructureObjectOrObjectOrMorphism
      6.2-2 IsStructureObjectOrObject
      6.2-3 IsStructureObject
      6.2-4 IsStructureObjectMorphism
      6.2-5 IsHomalgRingOrModule
    6.3 [33X[0;0YAttributes[133X
      6.3-1 RingFilter
      6.3-2 RingElementFilter
  7 [33X[0;0YPointers[133X
    7.1 [33X[0;0YWeak pointer objects[133X
      7.1-1 IsContainerForWeakPointers
      7.1-2 ContainerForWeakPointers
      7.1-3 UpdateContainerOfWeakPointers
      7.1-4 _AddElmWPObj_ForHomalg
      7.1-5 _AddTwoElmWPObj_ForHomalg
      7.1-6 _ElmWPObj_ForHomalg
    7.2 [33X[0;0YPointer objects[133X
      7.2-1 IsContainerForPointers
      7.2-2 ContainerForPointers
      7.2-3 UpdateContainerOfPointers
      7.2-4 _AddElmPObj_ForHomalg
      7.2-5 _AddTwoElmPObj_ForHomalg
      7.2-6 _ElmPObj_ForHomalg
  8 [33X[0;0YTools[133X
    8.1 [33X[0;0YFunctions[133X
      8.1-1 homalgTotalRuntimes
      8.1-2 AddLeftRightLogicalImplicationsForHomalg
      8.1-3 LogicalImplicationsForOneHomalgObject
      8.1-4 LogicalImplicationsForTwoHomalgBasicObjects
      8.1-5 InstallLogicalImplicationsForHomalgBasicObjects
      8.1-6 LeftRightAttributesForHomalg
      8.1-7 InstallLeftRightAttributesForHomalg
      8.1-8 MatchPropertiesAndAttributes
      8.1-9 InstallImmediateMethodToPullPropertyOrAttribute
      8.1-10 InstallImmediateMethodToConditionallyPullPropertyOrAttribute
      8.1-11 InstallImmediateMethodToPullPropertyOrAttributeWithDifferentName
      8.1-12 InstallImmediateMethodToPullPropertiesOrAttributes
      8.1-13 InstallImmediateMethodToPullTrueProperty
      8.1-14 InstallImmediateMethodToConditionallyPullTrueProperty
      8.1-15 InstallImmediateMethodToPullTruePropertyWithDifferentName
      8.1-16 InstallImmediateMethodToPullTrueProperties
      8.1-17 InstallImmediateMethodToPullFalseProperty
      8.1-18 InstallImmediateMethodToConditionallyPullFalseProperty
      8.1-19 InstallImmediateMethodToPullFalsePropertyWithDifferentName
      8.1-20 InstallImmediateMethodToPullFalseProperties
      8.1-21 InstallImmediateMethodToPushPropertyOrAttribute
      8.1-22 InstallImmediateMethodToConditionallyPushPropertyOrAttribute
      8.1-23 InstallImmediateMethodToPushPropertyOrAttributeWithDifferentName
      8.1-24 InstallImmediateMethodToPushPropertiesOrAttributes
      8.1-25 InstallImmediateMethodToPushTrueProperty
      8.1-26 InstallImmediateMethodToPushTruePropertyWithDifferentName
      8.1-27 InstallImmediateMethodToPushTrueProperties
      8.1-28 InstallImmediateMethodToPushFalseProperty
      8.1-29 InstallImmediateMethodToPushFalsePropertyWithDifferentName
      8.1-30 InstallImmediateMethodToPushFalseProperties
      8.1-31 DeclareAttributeWithCustomGetter
      8.1-32 AppendToAhomalgTable
      8.1-33 homalgNamesOfComponentsToIntLists
      8.1-34 IncreaseExistingCounterInObject
      8.1-35 IncreaseExistingCounterInObjectWithTiming
      8.1-36 IncreaseCounterInObject
      8.1-37 MemoryToString
      8.1-38 PrimePowerExponent
      8.1-39 ViewList
      8.1-40 homalgLaTeX
      8.1-41 IdenticalPosition
      8.1-42 PositionsOfMaximalObjects
      8.1-43 MaximalObjects
      8.1-44 CollectEntries
      8.1-45 MakeShowable
      8.1-46 MakeShowableWithLaTeX
      8.1-47 ReplacedStringViaRecord
      8.1-48 StartTimer
      8.1-49 StopTimer
      8.1-50 ResetTimer
      8.1-51 DisplayTimer
      8.1-52 ListImpliedFilters
      8.1-53 Breakpoint
      8.1-54 ReadPackageOnce
    8.2 [33X[0;0YExample functions[133X
      8.2-1 ExamplesForHomalg
      8.2-2 ExamplesForHomalg
  9 [33X[0;0YTrees[133X
    9.1 [33X[0;0YTrees[133X
      9.1-1 IsTree
      9.1-2 Content
      9.1-3 ListOfSuccessors
      9.1-4 Predecessor
      9.1-5 ListOfSentinels
      9.1-6 RemoveHead
      9.1-7 Tree
      9.1-8 Tree
      9.1-9 Add
      9.1-10 ContentListFromSentinelToHead
      9.1-11 PostOrder
  10 [33X[0;0YZ-functions[133X
    10.1 [33X[0;0YGap categories for Z functions[133X
      10.1-1 IsZFunction
      10.1-2 IsZFunctionWithInductiveSides
    10.2 [33X[0;0YCreating Z-functions[133X
      10.2-1 VoidZFunction
      10.2-2 AsZFunction
      10.2-3 UnderlyingFunction
      10.2-4 ZFunctionValue
      10.2-5 \[\]
      10.2-6 ZFunctionWithInductiveSides
      10.2-7 UpperFunction
      10.2-8 StableUpperValue
      10.2-9 IndexOfStableUpperValue
      10.2-10 SetStableUpperValue
      10.2-11 StableLowerValue
      10.2-12 IndexOfStableLowerValue
      10.2-13 SetStableLowerValue
      10.2-14 Reflection
      10.2-15 ApplyShift
      10.2-16 ApplyMap
      10.2-17 ApplyMap
      10.2-18 BaseZFunctions
      10.2-19 AppliedMap
      10.2-20 CombineZFunctions
      10.2-21 Replace
  
  
  [32X
