def test_gf_irreducible():
assert gf_irreducible_p(gf_irreducible(1, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(2, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(3, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(4, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(5, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(6, 11, ZZ), 11, ZZ) == True
assert gf_irreducible_p(gf_irreducible(7, 11, ZZ), 11, ZZ) == True
def test_gf_irreducible_p():
assert gf_irred_p_ben_or([7], 11, ZZ) == True
assert gf_irred_p_ben_or([7, 3], 11, ZZ) == True
assert gf_irred_p_ben_or([7, 3, 1], 11, ZZ) == False
assert gf_irred_p_rabin([7], 11, ZZ) == True
assert gf_irred_p_rabin([7, 3], 11, ZZ) == True
assert gf_irred_p_rabin([7, 3, 1], 11, ZZ) == False
assert gf_irreducible_p([7], 11, ZZ, method='ben-or') == True
assert gf_irreducible_p([7, 3], 11, ZZ, method='ben-or') == True
assert gf_irreducible_p([7, 3, 1], 11, ZZ, method='ben-or') == False
assert gf_irreducible_p([7], 11, ZZ, method='rabin') == True
assert gf_irreducible_p([7, 3], 11, ZZ, method='rabin') == True
assert gf_irreducible_p([7, 3, 1], 11, ZZ, method='rabin') == False
raises(KeyError, "gf_irreducible_p([7], 11, ZZ, method='other')")
f = [1, 9, 9, 13, 16, 15, 6, 7, 7, 7, 10]
g = [1, 7, 16, 7, 15, 13, 13, 11, 16, 10, 9]
h = gf_mul(f, g, 17, ZZ)
assert gf_irred_p_ben_or(f, 17, ZZ) == True
assert gf_irred_p_ben_or(g, 17, ZZ) == True
assert gf_irred_p_ben_or(h, 17, ZZ) == False
assert gf_irred_p_rabin(f, 17, ZZ) == True
assert gf_irred_p_rabin(g, 17, ZZ) == True
assert gf_irred_p_rabin(h, 17, ZZ) == False
def test_gf_irreducible_p():
assert gf_irred_p_ben_or([7], 11, ZZ) == True
assert gf_irred_p_ben_or([7,3], 11, ZZ) == True
assert gf_irred_p_ben_or([7,3,1], 11, ZZ) == False
assert gf_irred_p_rabin([7], 11, ZZ) == True
assert gf_irred_p_rabin([7,3], 11, ZZ) == True
assert gf_irred_p_rabin([7,3,1], 11, ZZ) == False
assert gf_irreducible_p([7], 11, ZZ, method='ben-or') == True
assert gf_irreducible_p([7,3], 11, ZZ, method='ben-or') == True
assert gf_irreducible_p([7,3,1], 11, ZZ, method='ben-or') == False
assert gf_irreducible_p([7], 11, ZZ, method='rabin') == True
assert gf_irreducible_p([7,3], 11, ZZ, method='rabin') == True
assert gf_irreducible_p([7,3,1], 11, ZZ, method='rabin') == False
raises(KeyError, "gf_irreducible_p([7], 11, ZZ, method='other')")
f = [1, 9, 9, 13, 16, 15, 6, 7, 7, 7, 10]
g = [1, 7, 16, 7, 15, 13, 13, 11, 16, 10, 9]
h = gf_mul(f, g, 17, ZZ)
assert gf_irred_p_ben_or(f, 17, ZZ) == True
assert gf_irred_p_ben_or(g, 17, ZZ) == True
assert gf_irred_p_ben_or(h, 17, ZZ) == False
assert gf_irred_p_rabin(f, 17, ZZ) == True
assert gf_irred_p_rabin(g, 17, ZZ) == True
assert gf_irred_p_rabin(h, 17, ZZ) == False
def __init__(self, p, n=1):
p, n = int(p), int(n)
if not isprime(p):
raise ValueError("p must be a prime number, not %s" % p)
if n <= 0:
raise ValueError("n must be a positive integer, not %s" % n)
self.p = p
self.n = n
if n == 1:
self.reducing = [1, 0]
else:
for c in itertools.product(range(p), repeat=n):
poly = (1, *c)
if gf_irreducible_p(poly, p, ZZ):
self.reducing = poly
break
def __init__(self, p: int, n: int = 1) -> None:
p, n = int(p), int(n)
self.check_p(p)
self.check_n(n)
self.flush()
self._p = p
self._n = n
if n == 1:
self.reducing = [1, 0]
else:
for c in itertools.product(range(p), repeat=n):
poly = (1, *c)
if gf_irreducible_p(poly, p, ZZ):
self.reducing = poly
break
def gen(self):
irr_poly = Poly(alpha ** self.m + alpha + 1, alpha).set_domain(GF(self.q))
if gf_irreducible_p([int(c) for c in irr_poly.all_coeffs()], self.q, ZZ):
quotient_size = len(power_dict(self.n, irr_poly, self.q))
else:
quotient_size = 0
log.info("irr(q_size: {}): {}".format(quotient_size, irr_poly))
while quotient_size < self.n:
irr_poly = Poly([int(c.numerator) for c in gf_irreducible(self.m, self.q, ZZ)], alpha)
quotient_size = len(power_dict(self.n, irr_poly, self.q))
log.info("irr(q_size: {}): {}".format(quotient_size, irr_poly))
g_poly = None
for i in range(self.b, self.b + self.d - 1):
if g_poly is None:
g_poly = minimal_poly(i, self.n, self.q, irr_poly)
else:
g_poly = lcm(g_poly, minimal_poly(i, self.n, self.q, irr_poly))
g_poly = g_poly.trunc(self.q)
log.info("g(x)={}".format(g_poly))
return irr_poly, g_poly
def __init__(self, p, n=None):
if n is None:
L = primeFact(p)
if len(set(L)) > 1:
raise ValueError('order must be a prime power')
p = L[0]
n = len(L)
p, n = int(p), int(n)
if not isprime(p):
raise ValueError("p must be a prime number, not %s" % p)
if n <= 0:
raise ValueError("n must be a positive integer, not %s" % n)
self.p = p
self.n = n
if n == 1:
self.reducing = [1, 0]
else:
for c in itertools.product(range(p), repeat=n):
poly = (1, *c)
if gf_irreducible_p(poly, p, ZZ):
self.reducing = poly
break
self.iterpos = 0
def test_gf_irreducible_p():
assert gf_irred_p_ben_or([7], 11, ZZ) == True
assert gf_irred_p_ben_or([7,3], 11, ZZ) == True
assert gf_irred_p_ben_or([7,3,1], 11, ZZ) == False
assert gf_irred_p_rabin([7], 11, ZZ) == True
assert gf_irred_p_rabin([7,3], 11, ZZ) == True
assert gf_irred_p_rabin([7,3,1], 11, ZZ) == False
config.setup('GF_IRRED_METHOD', 'ben-or')
assert gf_irreducible_p([7], 11, ZZ) == True
assert gf_irreducible_p([7,3], 11, ZZ) == True
assert gf_irreducible_p([7,3,1], 11, ZZ) == False
config.setup('GF_IRRED_METHOD', 'rabin')
assert gf_irreducible_p([7], 11, ZZ) == True
assert gf_irreducible_p([7,3], 11, ZZ) == True
assert gf_irreducible_p([7,3,1], 11, ZZ) == False
config.setup('GF_IRRED_METHOD', 'other')
raises(KeyError, lambda: gf_irreducible_p([7], 11, ZZ))
config.setup('GF_IRRED_METHOD')
f = [1, 9, 9, 13, 16, 15, 6, 7, 7, 7, 10]
g = [1, 7, 16, 7, 15, 13, 13, 11, 16, 10, 9]
h = gf_mul(f, g, 17, ZZ)
assert gf_irred_p_ben_or(f, 17, ZZ) == True
assert gf_irred_p_ben_or(g, 17, ZZ) == True
assert gf_irred_p_ben_or(h, 17, ZZ) == False
assert gf_irred_p_rabin(f, 17, ZZ) == True
assert gf_irred_p_rabin(g, 17, ZZ) == True
assert gf_irred_p_rabin(h, 17, ZZ) == False
def test_gf_irreducible_p():
assert gf_irred_p_ben_or(ZZ.map([7]), 11, ZZ) is True
assert gf_irred_p_ben_or(ZZ.map([7, 3]), 11, ZZ) is True
assert gf_irred_p_ben_or(ZZ.map([7, 3, 1]), 11, ZZ) is False
assert gf_irred_p_rabin(ZZ.map([7]), 11, ZZ) is True
assert gf_irred_p_rabin(ZZ.map([7, 3]), 11, ZZ) is True
assert gf_irred_p_rabin(ZZ.map([7, 3, 1]), 11, ZZ) is False
config.setup("GF_IRRED_METHOD", "ben-or")
assert gf_irreducible_p(ZZ.map([7]), 11, ZZ) is True
assert gf_irreducible_p(ZZ.map([7, 3]), 11, ZZ) is True
assert gf_irreducible_p(ZZ.map([7, 3, 1]), 11, ZZ) is False
config.setup("GF_IRRED_METHOD", "rabin")
assert gf_irreducible_p(ZZ.map([7]), 11, ZZ) is True
assert gf_irreducible_p(ZZ.map([7, 3]), 11, ZZ) is True
assert gf_irreducible_p(ZZ.map([7, 3, 1]), 11, ZZ) is False
config.setup("GF_IRRED_METHOD", "other")
raises(KeyError, lambda: gf_irreducible_p([7], 11, ZZ))
config.setup("GF_IRRED_METHOD")
f = ZZ.map([1, 9, 9, 13, 16, 15, 6, 7, 7, 7, 10])
g = ZZ.map([1, 7, 16, 7, 15, 13, 13, 11, 16, 10, 9])
h = gf_mul(f, g, 17, ZZ)
assert gf_irred_p_ben_or(f, 17, ZZ) is True
assert gf_irred_p_ben_or(g, 17, ZZ) is True
assert gf_irred_p_ben_or(h, 17, ZZ) is False
assert gf_irred_p_rabin(f, 17, ZZ) is True
assert gf_irred_p_rabin(g, 17, ZZ) is True
assert gf_irred_p_rabin(h, 17, ZZ) is False
def is_irreducible(f, p):
return gf_irreducible_p(f, p, ZZ)
def is_irreducible_poly(poly, p):
return gf_irreducible_p([int(c) for c in poly.all_coeffs()], p, ZZ)
