def zad_5():
ran = range(0, 1024)
result0 = Modular.ModuloEquatation(8, 8, 1024, ran)
print("NWD")
print(Modular.nwd(result0))
print('Sum of x')
print(np.sum(result0))
max_value = 0
max_power = 0
for i in range(len(result0)):
value = result0[i]
power = Modular.phi(value)
if max_power < power:
max_power = power
max_value = value
elif power < max_power:
a = pow(max_value, max_power)
b = pow(value, power)
if a < b:
max_power = power
max_value = value
print("max")
print(pow(max_value, max_power))
print('k')
print(len(result0))
def test_multiply_large_numbers(self):
first = pow(81723, 4)
second = pow(56789, 7)
mod = 123456789
result = Modular.mul_modulo(first, second, mod)
expected = 28459179
self.assertEqual(expected, result)
def test_multiply_by_modulo_multiple(self):
first = 10
second = 7
mod = 5
result = Modular.mul_modulo(first, second, mod)
expected = 0
self.assertEqual(expected, result)
def test_simple_multiply(self):
first = 2
second = 3
mod = 5
result = Modular.mul_modulo(first, second, mod)
expected = 1
self.assertEqual(expected, result)
def test_simple_power(self):
first = 5
second = 4
mod = 9
result = Modular.pow_modulo(first, second, mod)
expected = 4
self.assertEqual(expected, result)
def test_power_large_numbers(self):
first = 2018
second = 2018
mod = pow(2, 32) - 1
result = Modular.pow_modulo(first, second, mod)
expected = 2110863454
self.assertEqual(expected, result)
def zad_2():
base = 2018
power = 2018
mod = pow(2, 32) - 1
a = Modular.pow_modulo(base, power, mod)
t1 = int(pow(2, 16) - 1)
result1 = a % t1
print(" a mod( 2^16 -1)")
print(result1)
result2 = Modular.tau(a)
print(" tau(a)")
print(result2)
result3 = Modular.jota(a)
print(" jota(a)")
print(result3)
result4 = Modular.nwd([a, t1])
print(" nwd(a, 2^16 -1)")
print(result4)
result5 = Modular.nww([a, t1])
print(" nww(a, 2^16 -1)")
print(result5)
result61, result62 = Modular.pi_from_probability(a)
print(" pi(a)")
print(result61)
print(result62)
result7 = Modular.phi_by_kanon(a)
print(" euler(a)")
print(result7)
result8 = Modular.is_prime(a)
t2 = Modular.kanon(a)
print(" zad2.1")
print(result8)
print(min(t2))
result9 = Modular.nfermat(a)
print(" zad2.2")
print(result9)
print(t2)
def test_ModuloEquatation(self):
expected = [1, 129, 257, 385, 513, 641, 769, 897]
ran = range(0, 1025)
a = 8
b = 8
mod = 1024
result = Modular.ModuloEquatation(a, b, mod, ran)
self.assertEquals(expected, result)
def test_euklidesEquatation(self):
a = math.pow(2, 16) - 1
b = math.pow(2, 16) + 1
nwd, x, y = Modular.euklidesEquatation(a, b)
self.assertEquals(1, nwd)
self.assertEquals(math.pow(2, 15), x)
self.assertEquals(-math.pow(2, 15) + 1, y)
def zad_3():
n = 5
solutions = []
primes = Modular.nPrime(n)
ran = range(1, 2048)
for i in range(1, n + 1):
solutions.append(Modular.ModuloEquatation(1, i, primes[i - 1], ran))
base = set(solutions[0])
for i in range(1, n):
B = set(solutions[i])
base = base.intersection(B)
x = min(base)
print(x)
is_prime = Modular.is_prime(x)
print("is prime:", is_prime)
result1 = Modular.tau(x)
print(result1)
result2 = Modular.phi(x)
print(result2)
result3 = Modular.jota(x)
print(result3)
result4 = Modular.kanon(x)
print(result4)
def test_pow_modulo(self):
expected = 2110863454
a = 2018
n = 2018
mod = pow(2, 32) - 1
result = Modular.pow_modulo(a, n, mod)
self.assertEquals(expected, result)
def zad_4():
a = pow(2, 16) - 1
b = pow(2, 16) + 1
result1 = Modular.nwd([a, b])
print("nwd", result1)
result2 = pow(a, 32) * pow(b, 32) # nwd is 1
print("nww", result2)
print("phi", Modular.phi_by_kanon_pow(a, b))
nwd, x, y = Modular.euklidesEquatation(a, b)
kanonx = Modular.kanon(x)
kanony = Modular.kanon(y)
print("x:", x)
print("kanon x:", kanonx)
print("y:", y)
print("kanon y:", kanony)
def test_kanon3(self):
expected = {2: 1, 5: 1}
a = 10
result = Modular.kanon(a)
self.assertEqual(expected, result)
def test_pi2(self):
expected = 1
a = 2
self.assertEquals(expected, Modular.pi(a))
def test_pi1(self):
expected = 0
a = 1
self.assertEquals(expected, Modular.pi(a))
def test_nFermat_non(self):
expected = None
a = 4
self.assertEquals(expected, Modular.nfermat(a))
def test_nPrimeNumbers(self):
expected = [2, 3, 5, 7, 11]
n = 5
self.assertEquals(expected, Modular.nPrime(n))
def test_nFermat0(self):
expected = 0
a = 3
self.assertEquals(expected, Modular.nfermat(a))
def test_nFermat5(self):
expected = 5
a = 4294967297
self.assertEquals(expected, Modular.nfermat(a))
def test_Fermat7(self):
expected = 340282366920938463463374607431768211457
a = 7
self.assertEquals(expected, Modular.fermat(a))
def test_kanon4(self):
expected = {97: 1}
a = 97
result = Modular.kanon(a)
self.assertEqual(expected, result)
def test_NWD1(self):
expected = 1
a = 5
b = 12
self.assertEquals(expected, Modular.nwd([a, b]))
def test_jota(self):
expected = 1
a = 0
result = Modular.jota(a)
self.assertEquals(expected, result)
def test_pi3(self):
expected = 2
a = 3
self.assertEquals(expected, Modular.pi(a))
def test_tau2(self):
expected = 8
a = 30
result = Modular.tau(a)
self.assertEquals(expected, result)
def test_pi5(self):
expected = 8
a = 19
self.assertEquals(expected, Modular.pi(a))
def test_jota_negative(self):
expected = 3
a = -5
result = Modular.jota(a)
self.assertEquals(expected, result)
def test_Fermat0(self):
expected = 3
a = 0
self.assertEquals(expected, Modular.fermat(a))
def test_NWD2(self):
expected = 1
a = int(math.pow(2, 16) + 1)
b = int(math.pow(2, 16) - 1)
self.assertEquals(expected, Modular.nwd([a, b]))
def test_Fermat5(self):
expected = 4294967297
a = 5
self.assertEquals(expected, Modular.fermat(a))