Merge branch 'u/chapoton/11529' of ssh://trac.sagemath.org:22/sage in…

…to 11529

Conflicts:
	src/sage/combinat/all.py

src/doc/en/reference/combinat/index.rst

@@ -155,6 +155,7 @@ Combinatorics
    sage/combinat/abstract_tree
    sage/combinat/ordered_tree
    sage/combinat/binary_tree
+   sage/combinat/rooted_tree
 
 **Word**
 

src/sage/combinat/all.py

@@ -116,7 +116,10 @@
                           LabelledOrderedTree, LabelledOrderedTrees)
 from binary_tree import (BinaryTree, BinaryTrees,
                          LabelledBinaryTree, LabelledBinaryTrees)
+
 lazy_import('sage.combinat.interval_posets', ['TamariIntervalPoset', 'TamariIntervalPosets'])
+from rooted_tree import (RootedTree, RootedTrees,
+                         LabelledRootedTree, LabelledRootedTrees)
 
 from combination import Combinations
 from cartesian_product import CartesianProduct

src/sage/combinat/ordered_tree.py

@@ -22,6 +22,13 @@
 from sage.combinat.abstract_tree import (AbstractClonableTree,
                                          AbstractLabelledClonableTree)
 from sage.combinat.combinatorial_map import combinatorial_map
+from sage.misc.cachefunc import cached_method
+from sage.categories.sets_cat import Sets, EmptySetError
+from sage.rings.integer import Integer
+from sage.sets.non_negative_integers import NonNegativeIntegers
+from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets
+from sage.sets.family import Family
+from sage.misc.cachefunc import cached_method
 
 
 class OrderedTree(AbstractClonableTree, ClonableList):
@@ -511,12 +518,41 @@ def left_right_symmetry(self):
         children.reverse()
         return OrderedTree(children)
 
-from sage.categories.sets_cat import Sets, EmptySetError
-from sage.rings.integer import Integer
-from sage.sets.non_negative_integers import NonNegativeIntegers
-from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets
-from sage.sets.family import Family
-from sage.misc.cachefunc import cached_method
+    import sage.combinat.ranker
+    _cayley_ranker = sage.combinat.ranker.on_fly()
+
+    @cached_method
+    def cayley_normalize(self):
+        """
+        sage: (OrderedTree([[],[[]]]).cayley_normalize() ==
+        ...    OrderedTree([[[]],[]]).cayley_normalize())
+        True
+        """
+        rank, unrank = self._cayley_ranker
+        with self.clone() as res:
+            resl = res._get_list()
+            for i in range(len(resl)):
+                resl[i] = resl[i].cayley_normalize()
+            resl.sort(key = rank)
+        return unrank(rank(res))
+
+    # TODO !!!
+    def cayley_normalize_in_place(self):
+        """
+        In place cayley normalization
+
+        EXAMPLES::
+
+            sage: (OrderedTree([[],[[]]]).cayley_normalize() ==
+            ...    OrderedTree([[[]],[]]).cayley_normalize())
+            True
+        """
+        rank, unrank = self._cayley_ranker
+        resl = self._get_list()
+        for i in range(len(resl)):
+            resl[i] = resl[i].cayley_normalized()
+        resl.sort(key = rank)
+
 
 # Abstract class to serve as a Factory no instance are created.
 class OrderedTrees(UniqueRepresentation, Parent):
@@ -588,6 +624,7 @@ def leaf(self):
         """
         return self([])
 
+
 class OrderedTrees_all(DisjointUnionEnumeratedSets, OrderedTrees):
     """
     The set of all ordered trees.
@@ -659,7 +696,7 @@ def unlabelled_trees(self):
 
     def labelled_trees(self):
         """
-        Return the set of unlabelled trees associated to ``self``
+        Return the set of labelled trees associated to ``self``
 
         EXAMPLES::