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ToolsForHomalg

Special methods and knowledge propagation tools

2025.05-01

2 May 2025

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io
Address:
Walter-Flex-Str. 3
57072 Siegen
Germany

Sebastian Gutsche
Email: gutsche@mathematik.uni-siegen.de
Homepage: https://sebasguts.github.io
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57072 Siegen
Germany

Markus Lange-Hegermann
Email: markus.lange.hegermann@rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~markus/
Address:
Markus Lange-Hegermann
Lehrstuhl B fuer Mathematik, RWTH Aachen
Templergraben 64
52062 Aachen
Germany

Contents

1 Caches
 1.1 Object constructors

  1.1-1 CachingObject
  1.1-2 CachingObject
 1.2 Setters, getters

  1.2-1 CacheValue
  1.2-2 SetCacheValue
  1.2-3 IsEqualForCache
 1.3 Managing functions

  1.3-1 SetCachingObjectCrisp
  1.3-2 SetCachingObjectWeak
  1.3-3 DeactivateCachingObject
 1.4 Install functions

  1.4-1 InstallMethodWithCache
  1.4-2 InstallMethodWithCrispCache
  1.4-3 InstallMethodWithCacheFromObject
  1.4-4 FunctionWithCache
2 Lazy arrays
 2.1 GAP categories

  2.1-1 IsLazyArray
 2.2 Constructors

  2.2-1 LazyArrayWithValues
3 Lazy homogeneous lists
 3.1 GAP categories

  3.1-1 IsLazyHList
 3.2 Constructors

  3.2-1 LazyHList
4 Lists with attributes
 4.1 GAP categories

  4.1-1 IsListWithAttributes
 4.2 Constructors

  4.2-1 TypedListWithAttributes
  4.2-2 ListWithAttributes
5 ToDo-list
 5.1 Blueprints

  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 ToDo-list entries

  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 Category

  5.3-1 IsToDoList
 5.4 Constructor

  5.4-1 NewToDoList
 5.5 This is the magic

  5.5-1 Process_A_ToDo_List_Entry
  5.5-2 ProcessToDoList
 5.6 Methods for all objects

  5.6-1 ToDoList
 5.7 Proof tracking

  5.7-1 TraceProof
 5.8 Maintainance

  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 Basics
 6.1 Global variables

  6.1-1 HOMALG_TOOLS
 6.2 GAP Categories

  6.2-1 IsStructureObjectOrObjectOrMorphism
  6.2-2 IsStructureObjectOrObject
  6.2-3 IsStructureObject
  6.2-4 IsStructureObjectMorphism
  6.2-5 IsHomalgRingOrModule
 6.3 Attributes

  6.3-1 RingFilter
  6.3-2 RingElementFilter
7 Pointers
 7.1 Weak pointer objects

  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 Pointer objects

  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 Tools
 8.1 Functions

  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 Example functions

  8.2-1 ExamplesForHomalg
  8.2-2 ExamplesForHomalg
9 Trees
 9.1 Trees

  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 Z-functions
 10.1 Gap categories for Z functions

  10.1-1 IsZFunction
  10.1-2 IsZFunctionWithInductiveSides
 10.2 Creating Z-functions

  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
Index

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