def resolve_indication(a, b, l, m):
# find inverse and recount a
if get_inverse_of(m, b) is None:
raise RuntimeError('No solution!')
a = int(a * get_inverse_of(m, b) % m)
# find index and recount a
a = index = get_index_for(m, a)
# find betta as euler(m)
betta = get_euler(m)[0]
# check possible
nod = get_nod(l, betta)
if not is_solution_possible(index, nod):
raise RuntimeError("No solution, because (d,index) !=0")
# cut the equation
m = int(betta / nod)
a = int(a / nod)
b = int(b / nod)
l = int(l / nod)
# final cut
b = int(b * get_inverse_of(m, a) % m)
print(f'x = {find_root_and_system(m, False)[0]}^({b} + {m}k)')
return None
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_params(equation_str: str):
equations = []
# get parameters
for equation_str in equation_str.split(';'):
b = 0
m = 0
tmp_b = re.search(r'=[1-9][0-9]*\(', equation_str)
tmp_m = re.search(r'mod[1-9][0-9]*', equation_str)
# get parameter - b
if tmp_b is None:
raise RuntimeError(f'Ooops... Can not find parameter b.')
else:
b = tmp_b.group(0)[1:-1]
# get parameter - m
if tmp_m is None:
raise RuntimeError(f'Ooops... Can not find parameter m.')
else:
m = tmp_m.group(0)[3:]
equations.append(ChineseEquation(b, m, equation_str))
# validate nod
for i in range(len(equations) - 1):
nod_m1_m2 = nod_script_1_2.get_nod(equations[i].m, equations[i + 1].m)
if nod_m1_m2 != 1:
raise RuntimeError(f'Ooops... Equation has no solution because nod('
f'{equations[i].m},{equations[i + 1].m}) = {nod_m1_m2}.')
return equations
def compresParam(a, b, m, printSolution: bool):
# 74x=69(mod7) => 4x=6(mod7)
# 21x=35(mod14) => 7x=7x(mod14)
if abs(a) > m:
a = int(a % m)
if abs(b) > m:
b = int(b % m)
if nod_script_1_2.get_nod(m, a) == nod_script_1_2.get_nod(m, b):
tmp_m = int(m / nod_script_1_2.get_nod(m, a))
a = int(a / nod_script_1_2.get_nod(m, a))
b = int(b / nod_script_1_2.get_nod(m, b))
m = tmp_m
if printSolution:
print(f'compress: {a}x={b}(mod{m})')
return a, b, m
def order_addition_group(m: int):
elem_basis = []
if isPrimary(m):
return list(map(lambda a: f'ord({a})={m}', range(1, m + 1)))
for a in range(1, m + 1):
if get_nod(a, m) == 1:
elem_basis.append(f'ord({a})={m}')
else:
for k in range(1, m):
if a * k % m == 0:
elem_basis.append(f'ord({a})={k}')
break
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 resolve_degrees(a, b, m):
a = int(get_index_for(m, a))
b = int(get_index_for(m, b))
if a == 0 or b == 0:
raise RuntimeError('No solution!')
# find betta as euler(m)
betta = get_euler(m)[0]
# check possible
nod = get_nod(b, betta)
if not is_solution_possible(a, nod):
raise RuntimeError("No solution, because (a,index) !=0")
a = int(a / nod)
b = int(b / nod)
m = int(betta / nod)
# final cut
a = int(a * get_inverse_of(m, b) % m)
print(f'x = {a} + {m}k ')
def isPrimeNumber(numOne, numTwo, printSolution: bool = False):
nod_am = nod_script_1_2.get_nod(numOne, numTwo)
if printSolution:
print(f'nod({numOne},{numTwo}) = {nod_am}')
return nod_am == 1