def iteration(self, algorithm="breadth", tracking_words=True):
r"""
Return an iterator going through all elements in ``self``.
INPUT:
- ``algorithm`` (default: ``'breadth'``) -- must be one of
the following:
* ``'breadth'`` - iterate over in a linear extension of the
weak order
* ``'depth'`` - iterate by a depth-first-search
* ``'parabolic'`` - iterate by using parabolic subgroups
- ``tracking_words`` (default: ``True``) -- whether or not to keep
track of the reduced words and store them in ``_reduced_word``
.. NOTE::
The fastest iteration is the parabolic iteration and the
depth first algorithm without tracking words is second.
In particular, ``'depth'`` is ~1.5x faster than ``'breadth'``.
.. NOTE::
The ``'parabolic'`` iteration does not track words and requires
keeping the subgroup corresponding to `I \setminus \{i\}` in
memory (for each `i` individually).
EXAMPLES::
sage: W = ReflectionGroup(["B",2]) # optional - gap3
sage: for w in W.iteration("breadth",True): # optional - gap3
....: print("%s %s"%(w, w._reduced_word)) # optional - gap3
() []
(1,3)(2,6)(5,7) [1]
(1,5)(2,4)(6,8) [0]
(1,7,5,3)(2,4,6,8) [0, 1]
(1,3,5,7)(2,8,6,4) [1, 0]
(2,8)(3,7)(4,6) [1, 0, 1]
(1,7)(3,5)(4,8) [0, 1, 0]
(1,5)(2,6)(3,7)(4,8) [0, 1, 0, 1]
sage: for w in W.iteration("depth", False): w # optional - gap3
()
(1,3)(2,6)(5,7)
(1,5)(2,4)(6,8)
(1,3,5,7)(2,8,6,4)
(1,7)(3,5)(4,8)
(1,7,5,3)(2,4,6,8)
(2,8)(3,7)(4,6)
(1,5)(2,6)(3,7)(4,8)
"""
from sage.combinat.root_system.reflection_group_c import Iterator
return iter(
Iterator(self,
N=self.number_of_reflections(),
algorithm=algorithm,
tracking_words=tracking_words))
def iteration(self, algorithm="breadth", tracking_words=True):
r"""
Return an iterator going through all elements in ``self``.
INPUT:
- ``algorithm`` (default: ``'breadth'``) -- must be one of
the following:
* ``'breadth'`` - iterate over in a linear extension of the
weak order
* ``'depth'`` - iterate by a depth-first-search
- ``tracking_words`` (default: ``True``) -- whether or not to keep
track of the reduced words and store them in ``_reduced_word``
.. NOTE::
The fastest iteration is the depth first algorithm without
tracking words. In particular, ``'depth'`` is ~1.5x faster.
EXAMPLES::
sage: W = WeylGroup(["B",2], implementation="permutation")
sage: for w in W.iteration("breadth",True):
....: print("%s %s"%(w, w._reduced_word))
() []
(1,3)(2,6)(5,7) [1]
(1,5)(2,4)(6,8) [0]
(1,7,5,3)(2,4,6,8) [0, 1]
(1,3,5,7)(2,8,6,4) [1, 0]
(2,8)(3,7)(4,6) [1, 0, 1]
(1,7)(3,5)(4,8) [0, 1, 0]
(1,5)(2,6)(3,7)(4,8) [0, 1, 0, 1]
sage: for w in W.iteration("depth", False): w
()
(1,3)(2,6)(5,7)
(1,5)(2,4)(6,8)
(1,3,5,7)(2,8,6,4)
(1,7)(3,5)(4,8)
(1,7,5,3)(2,4,6,8)
(2,8)(3,7)(4,6)
(1,5)(2,6)(3,7)(4,8)
"""
from sage.combinat.root_system.reflection_group_c import Iterator
return iter(
Iterator(self,
N=self.number_of_reflections(),
algorithm=algorithm,
tracking_words=tracking_words))