115 lines
3.1 KiB
Python
115 lines
3.1 KiB
Python
from fractions import gcd
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class Polynomial():
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def __init__(self, lst, mod):
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self.poly = list(map(lambda x: x % mod, lst))
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self.mod = mod
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self.normalize()
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def normalize(self):
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while self.poly and self.poly[-1] == 0:
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self.poly.pop()
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#zwraca jednomian stopnia n
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@staticmethod
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def Monomial(n, c, mod):
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zeros = [0]*n
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zeros.append(c)
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return Polynomial(zeros, mod)
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def __add__(self, p2):
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p1 = self
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len_p1, len_p2= len(p1.poly), len(p2.poly)
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res = [0] * max(len_p1, len_p2)
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if len_p1 > len_p2:
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for _ in range(len_p1-len_p2):
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p2.poly.append(0)
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else:
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for _ in range(len_p2-len_p1):
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p1.poly.append(0)
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for i in range(len(res)):
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res[i] = (p1.poly[i] + p2.poly[i]) % self.mod
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return Polynomial(res, self.mod)
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def __sub__(self, p2):
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p1 = self
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res = []
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len_p2 = len(p2.poly)
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for i in range(len(p1.poly)):
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if i < len_p2:
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res.append(p1.poly[i] - p2.poly[i] % self.mod)
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else:
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res.append(p1.poly[i])
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return Polynomial(res, self.mod)
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def __mul__(self, p2):
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res = [0]*(len(self.poly)+len(p2.poly)-1)
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for i, x1 in enumerate(self.poly):
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for j, x2 in enumerate(p2.poly):
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res[i+j] += x1 * x2 % self.mod
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return Polynomial(res, self.mod)
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def __eq__(self, p2):
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p1 = self
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return p1.poly == p2.poly and p1.mod == p2.mod
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def __pow__(self, n):
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p1 = self
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for i in range(n):
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p1 = p1 * p1
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return p1
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def __mod__(self, p2):
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p1 = self
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m = self.mod
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if len(p1.poly) < len(p2.poly):
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return p1
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if len(p2.poly) == 0:
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raise ZeroDivisionError
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divisor_coeff = p2.poly[-1]
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divisor_exp = len(p2.poly) - 1
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while len(p1.poly) >= len(p2.poly):
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max_coeff_p1 = p1.poly[-1] #wspolczynnik przy najwyzszej potedze
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try:
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tmp_coeff = modDiv(max_coeff_p1, divisor_coeff, m)
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except ZeroDivisionError as e:
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raise e
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tmp_exp = len(p1.poly)-1 - divisor_exp
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tmp = [0] * tmp_exp
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tmp.append(tmp_coeff)
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sub = Polynomial(tmp, m) * p2
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p1 = p1 - sub
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p1.normalize()
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return Polynomial(p1.poly, m)
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def poly_gcd(self, p2):
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p1 = self
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try:
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divisible = p2
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except ZeroDivisionError as e:
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raise e
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if p2.poly == []:
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return p1
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return p2.poly_gcd(p1 % p2)
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def modDiv(a, b, m): # a*b^-1 (mod m)
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if gcd(b, m) != 1:
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raise ZeroDivisionError
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else:
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return (a * modinv(b, m)) % m
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#rozszerzony algorytm euklidesa
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def egcd(a, b):
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if a == 0:
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return (b, 0, 1)
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else:
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g, y, x = egcd(b % a, a)
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return (g, x - (b // a) * y, y)
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def modinv(a, m):
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g, x, y = egcd(a, m)
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return x % m |