def Origami(r,
u,
sparse=False,
check=True,
as_tuple=False,
positions=None,
name=None):
r"""
Constructor for origami
INPUT:
- ``r``, ``u`` - two permutations
- ``sparse`` - boolean (default: False)
- ``check`` - boolean (default: True) - whether or not check the input
- ``as_tuple`` - boolean (default: False) - if True, assume that ``r`` and
``u`` are tuples on [0,...,N-1] (time efficient)
- ``positions`` - list of 2-tuples (default: None) - position of the squares
for drawings
- ``name`` - an optional name to the origami
"""
if not as_tuple:
r = PermutationGroupElement(r, check=check)
u = PermutationGroupElement(u, check=check)
r = [i - 1 for i in r.domain()]
u = [i - 1 for i in u.domain()]
N = max(len(r), len(u))
r.extend(xrange(len(r), N))
u.extend(xrange(len(u), N))
elif check:
sr = set(r)
su = set(u)
N = len(r)
if len(u) != N:
raise ValueError("the two tuples must be of the same length")
for i in xrange(N):
if not i in sr:
raise ValueError("%d is not in r=%s" % (i, str(r)))
if not i in su:
raise ValueError("%d is not in u=%s" % (i, str(u)))
o = Origami_dense_pyx(tuple(r), tuple(u))
if check and not o.is_connected():
print "Warning: the origami is not connected"
if name is not None:
o.rename(name)
if positions is not None:
o.set_positions(positions)
return o
def Origami(r, u,
sparse=False,
check=True,
as_tuple=False,
positions=None, name=None):
r"""
Constructor for origami
INPUT:
- ``r``, ``u`` - two permutations
- ``sparse`` - boolean (default: False)
- ``check`` - boolean (default: True) - whether or not check the input
- ``as_tuple`` - boolean (default: False) - if True, assume that ``r`` and
``u`` are tuples on [0,...,N-1] (time efficient)
- ``positions`` - list of 2-tuples (default: None) - position of the squares
for drawings
- ``name`` - an optional name to the origami
"""
if not as_tuple:
r = PermutationGroupElement(r, check=check)
u = PermutationGroupElement(u, check=check)
r = [i-1 for i in r.domain()]
u = [i-1 for i in u.domain()]
N = max(len(r),len(u))
r.extend(xrange(len(r),N))
u.extend(xrange(len(u),N))
elif check:
sr = set(r)
su = set(u)
N = len(r)
if len(u) != N:
raise ValueError("the two tuples must be of the same length")
for i in xrange(N):
if not i in sr:
raise ValueError("%d is not in r=%s" %(i,str(r)))
if not i in su:
raise ValueError("%d is not in u=%s" %(i,str(u)))
o = Origami_dense_pyx(tuple(r),tuple(u))
if check and not o.is_connected():
print "Warning: the origami is not connected"
if name is not None:
o.rename(name)
if positions is not None:
o.set_positions(positions)
return o
def g(self,i=None):
r"""
Return the ``i``-th permutation that defines this pillowcase cover.
"""
if i is None:
return self.g(0), self.g(1), self.g(2), self.g(3)
i = int(i)
if i < 0 or i > 3:
raise IndexError("the index i (={}) must be in {{0,1,2,3}}".format(i))
return PermutationGroupElement([j+1 for j in self.g_tuple(i)], check=False)
def PillowcaseCover(g0, g1, g2, g3=None,
sparse=False,
check=True,
as_tuple=False,
positions=None, name=None):
r"""
Pillowcase cover constructor.
"""
if not as_tuple:
g0 = PermutationGroupElement(g0, check=check)
g1 = PermutationGroupElement(g1, check=check)
g2 = PermutationGroupElement(g2, check=check)
if g3 is None:
g3 = (~g2) * (~g1) * (~g0)
else:
g3 = PermutationGroupElement(g3, check=check)
g0 = [i-1 for i in g0.domain()]
g1 = [i-1 for i in g1.domain()]
g2 = [i-1 for i in g2.domain()]
g3 = [i-1 for i in g3.domain()]
N = max([len(g0),len(g1),len(g2),len(g3)])
g0.extend(xrange(len(g0),N))
g1.extend(xrange(len(g1),N))
g2.extend(xrange(len(g2),N))
g3.extend(xrange(len(g3),N))
elif check:
s0 = set(g0)
s1 = set(g1)
s2 = set(g2)
s3 = set(g3)
N = len(g0)
if len(g1) != N or len(g2) != N or len(g3) != N:
raise ValueError("the four tuples must be of the same length")
for i in xrange(N):
if not i in g0:
raise ValueError("%d is not in g0=%s" %(i,str(g0)))
if not i in g1:
raise ValueError("%d is not in g1=%s" %(i,str(g1)))
if not i in g2:
raise ValueError("%d is not in g2=%s"%(i,str(g2)))
if not i in g3:
raise ValueError("%d is not in g3=%s"%(i,str(g3)))
pcc = PillowcaseCover_dense(tuple(g0),tuple(g1),tuple(g2),tuple(g3))
if name is not None:
pcc.rename(name)
# if positions is not None:
# o.set_positions(positions)
if check:
pcc._check()
return pcc