def DC_char_to_gp_char(chi, G=None):
"""
If this function is to be called repeatedly with the same modulus it
is better to precompute G and pass it, so save recomputation:
"""
if G is None:
G = pari(chi.modulus()).znstar(1)
return G.znconreylog(DC.number(chi))
def char_orbit_index_to_DC_number(N, o):
"""Returns the index in the Dirichlet-Conrey numbering of one character in orbit number o"""
if o == 1:
return 1
global char_table_dict
if not char_table_dict:
char_table_dict = {}
try:
chartab = open("chartab.txt")
for L in chartab.readlines():
NN, oo, nn = [int(x) for x in L.split()]
if not NN in char_table_dict:
char_table_dict[NN] = {}
char_table_dict[NN][oo] = nn
chartab.close()
except IOError:
Chars = DirichletCharacterGaloisReps(N)
return DC.number(Chars[o - 1])
try:
return char_table_dict[N][o]
except KeyError: # N too big for precomputed table
Chars = DirichletCharacterGaloisReps(N)
return DC.number(Chars[o - 1])
def primitivize(label):
m, n = [ZZ(a) for a in label.split(".")]
char = DirichletCharacter_conrey(DirGroup(m), n).primitive_character()
return "%d.%d" % (char.modulus(), char.number())
def GP_DirichletCharacterGaloisReps(N):
G = pari(N).znstar(1)
return [
G.znconreylog(DC.number(chi))
for chi in DirichletCharacterGaloisReps(N)
]
def DC_char_to_gp_char(chi, G=None):
if G == None:
G = pari(chi.modulus()).znstar(1)
return G.znconreylog(DC.number(chi))
def OrderedConreyLabels(N):
return [DC.number(chi) for chi in DirichletCharacterGaloisReps(N)]
