def test_factoradics():
for i in range(100):
assert from_factoradic(to_factoradic(i)) == i
assert tuple(map(to_factoradic, range(10))) == (
(0,), (1, 0,), (1, 0, 0), (1, 1, 0), (2, 0, 0), (2, 1, 0),
(1, 0, 0, 0), (1, 0, 1, 0), (1, 1, 0, 0), (1, 1, 1, 0)
)
def __getitem__(self, i):
if isinstance(i, (slice, sequence_tools.CanonicalSlice)):
canonical_slice = sequence_tools.CanonicalSlice(
i, self.length, offset=self.canonical_slice.start)
return PermSpace(self.sequence,
domain=self.domain,
n_elements=self.n_elements,
fixed_map=self.fixed_map,
degrees=self.degrees,
is_combination=self.is_combination,
slice_=canonical_slice,
perm_type=self.perm_type)
assert isinstance(i, numbers.Integral)
if i <= -1:
i += self.length
if not (0 <= i < self.length):
raise IndexError
elif self.is_sliced:
return self.unsliced[i + self.canonical_slice.start]
elif self.is_dapplied:
return self.perm_type(self.undapplied[i], perm_space=self)
#######################################################################
elif self.is_degreed:
if self.is_rapplied:
assert not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
return self.perm_type(map(self.sequence.__getitem__,
self.unrapplied[i]),
perm_space=self)
assert not self.is_rapplied and not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
# If that wasn't an example of asserting one's dominance, I don't
# know what is.
available_values = list(self.free_values)
wip_perm_sequence_dict = dict(self.fixed_map)
wip_n_cycles_in_fixed_items = \
self._n_cycles_in_fixed_items_of_just_fixed
wip_i = i
for j in self.sequence:
if j in wip_perm_sequence_dict:
continue
for unused_value in available_values:
candidate_perm_sequence_dict = dict(wip_perm_sequence_dict)
candidate_perm_sequence_dict[j] = unused_value
### Checking whether we closed a cycle: ###################
# #
if j == unused_value:
closed_cycle = True
else:
current = j
while True:
current = candidate_perm_sequence_dict[current]
if current == j:
closed_cycle = True
break
elif current not in candidate_perm_sequence_dict:
closed_cycle = False
break
# #
### Finished checking whether we closed a cycle. ##########
candidate_n_cycles_in_fixed_items = \
wip_n_cycles_in_fixed_items + closed_cycle
candidate_fixed_perm_space_length = sum(
math_tools.abs_stirling(
self.sequence_length -
len(candidate_perm_sequence_dict),
self.sequence_length - degree -
candidate_n_cycles_in_fixed_items)
for degree in self.degrees)
if wip_i < candidate_fixed_perm_space_length:
available_values.remove(unused_value)
wip_perm_sequence_dict[j] = unused_value
wip_n_cycles_in_fixed_items = \
candidate_n_cycles_in_fixed_items
break
wip_i -= candidate_fixed_perm_space_length
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type(
(wip_perm_sequence_dict[k] for k in self.domain), self)
#######################################################################
elif self.is_recurrent:
assert not self.is_dapplied and not self.is_degreed and \
not self.is_sliced
available_values = list(self.sequence)
reserved_values = nifty_collections.Bag(self.fixed_map.values())
wip_perm_sequence_dict = dict(self.fixed_map)
wip_i = i
shit_set = set()
for j in range(self.n_elements):
if j in self.fixed_map:
available_values.remove(self.fixed_map[j])
reserved_values[self.fixed_map[j]] -= 1
continue
unused_values = [
item for item in
nifty_collections.OrderedBag(available_values) -
reserved_values if item not in shit_set
]
for unused_value in unused_values:
wip_perm_sequence_dict[j] = unused_value
candidate_sub_perm_space = \
PermSpace._create_with_cut_prefix(
self.sequence,
n_elements=self.n_elements,
fixed_map=wip_perm_sequence_dict,
is_combination=self.is_combination,
shit_set=shit_set, perm_type=self.perm_type
)
if wip_i < candidate_sub_perm_space.length:
available_values.remove(unused_value)
break
else:
wip_i -= candidate_sub_perm_space.length
if self.is_combination:
shit_set.add(wip_perm_sequence_dict[j])
del wip_perm_sequence_dict[j]
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type(
dict_tools.get_tuple(wip_perm_sequence_dict, self.domain),
self)
#######################################################################
elif self.is_fixed:
free_values_perm = self._free_values_unsliced_perm_space[i]
free_values_perm_iterator = iter(free_values_perm)
return self.perm_type(
tuple((self._undapplied_fixed_map[m] if (
m in self.fixed_indices
) else next(free_values_perm_iterator))
for m in self.indices), self)
#######################################################################
elif self.is_combination:
wip_number = self.length - 1 - i
wip_perm_sequence = []
for i in range(self.n_elements, 0, -1):
for j in range(self.sequence_length, i - 2, -1):
candidate = math_tools.binomial(j, i)
if candidate <= wip_number:
wip_perm_sequence.append(self.sequence[-(j + 1)])
wip_number -= candidate
break
else:
raise RuntimeError
result = tuple(wip_perm_sequence)
assert len(result) == self.n_elements
return self.perm_type(result, self)
#######################################################################
else:
factoradic_number = math_tools.to_factoradic(
i * math.factorial(self.n_unused_elements),
n_digits_pad=self.sequence_length)
if self.is_partial:
factoradic_number = factoradic_number[:-self.n_unused_elements]
unused_numbers = list(self.sequence)
result = tuple(
unused_numbers.pop(factoradic_digit)
for factoradic_digit in factoradic_number)
assert sequence_tools.get_length(result) == self.n_elements
return self.perm_type(result, self)
def __getitem__(self, i):
if isinstance(i, (slice, sequence_tools.CanonicalSlice)):
canonical_slice = sequence_tools.CanonicalSlice(
i, self.length, offset=self.canonical_slice.start
)
return PermSpace(
self.sequence, domain=self.domain, n_elements=self.n_elements,
fixed_map=self.fixed_map, degrees=self.degrees,
is_combination=self.is_combination, slice_=canonical_slice,
perm_type=self.perm_type
)
assert isinstance(i, numbers.Integral)
if i <= -1:
i += self.length
if not (0 <= i < self.length):
raise IndexError
elif self.is_sliced:
return self.unsliced[i + self.canonical_slice.start]
elif self.is_dapplied:
return self.perm_type(self.undapplied[i], perm_space=self)
#######################################################################
elif self.is_degreed:
if self.is_rapplied:
assert not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
return self.perm_type(map(self.sequence.__getitem__,
self.unrapplied[i]),
perm_space=self)
assert not self.is_rapplied and not self.is_recurrent and \
not self.is_partial and not self.is_combination and \
not self.is_dapplied and not self.is_sliced
# If that wasn't an example of asserting one's dominance, I don't
# know what is.
available_values = list(self.free_values)
wip_perm_sequence_dict = dict(self.fixed_map)
wip_n_cycles_in_fixed_items = \
self._n_cycles_in_fixed_items_of_just_fixed
wip_i = i
for j in self.sequence:
if j in wip_perm_sequence_dict:
continue
for unused_value in available_values:
candidate_perm_sequence_dict = dict(wip_perm_sequence_dict)
candidate_perm_sequence_dict[j] = unused_value
### Checking whether we closed a cycle: ###################
# #
if j == unused_value:
closed_cycle = True
else:
current = j
while True:
current = candidate_perm_sequence_dict[current]
if current == j:
closed_cycle = True
break
elif current not in candidate_perm_sequence_dict:
closed_cycle = False
break
# #
### Finished checking whether we closed a cycle. ##########
candidate_n_cycles_in_fixed_items = \
wip_n_cycles_in_fixed_items + closed_cycle
candidate_fixed_perm_space_length = sum(
math_tools.abs_stirling(
self.sequence_length -
len(candidate_perm_sequence_dict),
self.sequence_length - degree -
candidate_n_cycles_in_fixed_items
) for degree in self.degrees
)
if wip_i < candidate_fixed_perm_space_length:
available_values.remove(unused_value)
wip_perm_sequence_dict[j] = unused_value
wip_n_cycles_in_fixed_items = \
candidate_n_cycles_in_fixed_items
break
wip_i -= candidate_fixed_perm_space_length
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type((wip_perm_sequence_dict[k] for k in
self.domain), self)
#######################################################################
elif self.is_recurrent:
assert not self.is_dapplied and not self.is_degreed and \
not self.is_sliced
available_values = list(self.sequence)
reserved_values = nifty_collections.Bag(self.fixed_map.values())
wip_perm_sequence_dict = dict(self.fixed_map)
wip_i = i
shit_set = set()
for j in range(self.n_elements):
if j in self.fixed_map:
available_values.remove(self.fixed_map[j])
reserved_values[self.fixed_map[j]] -= 1
continue
unused_values = [
item for item in
nifty_collections.OrderedBag(available_values) -
reserved_values if item not in shit_set
]
for unused_value in unused_values:
wip_perm_sequence_dict[j] = unused_value
candidate_sub_perm_space = \
PermSpace._create_with_cut_prefix(
self.sequence,
n_elements=self.n_elements,
fixed_map=wip_perm_sequence_dict,
is_combination=self.is_combination,
shit_set=shit_set, perm_type=self.perm_type
)
if wip_i < candidate_sub_perm_space.length:
available_values.remove(unused_value)
break
else:
wip_i -= candidate_sub_perm_space.length
if self.is_combination:
shit_set.add(wip_perm_sequence_dict[j])
del wip_perm_sequence_dict[j]
else:
raise RuntimeError
assert wip_i == 0
return self.perm_type(
dict_tools.get_tuple(wip_perm_sequence_dict, self.domain),
self
)
#######################################################################
elif self.is_fixed:
free_values_perm = self._free_values_unsliced_perm_space[i]
free_values_perm_iterator = iter(free_values_perm)
return self.perm_type(
tuple(
(self._undapplied_fixed_map[m] if
(m in self.fixed_indices) else
next(free_values_perm_iterator))
for m in range(self.sequence_length)
),
self
)
#######################################################################
elif self.is_combination:
wip_number = self.length - 1 - i
wip_perm_sequence = []
for i in range(self.n_elements, 0, -1):
for j in range(self.sequence_length, i - 2, -1):
candidate = math_tools.binomial(j, i)
if candidate <= wip_number:
wip_perm_sequence.append(
self.sequence[-(j+1)]
)
wip_number -= candidate
break
else:
raise RuntimeError
result = tuple(wip_perm_sequence)
assert len(result) == self.n_elements
return self.perm_type(result, self)
#######################################################################
else:
factoradic_number = math_tools.to_factoradic(
i * math.factorial(
self.n_unused_elements),
n_digits_pad=self.sequence_length
)
if self.is_partial:
factoradic_number = factoradic_number[:-self.n_unused_elements]
unused_numbers = list(self.sequence)
result = tuple(unused_numbers.pop(factoradic_digit) for
factoradic_digit in factoradic_number)
assert sequence_tools.get_length(result) == self.n_elements
return self.perm_type(result, self)
