84 lines
2.7 KiB
Python
84 lines
2.7 KiB
Python
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from poly import Polynomial
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from sys import argv
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from ast import literal_eval
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from fractions import gcd
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class QuotientRing():
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def __init__(self, f, m):
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self.f = Polynomial(f, m)
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self.m = m
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self.remainders = self.remainders()
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self.reversibles = self.reversibles()
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self.zero_divisors = self.zero_divisors()
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self.idempotent = self.idempotent()
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self.nilpotent = self.nilpotent()
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def remainders(self): #n - exponent
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rems = [] #lista reszt
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m = self.m
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t = [0]
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i = 0
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while len(t) < len(self.f.poly):
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rems.append(Polynomial(t, m))
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i = (i + 1) % m
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t[0] = i
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if i == 0:
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if len(t) == 1:
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t.append(1)
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else:
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t[1] += 1
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for j in range(1, len(t)):
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if t[j] == 0 or t[j] % m != 0:
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break
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temp = t[j] % m
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t[j] = 0
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if temp == 0:
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if (j + 1) < len(t):
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t[j+1] += 1
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else:
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t.append(1)
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return rems
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def reversibles(self):
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return [ rem for rem in self.remainders if len(rem.poly_gcd(self.f).poly) == 1 ]
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#dopelnienie elementow odwracalnych
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def zero_divisors(self):
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return [ rem for rem in self.remainders if rem not in self.reversibles ]
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def idempotent(self):
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idems = []
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for rem in self.remainders:
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if (rem * rem / self.f) == (rem / self.f):
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idems.append(rem)
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try:
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if idems[0].poly == []: #implementacja wielomianow ucina zera
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idems[0].poly = [0]
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except IndexError:
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return idems
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return idems
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def nilpotent(self):
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nils = []
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phi = len([ i for i in range(1, self.m) if gcd(i, self.m) == 1 ])
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for zero_div in self.zero_divisors:
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for i in range(self.m):
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if len((zero_div ** i / self.f).poly) == 0:
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nils.append(zero_div)
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break
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return nils
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def main():
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m = int(argv[1])
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f = literal_eval(argv[2])
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qr = QuotientRing(f, m)
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out = [
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[ rev.poly for rev in qr.reversibles ],
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[ zero_div.poly for zero_div in qr.zero_divisors ],
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[ nil.poly for nil in qr.nilpotent ],
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[ idem.poly for idem in qr.idempotent ]
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]
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print(*out, sep='\n')
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if __name__ == '__main__':
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main()
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