Coverage for local/lib/python2.7/site-packages/sage/combinat/combinatorial_map.py : 69%
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""" Combinatorial maps
This module provides a decorator that can be used to add semantic to a Python method by marking it as implementing a *combinatorial map*, that is a map between two :class:`enumerated sets <EnumeratedSets>`::
sage: from sage.combinat.combinatorial_map import combinatorial_map sage: class MyPermutation(object): ....: ....: @combinatorial_map() ....: def reverse(self): ....: ''' ....: Reverse the permutation ....: ''' ....: # ... code ...
By default, this decorator is a no-op: it returns the decorated method as is::
sage: MyPermutation.reverse <unbound method MyPermutation.reverse>
See :func:`combinatorial_map_wrapper` for the various options this decorator can take.
Projects built on top of Sage are welcome to customize locally this hook to instrument the Sage code and exploit this semantic information. Typically, the decorator could be used to populate a database of maps. For a real-life application, see the project `FindStat <http://findstat.org/>`. As a basic example, a variant of the decorator is provided as :func:`combinatorial_map_wrapper`; it wraps the decorated method, so that one can later use :func:`combinatorial_maps_in_class` to query an object, or class thereof, for all the combinatorial maps that apply to it.
.. NOTE::
Since decorators are evaluated upon loading Python modules, customizing :obj:`combinatorial map` needs to be done before the modules using it are loaded. In the examples below, where we illustrate the customized ``combinatorial_map`` decorator on the :mod:`sage.combinat.permutation` module, we resort to force a reload of this module after dynamically changing ``sage.combinat.combinatorial_map.combinatorial_map``. This is good enough for those doctests, but remains fragile.
For real use cases it's probably best to just edit this source file statically (see below). """ #***************************************************************************** # Copyright (C) 2011 Christian Stump <christian.stump at gmail.com> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #*****************************************************************************
def combinatorial_map_trivial(f=None, order=None, name=None): r""" Combinatorial map decorator
See :ref:`sage.combinat.combinatorial_map` for a description of this decorator and its purpose. This default implementation does nothing.
INPUT:
- ``f`` -- (default: ``None``, if combinatorial_map is used as a decorator) a function - ``name`` -- (default: ``None``) the name for nicer outputs on combinatorial maps - ``order`` -- (default: ``None``) the order of the combinatorial map, if it is known. Is not used, but might be helpful later
OUTPUT:
- ``f`` unchanged
EXAMPLES::
sage: from sage.combinat.combinatorial_map import combinatorial_map_trivial as combinatorial_map sage: class MyPermutation(object): ....: ....: @combinatorial_map ....: def reverse(self): ....: ''' ....: Reverse the permutation ....: ''' ....: # ... code ... ....: ....: @combinatorial_map(name='descent set of permutation') ....: def descent_set(self): ....: ''' ....: The descent set of the permutation ....: ''' ....: # ... code ...
sage: MyPermutation.reverse <unbound method MyPermutation.reverse> sage: MyPermutation.descent_set <unbound method MyPermutation.descent_set> """ else:
def combinatorial_map_wrapper(f=None, order=None, name=None): r""" Combinatorial map decorator (basic example).
See :ref:`sage.combinat.combinatorial_map` for a description of the ``combinatorial_map`` decorator and its purpose. This implementation, together with :func:`combinatorial_maps_in_class` illustrates how to use this decorator as a hook to instrument the Sage code.
INPUT:
- ``f`` -- (default: ``None``, if combinatorial_map is used as a decorator) a function - ``name`` -- (default: ``None``) the name for nicer outputs on combinatorial maps - ``order`` -- (default: ``None``) the order of the combinatorial map, if it is known. Is not used, but might be helpful later
OUTPUT:
- A combinatorial map. This is an instance of the :class:`CombinatorialMap`.
EXAMPLES:
We define a class illustrating the use of this implementation of the :obj:`combinatorial_map` decorator with its various arguments::
sage: from sage.combinat.combinatorial_map import combinatorial_map_wrapper as combinatorial_map sage: class MyPermutation(object): ....: ....: @combinatorial_map() ....: def reverse(self): ....: ''' ....: Reverse the permutation ....: ''' ....: pass ....: ....: @combinatorial_map(order=2) ....: def inverse(self): ....: ''' ....: The inverse of the permutation ....: ''' ....: pass ....: ....: @combinatorial_map(name='descent set of permutation') ....: def descent_set(self): ....: ''' ....: The descent set of the permutation ....: ''' ....: pass ....: ....: def major_index(self): ....: ''' ....: The major index of the permutation ....: ''' ....: pass sage: MyPermutation.reverse Combinatorial map: reverse sage: MyPermutation.descent_set Combinatorial map: descent set of permutation sage: MyPermutation.inverse Combinatorial map: inverse
One can now determine all the combinatorial maps associated with a given object as follows::
sage: from sage.combinat.combinatorial_map import combinatorial_maps_in_class sage: X = combinatorial_maps_in_class(MyPermutation); X # random [Combinatorial map: reverse, Combinatorial map: descent set of permutation, Combinatorial map: inverse]
The method ``major_index`` defined about is not a combinatorial map::
sage: MyPermutation.major_index <unbound method MyPermutation.major_index>
But one can define a function that turns ``major_index`` into a combinatorial map::
sage: def major_index(p): ....: return p.major_index() ....: sage: major_index <function major_index at ...> sage: combinatorial_map(major_index) Combinatorial map: major_index
""" else:
############################################################################## # Edit here to customize the combinatorial_map hook ############################################################################## combinatorial_map = combinatorial_map_trivial #combinatorial_map = combinatorial_map_wrapper
class CombinatorialMap(object): r""" This is a wrapper class for methods that are *combinatorial maps*.
For further details and doctests, see :ref:`sage.combinat.combinatorial_map` and :func:`combinatorial_map_wrapper`. """ def __init__(self, f, order=None, name=None): """ Constructor for combinatorial maps
EXAMPLES::
sage: from sage.combinat.combinatorial_map import combinatorial_map_wrapper as combinatorial_map sage: def f(x): ....: "doc of f" ....: return x ....: sage: x = combinatorial_map(f); x Combinatorial map: f sage: x.__doc__ 'doc of f' sage: x.__name__ 'f' sage: x.__module__ '__main__' """ raise ValueError("Only plain functions are supported") else: self.__name__ = "..."
def __repr__(self): """ EXAMPLES::
sage: sage.combinat.combinatorial_map.combinatorial_map = sage.combinat.combinatorial_map.combinatorial_map_wrapper sage: import imp sage: _ = imp.reload(sage.combinat.permutation); sage: p = Permutation([1,3,2,4]) sage: p.left_tableau.__repr__() 'Combinatorial map: Robinson-Schensted insertion tableau' """
def _sage_src_lines_(self): r""" Return the source code location for the wrapped function.
EXAMPLES::
sage: sage.combinat.combinatorial_map.combinatorial_map = sage.combinat.combinatorial_map.combinatorial_map_wrapper sage: import imp sage: _ = imp.reload(sage.combinat.permutation) sage: p = Permutation([1,3,2,4]) sage: cm = p.left_tableau; cm Combinatorial map: Robinson-Schensted insertion tableau sage: (src, lines) = cm._sage_src_lines_() sage: src[0] " @combinatorial_map(name='Robinson-Schensted insertion tableau')\n" sage: lines # random 2653 """
def __get__(self, inst, cls=None): """ Bounds the method of self to the given instance.
EXAMPLES::
sage: sage.combinat.combinatorial_map.combinatorial_map = sage.combinat.combinatorial_map.combinatorial_map_wrapper sage: import imp sage: _ = imp.reload(sage.combinat.permutation); sage: p = Permutation([1,3,2,4]) sage: p.left_tableau #indirect doctest Combinatorial map: Robinson-Schensted insertion tableau """
def __call__(self, *args, **kwds): """ Calls the combinatorial map.
EXAMPLES::
sage: sage.combinat.combinatorial_map.combinatorial_map = sage.combinat.combinatorial_map.combinatorial_map_wrapper sage: import imp sage: _ = imp.reload(sage.combinat.permutation); sage: p = Permutation([1,3,2,4]) sage: cm = type(p).left_tableau; cm Combinatorial map: Robinson-Schensted insertion tableau sage: cm(p) [[1, 2, 4], [3]] sage: cm(Permutation([4,3,2,1])) [[1], [2], [3], [4]] """ return self._f(self._inst, *args, **kwds) else:
def unbounded_map(self): r""" Return the unbounded version of ``self``.
You can use this method to return a function which takes as input an element in the domain of the combinatorial map. See the example below.
EXAMPLES::
sage: sage.combinat.combinatorial_map.combinatorial_map = sage.combinat.combinatorial_map.combinatorial_map_wrapper sage: import imp sage: _ = imp.reload(sage.combinat.permutation); sage: from sage.combinat.permutation import Permutation sage: pi = Permutation([1,3,2]) sage: f = pi.reverse sage: F = f.unbounded_map() sage: F(pi) [2, 3, 1] """
def order(self): """ Returns the order of ``self``, or ``None`` if the order is not known.
EXAMPLES::
sage: from sage.combinat.combinatorial_map import combinatorial_map sage: class CombinatorialClass: ....: @combinatorial_map(order=2) ....: def to_self_1(): pass ....: @combinatorial_map() ....: def to_self_2(): pass sage: CombinatorialClass.to_self_1.order() 2 sage: CombinatorialClass.to_self_2.order() is None True """
def name(self): """ Returns the name of a combinatorial map. This is used for the string representation of ``self``.
EXAMPLES::
sage: from sage.combinat.combinatorial_map import combinatorial_map sage: class CombinatorialClass: ....: @combinatorial_map(name='map1') ....: def to_self_1(): pass ....: @combinatorial_map() ....: def to_self_2(): pass sage: CombinatorialClass.to_self_1.name() 'map1' sage: CombinatorialClass.to_self_2.name() 'to_self_2' """ else:
def combinatorial_maps_in_class(cls): """ Return the combinatorial maps of the class as a list of combinatorial maps.
For further details and doctests, see :ref:`sage.combinat.combinatorial_map` and :func:`combinatorial_map_wrapper`.
EXAMPLES::
sage: sage.combinat.combinatorial_map.combinatorial_map = sage.combinat.combinatorial_map.combinatorial_map_wrapper sage: import imp sage: _ = imp.reload(sage.combinat.permutation); sage: from sage.combinat.combinatorial_map import combinatorial_maps_in_class sage: p = Permutation([1,3,2,4]) sage: cmaps = combinatorial_maps_in_class(p) sage: cmaps # random [Combinatorial map: Robinson-Schensted insertion tableau, Combinatorial map: Robinson-Schensted recording tableau, Combinatorial map: Robinson-Schensted tableau shape, Combinatorial map: complement, Combinatorial map: descent composition, Combinatorial map: inverse, ...] sage: p.left_tableau in cmaps True sage: p.right_tableau in cmaps True sage: p.complement in cmaps True """ |