  
  [1X3 [33X[0;0YCaches[133X[101X
  
  
  [1X3.1 [33X[0;0YObject constructors[133X[101X
  
  [33X[0;0YCaches  are  objects which store for a fixed number of keys a value, so they
  are  a  map  Obj^k -> Obj, while the k is fixed. A cache ususally stores the
  result in a weak pointer list, which means that if the value which the cache
  should  store  is  not  referenced  in  the  system  anymore, it will not be
  remembered  by  the  cache.  However,  caches  can be set to store the value
  permanently  (crisp),  or  not  to store any new value at all (inaktive). In
  that  case, already stored values are still in the cache and can be accessed
  once the cache is set active again.[133X
  
  [1X3.1-1 CachingObject[101X
  
  [29X[2XCachingObject[102X( [[3Xk[103X, ][[3Xis_crisp[103X] ) [32X operation
  [29X[2XCachingObject[102X( [3Xarg[103X ) [32X operation
  [29X[2XCachingObject[102X( [3Xarg1[103X, [3Xarg2[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ya cache[133X
  
  [33X[0;0YIf  no  argument is given, the function returns a weak cache with key length
  one,  if  an  integer k is given, a weak cache with key length k, and if the
  bool is_crisp is true, a crisp cache with the corresponding length.[133X
  
  [1X3.1-2 CachingObject[101X
  
  [29X[2XCachingObject[102X( [3Xobject[103X, [3Xcache_name[103X, [3Xlength[103X[, [3Xis_crisp[103X] ) [32X operation
  [29X[2XCachingObject[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X, [3Xarg4[103X ) [32X operation
  
  [33X[0;0YThis   methods   are   not   installed,  they  serve  as  an  interface  for
  InstallMethodWithCacheFromObject.[133X
  
  
  [1X3.2 [33X[0;0YSetters, getters[133X[101X
  
  [1X3.2-1 CacheValue[101X
  
  [29X[2XCacheValue[102X( [3Xcache[103X, [3Xkey[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ystored value[133X
  
  [33X[0;0YIf  there  is a value stored in the cache for key, which can be a single key
  for caches with key length one or a list of keys depending on the key length
  of the cache, this method returns the value, otherwise SuPeRfail.[133X
  
  [1X3.2-2 SetCacheValue[101X
  
  [29X[2XSetCacheValue[102X( [3Xcache[103X, [3Xkey[103X, [3Xvalue[103X ) [32X operation
  
  [33X[0;0YSets the value of key of the cache to value.[133X
  
  [1X3.2-3 IsEqualForCache[101X
  
  [29X[2XIsEqualForCache[102X( [3Xobj1[103X, [3Xobj2[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ytrue or false[133X
  
  [33X[0;0YThis function is used to compare objects for the caches. The standard way is
  IsIdenticalObj,  and  lists are compared recursive with this function. It is
  possible and recommended to overload this function as needed.[133X
  
  
  [1X3.3 [33X[0;0YManaging functions[133X[101X
  
  [1X3.3-1 SetCachingObjectCrisp[101X
  
  [29X[2XSetCachingObjectCrisp[102X( [3Xcache[103X ) [32X function
  [29X[2XSetCachingObjectWeak[102X( [3Xarg[103X ) [32X function
  [29X[2XDeactivateCachingObject[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallMethodWithCache[102X( [3XLike[103X, [3XInstallMethod[103X ) [32X function
  [29X[2XInstallMethodWithCrispCache[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallMethodWithCacheFromObject[102X( [3XLike[103X, [3XInstallMethod[103X ) [32X function
  [29X[2XFunctionWithCache[102X( [3Xfunc[103X ) [32X function
  [29X[2XToDoListEntryToMaintainEqualAttributes[102X( [3Xindicator[103X, [3Xobjects[103X, [3Xattributes[103X ) [32X operation
  [29X[2XToDoListEntryToMaintainFollowingAttributes[102X( [3Xindicator[103X, [3Xobjects[103X, [3Xattributes[103X ) [32X operation
  [29X[2XToDoListEntry[102X( [3Xsource[103X, [3Xtarget_list[103X ) [32X operation
  [29X[2XToDoList_this_object[102X[32X global variable
  [29X[2XToDoListEntryToMaintainEqualAttributesBlueprint[102X( [3Xfilter[103X, [3Xindicator[103X, [3Xobjects[103X, [3Xattributes[103X ) [32X operation
  [29X[2XToDoListEntryToMaintainFollowingAttributesBlueprint[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X, [3Xarg4[103X ) [32X operation
  [29X[2XToDoListEntryBlueprint[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X ) [32X operation
  [29X[2XAddToToDoList[102X( [3XE[103X ) [32X operation
  [29X[2XSourcePart[102X( [3Xentry[103X ) [32X operation
  [29X[2XTargetPart[102X( [3Xentry[103X ) [32X operation
  [29X[2XProcessAToDoListEntry[102X( [3Xarg[103X ) [32X operation
  [29X[2XToDoListEntry[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X, [3Xarg4[103X ) [32X operation
  [29X[2XToDoListEntry[102X( [3Xarg1[103X, [3Xarg2[103X ) [32X operation
  [29X[2XSetTargetValueObject[102X( [3Xentry[103X, [3Xvalue[103X ) [32X operation
  [29X[2XSetTargetObject[102X( [3Xentry[103X, [3Xobj[103X ) [32X operation
  [29X[2XToDoListEntryWithContraposition[102X( [3Xsobj[103X, [3Xsource_prop[103X, [3Xsval[103X, [3Xtobj[103X, [3Xtarget[103X, [3Xtval[103X ) [32X operation
  [29X[2XDescriptionOfImplication[102X( [3Xarg[103X ) [32X attribute
  [29X[2XToDoListEntryForEqualAttributes[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X, [3Xarg4[103X ) [32X operation
  [29X[2XToDoListEntryForEquivalentAttributes[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X, [3Xarg4[103X, [3Xarg5[103X, [3Xarg6[103X ) [32X operation
  [29X[2XIsToDoList[102X( [3Xarg[103X ) [32X filter
  [29X[2XNewToDoList[102X( [3Xarg[103X ) [32X operation
  [29X[2XProcess_A_ToDo_List_Entry[102X( [3Xarg[103X ) [32X function
  [29X[2XToDoList[102X( [3Xarg[103X ) [32X attribute
  [29X[2XProcessToDoList[102X( [3XA[103X ) [32X attribute
  [29X[2XTraceProof[102X( [3Xobj[103X, [3Xname[103X, [3Xval[103X ) [32X operation
  [29X[2XActivateToDoList[102X( [3Xarg[103X ) [32X operation
  [29X[2XActivateToDoList[102X( [3Xarg[103X ) [32X operation
  [29X[2XDeactivateToDoList[102X( [3Xarg[103X ) [32X operation
  [29X[2XDeactivateToDoList[102X( [3Xarg[103X ) [32X operation
  [29X[2XActivateWhereInfosInEntries[102X( [3Xarg[103X ) [32X function
  [29X[2XDeactivateWhereInfosInEntries[102X( [3Xarg[103X ) [32X function
  [29X[2XHOMALG_TOOLS[102X[32X global variable
  [29X[2XIsStructureObjectOrObjectOrMorphism[102X( [3Xarg[103X ) [32X filter
  [29X[2XIsStructureObjectOrObject[102X( [3Xarg[103X ) [32X filter
  [29X[2XIsStructureObject[102X( [3Xarg[103X ) [32X filter
  [29X[2XIsStructureObjectMorphism[102X( [3Xarg[103X ) [32X filter
  [29X[2XIsHomalgRingOrModule[102X( [3Xarg[103X ) [32X filter
  [29X[2XIsContainerForWeakPointers[102X( [3Xarg[103X ) [32X filter
  [29X[2XIsContainerForPointers[102X( [3Xarg[103X ) [32X filter
  [29X[2XContainerForWeakPointers[102X( [3Xarg[103X ) [32X function
  [29X[2XhomalgTotalRuntimes[102X( [3Xarg[103X ) [32X function
  [29X[2XAddLeftRightLogicalImplicationsForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2XLogicalImplicationsForOneHomalgObject[102X( [3Xarg[103X ) [32X function
  [29X[2XLogicalImplicationsForTwoHomalgBasicObjects[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallLogicalImplicationsForHomalgBasicObjects[102X( [3Xarg[103X ) [32X function
  [29X[2XLeftRightAttributesForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallLeftRightAttributesForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2XMatchPropertiesAndAttributes[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullPropertyOrAttribute[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToConditionallyPullPropertyOrAttribute[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullPropertyOrAttributeWithDifferentName[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullPropertiesOrAttributes[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullTrueProperty[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToConditionallyPullTrueProperty[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullTruePropertyWithDifferentName[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullTrueProperties[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullFalseProperty[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToConditionallyPullFalseProperty[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullFalsePropertyWithDifferentName[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPullFalseProperties[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushPropertyOrAttribute[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToConditionallyPushPropertyOrAttribute[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushPropertyOrAttributeWithDifferentName[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushPropertiesOrAttributes[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushTrueProperty[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushTruePropertyWithDifferentName[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushTrueProperties[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushFalseProperty[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushFalsePropertyWithDifferentName[102X( [3Xarg[103X ) [32X function
  [29X[2XInstallImmediateMethodToPushFalseProperties[102X( [3Xarg[103X ) [32X function
  [29X[2XDeclareAttributeWithCustomGetter[102X( [3Xarg[103X ) [32X function
  [29X[2XAppendToAhomalgTable[102X( [3Xarg[103X ) [32X function
  [29X[2XhomalgNamesOfComponentsToIntLists[102X( [3Xarg[103X ) [32X function
  [29X[2XIncreaseExistingCounterInObject[102X( [3Xarg[103X ) [32X function
  [29X[2XIncreaseExistingCounterInObjectWithTiming[102X( [3Xarg[103X ) [32X function
  [29X[2XIncreaseCounterInObject[102X( [3Xarg[103X ) [32X function
  [29X[2XMemoryToString[102X( [3Xarg[103X ) [32X function
  [29X[2XPrimePowerExponent[102X( [3Xn[103X, [3Xp[103X ) [32X function
  [29X[2XViewList[102X( [3XL[103X ) [32X operation
  [29X[2XhomalgLaTeX[102X( [3Xarg[103X ) [32X operation
  [29X[2XExamplesForHomalg[102X( [3Xarg[103X ) [32X operation
  [29X[2XExamplesForHomalg[102X( [3Xarg[103X ) [32X operation
  [29X[2XUpdateContainerOfWeakPointers[102X( [3Xarg[103X ) [32X operation
  [29X[2X_AddElmWPObj_ForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2X_AddTwoElmWPObj_ForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2X_ElmWPObj_ForHomalg[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X ) [32X operation
  [29X[2XContainerForPointers[102X( [3Xarg[103X ) [32X function
  [29X[2XUpdateContainerOfPointers[102X( [3Xarg[103X ) [32X operation
  [29X[2X_AddElmPObj_ForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2X_AddTwoElmPObj_ForHomalg[102X( [3Xarg[103X ) [32X function
  [29X[2X_ElmPObj_ForHomalg[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X ) [32X operation
  [29X[2XTOOLS_FOR_HOMALG_GET_REAL_TIME_OF_FUNCTION_CALL[102X( [3Xfunction[103X, [3Xargs[103X ) [32X function
  [29X[2XIsTree[102X( [3Xarg[103X ) [32X filter
  [29X[2XContent[102X( [3Xarg[103X ) [32X attribute
  [29X[2XListOfSuccessors[102X( [3Xarg[103X ) [32X operation
  [29X[2XPredecessor[102X( [3Xarg[103X ) [32X operation
  [29X[2XListOfSentinels[102X( [3Xarg[103X ) [32X operation
  [29X[2XRemoveHead[102X( [3Xarg[103X ) [32X operation
  [29X[2XTree[102X( [3Xarg[103X ) [32X operation
  [29X[2XTree[102X( [3Xobj[103X ) [32X operation
  [29X[2XAdd[102X( [3Xtree[103X, [3Xnew_tree[103X ) [32X operation
  [29X[2XContentListFromSentinelToHead[102X( [3Xsent[103X ) [32X operation
  [29X[2XPostOrder[102X( [3Xarg[103X ) [32X operation
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YSets the caching to crisp, weak, or deativates the cache completely.[133X
  [33X[0;0YInstalls  a  method  like InstallMethod, but additionally puts a cache layer
  around  it so that the result is cached. It is possible to give the cache as
  the option Cache, to use the same cache for more than one method or store it
  somewhere to have access to the cache. Like InstallMethodWithCache, but with
  a  crisp cache. This works just like InstallMethodWithCache, but it extracts
  the  cache  via  the  CachingObject  method  from  one of its arguments. The
  CachingObject  must  then  be  implemented for one of the arguments, and the
  option  ArgumentNumber  can  specify  which  option  to  be  used. As second
  argument  for  CachingObject a string is used, which can identify the cache.
  Standard  is  the  name of the operation, for which the method is installed,
  but  it  can  be  specified  using  the  CacheName  option. Creates a cached
  function  out of a given function [3Xfunc[103X. If the option Cache is a cache, this
  cache  is  used.  If  the option Cache is the string crisp, a crisp cache is
  used.  All  other  values  for  this option lead to a single weak cache. The
  first  argument  is  the  [3Xindicator[103X.  It  is  a  list  of  sources  like  in
  ToDoListEntry.  Each  entry [3XSP[103X has to be a threetuple. First entry of [3XSP[103X has
  to  an object, for which the second entry of [3XSP[103X, which has to be the name of
  an  attribute, must become known. Once the attribute is known to the object,
  it  will  be  compared  to the third entry of the list. This can be a value,
  which  is  compared  directly  a  function, which is launched and its return
  value is compared, or a list, consisting of a function and arguments, so the
  return  value  of the function with given arguments is compared. If there is
  no  third  entry in [3XSP[103X, it is only looked up if the value is known. Once all
  entries  in  [3Xindicator[103X are processed like this, and all returned true in the
  comparasion,  a  list  of ToDoListEntryForEqualAttributes is installed. They
  are  installed  for  the two entries of the list [3Xobjects[103X which can either be
  the  objects  itself  or  a  list containing a function and arguments, which
  return  value  is  used.  For  each  entry  in  [3Xattributes[103X  such an entry is
  installed. Such an entry can be the name of an attribute, if both objects in
  [3Xobjects[103X  should  share the value between attributes with the same name, or a
  list  of  two  names,  if  the  attributes  do  not have the same name. This
  function  creates a ToDoListEntry which can install several ToDoListEntries.
  The  first  two  arguments,  [3Xindicator[103X and [3Xobjects[103X except that there will be
  only  ToDoListEntries  installed  between  the  two objects in [3Xobjects[103X. Each
  entry  in  [3Xattributes[103X  can either be a string which means that the attribute
  with  the  given  name  will  be  set from the first to the second object in
  [3Xobjects[103X  once  it  is  known.  The  third  argument  [3Xattributes[103X is a list of
  attributes  that  will  be  propagated by ToDoListEntries. Each entry [3XTP[103X can
  either  be a list consisting of a DescriptionOfImplication string and one of
  the  following or just one of the following lists: It can be a string, which
  means  that  the  Attribute  with the given name will be propagated from the
  first  to  the  second  object. It can be a list, consisting of two entries,
  where  the  first  entry  is a list of sources like in ToDoListEntry and the
  second  might  be  a  function which will be launched once the first part is
  fulfilled.  It can also be a threetuple which will serve as second to fourth
  argument  of  ToDoListEntry.  Or  it  can  be  a  string, which will set the
  attribute named like this of the first object to the one named in the second
  object  This  function  allows  to  create  more than one ToDoListEntry with
  identical  list  of sources at one time. First argument is a list of sources
  like  in  the  other  ToDoListEntry  functions  Second argument is a list of
  threetuples,  which serve as second to fourth argument of ToDoListEntry or a
  function,  which serves as second argument for ToDoListEntry or a tuple with
  a  description string and one of the above. Represents the objects for which
  the  blueprint  is  created  in  the  arguments  This  function  installs an
  immediate  method  which can install ToDoListEntryToMaintainEqualAttributes.
  First  argument  must  be  a  filter,  and  once the filter becomes true the
  ToDoListEntryToMaintainEqualAttributes  is  installed  with  the  second  to
  fourth  argument  as  first to third. In those attributes, at any point, the
  variable  ToDoList_this_object can be used. When the entry is installed This
  will be replaced with the object to which the filters became known, i.e. the
  one    which    triggered    the    immediate    method.    The    same   as
  ToDoListEntryToMaintainEqualAttributesBlueprint                          for
  ToDoListEntryToMaintainFollowingAttributes         The        same        as
  ToDoListEntryToMaintainEqualAttributesBlueprint  for  ToDoListEntry Adds the
  ToDo-list entry [3XE[103X to the ToDo-lists of it's source objects and creates a new
  one,  if this is needed. This function might be called with lists of entries
  Returns  the  a list of source parts of the ToDo-list entry [3Xentry[103X. This is a
  triple  of an object, a name of a filter/attribute, and a value to which the
  attribute has to be set to activate the entry Returns the target part of the
  ToDo-list  entry  [3Xentry[103X.  This  is  a  triple  of  an  object,  a  name of a
  filter/attribute,  and a value to which the specific filter/attribute should
  be set. The third entry of the list might also be a function to which return
  value  the  attribute  is  set.  Processes  a ToDo-list entry, i.e. sets the
  information  given  in  TargetPart  if  the  definitions  in  SourcePart are
  fulfilled. Returns a function if the entry could be processed, false if not,
  and  fail  if  SourcePart or TargetPart weren't availible anymore. The first
  argument  must  be  a list consisting of two, three or four-tuples where the
  first  entry  must be the object to which the attribute given as a string in
  the  second  entry must be known to process this entry. The second entry can
  also  be  a  list of strings, in that case all the attributes given as names
  must  be  known.  Also,  in  this  case,  only two entries in this tuple are
  allowed.  The  third part can be a value or a list, consisting of a function
  followed by arguments which will be computed by the time the attribute given
  as second entry becomes known to the first entry. If the second part is only
  a  string, and there is a third entry in the tuple the attribute is compared
  to  the  third  entry.  One  can set a comparating function as fourth entry,
  which  must  take  two entries and return false or true. If the value of the
  attribute matches the (computed) value in the third entry for all members of
  the  list  in the first argument the attribute given as third argument, also
  by  name, of the second argument is set to the value of the fourth argument.
  This can also be a list which has to be computed, or a function, which retun
  value  is  used  in  this case. The first argument is a list of three-tubles
  like  above.  Once  all preconditions become fulfilled the function given as
  second  argument  is  launched. If the given value of the target part is the
  return  value  of a function this command sets the target value of the entry
  to  a function. This is done to keep proof tracking availible. If the target
  object,  i.e.  the  first entry of the target part, was given as a function,
  this   method   can   set  this  entry  to  the  return  value  computed  in
  ProcessToDoListEntry.  This  happens  atomatically,  do  not worry about it.
  Creates  a ToDoListEntry which also installs a contraposition. The arguments
  [3Xsource_prop[103X  and  [3Xtarget[103X  need to be strings which name a property, and [3Xsval[103X
  and  [3Xtval[103X  need to be boolean values, i.e. true or false. Has to be set to a
  string,  which  describes  the  reason  for the conclusion. If the ToDo-list
  entry is displayed, the given string will be displayed with a because before
  it.  Creates a ToDoListEntry for two equal attributes, which means that both
  values  of the two attributes will be propagated in both directions. Creates
  a  ToDoListEntry for two equivalent attributes, which means that both values
  of  the  two  attributes  will be propagated in both directions. Please note
  that  this  one  does NOT implement contrapositions. This is the category of
  ToDo-lists.  Every  ToDo-list is an object of this category, which basically
  contains  the  ToDo-lists.  Creates  a new empty ToDo-list. Gets a ToDo-list
  entry,  which  is a pair of a list of strings and a weak pointer object, and
  processes  it.  If  the action was done, it returns true, if not, it returns
  false,  and  it  returns  fail  if the action is not possible anymore due to
  deleted  objects.  Returns the ToDo-list of an object, or creates a new one.
  This  is the magic! This attribute is never set. Creating an ToDo-list entry
  installs  an ImmediateMethod for this attribute for the specific category of
  the  object  to which ToDo-list is added, and the filter the entry contains.
  It  is  then  triggert if the filters become applicable, so the ToDo-list is
  processed  If  the  object [3Xobj[103X has the attribute [3Xname[103X, and its value is [3Xval[103X,
  and  the  knowledge  has  been obtained trough ToDoList-entries, this method
  traces  the way the property was set, and returns a tree which describes the
  full  way  of  how  the  attribute  became  known.  This operation activates
  ToDoLists  for  the  argument.  This  operation  activates ToDoLists for all
  objects.  This  operation  deactivates  ToDoLists  for  the  argument.  This
  operation  deactivates  ToDoLists  for  all  objects.  Note  that  it is not
  possible  to  activate  ToDoList  for  a  single  object  while they are not
  activated.  ToDoListEntries will yet be stored for all objects that can have
  ToDoLists.  All  objects  created  while  ToDoLists  are deactivated have by
  default  no  ToDoList.  Stores the result of Where( 100 ) in an entry if the
  entry  is  triggered.  This is not activated by default, since it might slow
  down  the  system. Deactives the storage of the result of Where( 100 ) if an
  entry is triggered. This is the default. A central place for configurations.
  ChapterInfo  Basics,  Variables  This  is the super super GAP-category which
  will    include    the    GAP-categories    IsStructureObjectOrObject    and
  IsHomalgObjectOrMorphism  This  is the super GAP-category which will include
  the  GAP-categories  IsHomalgRing,  IsHomalgModule, IsHomalgRingOrModule and
  IsHomalgComplex  This  is  the  super  GAP-category  which  will include the
  GAP-categories  IsHomalgRing we need this GAP-category to define things like
  Hom(M,R)  as  easy  as  Hom(M,N)  without  distinguishing  between structure
  objects   (e.g.  rings)  and  objects  (e.g.  modules)  This  is  the  super
  GAP-category  which  will  include  the GAP-categories IsHomalgRingMap, etc.
  this  is  the  super  GAP-category  which  will  include  the GAP-categories
  IsHomalgRing,  IsHomalgModule:  The  category  for  weak pointer objects The
  category  for  pointer objects The constructor for lists of weak pointers. A
  tool  to  compute  the  runtime  of  several  methods.  A  tool  to  install
  equivalence  between  filters.  Installs  a logical implication for one type
  with all it's contrapositions.[133X
  [33X[0;0YA  method  to  match  the properties and attributes of two objects. Installs
  methods  to  pull  new  known  properties  and attributes from one object to
  another  Installs  methods to pull new known properties and attributes under
  certain  conditions from one object to another. Installs an immediate method
  which  can  pull a property from one object to another with different names.
  Installs  an  immediate method to pull several properties or attributes from
  one object to another. Installs an immediate method to pull a property if it
  is  true.  Installs an immediate method which conditionally pulls a property
  if  it  is  true. Installs an immediate method which pulls a property with a
  different  name  if  it  is  true.  Installs an immediate method which pulls
  several  properties  if they are true Installs an immediate method to pull a
  property  if  it  is false. Installs an immediate method which conditionally
  pulls  a property if it is false. Installs an immediate method which pulls a
  property  with a different name if it is false. Installs an immediate method
  which  pulls  several  properties  if  they are false. Installs an immediate
  method  to push a property from one object to another. Installs an immediate
  method to conditionally push a property from one object to another. Installs
  an  immediate  method  which  can push a property from one object to another
  with   different  names.  Installs  an  immediate  method  to  push  several
  properties  or  attributes from one object to another. Installs an immediate
  method  to push a property if it is true. Installs an immediate method which
  pushes a property with a different name if it is true. Installs an immediate
  method  which  pushes  several  properties  if  they  are  true  Installs an
  immediate  method  to  push a property if it is false. Installs an immediate
  method  which  pushes  a  property  with  a  different  name if it is false.
  Installs  an  immediate  method  which  push  several properties if they are
  false.  Installs  an  attribute  with  a coustom getter function. Appends an
  entry  to  a  homalg  table.  Creates a list of integers out of the names of
  components.  Increases  an  existing  counter  in  an  object.  Increases an
  existiing counter on an object with timing. Increases a counter in an object
  and  creates  one  if  it  not exists Converts the current memory state to a
  string Returns the [3Xp[103X-exponent of the integer [3Xn[103X, where [3Xp[103X is a rational prime.
  Apply ViewObj to the list [3XL[103X.[133X
  [33X[0;0YRuns  the  examples  for  homalg  if the package is loadable. Runs the named
  example  for homalg Updates the weak pointers in a container and deletes the
  empty  ones Adds a weak pointer of an objects to a weak pointer list. Adds a
  weak pointer which depends on two objects to a list of weak pointers Creates
  a  weak  pointer  depending  on  two  objects  and adds it to the container.
  Creates a container for pointers. Updates the container of pointers, removes
  old. Adds a pointer to an object to a container for pointers. Adds a pointer
  to two objects to a container for pointers Returns an object which a pointer
  refers  to.  Returns real time seconds of the call function( args ) as first
  entry  of  list, result of call as second. The category of trees. A tree may
  have  a content, a list of successors, a predecessor and it knows if it is a
  leave  of a tree or not. The content of the tree. May be any object. Returns
  the list of successors of a tree. Returns the predecessor of a tree, or fail
  if  there  is  none. Returns a list of leaves of the tree. Returns the first
  successor of the tree, and adds all other successors of the tree to the tree
  that  is  returned. If the tree is a leave, it returns an empty tree. If the
  tree  is empty, it returns the tree itself. Returns an empty tree. Returns a
  tree  with argument [3Xobj[103X. Adds the [list of] tree[s] [3Xnew_tree[103X as successor to
  the  tree  [3Xtree[103X.  Returns a list of the contents of the trees from the leave
  [3Xsent[103X  up to the content of the head of the tree. Returns the contents of the
  nodes of the tree in post-order.[133X
  
