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+====== BigObject Lattice<Decoration, SeqType> ======
+//from application [[..:graph|graph]]//\\
+\\
+ A Lattice is a poset where join and meet exist for any two elements. It is realized as a directed graph.
+  ? Type Parameters:
+  :: ''Decoration'': additional data associated with each node.  Should be derived from ''[[..:graph#BasicDecoration |BasicDecoration]]''.
+  :: ''SeqType'': tag describing the node ordering, should be ''[[..:graph#Sequential |Sequential]]'' or ''[[..:graph#Nonsequential |Nonsequential]]''.
+  ? derived from:
+  : ''[[..:graph:Graph |Graph]]''
+  ? Specializations:
+  :: ''Lattice::BasicLattice'':  A ''[[..:graph:Lattice |Lattice]]'' with a ''[[..:graph#BasicDecoration |BasicDecoration]]'', which corresponds to the legacy HasseDiagram type
+===== Properties =====
+==== Combinatorics ====
+ These properties capture combinatorial information of the object.  Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.
+----
+{{anchor:bottom_node:}}
+  ?  **''BOTTOM_NODE''**
+  :: The index of the bottom node
+    ? Type:
+    :''[[..:common#Int |Int]]''
+    ? Example:
+    :: The following prints the bottom node of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->BOTTOM_NODE;
+</code>
+----
+{{anchor:decoration:}}
+  ?  **''DECORATION''**
+  :: This is the data associated to each node. The prototype for this is ''[[..:graph#BasicDecoration |BasicDecoration]]'', which consists of properties face and rank.
+    ? Type:
+    :''[[..:common#NodeMap |NodeMap]]<[[..:common#Directed |Directed]],Decoration>''
+    ? Example:
+    :: The following prints this property of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->DECORATION;
+ ({} 0)
+ ({0} 1)
+ ({1} 1)
+ ({2} 1)
+ ({1 2} 2)
+ ({0 2} 2)
+ ({0 1} 2)
+ ({0 1 2} 3)
+</code>
+----
+{{anchor:dims:}}
+  ?  **''DIMS''**
+  :: Kept only for backwards compatibility. Basically encodes the ''[[..:graph:Lattice#INVERSE_RANK_MAP |INVERSE_RANK_MAP]]'' in FaceLattice objects prior to 3.0.7
+    ? Type:
+    :''[[..:common#Array |Array]]<[[..:common#Int |Int]]>''
+----
+{{anchor:faces:}}
+  ?  **''FACES''**
+  :: The face of each node, realized as a NodeMap. This property is kept for two reasons: As a convenient way to access only the face part of the decoration (in this case the property is temporary) and for reasons of backwards compatibility.
+    ? Type:
+    :''[[..:common#NodeMap |NodeMap]]<[[..:common#Directed |Directed]],[[..:common#Set |Set]]<[[..:common#Int |Int]]%%>>%%''
+    ? Example:
+    :: The following prints the faces of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->FACES;
+ {}
+ {0}
+ {1}
+ {2}
+ {1 2}
+ {0 2}
+ {0 1}
+ {0 1 2}
+</code>
+----
+{{anchor:inverse_rank_map:}}
+  ?  **''INVERSE_RANK_MAP''**
+  :: This property provides an efficient way to enumerate all nodes of a given rank. Internally these are realized differently, depending on whether the Lattice is ''[[..:graph#Sequential |Sequential]]'' or ''[[..:graph#Nonsequential |Nonsequential]]''. Both provide the same user methods though.
+    ? Type:
+    :''[[..:graph#InverseRankMap |InverseRankMap]]<SeqType>''
+    ? Example:
+    :: The following prints this property of the face lattice of the 2-simplex (triangle), where the tuples represent the ranges of nodes belonging to a specific rank:
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->INVERSE_RANK_MAP;
+ {(0 (0 0)) (1 (1 3)) (2 (4 6)) (3 (7 7))}
+</code>
+----
+{{anchor:top_node:}}
+  ?  **''TOP_NODE''**
+  :: The index of the top node
+    ? Type:
+    :''[[..:common#Int |Int]]''
+    ? Example:
+    :: The following prints the top node of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->TOP_NODE;
+</code>
+----
+===== Methods =====
+==== Combinatorics ====
+ These methods capture combinatorial information of the object.  Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.
+----
+{{anchor:dual_faces:}}
+  ?  **''dual_faces()''**
+  ::
+    ? Returns:
+    :''[[..:common#Array |Array]]<[[..:common#Set |Set]]<[[..:common#Int |Int]]%%>>%%''
+    ? Example:
+    :: The following prints the dual faces of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->dual_faces();
+ {0 1 2}
+ {1 2}
+ {0 2}
+ {0 1}
+ {0}
+ {1}
+ {2}
+ {}
+</code>
+----
+{{anchor:nodes_of_rank:}}
+  ?  **''nodes_of_rank([[..:common#Int |Int]] r)''**
+  ::
+    ? Parameters:
+    :: ''[[..:common#Int |Int]]'' ''r''
+    ? Returns:
+    :''[[..:common#List |List]]<[[..:common#Int |Int]]>''
+    ? Example:
+    :: The following prints the nodes of rank 1 of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->nodes_of_rank(1);
+ {1 2 3}
+</code>
+----
+{{anchor:nodes_of_rank_range:}}
+  ?  **''nodes_of_rank_range([[..:common#Int |Int]] r1, [[..:common#Int |Int]] r2)''**
+  ::
+    ? Parameters:
+    :: ''[[..:common#Int |Int]]'' ''r1''
+    :: ''[[..:common#Int |Int]]'' ''r2''
+    ? Returns:
+    :''[[..:common#List |List]]<[[..:common#Int |Int]]>''
+    ? Example:
+    :: The following prints the nodes with rank between 1 and 2 of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->nodes_of_rank_range(1,2);
+ {1 2 3 4 5 6}
+</code>
+----
+{{anchor:rank:}}
+  ?  **''rank()''**
+  ::
+    ? Returns:
+    :''[[..:common#Int |Int]]''
+    ? Example:
+    :: The following prints the rank of the top node of the face lattice of the 2-simplex (triangle):
+    :: <code perl> > print simplex(2)->HASSE_DIAGRAM->rank();
+</code>
+----
+==== Visualization ====
+ These methods are for visualization.
+----
+{{anchor:visual:}}
+  ?  **''VISUAL()''**
+  :: Visualize the Lattice.
+    ? Options:
+    :
+    :: ''[[..:common#Int |Int]]'' ''seed'': random seed value for the node placement
+    : option list ''[[..:graph#Visual_Lattice_decorations |Visual::Lattice::decorations]]''
+    ? Returns:
+    :''[[..:graph:Visual_Lattice |Visual::Lattice]]''
+    ? Example:
+    :: The following visualizes the face lattice of the 2-simplex (triangle) with default settings:
+    :: <code perl> > simplex(2)->HASSE_DIAGRAM->VISUAL;
+</code>
+    ::  The following shows some modified visualization style of the same lattice:
+    :: <code perl> > simplex(2)->HASSE_DIAGRAM->VISUAL(NodeColor=>"green",EdgeThickness=>2,EdgeColor=>"purple");
+</code>
+----
+{{anchor:visual_dual:}}
+  ?  **''VISUAL_DUAL()''**
+  :: Visualize the dual Lattice. This only produces meaningful results for lattice where the codimension one nodes generate the lattice under intersection.
+    ? Options:
+    :
+    :: ''[[..:common#Int |Int]]'' ''seed'': random seed value for the node placement
+    : option list ''[[..:graph#Visual_Lattice_decorations |Visual::Lattice::decorations]]''
+    ? Returns:
+    :''[[..:graph:Visual_Lattice |Visual::Lattice]]''
+    ? Example:
+    :: The following visualizes the dual face lattice of the 2-simplex (triangle) with default settings:
+    :: <code perl> > simplex(2)->HASSE_DIAGRAM->VISUAL_DUAL;
+</code>
+    ::  The following shows some modified visualization style of the same lattice:
+    :: <code perl> > simplex(2)->HASSE_DIAGRAM->VISUAL_DUAL(NodeColor=>"green",EdgeThickness=>2,EdgeColor=>"purple");
+</code>
+----