def test_totatives(z):
assert isinstance(Integer(z).totatives, set)
if z <= 0:
assert not Integer(z).totatives
else:
assert Integer(z).totatives == {x for x in range(1, z + 1)
if Integer.gcd(z, x) == 1}
def test_primalidad(n, k):
two = Integer("2")
one = Integer("1")
zero = Integer("0")
if (n.equals(two)):
return "PRIMO"
elif (n.is_even() or n.is_power()):
return "COMPUESTO"
else:
a = []
for i in range(0, k):
a.append(random.randint(1, n.to_int() - 1))
b = []
for a_i in a:
integer_ai = Integer(str(a_i))
gcd_i = integer_ai.gcd(n)
if (gcd_i.greater_than(one)):
return "COMPUESTO"
else:
exponent = n.substract(one).divide(two)[0]
b_i = integer_ai.exp_mod(exponent, n)
b.append(b_i)
neg = 0
for b_i in b:
if (b_i.add(one).module(n).equals(zero)):
neg += 1
elif (not b_i.substract(one).module(n).equals(zero)):
return "COMPUESTO"
if (neg == 0):
print("-------------break 4-------------------")
return "COMPUESTO"
else:
return "PRIMO"
def test_gcd(a, b):
assert Integer.gcd(a, b) == math.gcd(a, b)