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Author SHA1 Message Date
78f79da83c Zaktualizuj 'wielomiany.py' 2018-06-07 08:06:57 +00:00
448979c654 Dodaj 'wielomiany.py' 2018-06-06 23:25:32 +00:00
24087c2bb4 Prześlij pliki do '' 2018-05-30 18:35:47 +00:00
2 changed files with 138 additions and 0 deletions

48
Ring.py Normal file
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from fractions import gcd
class Modulo:
def __init__(self, n):
self.n = int(n)
self.modulo_set = list(range(self.n))
self.answer = []
def get_inverse_elements(self):
self.inverse_elements = []
for i in self.modulo_set:
if gcd(i, self.n) == 1:
self.inverse_elements.append(i)
self.answer.append(self.inverse_elements)
def get_zero_divisors(self):
self.zero_divisors = []
for i in self.modulo_set:
for j in self.modulo_set:
if (i * j) % self.n == 0 and i != 0 and j != 0:
self.zero_divisors.append(i)
self.answer.append(list(set(self.zero_divisors)))
def get_nilpotent_elements(self):
self.nilpotent_elements = []
for i in self.modulo_set:
for j in range(1, len(self.inverse_elements) + 1):
if (i**j) % self.n == 0 and i != 0:
self.nilpotent_elements.append(i)
self.answer.append(list(set(self.nilpotent_elements)))
def get_idempotent_elements(self):
self.idempotent_elements = []
for i in self.modulo_set:
if (i*i) % self.n == i:
self.idempotent_elements.append(i)
self.answer.append(self.idempotent_elements)
def get_all(self):
self.get_inverse_elements()
self.get_zero_divisors()
self.get_nilpotent_elements()
self.get_idempotent_elements()
return self.answer
s = Modulo(input("Enter n: "))
print(s.get_all())

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