def check_order_parity(self, rec, verbose=False):
"""
check order and parity by constructing a Conrey character in Sage (use the first index in galois_orbit)
"""
# TIME about 30000s for full table
char = ConreyCharacter(rec['modulus'], rec['galois_orbit'][0])
parity = 1 if char.is_even() else -1
success = (parity == rec['parity']
and char.conductor() == rec['conductor']
and char.multiplicative_order() == rec['order'])
if verbose and not success:
print("Order-parity failure", parity, rec['parity'],
char.conductor(), rec['conductor'],
char.multiplicative_order(), rec['order'])
return success
def get_character_modulus(a, b, limit=7):
""" this function is also used by lfunctions/LfunctionPlot.py """
headers = list(range(1, limit))
headers.append("more")
entries = {}
rows = list(range(a, b + 1))
for row in rows:
if row != 1:
G = Integers(row).list_of_elements_of_multiplicative_group()
else:
G = [1]
for chi_n in G:
chi = ConreyCharacter(row, chi_n)
multorder = chi.multiplicative_order()
if multorder <= limit:
el = chi
col = multorder
entry = entries.get((row, col), [])
entry.append(el)
entries[(row, col)] = entry
entries2 = {}
out = lambda chi: (chi.number, chi.is_primitive(),
chi.multiplicative_order(), chi.is_even())
for k, v in entries.items():
l = []
v = sorted(v, key=lambda x: x.number)
while v:
e1 = v.pop(0)
e1_num = e1.number
inv_num = 1 if e1_num == 1 else e1_num.inverse_mod(e1.modulus)
inv = ConreyCharacter(e1.modulus, inv_num)
if e1_num == inv_num:
l.append((out(e1), ))
else:
l.append((out(e1), out(inv)))
v = [
x for x in v
if (x.modulus, x.number) != (inv.modulus, inv.number)
]
if k[1] == "more":
l = sorted(l, key=lambda e: e[0][2])
entries2[k] = l
cols = headers
return headers, entries2, rows, cols