87 lines
2.3 KiB
Python
87 lines
2.3 KiB
Python
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class Polynomial:
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n = 0
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def __init__(self, *args):
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self.degree = len(args) - 1
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self.coefficients = list(args)
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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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n = input("Enter n: ")
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Polynomial.n = int(n)
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c1 = [int(x) for x in input("Enter 1st polynomial (coefficients divided by space): ").split()]
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c1 = [x % Polynomial.n for x in c1]
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c2 = [int(x) for x in input("Enter 2nd polynomial: ").split()]
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c2 = [x % Polynomial.n for x in c2]
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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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