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 show():
args = request.args
objLinks = args # an immutable dict of links to objects to tp
objPaths = []
for k, v in objLinks.items():
objPaths.append(v.split('/'))
galoisRepObjs = []
for p in objPaths:
galoisRepObjs.append(galois_rep_from_path(p))
if len(galoisRepObjs)==1:
gr = galoisRepObjs[0]
gr.lfunction()
info = {}
info['dirichlet'] = lfuncDShtml(gr, "analytic")
info['eulerproduct'] = lfuncEPtex(gr, "abstract")
info['functionalequation'] = lfuncFEtex(gr, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(gr, "selberg")
info['bread'] = get_bread()
return render_template('Lfunction.html', **info)
# currently only implemented tp of two things
if len(galoisRepObjs)==2:
try:
tp = GaloisRepresentation([galoisRepObjs[0], galoisRepObjs[1]])
tp.lfunction()
info = {}
info['dirichlet'] = lfuncDShtml(tp, "analytic")
info['eulerproduct'] = lfuncEPtex(tp, "abstract")
info['functionalequation'] = lfuncFEtex(tp, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(tp, "selberg")
properties = [('Root number', '$'+str(tp.root_number()).replace('*','').replace('I','i')+'$'),
('Dimension', '$'+str(tp.dimension())+'$'),
('Conductor', '$'+str(tp.cond())+'$')]
info['properties'] = properties
if (tp.numcoeff > len(tp.dirichlet_coefficients)+10):
info['zeroswarning'] = 'These zeros may be inaccurate because we use only %s terms rather than the theoretically required %s terms' %(len(tp.dirichlet_coefficients), tp.numcoeff)
info['svwarning'] = 'These special values may also be inaccurate, for the same reason.'
else:
info['zeroswarning'] = ''
info['svwarning'] = ''
info['tpzeroslink'] = zeros(tp)
info['sv_edge'] = specialValueString(tp, 1, '1')
info['sv_critical'] = specialValueString(tp, 0.5, '1/2')
# friends = []
# friends.append(('L-function of first object', url_for('.show', obj1=objLinks[0])))
# friends.append(('L-function of second object', url_for('.show', obj2=objLinks[1])))
# info['friends'] = friends
info['eulerproduct'] = 'L(s, V \otimes W) = \prod_{p} \det(1 - Frob_p p^{-s} | (V \otimes W)^{I_p})^{-1}'
info['bread'] = get_bread()
return render_template('Lfunction.html', **info)
except (KeyError,ValueError,RuntimeError,NotImplementedError) as err:
return render_lfunction_exception(err)
else:
return render_template("not_yet_implemented.html")
def show():
args = request.args
bread = get_bread()
objLinks = args # an immutable dict of links to objects to tp
objPaths = []
for k, v in objLinks.items():
objPaths.append(v.split('/'))
galoisRepObjs = []
for p in objPaths:
galoisRepObjs.append(galois_rep_from_path(p))
if len(galoisRepObjs)==1:
gr = galoisRepObjs[0]
gr.lfunction()
info = {}
info['dirichlet'] = lfuncDShtml(tp, "analytic")
info['eulerproduct'] = lfuncEPtex(tp, "abstract")
info['functionalequation'] = lfuncFEtex(tp, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(tp, "selberg")
return render_template('Lfunction.html', **info)
# currently only implemented tp of two things
if len(galoisRepObjs)==2:
try:
tp = GaloisRepresentation([galoisRepObjs[0], galoisRepObjs[1]])
tp.lfunction()
info = {}
info['dirichlet'] = lfuncDShtml(tp, "analytic")
info['eulerproduct'] = lfuncEPtex(tp, "abstract")
info['functionalequation'] = lfuncFEtex(tp, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(tp, "selberg")
properties2 = [('Root number', '$'+str(tp.root_number()).replace('*','').replace('I','i')+'$'),
('Dimension', '$'+str(tp.dimension())+'$'),
('Conductor', '$'+str(tp.cond())+'$')]
info['properties2'] = properties2
if (tp.numcoeff > len(tp.dirichlet_coefficients)+10):
info['zeroswarning'] = 'These zeros may be inaccurate because we use only %s terms rather than the theoretically required %s terms' %(len(tp.dirichlet_coefficients), tp.numcoeff)
info['svwarning'] = 'These special values may also be inaccurate, for the same reason.'
else:
info['zeroswarning'] = ''
info['svwarning'] = ''
info['tpzeroslink'] = zeros(tp)
info['sv_edge'] = specialValueString(tp, 1, '1')
info['sv_critical'] = specialValueString(tp, 0.5, '1/2')
# friends = []
# friends.append(('L-function of first object', url_for('.show', obj1=objLinks[0])))
# friends.append(('L-function of second object', url_for('.show', obj2=objLinks[1])))
# info['friends'] = friends
info['eulerproduct'] = 'L(s, V \otimes W) = \prod_{p} \det(1 - Frob_p p^{-s} | (V \otimes W)^{I_p})^{-1}'
return render_template('Lfunction.html', **info)
except Exception as ex:
info = {'content': 'Sorry, there was a problem: ' + str(ex.args), 'title':'Error'}
return render_template('LfunctionSimple.html', **info)
else:
return render_template("not_yet_implemented.html")