def has_inssch(self):
types = [
PermSet([Permutation(321),
Permutation(2143),
Permutation(2413)]),
PermSet([Permutation(123),
Permutation(3142),
Permutation(3412)]),
PermSet([Permutation(132), Permutation(312)]),
PermSet([Permutation(213), Permutation(231)])
]
return all([
any([all([b.avoids(p) for p in B]) for b in self._basis])
for B in types
])
def is_identity(perm):
"""Checks if the permutation is the identity.
>>> p = Permutation.random(10)
>>> (p * p.inverse()).is_identity()
True
"""
return perm == Permutation.identity(len(perm))
def is_identity(perm):
"""Checks if the permutation is the identity.
>>> p = Permutation.random(10)
>>> (p * p.inverse()).is_identity()
True
"""
return perm == Permutation.identity(len(perm))
def threepats(perm):
p = list(perm)
n = perm.__len__()
patnums = {'123': 0, '132': 0, '213': 0, '231': 0, '312': 0, '321': 0}
for i in range(n - 2):
for j in range(i + 1, n - 1):
for k in range(j + 1, n):
patnums[''.join(
map(lambda x: str(x + 1), Permutation([p[i], p[j],
p[k]])))] += 1
return patnums
def __init__(self, basis, length=8, verbose=0):
list.__init__(self, [PermSet() for i in range(0, length + 1)])
self.length = length
temp_basis = []
for P in basis:
temp_basis.append(Permutation(P))
basis = temp_basis
self.basis = basis
if length >= 1:
self[1].add(Permutation([1]))
for n in range(2, length + 1):
k = 0
outof = len(self[n - 1])
for P in self[n - 1]:
k += 1
if verbose > 0 and k % verbose == 0:
# print '\t\t\t\tRight Extensions:',k,'/',outof,'\t( length',n,')'
print(
'\t\t\t\tRight Extenstions: {}/{}\t( length {}'.format(
k, outof, n))
insertion_locations = P.insertion_locations
add_this_time = []
for Q in P.right_extensions():
is_good = True
for B in basis:
if B.involved_in(Q, last_require=2):
is_good = False
insertion_locations[Q[-1]] = 0
# break
if is_good:
add_this_time.append(Q)
for Q in add_this_time:
# print Q,'is good'
# print '\tchanging IL from ',Q.insertion_locations,'to',(insertion_locations[:Q[-1]+1]+ insertion_locations[Q[-1]:])
Q.insertion_locations = insertion_locations[:Q[
-1] + 1] + insertion_locations[Q[-1]:]
self[n].add(Q)
def all(cls, length):
"""Builds the set of all permutations of a given length.
Parameters:
-----------
length : int
the length of the permutations
Examples
--------
>>> p = Permutation(12); q = Permutation(21)
>>> PermSet.all(2) == PermSet([p, q])
True
"""
return PermSet(Permutation.listall(length))
def all(cls, length):
"""Builds the set of all permutations of a given length.
Parameters:
-----------
length : int
the length of the permutations
Examples
--------
>>> p = Permutation(12); q = Permutation(21)
>>> PermSet.all(2) == PermSet([p, q])
True
"""
return PermSet(Permutation.listall(length))
def othercycles(perm):
# builds a permutation induced by the black and gray edges separately, and
# counts the number of cycles in their product
p = list(perm)
n = perm.__len__()
q = [0] + [p[i] + 1 for i in range(n)]
grayperm = [n] + range(n)
blackperm = [0 for i in range(n + 1)]
for i in range(n + 1):
ind = q.index(i)
blackperm[i] = q[ind - 1]
newperm = []
for i in range(n + 1):
k = blackperm[i]
j = grayperm[k]
newperm.append(j)
return Permutation(newperm).numcycles()
def fourpats(perm):
p = list(perm)
n = perm.__len__()
patnums = {
'1234': 0,
'1243': 0,
'1324': 0,
'1342': 0,
'1423': 0,
'1432': 0,
'2134': 0,
'2143': 0,
'2314': 0,
'2341': 0,
'2413': 0,
'2431': 0,
'3124': 0,
'3142': 0,
'3214': 0,
'3241': 0,
'3412': 0,
'3421': 0,
'4123': 0,
'4132': 0,
'4213': 0,
'4231': 0,
'4312': 0,
'4321': 0
}
for i in range(n - 3):
for j in range(i + 1, n - 2):
for k in range(j + 1, n - 1):
for m in range(k + 1, n):
patnums[''.join(
map(lambda x: str(x + 1),
list(Permutation([p[i], p[j], p[k], p[m]]))))] += 1
return patnums
def right_juxtaposition(self, C, generate_perms=True):
A = permset.PermSet()
max_length = max([len(P) for P in self.basis]) + max(
[len(P) for P in C.basis])
for n in range(2, max_length + 1):
for i in range(0, factorial(n)):
P = Permutation(i, n)
for Q in self.basis:
for R in C.basis:
if len(Q) + len(R) == n:
if (Q == Permutation(P[0:len(Q)])
and R == Permutation(P[len(Q):n])):
A.add(P)
elif len(Q) + len(R) - 1 == n:
if (Q == Permutation(P[0:len(Q)])
and Permutation(R) == Permutation(
P[len(Q) - 1:n])):
A.add(P)
return AvClass(list(A.minimal_elements()),
length=(8 if generate_perms else 0))
def ltrmax(perm):
return [len(perm) - i - 1 for i in Permutation(perm[::-1]).rtlmax()][::-1]