def __init__(self, basis, quiet=False):
self._basis = basis
self._max_basis_length = max([len(b) for b in self._basis])
self._class = AvClass(basis, 1)
self._configs_checked = set()
self._automaton_ready = False
self._root = Configuration((0, ), self._basis, 'm')
self._perm = Configuration((1, ), self._basis, 'f')
self._tree = {self._root: self._root.children()}
self._automaton = {self._root: list(self._root.children())}
self._has_inssch = False
self._reductions = {}
self._automaton_ready = False
if self.has_inssch():
self._has_inssch = True
else:
syms = PermSet(self._basis).all_syms()
for S in syms:
self._basis = S
if self.has_inssch():
self._has_inssch = True
if not quiet:
print(
'Av({}) does not have an insertion scheme, but its symmetry Av({}) does.'
.format(basis, S))
break
if not self._has_inssch:
if not quiet:
print(
'Neither this class nor its symmetries has an insertion scheme.'
)
def __init__(self, basis, quiet=False):
self._basis = basis
self._max_basis_length = max([len(b) for b in self._basis])
self._class = AvClass(basis, 1)
self._configs_checked = set()
self._automaton_ready = False
self._root = Configuration((0,), self._basis, 'm')
self._perm = Configuration((1,), self._basis, 'f')
self._tree = {self._root: self._root.children()}
self._automaton = {self._root: list(self._root.children())}
self._has_inssch = False
self._reductions = {}
self._automaton_ready = False
if self.has_inssch():
self._has_inssch = True
else:
syms = PermSet(self._basis).all_syms()
for S in syms:
self._basis = S
if self.has_inssch():
self._has_inssch = True
if not quiet:
print('Av({}) does not have an insertion scheme, but its symmetry Av({}) does.'.format(basis, S))
break
if not self._has_inssch:
if not quiet:
print('Neither this class nor its symmetries has an insertion scheme.')
class InsertionScheme():
_tree = {}
_basis = []
_max_basis_length = 0
_automaton = {}
_root = None
_configs_checked = set()
_automaton_ready = False
_has_inssch = False
_reductions = {}
_class = []
def __init__(self, basis, quiet=False):
self._basis = basis
self._max_basis_length = max([len(b) for b in self._basis])
self._class = AvClass(basis, 1)
self._configs_checked = set()
self._automaton_ready = False
self._root = Configuration((0,), self._basis, 'm')
self._perm = Configuration((1,), self._basis, 'f')
self._tree = {self._root: self._root.children()}
self._automaton = {self._root: list(self._root.children())}
self._has_inssch = False
self._reductions = {}
self._automaton_ready = False
if self.has_inssch():
self._has_inssch = True
else:
syms = PermSet(self._basis).all_syms()
for S in syms:
self._basis = S
if self.has_inssch():
self._has_inssch = True
if not quiet:
print('Av({}) does not have an insertion scheme, but its symmetry Av({}) does.'.format(basis, S))
break
if not self._has_inssch:
if not quiet:
print('Neither this class nor its symmetries has an insertion scheme.')
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 follow_reduce(self,config):
while config in self._reductions.keys():
config = self._reductions[config]
return config
def build_rules(self, verbose=True, make_class=False, class_bound=100):
configs_to_check = [Configuration((0,), self._basis)]
while len(configs_to_check) > 0:
if verbose:
# print '\tstates to check:',len(configs_to_check),', nodes in tree:',len(self._tree.keys()),', states:', len(self._automaton)
s_to_print = '\tstates to check: {}, nodes in tree: {}, states: {}'.format(
len(configs_to_check), len(self._tree.keys()), len(self._automaton))
print(s_to_print)
configs_to_check.sort(key=len)
current_config = configs_to_check[0]
if verbose:
print('\nChecking: ',current_config)
self._configs_checked.add(current_config)
if current_config.is_permutation():
if verbose:
print(current_config,' is not reducible')
configs_to_check.remove(current_config)
continue
length_to_check = self._max_basis_length + current_config.num_slots() - 2
reducible = False
order_to_check = sorted(range(len(current_config)), key=lambda i : current_config[i], reverse=True)
checked_already = list()
for i in order_to_check:
if current_config[i] == 0 or (i > 0 and i < len(current_config)-1 and current_config[i-1] == 0 and current_config[i+1] == 0):
continue
second_config = Configuration(current_config[:i]+current_config[i+1:], self._basis, '?')
if second_config in checked_already:
continue
checked_already.append(second_config)
if verbose:
# print 'Checking isomorphism (depth='+str(length_to_check)+'):',current_config, '<->', second_config
print('Checking isomorphism (depth={}): {} <-> {}'.format(
length_to_check, current_config, second_config))
if self.check_isomorphism(current_config, second_config, length_to_check, make_class, class_bound):
self._reductions[current_config] = second_config
if verbose:
print(current_config,' is reducible to ',second_config)
if current_config in self._automaton.keys():
del self._automaton[current_config]
for config in self._automaton.keys():
if current_config in self._automaton[config]:
self._automaton[config].remove(current_config)
self._automaton[config].append(self.follow_reduce(second_config))
configs_to_check.append(second_config)
reducible = True
break
if not reducible:
if verbose:
print(current_config,'is not reducible')
if make_class and len(self._class) < len(current_config) + 2 and len(current_config) + 2 <= class_bound:
if verbose:
# print '\t\t\tExtending class length from ', (len(self._class) - 1), 'to', (len(current_config) + 2), 'for', current_config, '(!)'
print('\t\t\tExtending class length from {} to {} for {} (!)'.format(
len(self._class - 1), len(current_config) + 2, current_config))
self._class.extend_to_length(len(current_config)+2)
if verbose:
print('\t\t\t\tDone!')
# print '3'
TTT = current_config.valid_children(self._class)
self._automaton[current_config] = list(TTT)
configs_to_check.extend(TTT)
configs_to_check.remove(current_config)
configs_to_check = list(set(configs_to_check).difference(self._configs_checked))
self.standardize_perms()
self._automaton_ready = True
def standardize_perms(self):
for config in self._automaton.keys():
for c in self._automaton[config]:
if c.is_permutation():
self._automaton[config].remove(c)
self._automaton[config].append(self._perm)
def check_isomorphism(self, c1, c2, depth, make_class=False, class_bound=100):
# print '\t\tCI:',depth,c1,c2,len(self._tree.keys())
if depth == 0 or c1.is_permutation() or c2.is_permutation():
if c1.is_permutation() != c2.is_permutation():
pass
# print c1,c2
return c1.is_permutation() == c2.is_permutation()
if c1 not in self._tree.keys():
if make_class and len(self._class) < len(c1) + 3 and len(c1) + 2 <= class_bound:
print('\t\t\tExtending class length from ', (len(self._class)-1), 'to', (len(c1) + 2), 'for', c1, '(@)')
self._class.extend_to_length(len(c1)+2)
print('\t\t\t\tDone!')
# print '1',c1,len(c1)
self._tree[c1] = c1.valid_children(self._class)
if c2 not in self._tree.keys():
if make_class and len(self._class) < len(c2) + 3 and len(c2) + 2 <= class_bound:
print('\t\t\tExtending class length from ', (len(self._class)-1), 'to', (len(c2) + 2), 'for', c2, '(#)')
self._class.extend_to_length(len(c2)+2)
print('\t\t\t\tDone!')
# print '2'
self._tree[c2] = c2.valid_children(self._class)
c1kids = {c._type : c for c in self._tree[c1]}
c2kids = {c._type : c for c in self._tree[c2]}
if set(c1kids.keys()) != set(c2kids.keys()):
# print c1,c2,c1kids,c2kids
return False
# if random.randint(1,1000) == 535:
# print '\tnum states:',len(self._tree), '\tdepth:',depth
return all([self.check_isomorphism(c1kids[i], c2kids[i], depth-1, make_class, class_bound) for i in c1kids.keys()])
def gf(self, verbose=False, show_series=False):
if not self._automaton_ready:
self.build_rules(verbose=verbose)
states = self._automaton.keys()
states.append(self._perm)
x = sympy.Symbol('x')
transitions = []
for s1 in states:
t = []
for s2 in states:
if s1 in self._automaton.keys() and s2 in self._automaton[s1]:
t.append(self._automaton[s1].count(s2)*x)
else:
t.append(0)
transitions.append(t)
M = (sympy.eye(len(states))-sympy.Matrix(transitions)) ** -1
f = (1+M[states.index(self._root),states.index(self._perm)]).factor()
if show_series:
print(f.series(x,0,11))
return f
class InsertionScheme():
_tree = {}
_basis = []
_max_basis_length = 0
_automaton = {}
_root = None
_configs_checked = set()
_automaton_ready = False
_has_inssch = False
_reductions = {}
_class = []
def __init__(self, basis, quiet=False):
self._basis = basis
self._max_basis_length = max([len(b) for b in self._basis])
self._class = AvClass(basis, 1)
self._configs_checked = set()
self._automaton_ready = False
self._root = Configuration((0, ), self._basis, 'm')
self._perm = Configuration((1, ), self._basis, 'f')
self._tree = {self._root: self._root.children()}
self._automaton = {self._root: list(self._root.children())}
self._has_inssch = False
self._reductions = {}
self._automaton_ready = False
if self.has_inssch():
self._has_inssch = True
else:
syms = PermSet(self._basis).all_syms()
for S in syms:
self._basis = S
if self.has_inssch():
self._has_inssch = True
if not quiet:
print(
'Av({}) does not have an insertion scheme, but its symmetry Av({}) does.'
.format(basis, S))
break
if not self._has_inssch:
if not quiet:
print(
'Neither this class nor its symmetries has an insertion scheme.'
)
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 follow_reduce(self, config):
while config in self._reductions.keys():
config = self._reductions[config]
return config
def build_rules(self, verbose=True, make_class=False, class_bound=100):
configs_to_check = [Configuration((0, ), self._basis)]
while len(configs_to_check) > 0:
if verbose:
# print '\tstates to check:',len(configs_to_check),', nodes in tree:',len(self._tree.keys()),', states:', len(self._automaton)
s_to_print = '\tstates to check: {}, nodes in tree: {}, states: {}'.format(
len(configs_to_check), len(self._tree.keys()),
len(self._automaton))
print(s_to_print)
configs_to_check.sort(key=len)
current_config = configs_to_check[0]
if verbose:
print('\nChecking: ', current_config)
self._configs_checked.add(current_config)
if current_config.is_permutation():
if verbose:
print(current_config, ' is not reducible')
configs_to_check.remove(current_config)
continue
length_to_check = self._max_basis_length + current_config.num_slots(
) - 2
reducible = False
order_to_check = sorted(range(len(current_config)),
key=lambda i: current_config[i],
reverse=True)
checked_already = list()
for i in order_to_check:
if current_config[i] == 0 or (i > 0
and i < len(current_config) - 1
and current_config[i - 1] == 0
and current_config[i + 1] == 0):
continue
second_config = Configuration(
current_config[:i] + current_config[i + 1:], self._basis,
'?')
if second_config in checked_already:
continue
checked_already.append(second_config)
if verbose:
# print 'Checking isomorphism (depth='+str(length_to_check)+'):',current_config, '<->', second_config
print('Checking isomorphism (depth={}): {} <-> {}'.format(
length_to_check, current_config, second_config))
if self.check_isomorphism(current_config, second_config,
length_to_check, make_class,
class_bound):
self._reductions[current_config] = second_config
if verbose:
print(current_config, ' is reducible to ',
second_config)
if current_config in self._automaton.keys():
del self._automaton[current_config]
for config in self._automaton.keys():
if current_config in self._automaton[config]:
self._automaton[config].remove(current_config)
self._automaton[config].append(
self.follow_reduce(second_config))
configs_to_check.append(second_config)
reducible = True
break
if not reducible:
if verbose:
print(current_config, 'is not reducible')
if make_class and len(
self._class) < len(current_config) + 2 and len(
current_config) + 2 <= class_bound:
if verbose:
# print '\t\t\tExtending class length from ', (len(self._class) - 1), 'to', (len(current_config) + 2), 'for', current_config, '(!)'
print(
'\t\t\tExtending class length from {} to {} for {} (!)'
.format(len(self._class - 1),
len(current_config) + 2, current_config))
self._class.extend_to_length(len(current_config) + 2)
if verbose:
print('\t\t\t\tDone!')
# print '3'
TTT = current_config.valid_children(self._class)
self._automaton[current_config] = list(TTT)
configs_to_check.extend(TTT)
configs_to_check.remove(current_config)
configs_to_check = list(
set(configs_to_check).difference(self._configs_checked))
self.standardize_perms()
self._automaton_ready = True
def standardize_perms(self):
for config in self._automaton.keys():
for c in self._automaton[config]:
if c.is_permutation():
self._automaton[config].remove(c)
self._automaton[config].append(self._perm)
def check_isomorphism(self,
c1,
c2,
depth,
make_class=False,
class_bound=100):
# print '\t\tCI:',depth,c1,c2,len(self._tree.keys())
if depth == 0 or c1.is_permutation() or c2.is_permutation():
if c1.is_permutation() != c2.is_permutation():
pass
# print c1,c2
return c1.is_permutation() == c2.is_permutation()
if c1 not in self._tree.keys():
if make_class and len(
self._class) < len(c1) + 3 and len(c1) + 2 <= class_bound:
print('\t\t\tExtending class length from ',
(len(self._class) - 1), 'to', (len(c1) + 2), 'for', c1,
'(@)')
self._class.extend_to_length(len(c1) + 2)
print('\t\t\t\tDone!')
# print '1',c1,len(c1)
self._tree[c1] = c1.valid_children(self._class)
if c2 not in self._tree.keys():
if make_class and len(
self._class) < len(c2) + 3 and len(c2) + 2 <= class_bound:
print('\t\t\tExtending class length from ',
(len(self._class) - 1), 'to', (len(c2) + 2), 'for', c2,
'(#)')
self._class.extend_to_length(len(c2) + 2)
print('\t\t\t\tDone!')
# print '2'
self._tree[c2] = c2.valid_children(self._class)
c1kids = {c._type: c for c in self._tree[c1]}
c2kids = {c._type: c for c in self._tree[c2]}
if set(c1kids.keys()) != set(c2kids.keys()):
# print c1,c2,c1kids,c2kids
return False
# if random.randint(1,1000) == 535:
# print '\tnum states:',len(self._tree), '\tdepth:',depth
return all([
self.check_isomorphism(c1kids[i], c2kids[i], depth - 1, make_class,
class_bound) for i in c1kids.keys()
])
def gf(self, verbose=False, show_series=False):
if not self._automaton_ready:
self.build_rules(verbose=verbose)
states = self._automaton.keys()
states.append(self._perm)
x = sympy.Symbol('x')
transitions = []
for s1 in states:
t = []
for s2 in states:
if s1 in self._automaton.keys() and s2 in self._automaton[s1]:
t.append(self._automaton[s1].count(s2) * x)
else:
t.append(0)
transitions.append(t)
M = (sympy.eye(len(states)) - sympy.Matrix(transitions))**-1
f = (1 + M[states.index(self._root),
states.index(self._perm)]).factor()
if show_series:
print(f.series(x, 0, 11))
return f
