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__truediv__ to __mod__

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Aleksy Wróblewski 2018-06-27 17:48:31 +00:00
parent f4885f813b
commit d2187f2dbb
1 changed files with 114 additions and 114 deletions
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228
poly.py
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@ -1,115 +1,115 @@
from fractions import gcd from fractions import gcd
class Polynomial(): class Polynomial():
def __init__(self, lst, mod): def __init__(self, lst, mod):
self.poly = list(map(lambda x: x % mod, lst)) self.poly = list(map(lambda x: x % mod, lst))
self.mod = mod self.mod = mod
self.normalize() self.normalize()
def normalize(self): def normalize(self):
while self.poly and self.poly[-1] == 0: while self.poly and self.poly[-1] == 0:
self.poly.pop() self.poly.pop()
#zwraca jednomian stopnia n #zwraca jednomian stopnia n
@staticmethod @staticmethod
def Monomial(n, c, mod): def Monomial(n, c, mod):
zeros = [0]*n zeros = [0]*n
zeros.append(c) zeros.append(c)
return Polynomial(zeros, mod) return Polynomial(zeros, mod)
def __add__(self, p2): def __add__(self, p2):
p1 = self p1 = self
len_p1, len_p2= len(p1.poly), len(p2.poly) len_p1, len_p2= len(p1.poly), len(p2.poly)
res = [0] * max(len_p1, len_p2) res = [0] * max(len_p1, len_p2)
if len_p1 > len_p2: if len_p1 > len_p2:
for _ in range(len_p1-len_p2): for _ in range(len_p1-len_p2):
p2.poly.append(0) p2.poly.append(0)
else: else:
for _ in range(len_p2-len_p1): for _ in range(len_p2-len_p1):
p1.poly.append(0) p1.poly.append(0)
for i in range(len(res)): for i in range(len(res)):
res[i] = (p1.poly[i] + p2.poly[i]) % self.mod res[i] = (p1.poly[i] + p2.poly[i]) % self.mod
return Polynomial(res, self.mod) return Polynomial(res, self.mod)
def __sub__(self, p2): def __sub__(self, p2):
p1 = self p1 = self
res = [] res = []
len_p2 = len(p2.poly) len_p2 = len(p2.poly)
for i in range(len(p1.poly)): for i in range(len(p1.poly)):
if i < len_p2: if i < len_p2:
res.append(p1.poly[i] - p2.poly[i] % self.mod) res.append(p1.poly[i] - p2.poly[i] % self.mod)
else: else:
res.append(p1.poly[i]) res.append(p1.poly[i])
return Polynomial(res, self.mod) return Polynomial(res, self.mod)
def __mul__(self, p2): def __mul__(self, p2):
res = [0]*(len(self.poly)+len(p2.poly)-1) res = [0]*(len(self.poly)+len(p2.poly)-1)
for i, x1 in enumerate(self.poly): for i, x1 in enumerate(self.poly):
for j, x2 in enumerate(p2.poly): for j, x2 in enumerate(p2.poly):
res[i+j] += x1 * x2 % self.mod res[i+j] += x1 * x2 % self.mod
return Polynomial(res, self.mod) return Polynomial(res, self.mod)
def __eq__(self, p2): def __eq__(self, p2):
p1 = self p1 = self
return p1.poly == p2.poly and p1.mod == p2.mod return p1.poly == p2.poly and p1.mod == p2.mod
def __pow__(self, n): def __pow__(self, n):
p1 = self p1 = self
for i in range(n): for i in range(n):
p1 = p1 * p1 p1 = p1 * p1
return p1 return p1
def __truediv__(self, p2): def __mod__(self, p2):
p1 = self p1 = self
m = self.mod m = self.mod
if len(p1.poly) < len(p2.poly): if len(p1.poly) < len(p2.poly):
return p1 return p1
if len(p2.poly) == 0: if len(p2.poly) == 0:
raise ZeroDivisionError raise ZeroDivisionError
divisor_coeff = p2.poly[-1] divisor_coeff = p2.poly[-1]
divisor_exp = len(p2.poly) - 1 divisor_exp = len(p2.poly) - 1
while len(p1.poly) >= len(p2.poly): while len(p1.poly) >= len(p2.poly):
max_coeff_p1 = p1.poly[-1] #wspolczynnik przy najwyzszej potedze max_coeff_p1 = p1.poly[-1] #wspolczynnik przy najwyzszej potedze
try: try:
tmp_coeff = modDiv(max_coeff_p1, divisor_coeff, m) tmp_coeff = modDiv(max_coeff_p1, divisor_coeff, m)
except ZeroDivisionError as e: except ZeroDivisionError as e:
raise e raise e
tmp_exp = len(p1.poly)-1 - divisor_exp tmp_exp = len(p1.poly)-1 - divisor_exp
tmp = [0] * tmp_exp tmp = [0] * tmp_exp
tmp.append(tmp_coeff) tmp.append(tmp_coeff)
sub = Polynomial(tmp, m) * p2 sub = Polynomial(tmp, m) * p2
p1 = p1 - sub p1 = p1 - sub
p1.normalize() p1.normalize()
return Polynomial(p1.poly, m) return Polynomial(p1.poly, m)
def poly_gcd(self, p2): def poly_gcd(self, p2):
p1 = self p1 = self
try: try:
divisible = p2 divisible = p2
except ZeroDivisionError as e: except ZeroDivisionError as e:
raise e raise e
if p2.poly == []: if p2.poly == []:
return p1 return p1
return p2.poly_gcd(p1 / p2) return p2.poly_gcd(p1 % p2)
def modDiv(a, b, m): # a*b^-1 (mod m) def modDiv(a, b, m): # a*b^-1 (mod m)
if gcd(b, m) != 1: if gcd(b, m) != 1:
raise ZeroDivisionError raise ZeroDivisionError
else: else:
return (a * modinv(b, m)) % m return (a * modinv(b, m)) % m
#rozszerzony algorytm euklidesa #rozszerzony algorytm euklidesa
def egcd(a, b): def egcd(a, b):
if a == 0: if a == 0:
return (b, 0, 1) return (b, 0, 1)
else: else:
g, y, x = egcd(b % a, a) g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y) return (g, x - (b // a) * y, y)
def modinv(a, m): def modinv(a, m):
g, x, y = egcd(a, m) g, x, y = egcd(a, m)
return x % m return x % m