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 = WebDirichletCharacter(**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 flask.abort(404)
try:
if calc == 'value':
return WebDirichletCharacter(**args).value(val)
if calc == 'gauss':
return WebDirichletCharacter(**args).gauss_sum(val)
elif calc == 'jacobi':
return WebDirichletCharacter(**args).jacobi_sum(val)
elif calc == 'kloosterman':
return WebDirichletCharacter(**args).kloosterman_sum(val)
else:
return flask.abort(404)
except Warning, e:
return "<span style='color:gray;'>%s</span>" % e
def line(n):
l = []
count = 0
q = n
while count < limit:
if modn_exponent(q) % n == 0:
G = DirichletGroup_conrey(q)
for chi in G:
j = chi.number()
c = WebDirichletCharacter(modulus = q, number = j)
if chi.multiplicative_order() == n:
l.append((q, j, chi.is_primitive(), chi.multiplicative_order(), c.symbol))
count += 1
if count == limit:
break
q += 1
return l
def line(N):
l = []
if N%4 == 2:
return l
count = 0
q = N
while count < limit:
if q % N == 0:
G = DirichletGroup_conrey(q)
for chi in G:
j = chi.number()
c = WebDirichletCharacter(modulus = q, number = j)
if chi.conductor() == q:
l.append((q, j, chi.is_primitive(), chi.multiplicative_order(), c.symbol))
count += 1
if count == limit:
break
q += N
return l