84 lines
2.3 KiB
Python
84 lines
2.3 KiB
Python
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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, coeff_list):
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self.degree = len(coeff_list) - 1
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self.coefficients = [x % Polynomial.n for x in coeff_list]
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def __pow__(self, n):
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result = self
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for i in range(n):
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result = Polynomial.multiply(result, result)
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return result
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@staticmethod
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def add(p1, p2):
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result = []
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f = p1.coefficients
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g = p2.coefficients
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if len(f) >= len(g):
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result = f
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for i in range(len(g)):
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result[i] = f[i] + g[i]
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else:
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result = g
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for i in range(len(f)):
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result[i] = f[i] + g[i]
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result = [x % int(Polynomial.n) for x in result]
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return Polynomial(result)
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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(len(f)):
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for j in range(len(g)):
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result[i+j] += f[i] * g[j]
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result = [x % int(Polynomial.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(Polynomial.n)):
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r = (i * x) % int(Polynomial.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 _ 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(Polynomial.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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