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3 Commits
Author | SHA1 | Date | |
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78f79da83c | |||
448979c654 | |||
24087c2bb4 |
48
Ring.py
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48
Ring.py
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@ -0,0 +1,48 @@
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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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90
wielomiany.py
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90
wielomiany.py
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@ -0,0 +1,90 @@
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import sys
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import ast
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class Polynomial:
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n = 0
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def __init__(self, coef_list):
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self.degree = len(coef_list) - 1
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self.coefficients = coef_list
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@staticmethod
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def multiply(p1, p2):
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result = [0] * (p1.degree + p2.degree + 1)
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f = p1.coefficients
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g = p2.coefficients
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for i in range(0, len(f)):
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for j in range(0, len(g)):
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result[i+j] += f[i] * g[j]
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result = [x % int(n) for x in result]
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return Polynomial(result)
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@staticmethod
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def divide(p1, p2):
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def inverse(x):
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for i in range(1, int(n)):
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r = (i * x) % int(n)
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if r == 1:
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break
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else:
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raise ZeroDivisionError
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return i
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if p1.degree < p2.degree:
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return p1
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f = p1.coefficients
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g = p2.coefficients
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g_lead_coef = g[-1]
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g_deg = p2.degree
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while len(f) >= len(g):
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f_lead_coef = f[-1]
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tmp_coef = f_lead_coef * inverse(g_lead_coef)
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tmp_exp = len(f) - 1 - g_deg
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tmp = []
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for i in range(tmp_exp):
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tmp.append(0)
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tmp.append(tmp_coef)
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tmp_poly = Polynomial(tmp)
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sub = Polynomial.multiply(p2, tmp_poly)
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f = [x - y for x, y in zip(f, sub.coefficients)]
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f = [x % int(n) for x in f]
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while f and f[-1] == 0:
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f.pop()
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return Polynomial(f)
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@staticmethod
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def gcd(p1, p2):
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if len(p2.coefficients) == 0:
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return p1
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return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
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def main():
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c1 = ast.literal_eval(sys.argv[2])
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c2 = ast.literal_eval(sys.argv[3])
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f = Polynomial(c1)
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g = Polynomial(c2)
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ans = []
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mul = Polynomial.multiply(f, g)
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ans.append(mul.coefficients)
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try:
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div = Polynomial.divide(f, g)
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ans.append(div.coefficients)
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except ZeroDivisionError as e:
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ans.append(e)
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try:
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gcd = Polynomial.gcd(f, g)
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ans.append(gcd.coefficients)
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except ZeroDivisionError as e:
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ans.append(e)
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print(ans)
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if __name__ == "__main__":
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n = int(sys.argv[1])
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main()
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