def find_adjacent_classes(self, m):
result = []
if self.type == OperationType.MULTIPLE:
count_anjacent_classes = euler(m)[0] / len(self.elements) - 1
for i in range(1, m):
if count_anjacent_classes == 0:
break
if get_nod(i, m) != 1 or i in self.elements:
continue
tmp = []
for each in self.elements:
tmp.append(each * i % m)
count_anjacent_classes -= 1
result.append(tmp)
elif self.type == OperationType.ADDITION:
if euler(m)[0] == m - 1:
return []
for i in range(1, int(m / len(self.elements))):
tmp = []
for each in self.elements:
tmp.append(int((each + i) % m))
result.append(tmp)
return result
def get_inverse_of(m: int, a: int):
subtract = getSubtractClassFor(m)
if a > m:
a = a % m
if a == 0:
raise ValueError(f'Can not find inverse element for {a} by m = {m}')
# SKIP 1?
for each in subtract:
if a == each:
tmp_euler = euler(m)[0]
u = each**(tmp_euler - 1)
return u % m
def getInverseOf(m: int, a: int):
answ = {}
subtract = getSubtractClassFor(m)
if abs(a) > m:
a = a % m
# SKIP 1?
for each in subtract:
if a == each or (a < 0 and a + m == each):
tmp_euler = euler(m)[0]
u = each**(tmp_euler - 1)
answ[a] = u % m
# return dictionary [K:V],
# K - a
# V - u
return answ
def getAllInverseOf(m: int):
answ = {}
subtract = getSubtractClassFor(m)
# SKIP 1?
for each in subtract:
if each == 1:
answ[1] = 1
else:
tmp_euler = euler(m)[0]
u = each**(tmp_euler - 1)
answ[each] = u % m
# return dictionary [K:V],
# K - a
# V - u
return answ
def order_multiple_group(m: int):
eul = euler_script_5.euler(m)[0]
canon = canonic_view_script_4.prime_factors_list(eul)
elem_basis = []
# find order for each elem
for a in range(1, m):
ri = []
# bypass prime list
for prime_elem in canon.keys():
w = canon[prime_elem] # get max W
for wi in reversed(range(w + 1)):
if (a**((m - 1) / (prime_elem**wi))) % m == 1 or wi == 0:
ri.append(prime_elem**(w - wi))
break
elem_basis.append(f'ord({a}):={reduce(lambda x, y: x * y, ri)}')
return elem_basis
def find_root_and_system(m: int, print_solution: bool):
eul = euler_script_5.euler(m)[0]
canonic_number = canonic_view_script_4.to_list_prime(canonic_view_script_4.prime_factors_list(eul))
if print_solution:
print(f'Euler: φ({m}) = {eul}')
print(f'Canon view: {eul} = {canonic_view_script_4.pretty_str(canonic_view_script_4.prime_factors_list(eul))}')
a = 2
while a < eul:
isRoot = True
for each in canonic_number:
if isRoot:
degree = int(eul / each)
if (a ** degree) % m == 1:
isRoot = False
else:
break
if isRoot and nod_script_1_2.get_nod(a, m) == 1:
system = get_system(a, canonic_view_script_4.get_all_prime(m), m)
return a, system
a += 1
return -1, []
def get_euler(m):
return euler(m)[0]