def left_rauzy_move(self, winner):
r"""
Performs a Rauzy move on the left.
EXAMPLES:
::
sage: p = iet.Permutation('a b c','c b a',reduced=True)
sage: p.left_rauzy_move(0)
a b c
b c a
sage: p.right_rauzy_move(1)
a b c
b c a
::
sage: p = iet.GeneralizedPermutation('a a','b b c c',reduced=True)
sage: p.left_rauzy_move(0)
a a b
b c c
"""
winner = interval_conversion(winner)
result = copy(self)
result._reversed()
result = result.right_rauzy_move(winner)
result._reversed()
return result
def has_rauzy_move(self, winner, side='right'):
r"""
Tests if the permutation is rauzy_movable on the left.
EXAMPLES:
::
sage: p = iet.Permutation('a b c','a c b',reduced=True)
sage: p.has_rauzy_move(0,'right')
True
sage: p.has_rauzy_move(0,'left')
False
sage: p.has_rauzy_move(1,'right')
True
sage: p.has_rauzy_move(1,'left')
False
::
sage: p = iet.Permutation('a b c d','c a b d',reduced=True)
sage: p.has_rauzy_move(0,'right')
False
sage: p.has_rauzy_move(0,'left')
True
sage: p.has_rauzy_move(1,'right')
False
sage: p.has_rauzy_move(1,'left')
True
"""
side = side_conversion(side)
winner = interval_conversion(winner)
return self._twin[winner][side] % len(self) != side % len(self)
def length(self, interval=None):
r"""
Returns the 2-uple of lengths.
p.length() is identical to (p.length_top(), p.length_bottom())
If an interval is specified, it returns the length of the specified
interval.
INPUT:
- ``interval`` - None, 'top' (or 't' or 0) or 'bottom' (or 'b' or 1)
OUTPUT:
integer or 2-uple of integers -- the corresponding lengths
EXAMPLES::
sage: p = iet.Permutation('a b c','c b a')
sage: p.length()
(3, 3)
sage: p = iet.GeneralizedPermutation('a a b','c d c b d')
sage: p.length()
(3, 5)
"""
if interval is None :
return len(self._twin[0]),len(self._twin[1])
else :
interval = interval_conversion(interval)
return len(self._twin[interval])
def right_rauzy_move(self, winner):
r"""
Performs a Rauzy move on the right.
EXAMPLES:
::
sage: p = iet.Permutation('a b c','c b a',reduced=True)
sage: p.right_rauzy_move(0)
a b c
c a b
sage: p.right_rauzy_move(1)
a b c
b c a
::
sage: p = iet.GeneralizedPermutation('a a','b b c c',reduced=True)
sage: p.right_rauzy_move(0)
a b b
c c a
"""
winner = interval_conversion(winner)
result = copy(self)
loser_to = result._get_loser_to(winner)
# beware here, loser_to can contain 2 or 3 items
# (depending on the presence of flip)
result._twin_rauzy_move(winner, loser_to)
return result
def rauzy_move_relabel(self, winner, side='right'):
r"""
Returns the relabelization obtained from this move.
EXAMPLE::
sage: from surface_dynamics.all import *
sage: p = iet.Permutation('a b c d','d c b a')
sage: q = p.reduced()
sage: p_t = p.rauzy_move('t')
sage: q_t = q.rauzy_move('t')
sage: s_t = q.rauzy_move_relabel('t')
sage: print s_t
a->a, b->b, c->c, d->d
sage: map(s_t, p_t[0]) == map(Word, q_t[0])
True
sage: map(s_t, p_t[1]) == map(Word, q_t[1])
True
sage: p_b = p.rauzy_move('b')
sage: q_b = q.rauzy_move('b')
sage: s_b = q.rauzy_move_relabel('b')
sage: print s_b
a->a, b->d, c->b, d->c
sage: map(s_b, q_b[0]) == map(Word, p_b[0])
True
sage: map(s_b, q_b[1]) == map(Word, p_b[1])
True
"""
from surface_dynamics.interval_exchanges.labelled import LabelledPermutationIET
from sage.combinat.words.morphism import WordMorphism
winner = interval_conversion(winner)
side = side_conversion(side)
p = LabelledPermutationIET(self.list())
l0_q = p.rauzy_move(winner, side).list()[0]
d = dict([(self._alphabet[i],l0_q[i]) for i in range(len(self))])
return WordMorphism(d)
def rauzy_move_relabel(self, winner, side='right'):
r"""
Returns the relabelization obtained from this move.
EXAMPLE::
sage: from surface_dynamics.all import *
sage: p = iet.Permutation('a b c d','d c b a')
sage: q = p.reduced()
sage: p_t = p.rauzy_move('t')
sage: q_t = q.rauzy_move('t')
sage: s_t = q.rauzy_move_relabel('t')
sage: print s_t
a->a, b->b, c->c, d->d
sage: map(s_t, p_t[0]) == map(Word, q_t[0])
True
sage: map(s_t, p_t[1]) == map(Word, q_t[1])
True
sage: p_b = p.rauzy_move('b')
sage: q_b = q.rauzy_move('b')
sage: s_b = q.rauzy_move_relabel('b')
sage: print s_b
a->a, b->d, c->b, d->c
sage: map(s_b, q_b[0]) == map(Word, p_b[0])
True
sage: map(s_b, q_b[1]) == map(Word, p_b[1])
True
"""
from surface_dynamics.interval_exchanges.labelled import LabelledPermutationIET
from sage.combinat.words.morphism import WordMorphism
winner = interval_conversion(winner)
side = side_conversion(side)
p = LabelledPermutationIET(self.list())
l0_q = p.rauzy_move(winner, side).list()[0]
d = dict([(self._alphabet[i],l0_q[i]) for i in range(len(self))])
return WordMorphism(d)
def right_rauzy_move(self, winner):
r"""
Performs a Rauzy move on the right.
EXAMPLE::
sage: p = iet.Permutation('a b c','c b a',reduced=True,flips='c')
sage: p.right_rauzy_move('top')
-a b -c
-a -c b
"""
winner = interval_conversion(winner)
result = copy(self)
loser_to = result._get_loser_to(winner)
result._flip_rauzy_move(winner, loser_to)
result._twin_rauzy_move(winner, loser_to)
return result
def in_which_interval(self, x, interval=0):
r"""
Returns the letter for which x is in this interval.
INPUT:
- ``x`` - a positive number
- ``interval`` - (default: 'top') 'top' or 'bottom'
OUTPUT:
label -- a label corresponding to an interval
TEST:
::
sage: t = iet.IntervalExchangeTransformation(('a b c','c b a'),[1,1,1])
sage: t.in_which_interval(0)
'a'
sage: t.in_which_interval(0.3)
'a'
sage: t.in_which_interval(1)
'b'
sage: t.in_which_interval(1.9)
'b'
sage: t.in_which_interval(2)
'c'
sage: t.in_which_interval(2.1)
'c'
sage: t.in_which_interval(3)
Traceback (most recent call last):
...
ValueError: your value does not lie in [0;l[
.. and for the bottom interval::
sage: t.in_which_interval(0,'bottom')
'c'
sage: t.in_which_interval(1.2,'bottom')
'b'
sage: t.in_which_interval(2.9,'bottom')
'a'
TESTS::
sage: t.in_which_interval(-2.9,'bottom')
Traceback (most recent call last):
...
ValueError: your value does not lie in [0;l[
"""
interval = interval_conversion(interval)
if x < 0 or x >= self.length():
raise ValueError("your value does not lie in [0;l[")
i = 0
while x >= 0:
x -= self._lengths[self._permutation._intervals[interval][i]]
i += 1
i -= 1
x += self._lengths[self._permutation._intervals[interval][i]]
j = self._permutation._intervals[interval][i]
return self._permutation._alphabet.unrank(j)
def in_which_interval(self, x, interval=0):
r"""
Returns the letter for which x is in this interval.
INPUT:
- ``x`` - a positive number
- ``interval`` - (default: 'top') 'top' or 'bottom'
OUTPUT:
label -- a label corresponding to an interval
TEST:
::
sage: t = iet.IntervalExchangeTransformation(('a b c','c b a'),[1,1,1])
sage: t.in_which_interval(0)
'a'
sage: t.in_which_interval(0.3)
'a'
sage: t.in_which_interval(1)
'b'
sage: t.in_which_interval(1.9)
'b'
sage: t.in_which_interval(2)
'c'
sage: t.in_which_interval(2.1)
'c'
sage: t.in_which_interval(3)
Traceback (most recent call last):
...
ValueError: your value does not lie in [0;l[
.. and for the bottom interval::
sage: t.in_which_interval(0,'bottom')
'c'
sage: t.in_which_interval(1.2,'bottom')
'b'
sage: t.in_which_interval(2.9,'bottom')
'a'
"""
interval = interval_conversion(interval)
if x < 0 or x >= self.length():
raise ValueError, "your value does not lie in [0;l["
i = 0
while x >= 0:
x -= self._lengths[self._permutation._intervals[interval][i]]
i += 1
i -= 1
x += self._lengths[self._permutation._intervals[interval][i]]
j = self._permutation._intervals[interval][i]
return self._permutation._alphabet.unrank(j)
