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Aleksy Wróblewski 2018-06-27 17:48:59 +00:00
parent d2187f2dbb
commit b34b9a42fb
1 changed files with 83 additions and 83 deletions
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hw4.py
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@ -1,84 +1,84 @@
from poly import Polynomial from poly import Polynomial
from sys import argv from sys import argv
from ast import literal_eval from ast import literal_eval
from fractions import gcd from fractions import gcd
class QuotientRing(): class QuotientRing():
def __init__(self, f, m): def __init__(self, f, m):
self.f = Polynomial(f, m) self.f = Polynomial(f, m)
self.m = m self.m = m
self.remainders = self.remainders() self.remainders = self.remainders()
self.reversibles = self.reversibles() self.reversibles = self.reversibles()
self.zero_divisors = self.zero_divisors() self.zero_divisors = self.zero_divisors()
self.idempotent = self.idempotent() self.idempotent = self.idempotent()
self.nilpotent = self.nilpotent() self.nilpotent = self.nilpotent()
def remainders(self): #n - exponent def remainders(self): #n - exponent
rems = [] #lista reszt rems = [] #lista reszt
m = self.m m = self.m
t = [0] t = [0]
i = 0 i = 0
while len(t) < len(self.f.poly): while len(t) < len(self.f.poly):
rems.append(Polynomial(t, m)) rems.append(Polynomial(t, m))
i = (i + 1) % m i = (i + 1) % m
t[0] = i t[0] = i
if i == 0: if i == 0:
if len(t) == 1: if len(t) == 1:
t.append(1) t.append(1)
else: else:
t[1] += 1 t[1] += 1
for j in range(1, len(t)): for j in range(1, len(t)):
if t[j] == 0 or t[j] % m != 0: if t[j] == 0 or t[j] % m != 0:
break break
temp = t[j] % m temp = t[j] % m
t[j] = 0 t[j] = 0
if temp == 0: if temp == 0:
if (j + 1) < len(t): if (j + 1) < len(t):
t[j+1] += 1 t[j+1] += 1
else: else:
t.append(1) t.append(1)
return rems return rems
def reversibles(self): def reversibles(self):
return [ rem for rem in self.remainders if len(rem.poly_gcd(self.f).poly) == 1 ] return [ rem for rem in self.remainders if len(rem.poly_gcd(self.f).poly) == 1 ]
#dopelnienie elementow odwracalnych #dopelnienie elementow odwracalnych
def zero_divisors(self): def zero_divisors(self):
return [ rem for rem in self.remainders if rem not in self.reversibles ] return [ rem for rem in self.remainders if rem not in self.reversibles ]
def idempotent(self): def idempotent(self):
idems = [] idems = []
for rem in self.remainders: for rem in self.remainders:
if (rem * rem / self.f) == (rem / self.f): if (rem * rem % self.f) == (rem % self.f):
idems.append(rem) idems.append(rem)
try: try:
if idems[0].poly == []: #implementacja wielomianow ucina zera if idems[0].poly == []: #implementacja wielomianow ucina zera
idems[0].poly = [0] idems[0].poly = [0]
except IndexError: except IndexError:
return idems return idems
return idems return idems
def nilpotent(self): def nilpotent(self):
nils = [] nils = []
phi = len([ i for i in range(1, self.m) if gcd(i, self.m) == 1 ]) phi = len([ i for i in range(1, self.m) if gcd(i, self.m) == 1 ])
for zero_div in self.zero_divisors: for zero_div in self.zero_divisors:
for i in range(self.m): for i in range(self.m):
if len((zero_div ** i / self.f).poly) == 0: if len((zero_div ** i % self.f).poly) == 0:
nils.append(zero_div) nils.append(zero_div)
break break
return nils return nils
def main(): def main():
m = int(argv[1]) m = int(argv[1])
f = literal_eval(argv[2]) f = literal_eval(argv[2])
qr = QuotientRing(f, m) qr = QuotientRing(f, m)
out = [ out = [
[ rev.poly for rev in qr.reversibles ], [ rev.poly for rev in qr.reversibles ],
[ zero_div.poly for zero_div in qr.zero_divisors ], [ zero_div.poly for zero_div in qr.zero_divisors ],
[ nil.poly for nil in qr.nilpotent ], [ nil.poly for nil in qr.nilpotent ],
[ idem.poly for idem in qr.idempotent ] [ idem.poly for idem in qr.idempotent ]
] ]
print(*out, sep='\n') print(*out, sep='\n')
if __name__ == '__main__': if __name__ == '__main__':
main() main()