88 lines
2.8 KiB
Python
88 lines
2.8 KiB
Python
from poly import Polynomial as P
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import sys
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import ast
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class QuotientRing:
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def __init__(self, coeffs):
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self.fx = P(coeffs)
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self.remainder_set = self.create_remainder_set()
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self.invertible_elements = self.get_invertible_elements()
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self.zero_divisors = self.get_zero_divisors()
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self.nilpotent_elements = self.get_nilpotent_elements()
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self.idempotent_elements = self.get_idempotent_elements()
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def create_remainder_set(self):
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remainders = []
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rem = [0]
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i = 0
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while len(rem) < len(self.fx.coefficients):
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remainders.append(P(rem))
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i = (i + 1) % P.n
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rem[0] = i
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if i == 0:
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if len(rem) == 1:
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rem.append(1)
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else:
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rem[1] += 1
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for j in range(1, len(rem)):
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if rem[j] == 0 or rem[j] % P.n != 0:
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break
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tmp = rem[j] % P.n
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rem[j] = 0
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if tmp == 0:
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if (j + 1) < len(rem):
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rem[j+1] += 1
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else:
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rem.append(1)
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return remainders
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def get_invertible_elements(self):
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invertible_elements = []
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for i in self.remainder_set:
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if i.coefficients != [0] and len(P.gcd(self.fx, i).coefficients) == 1:
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invertible_elements.append(i)
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return invertible_elements
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def get_zero_divisors(self):
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zero_diviors = []
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for i in self.remainder_set:
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if i not in self.invertible_elements:
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zero_diviors.append(i)
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return zero_diviors
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def get_nilpotent_elements(self):
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nilpotent_elements = []
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for i in self.zero_divisors:
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for j in range(1, len(self.invertible_elements) + 1):
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if i.coefficients == [0] or len(P.divide(i**j, self.fx).coefficients) == 0:
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nilpotent_elements.append(i)
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break
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return nilpotent_elements
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def get_idempotent_elements(self):
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idempotent_elements = []
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for i in self.remainder_set:
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if P.divide(i**2, self.fx).coefficients == P.divide(i, self.fx).coefficients:
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idempotent_elements.append(i)
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return idempotent_elements
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def main():
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P.n = int(sys.argv[1])
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coeffs = ast.literal_eval(sys.argv[2])
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Q = QuotientRing(coeffs)
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ans = [
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[x.coefficients for x in Q.invertible_elements],
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[x.coefficients for x in Q.zero_divisors],
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[x.coefficients for x in Q.nilpotent_elements],
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[x.coefficients for x in Q.idempotent_elements]
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]
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for i in range(len(ans)):
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print(ans[i])
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if __name__ == '__main__':
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main() |