def check_character_values(self, rec, verbose=False):
"""
The x's listed in values and values_gens should be coprime to the modulus N in the label.
For x's that appear in both values and values_gens, the value should be the same.
"""
# TIME about 3000s for full table
N = Integer(rec['modulus'])
v2, u2 = N.val_unit(2)
if v2 == 1:
# Z/2 doesn't contribute generators, but 2 divides N
adjust2 = -1
elif v2 >= 3:
# Z/8 and above requires two generators
adjust2 = 1
else:
adjust2 = 0
if N == 1:
# The character stores a value in the case N=1
ngens = 1
else:
ngens = len(N.factor()) + adjust2
vals = rec['values']
val_gens = rec['values_gens']
val_gens_dict = dict(val_gens)
if len(vals) != min(12, euler_phi(N)) or len(val_gens) != ngens:
if verbose:
print "Length failure", len(vals), euler_phi(N), len(
val_gens), ngens
return False
if N > 2 and (vals[0][0] != N - 1 or vals[1][0] != 1 or vals[1][1] != 0
or vals[0][1] not in [0, rec['order'] // 2]):
if verbose:
print "Initial value failure", N, rec['order'], vals[:2]
return False
if any(N.gcd(g) > 1 for g, gval in val_gens + vals):
if verbose:
print "gcd failure", [
g for g, gval in val_gens + vals if N.gcd(g) > 1
]
return False
for g, val in vals:
if g in val_gens_dict and val != val_gens_dict[g]:
if verbose:
print "Mismatch failure", g, val, val_gens_dict[g]
return False
return True
def check_character_values(self, rec, verbose=False):
"""
The x's listed in values and values_gens should be coprime to the modulus N in the label.
For x's that appear in both values and values_gens, the value should be the same.
"""
# TIME about 3000s for full table
N = Integer(rec['modulus'])
v2, u2 = N.val_unit(2)
if v2 == 1:
# Z/2 doesn't contribute generators, but 2 divides N
adjust2 = -1
elif v2 >= 3:
# Z/8 and above requires two generators
adjust2 = 1
else:
adjust2 = 0
if N == 1:
# The character stores a value in the case N=1
ngens = 1
else:
ngens = len(N.factor()) + adjust2
vals = rec['values']
val_gens = rec['values_gens']
val_gens_dict = dict(val_gens)
if len(vals) != min(12, euler_phi(N)) or len(val_gens) != ngens:
if verbose:
print "Length failure", len(vals), euler_phi(N), len(val_gens), ngens
return False
if N > 2 and (vals[0][0] != N-1 or vals[1][0] != 1 or vals[1][1] != 0 or vals[0][1] not in [0, rec['order']//2]):
if verbose:
print "Initial value failure", N, rec['order'], vals[:2]
return False
if any(N.gcd(g) > 1 for g, gval in val_gens+vals):
if verbose:
print "gcd failure", [g for g, gval in val_gens+vals if N.gcd(g) > 1]
return False
for g, val in vals:
if g in val_gens_dict and val != val_gens_dict[g]:
if verbose:
print "Mismatch failure", g, val, val_gens_dict[g]
return False
return True
