def rubik():
n = 48
base = Permutation.identity(n)
L = [(1, 3, 8, 6), (2, 5, 7, 4), (33, 9, 41, 32), (36, 12, 44, 29),
(38, 14, 46, 27)]
F = [(9, 11, 16, 14), (10, 13, 15, 12), (38, 17, 43, 8), (39, 20, 42, 5),
(40, 22, 41, 3)]
R = [(17, 19, 24, 22), (18, 21, 23, 20), (48, 16, 40, 25),
(45, 13, 37, 28), (43, 11, 35, 30)]
B = [(25, 27, 32, 30), (26, 29, 31, 28), (19, 33, 6, 48), (21, 34, 4, 47),
(24, 35, 1, 46)]
U = [(33, 35, 40, 38), (34, 37, 39, 36), (25, 17, 9, 1), (26, 18, 10, 2),
(27, 19, 11, 3)]
D = [(41, 43, 48, 46), (42, 45, 47, 44), (6, 14, 22, 30), (7, 15, 23, 31),
(8, 16, 24, 32)]
generator_set = [L, F, R, B, U, D]
generator_set = [
Permutation.from_cycles(n, move) for move in generator_set
]
example = Schreier.Algorithm(n, generator_set, base)
example.run()
print(example.get_order())
def listAll(anInt):
theList = []
for k in range(anInt):
theList.append(k)
z = Permutation(theList)
for k in range(factorial(len(z.data))):
b = factoradic(k,len(z.data))
c = z.permutation(k)
d = z.getPermutationIndex(c)
print "%s\t%s\t%s\t%s" % (k,b,c,d)
def rec(self, pos):
self.stab_chain[pos].build_tree()
schreier_generators = self.stab_chain[pos].get_schreier_generators()
for h in schreier_generators:
residue, break_pos = self.check_element(h)
if residue != Permutation.identity(self.n):
if break_pos == len(self.stab_chain) - 1:
self.stab_chain.append(
self.ChainSegment(self.n, [Permutation.identity(self.n)], self.base[len(self.stab_chain) + 1]))
for broken in range(break_pos, pos, -1):
self.stab_chain[broken].stab_gen.append(residue)
self.rec(broken)
def getPermutedFeynmans(self):
# This method finds all possible permutaions of a list of photon
# objects, returns a list of Feynman objects, each with a different
# possible permutation
feyn_list = [] #list of feynman diagrams
photon_list = self.getTupleSet()
N_photons = len(photon_list)
permuted_photons = Permutation.getPermutations(photon_list)
N_permutations = len(permuted_photons)
# create list of feynman objects for each permutation
for i in range(N_permutations):
temp_feyn = Feynman() #new feynman diagram
for j in range(N_photons):
# generate temp_photon from permutation
temp_tuple = permuted_photons[i][j]
temp_photon = Photon.Photon(temp_tuple[0],temp_tuple[1])
#add new photon to new feynman diagram
temp_feyn.addPhoton(temp_photon)
# make Omegas and Mus consistent for all permutations of feyn
temp_feyn.linkMolecule(self.linkedMol)
# add new feynman diagram to list of feynman diagrams
feyn_list.append(temp_feyn)
return feyn_list
def testPermutation(self):
print("\n%%%%%%% Testing Permutation")
expectedResult = 336
result = Permutation.permutation(8, 3)
print("permutation(8,3)=" + str(result))
self.assertEqual(result, expectedResult, msg="Permutation(8,3)")
expectedResult = 120
result = Permutation.permutation(5, 5)
print("permutation(5,5)=" + str(result))
self.assertEqual(result, expectedResult, msg="Permutation(5,5)")
expectedResult = 132
result = Permutation.permutation(12, 2)
print("permutation(12,2)=" + str(result))
self.assertEqual(result, expectedResult, msg="Permutation(12,2)")
def example_A_5():
print('Пример работы с группой A_5\n')
a = Permutation([2, 3, 1, 4, 5])
b = Permutation([1, 3, 4, 2, 5])
c = Permutation([1, 2, 4, 5, 3])
print('Образующие A_5:')
print('a =', a)
print('b =', b)
print('c =', c)
print()
A_5 = StabilizerChain([a, b, c])
print('|A_5| =', A_5.ord())
print()
print('Орбита 1: ', A_5.get_orbit(1))
print('Орбита 2 в Stab_1:', A_5[1].tree.get_orbit())
print('Образующие Stab_{1, 2}:', A_5.get_gen_set(2))
print()
print('Сильное порождающее множество для A_5:')
print(A_5.get_strong_gen_set())
print()
sigma = Permutation([2, 1, 3, 4, 5])
print('Сожержится ли', sigma, 'в A_5?', A_5.contains(sigma))
print()
sigma = Permutation([2, 1, 4, 3, 5])
print('Содержится ли', sigma, 'в A_5?', A_5.contains(sigma))
print()
print('Разложение через Сильное порождающее множество:')
print(sigma, '=', A_5.contains(sigma, need_decomp=True))
print('\n- - - - - - - - - - - - - - - - - - - - - - - - -\n')
return A_5
def example_permutations():
print('\n- - - - - - - - - - - - - - - - - - - - - - - - -\n')
print('Пример работы с перестановками\n')
a = Permutation([3, 4, 1, 2, 6, 7, 5])
print('a =', a)
b = to_perm([1, 5, 4, 3, 2])
print('b =', b)
c = to_perm('(5 7 1 4 8)')
print('c =', c)
print()
print('a * b =', a * b)
print('b * a =', b * a)
print()
print('b * c =', b * c)
print('c * b =', c * b)
print()
print('a ^ 0 =', a**0)
print('a ^ 1 =', a**1)
print('a ^ 3 =', a**3)
print('a ^ 226 =', a**226)
print('a ^ 123456789 =', a**123456789)
print('a ^ -1 =', a**-1)
print('a ^ -2 =', a**-2)
print()
print('ord(a) =', a.ord())
print('ord(b) =', b.ord())
print()
print('a = b ?', a == b)
print('c = (8 5 7 1 4) ?', c == to_perm('(8 5 7 1 4)'))
print('\n- - - - - - - - - - - - - - - - - - - - - - - - -\n')
def task():
n = 56
rows = 7
cols = 8
swap_rows_cols = []
for i in range(rows):
for j in range(cols):
swap_rows_cols.append(j * rows + i + 1)
swap_rows_cols = Permutation.Perm(swap_rows_cols)
print(swap_rows_cols.as_cycles()) # first generator
swap_halves = Permutation.Perm([(n // 2 + i) % n + 1 for i in range(n)])
print(swap_halves.as_cycles()) # second generator
generator_set = [swap_rows_cols, swap_halves]
# top cards in right order
print("Enter top cards order")
print("example: 1 3 2 4 will check deck with these cards on the top")
order = list(map(int, input().split()))
base = order.copy()
for i in range(1, n + 1):
if i not in base:
base.append(i)
base = Permutation.Perm(base)
print(order)
cards = Schreier.Algorithm(n, generator_set, base)
cards.run()
print(cards.get_order()) # order of group
print(cards.stab_chain[1].stab_gen) # generators of stabilizer of point 1
residue, level = cards.check_element(base)
print(residue, level)
if level >= len(order):
print("Possible")
else:
print("Impossible")
def summary(self):
x_features = self.x
if self.xbin and self.x_bin != 0: # x bins
x_freq = equal_freq(x_features, self.x_bin) \
if self.bin_type == 'freq' \
else equal_width(x_features, self.x_bin)
else:
x_freq = x_features
if self.ybin and self.y_bin != 0: # y bins
y_freq = equal_freq(self.y, self.y_bin) \
if self.bin_type == 'freq' \
else equal_width(self.y, self.y_bin)
else:
y_freq = self.y
mi = fGain(x_freq, y_freq) if self.fraction else gain(x_freq, y_freq)
if self.permut:
permut = Permutation(x_freq, y_freq).summary()
permut = permut / entropy(y_freq) if self.fraction else permut
mi -= permut
return mi
import Permutation
prime = [0, 2, 3, 5, 7, 11, 13, 17]
num = [str(i) for i in range(10)]
allnums = []
while not Permutation.isEnd(num):
isPan = True
for k in range(1, 8):
if int(''.join(num[k:k + 3]).lstrip('0')) % prime[k] != 0:
isPan = False
break
if isPan:
print(int(''.join(num)))
allnums.append(int(''.join(num)))
num = Permutation.nextPermuteStr(num)
sum = 0
for n in allnums:
sum += n
print(sum)
import MathUtils
import Permutation as permutation
num = 987654321
max = 2
while num > 0:
if MathUtils.isPrime(num):
max = num
print("max prime: {}".format(num))
break
if permutation.isBegin(list(str(num))):
num = list(str(num / 10)).sort(reverse=True)
num = int(str(num))
else:
num = int(''.join(permutation.lastPermuteStr(list(str(num)))))
def my_task():
'''
Условие задачи
Цыганка гадает вам на картах. Она раскладывает 56 карт из младшей колоды таро на столе в семь рядов по 8 карт в каждом (сначала она заполняет верхний ряд слева направо, а потом переходит к следующему и т.д.). Потом она собирает карты обратно в колоду по столбцам (сверху оказывается карта в левом верхнем углу, снизу в правом нижнем). Собирая карты, цыганка может немного их перемешать, снимая верхнюю половину колоды и кладя её под низ.
Цыганка хочет добиться воспроизводимости гадания (полезно для бизнеса).
1). Какими способами она может тасовать карты так, чтобы сверху оставалась та же карта, которая была там до тасования?
2). Может ли она при этом подложить под верхнюю карту любую другую заранее выбранную, и если да, то каким количеством способов?
'''
print('Тестовая задача\n')
print('Перестановки, порождающие группу TG: ') # как я понял из условия
a = Permutation([
1, 9, 17, 25, 33, 41, 49, 2, 10, 18, 26, 34, 42, 50, 3, 11, 19, 27, 35,
43, 51, 4, 12, 20, 28, 36, 44, 52, 5, 13, 21, 29, 37, 45, 53, 6, 14,
22, 30, 38, 46, 54, 7, 15, 23, 31, 39, 47, 55, 8, 16, 24, 32, 40, 48,
56
])
b = Permutation([
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46,
47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28
])
print('a =', a) # (2 ... 8)(4 ... 22)(6 ... 36)(12 ... 23)
print('b =', b) # (1 29)(2 30)(3 31)(4 32)...(27 55)(28 56)
print()
stdout.flush()
# Строим полную цепочку стабилизаторов
TG = StabilizerChain([a, b])
print('|TG| =', TG.ord()) # 20460710453732638271310403731456000000
stab_1 = TG.ord() // len(TG[0].tree)
print('|Stab_1| =', stab_1) # 365369829530939969130542923776000000
print()
print('Орбита второй карты в Stab_1 =',
TG[1].tree.get_orbit()) # {2, 3, 4, ..., 54, 55}
# -> Для всех чисел, кроме {1, 56} ответ на 2-ой вопрос - Можно
print()
stab_12 = TG.ord() // len(TG[0].tree) // len(TG[1].tree)
print('|Stab_{1, 2}| =', stab_12) # 6766107954276666095010054144000000
print()
x = int(input('Введите карту, которую нужно поместить под 1-ую: '))
answer_x = stab_12
if x in [1, 56]:
answer_x = 0
print('Количество способов поместить карту', x, 'под 1-ую =', answer_x)
print('\n- - - - - - - - - - - - - - - - - - - - - - - - -\n')
return TG
# Am * Bn = Cm+n where 2*(m + n) = 9
# or Am * Bn = Cm+n+1 2*(m + n) + 1= 9
# => m + n = 4
import math
import Permutation as lp
numbers = [i for i in range(1, 10)]
ans = set([])
while (not lp.isEnd(numbers)):
C = numbers[0] + numbers[1] * 10 + numbers[2] * 100 + numbers[3] * 1000
A = numbers[4] + numbers[5] * 10
B = numbers[6] + numbers[7] * 10 + numbers[8] * 100
if A * B == C:
ans.add(C)
A = numbers[4]
B = numbers[5] + numbers[6] * 10 + numbers[7] * 100 + numbers[8] * 1000
if A * B == C:
ans.add(C)
numbers = lp.nextPermuteStr(numbers)
res = 0
ans = list(ans)
for i in range(len(ans)):
res += ans[i]
print(res)
subs_count = {}
for i in range(0, len(lst) - 2):
for j in range(i + 1, len(lst) - 1):
for k in range(j + 1, len(lst)):
if lst[k] - lst[j] == lst[j] - lst[i]:
print(lst[i], lst[j], lst[k])
return
sequence_set = set([])
all_set = set([])
for prime in prime_tab:
all_set.add(prime)
sequence_set.add(prime)
next_permutation = pmt.nextPermuteStr([int(i) for i in str(prime)])
next_num = tmp_convert(next_permutation)
while (not pmt.isEnd(next_permutation)):
if next_num == prime or next_num in all_set:
sequence_set.clear()
break
if next_num in prime_tab:
sequence_set.add(next_num)
all_set.add(next_num)
next_permutation = pmt.nextPermuteStr(next_permutation)
next_num = tmp_convert(next_permutation)
if len(sequence_set) > 2:
def __init__(self, n, generator_set, base):
self.n = n
self.base = base
self.stab_chain = [self.ChainSegment(n, generator_set, base[1]),
self.ChainSegment(n, [Permutation.identity(n)], base[2])]
def summary(self, scores=False):
if self.individual:
d = len(self.x[0]) if type(
self.x[0]) in [np.array, np.ndarray, list] else 1
for j in range(d):
x_features = self.x[:, j] if d != 1 else self.x
if self.xbin and self.x_bin != 0: # x bins
x_freq = equal_freq(x_features, self.x_bin) \
if self.bin_type == 'freq' \
else equal_width(x_features, self.x_bin)
else:
x_freq = x_features
if self.ybin and self.y_bin != 0: # y bins
y_freq = equal_freq(self.y, self.y_bin) \
if self.bin_type == 'freq' \
else equal_width(self.y, self.y_bin)
else:
y_freq = self.y
mi = fGain(x_freq, y_freq) if self.fraction else gain(
x_freq, y_freq)
if self.permut:
permut = Permutation(x_freq, y_freq).summary()
permut = permut / entropy(
y_freq) if self.fraction else permut
mi -= permut
self.mi_list.append((mi, str('X' + str(j))))
self.mi_list.sort(reverse=True)
if scores:
self.indi_variables = [
(each[0], int(each[1][1:]))
for each in self.mi_list[:self.num_features]
]
else:
self.indi_variables = [
int(each[1][1:])
for each in self.mi_list[:self.num_features]
]
return self.mi_list
if self.interaction:
all_interactions = list(
itertools.combinations([_ for _ in range(len(self.x[0]))],
self.x_bin))
for cell in all_interactions:
if self.xbin and self.x_bin != 0:
x_freq = equal_freq(self.x[:, cell], self.x_bin) \
if self.bin_type == 'freq' \
else equal_width(self.x[:, cell], self.x_bin)
else:
x_freq = self.x[:, list(cell)]
if self.ybin and self.y_bin != 0:
y_freq = equal_freq(self.y, self.y_bin) \
if self.bin_type == 'freq' \
else equal_freq(self.y, self.y_bin)
else:
y_freq = self.y
gains = 0
for each in cell:
gains += fGain(self.x[:, each], y_freq)
entro = fGain(x_freq, y_freq) - gains
if self.x_bin and self.permut:
permut = Permutation(x_freq,
y_freq).summary() / entropy(y_freq)
mi -= permut
self.inter_list.append((entro, "-".join(list([str(each) for each in cell])))) \
if entro >= 0.05 \
else self.inter_list
self.inter_list.sort(reverse=True)
if scores:
self.inter_variables = [
(each[0], [int(sub) for sub in each[1].split('-')])
for each in self.inter_list[:self.num_features]
]
else:
self.inter_variables = [[
int(sub) for sub in each[1].split('-')
] for each in self.inter_list[:self.num_features]]
return self.indi_variables, self.inter_variables