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
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 galois_rep_from_path(p):
C = getDBConnection()
if p[0] == 'EllipticCurve':
# create the sage elliptic curve then create Galois rep object
data = C.elliptic_curves.curves.find_one(
{'lmfdb_label': p[2] + "." + p[3] + p[4]})
ainvs = [int(a) for a in data['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'):
N = int(p[4])
k = int(p[5])
chi = p[6] # this should be zero; TODO check this is the case
label = p[7] # this is a, b, c, etc.; chooses the galois orbit
embedding = p[8] # this is the embedding of that galois orbit
form = WebNewForm(N, k, chi=chi, label=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 render_Dirichletwebpage(modulus=None, number=None):
if modulus == None:
return render_DirichletNavigation()
modulus = modulus.replace(' ','')
if number == None and re.match('^[1-9][0-9]*\.[1-9][0-9]*$', modulus):
return redirect(url_for(".render_Dirichletwebpage", label=modulus), 301)
args={}
args['type'] = 'Dirichlet'
args['modulus'] = modulus
args['number'] = number
try:
modulus = int(modulus)
except ValueError:
modulus = 0
if modulus <= 0:
flash_error ("%s is not a valid modulus for a Dirichlet character. It should be a positive integer.", args['modulus'])
return redirect(url_for(".render_Dirichletwebpage"))
if modulus > 10**20:
flash_error ("specified modulus %s is too large, it should be less than $10^{20}$.", modulus)
return redirect(url_for(".render_Dirichletwebpage"))
if number == None:
if modulus < 10000:
info = WebDBDirichletGroup(**args).to_dict()
info['show_orbit_label'] = True
elif modulus < 100000:
info = WebDirichletGroup(**args).to_dict()
else:
info = WebSmallDirichletGroup(**args).to_dict()
info['title'] = 'Group of Dirichlet Characters of Modulus ' + str(modulus)
info['bread'] = [('Characters', url_for(".render_characterNavigation")),
('Dirichlet', url_for(".render_Dirichletwebpage")),
('%d'%modulus, url_for(".render_Dirichletwebpage", modulus=modulus))]
info['learnmore'] = learn()
info['code'] = dict([(k[4:],info[k]) for k in info if k[0:4] == "code"])
info['code']['show'] = { lang:'' for lang in info['codelangs'] } # use default show names
if 'gens' in info:
info['generators'] = ', '.join([r'<a href="%s">$\chi_{%s}(%s,\cdot)$'%(url_for(".render_Dirichletwebpage",modulus=modulus,number=g),modulus,g) for g in info['gens']])
return render_template('CharGroup.html', **info)
try:
number = int(number)
except ValueError:
number = 0;
if number <= 0 or gcd(modulus,number) != 1 or number > modulus:
flash_error("the value %s is invalid. It should be a positive integer coprime to and no greater than the modulus %s.", args['number'],args['modulus'])
return redirect(url_for(".render_Dirichletwebpage"))
if modulus < 10000:
webchar = WebDBDirichletCharacter(**args)
info = webchar.to_dict()
elif modulus < 100000:
webchar = WebDirichletCharacter(**args)
info = webchar.to_dict()
else:
info = WebSmallDirichletCharacter(**args).to_dict()
info['bread'] = [('Characters', url_for(".render_characterNavigation")),
('Dirichlet', url_for(".render_Dirichletwebpage")),
('%s'%modulus, url_for(".render_Dirichletwebpage", modulus=modulus)),
('%s'%number, url_for(".render_Dirichletwebpage", modulus=modulus, number=number)) ]
info['learnmore'] = learn()
info['code'] = dict([(k[4:],info[k]) for k in info if k[0:4] == "code"])
info['code']['show'] = { lang:'' for lang in info['codelangs'] } # use default show names
return render_template('Character.html', **info)