def __init__(self, *x, **data_dict):
if len(x) == 0:
# Just passing named arguments
self._data = data_dict["data"]
label = self._data['label']
else:
if len(x) == 1: # Assume we got a label
label = x[0]
parts = x[0].split(".")
base = "%s.%s.%s.%s" % tuple(parts[j] for j in (0, 1, 2, 3))
if len(parts) < 5: # Galois orbit
conjindex = 1
else:
conjindex = letters2num(parts[4])
elif len(x) == 2: # base and gorb index
base = x[0]
conjindex = x[1]
label = "%s.%s" % (str(x[0]), num2letters(x[1]))
else:
raise ValueError("Invalid number of positional arguments")
self._data = db.artin_reps.lucky({'Baselabel': str(base)})
conjs = self._data["GaloisConjugates"]
conj = [xx for xx in conjs if xx['GalOrbIndex'] == conjindex]
self._data['label'] = label
self._data.update(conj[0])
def friends(self):
from lmfdb.lfunctions.LfunctionDatabase import get_lfunction_by_url
friendlist = []
cglink = url_character(type=self.type, modulus=self.modulus)
friendlist.append(("Character group", cglink))
gal_orb_link = url_character(type=self.type,
modulus=self.modulus,
orbit_label=self.orbit_label)
friendlist.append(("Character orbit", gal_orb_link))
if self.type == "Dirichlet" and self.isprimitive == bool_string(True):
url = url_character(type=self.type,
number_field=None,
modulus=self.modulus,
number=self.number)
if get_lfunction_by_url(url[1:]):
friendlist.append(('L-function', '/L' + url))
else:
if self.conductor == 1:
friendlist.append(('L-function', '/L/Riemann'))
friendlist.append(
('Sato-Tate group', '/SatoTateGroup/0.1.%d' % self.order))
if len(self.vflabel) > 0:
friendlist.append(("Value field", '/NumberField/' + self.vflabel))
if self.symbol_numerator():
if self.symbol_numerator() > 0:
assoclabel = '2.2.%d.1' % self.symbol_numerator()
else:
assoclabel = '2.0.%d.1' % -self.symbol_numerator()
friendlist.append(
("Associated quadratic field", '/NumberField/' + assoclabel))
label = "%s.%s" % (self.modulus, self.number)
myrep = db.artin_reps.lucky({'Dets': {'$contains': label}})
if myrep is not None:
j = myrep['Dets'].index(label)
artlabel = myrep['Baselabel'] + '.' + num2letters(j + 1)
friendlist.append((
'Artin representation ' + artlabel,
url_for(
'artin_representations.render_artin_representation_webpage',
label=artlabel)))
if self.type == "Dirichlet" and self.isprimitive == bool_string(False):
friendlist.append(('Primitive character ' + self.inducing,
url_for('characters.render_Dirichletwebpage',
modulus=self.conductor,
number=self.indlabel)))
return friendlist
