def make_webchar(args, get_bread=False):
modulus = int(args['modulus'])
number = int(args['number']) if 'number' in args else None
orbit_label = args.get('orbit_label', None)
if modulus <= 10000:
if number is None:
if get_bread:
bread_crumbs = bread(
[('%s' % modulus, url_for(".render_Dirichletwebpage", modulus=modulus)),
('%s' % orbit_label, url_for(".render_Dirichletwebpage", modulus=modulus, orbit_label=orbit_label))])
return WebDBDirichletOrbit(**args), bread_crumbs
return WebDBDirichletOrbit(**args)
if args.get('orbit_label') is None:
db_orbit_label = db.char_dir_values.lookup("{}.{}".format(modulus, number), projection='orbit_label')
orbit_label = cremona_letter_code(int(db_orbit_label.partition('.')[-1]) - 1)
args['orbit_label'] = orbit_label
if get_bread:
bread_crumbs = bread(
[('%s' % modulus, url_for(".render_Dirichletwebpage", modulus=modulus)),
('%s' % orbit_label, url_for(".render_Dirichletwebpage", modulus=modulus, orbit_label=orbit_label)),
('%s' % number, url_for(".render_Dirichletwebpage", modulus=modulus, orbit_label=orbit_label, number=number))])
return WebDBDirichletCharacter(**args), bread_crumbs
return WebDBDirichletCharacter(**args)
else:
if get_bread:
bread_crumbs = bread(
[('%s' % modulus, url_for(".render_Dirichletwebpage", modulus=modulus)),
('%s' % number, url_for(".render_Dirichletwebpage", modulus=modulus, number=number))])
return WebSmallDirichletCharacter(**args), bread_crumbs
return WebSmallDirichletCharacter(**args)
def galois_rep_from_path(p):
if p[0]=='EllipticCurve':
# create the sage elliptic curve then create Galois rep object
ainvs = db.ec_curves.lucky({'lmfdb_label':p[2]+"."+p[3]+p[4]}, 'ainvs')
E = EllipticCurve(ainvs)
return GaloisRepresentation(E)
elif (p[0]=='Character' and p[1]=='Dirichlet'):
dirichletArgs = {'type':'Dirichlet', 'modulus':int(p[2]), 'number':int(p[3])}
chi = WebSmallDirichletCharacter(**dirichletArgs)
return GaloisRepresentation(chi)
elif (p[0]=='ModularForm'):
level = int(p[4])
weight = int(p[5])
conrey_label = p[6] # this should be zero; TODO check this is the case
hecke_orbit = p[7] # this is a, b, c, etc.; chooses the galois orbit
embedding = p[8] # this is the embedding of that galois orbit
label = convert_newformlabel_from_conrey(str(level)+"."+str(weight)+"."+str(conrey_label)+"."+hecke_orbit)
form = WebNewform(label)
return GaloisRepresentation([form, ZZ(embedding)])
elif (p[0]=='ArtinRepresentation'):
dim = p[1]
conductor = p[2]
index = p[3]
rho = ArtinRepresentation(dim, conductor, index)
return GaloisRepresentation(rho)
else:
return
def make_webchar(args):
modulus = int(args['modulus'])
if modulus < 10000:
return WebDBDirichletCharacter(**args)
elif modulus < 100000:
return WebDirichletCharacter(**args)
else:
return WebSmallDirichletCharacter(**args)
def dc_calc(calc, modulus, number):
val = request.args.get("val", [])
args = {'type': 'Dirichlet', 'modulus': modulus, 'number': number}
if not val:
return abort(404)
try:
if calc == 'value':
return WebSmallDirichletCharacter(**args).value(val)
if calc == 'gauss':
return WebSmallDirichletCharacter(**args).gauss_sum(val)
elif calc == 'jacobi':
return WebSmallDirichletCharacter(**args).jacobi_sum(val)
elif calc == 'kloosterman':
return WebSmallDirichletCharacter(**args).kloosterman_sum(val)
else:
return abort(404)
except Warning as e:
return "<span style='color:gray;'>%s</span>" % e
except Exception:
return "<span style='color:red;'>Error: bad input</span>"
def determinant(self):
if self._data['Dets']:
parts = self.label().split("c")
thischar = str( self._data['Dets'][int(parts[1])-1] )
if self.dimension()==1:
wc = thischar.split(r'.')
self._data['central_character'] = WebSmallDirichletCharacter(modulus=wc[0], number=wc[1])
return self._data['central_character']
return(thischar)
# Not in the database
if self.dimension()==1:
return self.central_character()
return self.central_character_as_artin_rep().label()
def central_character(self):
"""
Returns the central character, i.e., determinant character
as a web character.
"""
if 'central_character' in self._data:
return self._data['central_character']
# Build it as a python function, id it, make a lmfdb character
# But, if the conductor is too large, this can stall because
# the function has to factor arbitrary integers modulo N
if Integer(self.conductor()) > 10**40:
return None
myfunc = self.central_char_function()
wc = id_dirichlet(myfunc, self.conductor(), 2 * self.character_field())
wc = WebSmallDirichletCharacter(modulus=wc[0], number=wc[1])
self._data['central_character'] = wc
return wc