forked from kalmar/DALGLI0
48 lines
1.8 KiB
Python
48 lines
1.8 KiB
Python
from fractions import gcd
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class Modulo:
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def __init__(self, n):
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self.elems = list(range(n))
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self.n = n
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self.reversibles = self.get_reversibles()
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self.idempotent = self.get_idempotent()
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self.zero_divisors = self.get_zero_divisors()
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self.nilpotent = self.get_nilpotent()
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'''elementy odwracalne to te, ktorych nwd z n jest rowne 1'''
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def get_reversibles(self):
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return list(filter(lambda x: gcd(x, self.n) == 1, self.elems))
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'''nie rozwazamy elementow odwracalnych ani liczby 0
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#dzielnik zera nie moze byc elementem odwracalnym'''
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def get_zero_divisors(self):
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potential_zeros = [ elem for elem in self.elems if elem not in self.reversibles ][1:]
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results = []
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for elem in potential_zeros:
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for elem2 in potential_zeros:
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if (elem * elem2) % self.n == 0:
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results.append(elem)
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break
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return list(results)
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def get_idempotent(self):
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'''element idempotentny => a^2 przystaje do a'''
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return list(filter(lambda x: x*x % self.n == x, self.elems))
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def get_nilpotent(self):
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'''jesli pierscien nie zawiera dzielnikow zera, to nie zawiera takze elementow
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nilpotentnych; wystarczy sprawdzic wsrod dzielnikow zera '''
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potential_nils = self.zero_divisors
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phi = len(self.reversibles) #funkcja fi
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results = []
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for elem in potential_nils:
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for i in range(1, phi+1):
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if elem**i % self.n == 0:
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results.append(elem)
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break
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return results
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def main():
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m = Modulo(int(input()))
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print([m.reversibles, m.zero_divisors, m.nilpotent, m.idempotent])
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if __name__ == '__main__':
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main()
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