49 lines
1.6 KiB
Python
49 lines
1.6 KiB
Python
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from fractions import gcd
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class Modulo:
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def __init__(self, n):
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self.n = int(n)
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self.modulo_set = list(range(self.n))
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self.answer = []
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def get_inverse_elements(self):
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self.inverse_elements = []
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for i in self.modulo_set:
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if gcd(i, self.n) == 1:
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self.inverse_elements.append(i)
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self.answer.append(self.inverse_elements)
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def get_zero_divisors(self):
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self.zero_divisors = []
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for i in self.modulo_set:
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for j in self.modulo_set:
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if (i * j) % self.n == 0 and i != 0 and j != 0:
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self.zero_divisors.append(i)
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self.answer.append(list(set(self.zero_divisors)))
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def get_nilpotent_elements(self):
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self.nilpotent_elements = []
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for i in self.modulo_set:
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for j in range(1, len(self.inverse_elements) + 1):
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if (i**j) % self.n == 0 and i != 0:
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self.nilpotent_elements.append(i)
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self.answer.append(list(set(self.nilpotent_elements)))
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def get_idempotent_elements(self):
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self.idempotent_elements = []
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for i in self.modulo_set:
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if (i*i) % self.n == i:
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self.idempotent_elements.append(i)
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self.answer.append(self.idempotent_elements)
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def get_all(self):
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self.get_inverse_elements()
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self.get_zero_divisors()
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self.get_nilpotent_elements()
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self.get_idempotent_elements()
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return self.answer
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s = Modulo(input("Enter n: "))
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print(s.get_all())
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