  
  [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
  
  [33X[1;0Y[29X[2XCachingObject[102X( [[3Xk[103X, ][[3Xis_crisp[103X] ) [32X operation[133X
  [33X[1;0Y[29X[2XCachingObject[102X( [3Xarg[103X ) [32X operation[133X
  [33X[1;0Y[29X[2XCachingObject[102X( [3Xarg1[103X, [3Xarg2[103X ) [32X operation[133X
  [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
  
  [33X[1;0Y[29X[2XCachingObject[102X( [3Xobject[103X, [3Xcache_name[103X, [3Xlength[103X[, [3Xis_crisp[103X] ) [32X operation[133X
  [33X[1;0Y[29X[2XCachingObject[102X( [3Xarg1[103X, [3Xarg2[103X, [3Xarg3[103X, [3Xarg4[103X ) [32X operation[133X
  
  [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
  
  [33X[1;0Y[29X[2XCacheValue[102X( [3Xcache[103X, [3Xkey[103X ) [32X operation[133X
  [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  a  list  only contraining the value,
  otherwise an empty list.[133X
  
  [1X3.2-2 SetCacheValue[101X
  
  [33X[1;0Y[29X[2XSetCacheValue[102X( [3Xcache[103X, [3Xkey[103X, [3Xvalue[103X ) [32X operation[133X
  
  [33X[0;0YSets the value of key of the cache to value.[133X
  
  [1X3.2-3 IsEqualForCache[101X
  
  [33X[1;0Y[29X[2XIsEqualForCache[102X( [3Xobj1[103X, [3Xobj2[103X ) [32X operation[133X
  [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
  
  [33X[1;0Y[29X[2XSetCachingObjectCrisp[102X( [3Xcache[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YSets the caching to crisp, weak, or deativates the cache completely.[133X
  
  [1X3.3-2 SetCachingObjectWeak[101X
  
  [33X[1;0Y[29X[2XSetCachingObjectWeak[102X( [3Xarg[103X ) [32X function[133X
  
  [1X3.3-3 DeactivateCachingObject[101X
  
  [33X[1;0Y[29X[2XDeactivateCachingObject[102X( [3Xarg[103X ) [32X function[133X
  
  
  [1X3.4 [33X[0;0YInstall functions[133X[101X
  
  [1X3.4-1 InstallMethodWithCache[101X
  
  [33X[1;0Y[29X[2XInstallMethodWithCache[102X( [3XLike[103X, [3XInstallMethod[103X ) [32X function[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.[133X
  
  [1X3.4-2 InstallMethodWithCrispCache[101X
  
  [33X[1;0Y[29X[2XInstallMethodWithCrispCache[102X( [3Xarg[103X ) [32X function[133X
  
  [33X[0;0YLike InstallMethodWithCache, but with a crisp cache.[133X
  
  [1X3.4-3 InstallMethodWithCacheFromObject[101X
  
  [33X[1;0Y[29X[2XInstallMethodWithCacheFromObject[102X( [3XLike[103X, [3XInstallMethod[103X ) [32X function[133X
  
  [33X[0;0YThis  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.[133X
  
  [1X3.4-4 FunctionWithCache[101X
  
  [33X[1;0Y[29X[2XFunctionWithCache[102X( [3Xfunc[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya function[133X
  
  [33X[0;0YCreates  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.[133X
  
