def is_complete(self):
r"""
Return whether that all winners appear.
EXAMPLES::
sage: from surface_dynamics import iet
sage: p = iet.Permutation('a b c d e f', 'f e d c b a')
sage: q = p.rauzy_move('t').rauzy_move('b').rauzy_move('t')
sage: f = iet.FlipSequence(q, ['t', 't', 'b', 'b', 'b', 't', 'b', 't'],
....: top_bottom_inverse=True,
....: left_right_inverse=True)
sage: f.close()
sage: f.is_complete()
True
"""
if not self._start == self._end:
raise ValueError('not a loop')
n = len(self._start)
moved = set()
for p, winner, side in self:
moved.update(perm_orbit(self._relabelling, p._labels[winner][side]))
if len(moved) == n:
return True
return False
def face_orbit(self, i):
r"""
Return the orbit of ``i`` under the permutation associated to faces.
"""
if self._active_darts[i]:
return perm_orbit(self._faces,i)
return None
def face_orbit(self, i):
r"""
Return the orbit of ``i`` under the permutation associated to faces.
"""
if self._active_darts[i]:
return perm_orbit(self._faces,i)
return None
def edge_orbit(self, i):
r"""
Return the orbit of the dart ``i`` under the permutation that defines
the edges.
"""
if self._active_darts[i]:
return perm_orbit(self._edges,i)
return None
def vertex_orbit(self, i):
r"""
Return the orbit of ``i`` under the permutation that define the
vertices.
"""
if self._active_darts[i]:
return perm_orbit(self._vertices,i)
return None
def edge_orbit(self, i):
r"""
Return the orbit of the dart ``i`` under the permutation that defines
the edges.
"""
if self._active_darts[i]:
return perm_orbit(self._edges,i)
return None
def vertex_orbit(self, i):
r"""
Return the orbit of ``i`` under the permutation that define the
vertices.
"""
if self._active_darts[i]:
return perm_orbit(self._vertices,i)
return None
