Removed TODO in doc

Author: hivert

src/sage/sets/recursively_enumerated_set.pyx

@@ -21,121 +21,6 @@ AUTHORS:
 
 EXAMPLES:
 
-.. TODO:: Merge in the following documentation by Florent:
-
-    How to define a set using those classes ?
-
-    Only two things are necessary to define a set using a
-    :class:`RecursivelyEnumeratedSet` object (the other classes being very similar) :
-
-    .. MATH::
-
-        \begin{picture}(-300,0)(600,0)
-        % Root
-        \put(0,0){\circle*{7}}
-        \put(0,10){\makebox(0,10){``\ ''}}
-        % First Children
-        \put(-150,-60){\makebox(0,10){``a''}}
-        \put(0,-60){\makebox(0,10){``b''}}
-        \put(150,-60){\makebox(0,10){``c''}}
-        \multiput(-150,-70)(150,0){3}{\circle*{7}}
-        % Second children
-        \put(-200,-130){\makebox(0,10){``aa''}}
-        \put(-150,-130){\makebox(0,10){``ab''}}
-        \put(-100,-130){\makebox(0,10){``ac''}}
-        \put(-50,-130){\makebox(0,10){``ba''}}
-        \put(0,-130){\makebox(0,10){``bb''}}
-        \put(50,-130){\makebox(0,10){``bc''}}
-        \put(100,-130){\makebox(0,10){``ca''}}
-        \put(150,-130){\makebox(0,10){``cb''}}
-        \put(200,-130){\makebox(0,10){``cc''}}
-        \multiput(-200,-140)(50,0){9}{\circle*{7}}
-        % Legend
-        \put(100,-5){\makebox(0,10)[l]{1) An initial element}}
-        \put(-250,-5){\makebox(0,10)[l]{2) A function of an element enumerating}}
-        \put(-235,-20){\makebox(0,10)[l]{its children (if any)}}
-        % Arrows
-        \thicklines
-        \put(0,-10){\vector(0,-1){30}}
-        \put(-15,-5){\vector(-2,-1){110}}
-        \put(15,-5){\vector(2,-1){110}}
-        \multiput(-150,-80)(150,0){3}{\vector(0,-1){30}}
-        \multiput(-160,-80)(150,0){3}{\vector(-1,-1){30}}
-        \multiput(-140,-80)(150,0){3}{\vector(1,-1){30}}
-        \put(90,0){\vector(-1,0){70}}
-        \put(-215,-30){\vector(1,-1){40}}
-        \end{picture}
-
-    For the previous example, the two necessary pieces of information are :
-
-    - The initial element ``""``
-
-    - The function ``lambda x : [x+letter for letter in ['a', 'b', 'c']``
-
-    Err.. Well, this would actually describe an **infinite** set, as such rules
-    describes "all words" on 3 letters. Hence, it is a good idea to replace the
-    function by
-
-        ``lambda x : [x+letter for letter in ['a', 'b', 'c']] if len(x) < 2 else []``
-
-    or even::
-
-        sage: def children(x):
-        ....:     if len(x) < 2:
-        ....:         for letter in ['a', 'b', 'c']:
-        ....:             yield x+letter
-
-    We can then create the :class:`RecursivelyEnumeratedSet` object with either ::
-
-        sage: S = RecursivelyEnumeratedSet( [''],
-        ....:     lambda x: [x+letter for letter in ['a', 'b', 'c']]
-        ....:               if len(x) < 2 else [],
-        ....:     structure='forest', enumeration='depth',
-        ....:     category=FiniteEnumeratedSets())
-        sage: S.list()
-        ['', 'a', 'aa', 'ab', 'ac', 'b', 'ba', 'bb', 'bc', 'c', 'ca', 'cb', 'cc']
-
-    Or::
-
-        sage: S = RecursivelyEnumeratedSet( [''], children,
-        ....:     structure='forest', enumeration='depth',
-        ....:     category=FiniteEnumeratedSets())
-        sage: S.list()
-        ['', 'a', 'aa', 'ab', 'ac', 'b', 'ba', 'bb', 'bc', 'c', 'ca', 'cb', 'cc']
-
-    Here is a little more involved example. We want to iterate through all
-    permutations of a given set S. One solution is to take elements of S one by
-    one an insert them at every positions. So a node of the generating tree
-    contains two informations
-
-    - the list ``lst`` of already inserted element;
-    - the set ``st`` of the yet to be inserted element.
-
-    We want to generate a permutation only if ``st`` is empty (leaves on the
-    tree). Also suppose for the sake of the example, that instead of list we want
-    to generate tuples. This selection of some nodes and final mapping of a
-    function to the element is done by the ``post_process = f`` argument. The
-    convention is that the generated elements are the ``s := f(n)``, except when
-    ``s`` not ``None`` when no element is generated at all. Here is the code::
-
-        sage: def children((lst, st)):
-        ....:     st = set(st) # make a copy
-        ....:     if st:
-        ....:        el = st.pop()
-        ....:        for i in range(0, len(lst)+1):
-        ....:            yield (lst[0:i]+[el]+lst[i:], st)
-        sage: list(children(([1,2], {3,7,9})))
-        [([9, 1, 2], {3, 7}), ([1, 9, 2], {3, 7}), ([1, 2, 9], {3, 7})]
-        sage: S = RecursivelyEnumeratedSet( [([], {1,3,6,8})],
-        ....:     children,
-        ....:     post_process = lambda (l, s): tuple(l) if not s else None,
-        ....:     structure='forest', enumeration='depth',
-        ....:     category=FiniteEnumeratedSets())
-        sage: S.list()
-        [(6, 3, 1, 8), (3, 6, 1, 8), (3, 1, 6, 8), (3, 1, 8, 6), (6, 1, 3, 8), (1, 6, 3, 8), (1, 3, 6, 8), (1, 3, 8, 6), (6, 1, 8, 3), (1, 6, 8, 3), (1, 8, 6, 3), (1, 8, 3, 6), (6, 3, 8, 1), (3, 6, 8, 1), (3, 8, 6, 1), (3, 8, 1, 6), (6, 8, 3, 1), (8, 6, 3, 1), (8, 3, 6, 1), (8, 3, 1, 6), (6, 8, 1, 3), (8, 6, 1, 3), (8, 1, 6, 3), (8, 1, 3, 6)]
-        sage: S.cardinality()
-        24
-
 Forest structure
 ----------------