def nextprimchar(m, n):
if m < 3:
return 3, 2
while 1:
n += 1
if n >= m:
m, n = m + 1, 2
if gcd(m, n) != 1:
continue
# we have a character, test if it is primitive
chi = ConreyCharacter(m,n)
if chi.is_primitive():
return m, n
def prevprimchar(m, n):
if m <= 3:
return 1, 1
while True:
n -= 1
if n <= 1: # (m,1) is never primitive for m>1
m, n = m - 1, m - 1
if m <= 2:
return 1, 1
if gcd(m, n) != 1:
continue
# we have a character, test if it is primitive
chi = ConreyCharacter(m,n)
if chi.is_primitive():
return m, n
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