#11529: Rooted trees
-------------------------------------+-------------------------------------
       Reporter:  hivert             |        Owner:  hivert
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.5
      Component:  combinatorics      |   Resolution:
       Keywords:  rooted trees,      |    Merged in:
  Cayley                             |    Reviewers:
        Authors:  Florent Hivert     |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  76f695772807e9cad8d48a6fb0fc14e78289a2aa
  u/chapoton/11529_alone             |     Stopgaps:
   Dependencies:  #11407             |
-------------------------------------+-------------------------------------

Comment (by darij):

 OK. Are you sure `on_fly` is a good idea? It reeks of nondeterminism to
 me:
 {{{
 sage: OT = OrderedTree
 sage: OT([[[],[]], [[],[],[]]]).normalize()
 [[[], []], [[], [], []]]
 sage: OT([[[],[],[]], [[],[]]]).normalize()
 [[[], []], [[], [], []]]
 sage:
 Exiting Sage (CPU time 0m0.29s, Wall time 1m31.05s).
 skraeling@angband ~/sage $ ./sage
 ┌────────────────────────────────────────────────────────────────────┐
 │ Sage Version 6.5.rc1, Release Date: 2015-02-08                     │
 │ Type "notebook()" for the browser-based notebook interface.        │
 │ Type "help()" for help.                                            │
 └────────────────────────────────────────────────────────────────────┘
 ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
 ┃ Warning: this is a prerelease version, and it may be unstable.     ┃
 ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
 sage: OT = OrderedTree
 sage: OT([[[],[],[]], [[],[]]]).normalize()
 [[[], [], []], [[], []]]
 sage: OT([[[],[]], [[],[],[]]]).normalize()
 [[[], [], []], [[], []]]
 }}}
 Is this what we want? And does it behave well in regard to the other
 features of our tree classes, such as the `clone` context manager?

 Also, the doc of `LabelledRootedTrees` says that this class is a parent
 stub to be inherited from by classes of labelled rooted trees with
 specific properties; but the `unlabelled_trees` and `cardinality` methods
 look like they are specific to the class of *all* labelled rooted trees.
 Shouldn't they go into `LabelledRootedTrees_all`?

--
Ticket URL: <http://trac.sagemath.org/ticket/11529#comment:22>
Sage <http://www.sagemath.org>
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