def set_navi(L):
''' Returns the data for navigation to previous/next
L-function when this makes sense. If not it returns None
'''
prev_data = None
if L.Ltype() == 'maass' and L.group == 'GL2':
next_form_id = L.mf.next_maassform_id()
if next_form_id:
next_data = ("next",r"$L(s,f_{\text next})$", '/L' +
url_for('mwf.render_one_maass_waveform',
maass_id = next_form_id) )
else:
next_data = ('','','')
prev_form_id = L.mf.prev_maassform_id()
if prev_form_id:
prev_data = ("previous", r"$L(s,f_{\text prev}$)", '/L' +
url_for('mwf.render_one_maass_waveform',
maass_id = prev_form_id) )
else:
prev_data = ('','','')
elif L.Ltype() == 'dirichlet':
mod, num = L.charactermodulus, L.characternumber
Lpattern = r"\(L(s,\chi_{%s}(%s,·))\)"
if mod > 1:
pmod,pnum = WebDirichlet.prevprimchar(mod, num)
prev_data = ("previous",Lpattern%(pmod,pnum) if pmod > 1 else r"\(\zeta(s)\)",
url_for('.l_function_dirichlet_page',
modulus=pmod,number=pnum))
else:
prev_data = ('','','')
nmod,nnum = WebDirichlet.nextprimchar(mod, num)
next_data = ("next",Lpattern%(nmod,nnum) if nmod > 1 else r"\(\zeta(s)\)",
url_for('.l_function_dirichlet_page',
modulus=nmod,number=nnum))
if prev_data is None:
return None
else:
return ( prev_data, next_data )
def info_from_db_orbit(orbit):
mod = orbit['modulus']
conductor = orbit['conductor']
orbit_index = orbit['orbit_index']
orbit_letter = cremona_letter_code(orbit_index - 1)
orbit_label = "{}.{}".format(mod, orbit_letter)
order = orbit['order']
is_odd = 'Odd' if _is_odd(orbit['parity']) else 'Even'
is_prim = _is_primitive(orbit['is_primitive'])
results = []
for num in orbit['galois_orbit']:
results.append(
(mod, num, conductor, orbit_label, order, is_odd, is_prim,
WebDirichlet.char2tex(mod, num)))
return results
def info_from_db_orbit(orbit):
mod = orbit['modulus']
conductor = orbit['conductor']
orbit_index = orbit['orbit_index']
orbit_letter = cremona_letter_code(orbit_index - 1)
orbit_label = "{}.{}".format(mod, orbit_letter)
order = orbit['order']
is_odd = 'Odd' if _is_odd(orbit['parity']) else 'Even'
is_prim = _is_primitive(orbit['is_primitive'])
results = []
for num in orbit['galois_orbit']:
results.append((
mod,
num,
conductor,
orbit_label,
order,
is_odd,
is_prim,
WebDirichlet.char2tex(mod, num)
))
return results
def initLfunction(L, args, request):
''' Sets the properties to show on the homepage of an L-function page.
'''
info = {'title': L.title}
try:
info['citation'] = L.citation
except AttributeError:
info['citation'] = ""
try:
info['support'] = L.support
except AttributeError:
info['support'] = ""
info['Ltype'] = L.Ltype()
# Here we should decide which values are indeed special values
# According to Brian, odd degree has special value at 1, and even
# degree has special value at 1/2.
# (however, I'm not sure this is true if L is not primitive -- GT)
# Now we usually display both
if L.Ltype() != "artin" or (L.Ltype() == "artin" and L.sign != 0):
# if is_even(L.degree) :
# info['sv12'] = specialValueString(L, 0.5, '1/2')
# if is_odd(L.degree):
# info['sv1'] = specialValueString(L, 1, '1')
info['sv1'] = specialValueString(L, 1, '1')
info['sv12'] = specialValueString(L, 0.5, '1/2')
info['args'] = args
info['credit'] = L.credit
# info['citation'] = L.citation
try:
info['factorization'] = L.factorization
except:
pass
try:
info['url'] = L.url
except:
info['url'] = ''
info['degree'] = int(L.degree)
info['zeroeslink'] = (request.url.replace('/L/', '/L/Zeros/').
replace('/Lfunction/', '/L/Zeros/').
replace('/L-function/', '/L/Zeros/')) # url_for('zeroesLfunction', **args)
info['plotlink'] = (request.url.replace('/L/', '/L/Plot/').
replace('/Lfunction/', '/L/Plot/').
replace('/L-function/', '/L/Plot/')) # info['plotlink'] = url_for('plotLfunction', **args)
info['bread'] = []
info['properties2'] = set_gaga_properties(L)
# Create friendlink by removing 'L/' and ending '/'
friendlink = request.url.replace('/L/', '/').replace('/L-function/', '/').replace('/Lfunction/', '/')
splitlink = friendlink.rpartition('/')
friendlink = splitlink[0] + splitlink[2]
logger.debug(L.Ltype())
if L.Ltype() == 'maass':
if L.group == 'GL2':
minNumberOfCoefficients = 100 # TODO: Fix this to take level into account
if len(L.dirichlet_coefficients) < minNumberOfCoefficients:
info['zeroeslink'] = ''
info['plotlink'] = ''
info['bread'] = get_bread(2, [('Maass Form',
url_for('.l_function_maass_browse_page')),
('\(' + L.texname + '\)', request.url)])
info['friends'] = [('Maass Form ', friendlink)]
else:
info['bread'] = get_bread(L.degree,
[('Maass Form', url_for('.l_function_maass_gln_browse_page',
degree='degree' + str(L.degree))),
(L.dbid, request.url)])
elif L.Ltype() == 'riemann':
info['bread'] = get_bread(1, [('Riemann Zeta', request.url)])
info['friends'] = [('\(\mathbb Q\)', url_for('number_fields.by_label', label='1.1.1.1')), ('Dirichlet Character \(\\chi_{1}(1,\\cdot)\)',
url_character(type='Dirichlet', modulus=1, number=1))]
elif L.Ltype() == 'dirichlet':
mod, num = L.charactermodulus, L.characternumber
Lpattern = r"\(L(s,\chi_{%s}(%s,·))\)"
if mod > 1:
pmod,pnum = WebDirichlet.prevprimchar(mod, num)
Lprev = (Lpattern%(pmod,pnum),url_for('.l_function_dirichlet_page',modulus=pmod,number=pnum))
else:
Lprev = ('','')
nmod,nnum = WebDirichlet.nextprimchar(mod, num)
Lnext = (Lpattern%(nmod,nnum),url_for('.l_function_dirichlet_page',modulus=nmod,number=nnum))
info['navi'] = (Lprev,Lnext)
snum = str(L.characternumber)
smod = str(L.charactermodulus)
charname = WebDirichlet.char2tex(smod, snum)
info['bread'] = get_bread(1, [(charname, request.url)])
info['friends'] = [('Dirichlet Character ' + str(charname), friendlink)]
elif L.Ltype() == 'ellipticcurveQ':
label = L.label
while friendlink[len(friendlink) - 1].isdigit(): # Remove any number at the end to get isogeny class url
friendlink = friendlink[0:len(friendlink) - 1]
info['friends'] = [('Isogeny class ' + label, friendlink)]
for i in range(1, L.nr_of_curves_in_class + 1):
info['friends'].append(('Elliptic curve ' + label + str(i), friendlink + str(i)))
if L.modform:
info['friends'].append(('Modular form ' + label.replace('.', '.2'), url_for("emf.render_elliptic_modular_forms",
level=L.modform['level'], weight=2, character=0, label=L.modform['iso'])))
info['friends'].append(('L-function ' + label.replace('.', '.2'),
url_for('.l_function_emf_page', level=L.modform['level'],
weight=2, character=0, label=L.modform['iso'], number=0)))
info['friends'].append(
('Symmetric square L-function', url_for(".l_function_ec_sym_page", power='2', label=label)))
info['friends'].append(
('Symmetric cube L-function', url_for(".l_function_ec_sym_page", power='3', label=label)))
info['bread'] = get_bread(2, [('Elliptic curve', url_for('.l_function_ec_browse_page')),
(label, url_for('.l_function_ec_page', label=label))])
elif L.Ltype() == 'ellipticmodularform':
friendlink = friendlink + L.addToLink # Strips off the embedding
friendlink = friendlink.rpartition('/')[0] # number for the L-function
if L.character:
info['friends'] = [('Modular form ' + str(
L.level) + '.' + str(L.weight) + '.' + str(L.character) + str(L.label), friendlink)]
else:
info['friends'] = [('Modular form ' + str(L.level) + '.' + str(L.weight) + str(
L.label), friendlink)]
if L.ellipticcurve:
info['friends'].append(
('EC isogeny class ' + L.ellipticcurve, url_for("by_ec_label", label=L.ellipticcurve)))
info['friends'].append(('L-function ' + str(L.level) + '.' + str(L.label),
url_for('.l_function_ec_page', label=L.ellipticcurve)))
for i in range(1, L.nr_of_curves_in_class + 1):
info['friends'].append(('Elliptic curve ' + L.ellipticcurve + str(i),
url_for("by_ec_label", label=L.ellipticcurve + str(i))))
info['friends'].append(
('Symmetric square L-function', url_for(".l_function_ec_sym_page", power='2', label=label)))
info['friends'].append(
('Symmetric cube L-function', url_for(".l_function_ec_sym_page", power='3', label=label)))
elif L.Ltype() == 'hilbertmodularform':
friendlink = '/'.join(friendlink.split('/')[:-1])
info['friends'] = [('Hilbert Modular Form', friendlink.rpartition('/')[0])]
elif L.Ltype() == 'dedekindzeta':
info['friends'] = [('Number Field', friendlink)]
elif L.Ltype() in ['lcalcurl', 'lcalcfile']:
info['bread'] = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == 'SymmetricPower':
def ordinal(n):
if n == 2:
return "Square"
elif n == 3:
return "Cube"
elif 10 <= n % 100 < 20:
return str(n) + "th Power"
else:
return str(n) + {1: 'st', 2: 'nd', 3: 'rd'}.get(n % 10, "th") + " Power"
if L.m == 2:
info['bread'] = get_bread(3, [("Symmetric square of Elliptic curve",
url_for('.l_function_ec_sym2_browse_page')),
(L.label, url_for('.l_function_ec_sym_page',
label=L.label,power=L.m))])
elif L.m == 3:
info['bread'] = get_bread(4, [("Symmetric cube of Elliptic curve",
url_for('.l_function_ec_sym3_browse_page')),
(L.label, url_for('.l_function_ec_sym_page',
label=L.label,power=L.m))])
else:
info['bread'] = [('L-functions', url_for('.l_function_top_page')),
('Symmetric %s of Elliptic curve ' % ordinal(L.m)
+ str(L.label),
url_for('.l_function_ec_sym_page',
label=L.label,power=L.m))]
friendlink = request.url.replace('/L/SymmetricPower/%d/' % L.m, '/')
splitlink = friendlink.rpartition('/')
friendlink = splitlink[0] + splitlink[2]
friendlink2 = request.url.replace('/L/SymmetricPower/%d/' % L.m, '/L/')
splitlink = friendlink2.rpartition('/')
friendlink2 = splitlink[0] + splitlink[2]
info['friends'] = [('Isogeny class ' + L.label, friendlink), ('Symmetric 1st Power', friendlink2)]
for j in range(2, L.m + 2):
if j != L.m:
friendlink3 = request.url.replace('/L/SymmetricPower/%d/' % L.m, '/L/SymmetricPower/%d/' % j)
info['friends'].append(('Symmetric %s' % ordinal(j), friendlink3))
elif L.Ltype() == 'siegelnonlift' or L.Ltype() == 'siegeleisenstein' or L.Ltype() == 'siegelklingeneisenstein' or L.Ltype() == 'siegelmaasslift':
weight = str(L.weight)
number = str(L.number)
info['friends'] = [('Siegel Modular Form', friendlink)]
elif L.Ltype() == "artin":
# info['zeroeslink'] = ''
# info['plotlink'] = ''
info['friends'] = [('Artin representation', L.artin.url_for())]
if L.sign == 0: # The root number is now unknown
info['zeroeslink'] = ''
info['plotlink'] = ''
info['dirichlet'] = lfuncDStex(L, "analytic")
info['eulerproduct'] = lfuncEPtex(L, "abstract")
info['functionalequation'] = lfuncFEtex(L, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(L, "selberg")
if len(request.args) == 0:
lcalcUrl = request.url + '?download=lcalcfile'
else:
lcalcUrl = request.url + '&download=lcalcfile'
info['downloads'] = [('Lcalcfile', lcalcUrl)]
return info
def charinfo(chi):
""" return data associated to the WebDirichletCharacter chi """
return (chi.modulus(), chi.number(), chi.conductor(),
chi.multiplicative_order(), chi.is_odd(), chi.is_primitive(),
WebDirichlet.char2tex(chi.modulus(), chi.number()))
def charinfo(chi):
""" return data associated to the WebDirichletCharacter chi """
return (chi.modulus(), chi.number(), chi.conductor(), chi.multiplicative_order(), chi.is_odd(), chi.is_primitive(), WebDirichlet.char2tex(chi.modulus(), chi.number()))
def set_bread_and_friends(L, request):
''' Returns the list of friends to link to and the bread crumbs.
Depends on the type of L-function and needs to be added to for new types
'''
bread = []
friends = []
origins = []
factors = []
instances = []
# Create default friendlink by removing 'L/' and ending '/'
friendlink = request.path.replace('/L/', '/').replace('/L-function/', '/').replace('/Lfunction/', '/')
splitlink = friendlink.rpartition('/')
friendlink = splitlink[0] + splitlink[2]
if L.Ltype() == 'riemann':
friends = [('\(\mathbb Q\)', url_for('number_fields.by_label', label='1.1.1.1')),
('Dirichlet Character \(\\chi_{1}(1,\\cdot)\)',url_for('characters.render_Dirichletwebpage',
modulus=1, number=1))]
bread = get_bread(1, [('Riemann Zeta', request.path)])
elif L.Ltype() == 'dirichlet':
snum = str(L.characternumber)
smod = str(L.charactermodulus)
charname = WebDirichlet.char2tex(smod, snum)
friends = [('Dirichlet Character ' + str(charname), friendlink)]
if L.fromDB and not L.selfdual:
friends.append(('Dual L-function', L.dual_link))
bread = get_bread(1, [(charname, request.path)])
elif L.Ltype() == 'ellipticcurve':
bread = L.bread
origins = L.origins
friends = L.friends
factors = L.factors
instances = L.instances
elif L.Ltype() == 'ellipticmodularform':
friendlink = friendlink.rpartition('/')[0] # Strips off the embedding
# number for the L-function
if L.character: # TODO: Probably always true now
full_label = ( str(L.level) + '.' + str(L.weight) + '.' + str(L.character) +
str(L.label) )
else:
full_label = str(L.level) + '.' + str(L.weight) + str(L.label)
origins = [('Modular form ' + full_label, friendlink)]
if L.ellipticcurve:
origins.append(
('Isogeny class ' + L.ellipticcurve,
url_for("ec.by_ec_label", label=L.ellipticcurve)))
# DEPRECATED
#for i in range(1, L.nr_of_curves_in_class + 1):
# friends.append(('Elliptic curve ' + L.ellipticcurve + str(i),
# url_for("ec.by_ec_label", label=L.ellipticcurve + str(i))))
if not isogeny_class_cm(L.ellipticcurve):
friends.append(
('Symmetric square L-function',
url_for(".l_function_ec_sym_page_label", power='2',
label=L.ellipticcurve)))
friends.append(
('Symmetric cube L-function',
url_for(".l_function_ec_sym_page_label", power='3',
label=L.ellipticcurve)))
bread = get_bread(2, [('Cusp Form', url_for('.l_function_cuspform_browse_page')),
(full_label, request.path)])
elif L.Ltype() == 'maass':
if L.group == 'GL2':
friends = [('Maass Form ', friendlink)]
bread = get_bread(2, [('Maass Form',
url_for('.l_function_maass_browse_page')),
('\(' + L.texname + '\)', request.path)])
else:
if L.fromDB and not L.selfdual:
friends = [('Dual L-function', L.dual_link)]
bread = get_bread(L.degree,
[('Maass Form', url_for('.l_function_maass_gln_browse_page',
degree='degree' + str(L.degree))),
(L.maass_id.partition('/')[2], request.path)])
elif L.Ltype() == 'hilbertmodularform':
friendlink = '/'.join(friendlink.split('/')[:-1])
friends = [('Hilbert modular form ' + L.label, friendlink.rpartition('/')[0])]
if L.degree == 4:
bread = get_bread(4, [(L.label, request.path)])
else:
bread = [('L-functions', url_for('.l_function_top_page'))]
elif (L.Ltype() == 'siegelnonlift' or L.Ltype() == 'siegeleisenstein' or
L.Ltype() == 'siegelklingeneisenstein' or L.Ltype() == 'siegelmaasslift'):
weight = str(L.weight)
label = 'Sp4Z.' + weight + '_' + L.orbit
friendlink = '/'.join(friendlink.split('/')[:-3]) + '.' + weight + '_' + L.orbit
friends = [('Siegel Modular Form ' + label, friendlink)]
if L.degree == 4:
bread = get_bread(4, [(label, request.path)])
else:
bread = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == 'genus2curveQ':
(cond, dummy, alpha) = L.label.partition('.')
friends = [('Isogeny class ' + L.label, url_for('g2c.by_url_isogeny_class_label',
cond = cond, alpha = alpha))]
bread = get_bread(4, [(L.label, request.path)])
elif L.Ltype() == 'dedekindzeta':
friends = [('Number Field', friendlink)]
if L.degree <= 4:
bread = get_bread(L.degree, [(L.label, request.path)])
else:
bread = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == "artin":
friends = [('Artin representation', L.artin.url_for())]
if L.degree <= 4:
bread = get_bread(L.degree, [(L.label, request.path)])
else:
bread = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == "hgmQ":
# The /L/ trick breaks down for motives,
# because we have a scheme for the L-functions themselves
newlink = friendlink.rpartition('t')
friendlink = newlink[0]+'/t'+newlink[2]
friends = [('Hypergeometric motive ', friendlink)]
if L.degree <= 4:
bread = get_bread(L.degree, [(L.label, request.path)])
else:
bread = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == 'SymmetricPower':
def ordinal(n):
if n == 2:
return "Square"
elif n == 3:
return "Cube"
elif 10 <= n % 100 < 20:
return str(n) + "th Power"
else:
return str(n) + {1: 'st', 2: 'nd', 3: 'rd'}.get(n % 10, "th") + " Power"
if L.m == 2:
bread = get_bread(3, [("Symmetric square of Elliptic curve",
url_for('.l_function_ec_sym2_browse_page')),
(L.label, url_for('.l_function_ec_sym_page_label',
label=L.label,power=L.m))])
elif L.m == 3:
bread = get_bread(4, [("Symmetric Cube of Elliptic Curve",
url_for('.l_function_ec_sym3_browse_page')),
(L.label, url_for('.l_function_ec_sym_page_label',
label=L.label,power=L.m))])
else:
bread = [('L-functions', url_for('.l_function_top_page')),
('Symmetric %s of Elliptic Curve ' % ordinal(L.m)
+ str(L.label),
url_for('.l_function_ec_sym_page_label',
label=L.label,power=L.m))]
friendlink = request.path.replace('/L/SymmetricPower/%d/' % L.m, '/')
splitlink = friendlink.rpartition('/')
friendlink = splitlink[0] + splitlink[2]
friendlink2 = request.path.replace('/L/SymmetricPower/%d/' % L.m, '/L/')
splitlink = friendlink2.rpartition('/')
friendlink2 = splitlink[0] + splitlink[2]
friends = [('Isogeny class ' + L.label, friendlink), ('Symmetric 1st Power', friendlink2)]
for j in range(2, L.m + 2):
if j != L.m:
friendlink3 = request.path.replace('/L/SymmetricPower/%d/' % L.m, '/L/SymmetricPower/%d/' % j)
friends.append(('Symmetric %s' % ordinal(j), friendlink3))
elif L.Ltype() in ['lcalcurl', 'lcalcfile']:
if L.degree <= 4:
bread = get_bread(L.degree, [])
else:
bread = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == "general":
bread = L.bread
origins = L.origins
friends = L.friends
factors = L.factors
instances = L.instances
return (bread, origins, friends, factors, instances)
def texname(self):
from lmfdb.WebCharacter import WebDirichlet
return WebDirichlet.char2tex(self.modulus, self.number)
def test_Dirichletmethods(self):
modlabel, numlabel = 14, 5
mod = WebDirichlet.label2ideal(modlabel)
assert WebDirichlet.ideal2label(mod) == modlabel
num = WebDirichlet.label2number(numlabel)
assert WebDirichlet.number2label(num) == numlabel
def test_Dirichletmethods(self):
modlabel, numlabel = 14, 5
mod = WebDirichlet.label2ideal(modlabel)
assert WebDirichlet.ideal2label(mod) == modlabel
num = WebDirichlet.label2number(numlabel)
assert WebDirichlet.number2label(num) == numlabel
def texname(self):
from lmfdb.WebCharacter import WebDirichlet
return WebDirichlet.char2tex(self.modulus, self.number)
def initLfunction(L, args, request):
''' Sets the properties to show on the homepage of an L-function page.
'''
info = {'title': L.title}
try:
info['citation'] = L.citation
except AttributeError:
info['citation'] = ""
try:
info['support'] = L.support
except AttributeError:
info['support'] = ""
info['Ltype'] = L.Ltype()
# Here we should decide which values are indeed special values
# According to Brian, odd degree has special value at 1, and even
# degree has special value at 1/2.
# (however, I'm not sure this is true if L is not primitive -- GT)
# Now we usually display both
if L.Ltype() != "artin" or (L.Ltype() == "artin" and L.sign != 0):
# if is_even(L.degree) :
# info['sv12'] = specialValueString(L, 0.5, '1/2')
# if is_odd(L.degree):
# info['sv1'] = specialValueString(L, 1, '1')
info['sv1'] = specialValueString(L, 1, '1')
info['sv12'] = specialValueString(L, 0.5, '1/2')
info['args'] = args
info['credit'] = L.credit
# info['citation'] = L.citation
try:
info['factorization'] = L.factorization
except:
pass
try:
info['url'] = L.url
except:
info['url'] = ''
info['degree'] = int(L.degree)
info['zeroeslink'] = (request.url.replace('/L/', '/L/Zeros/').replace(
'/Lfunction/', '/L/Zeros/').replace('/L-function/', '/L/Zeros/')
) # url_for('zeroesLfunction', **args)
info['plotlink'] = (
request.url.replace('/L/', '/L/Plot/').replace(
'/Lfunction/', '/L/Plot/').replace('/L-function/', '/L/Plot/')
) # info['plotlink'] = url_for('plotLfunction', **args)
info['bread'] = []
info['properties2'] = set_gaga_properties(L)
# Create friendlink by removing 'L/' and ending '/'
friendlink = request.url.replace('/L/',
'/').replace('/L-function/', '/').replace(
'/Lfunction/', '/')
splitlink = friendlink.rpartition('/')
friendlink = splitlink[0] + splitlink[2]
logger.debug(L.Ltype())
if L.Ltype() == 'maass':
if L.group == 'GL2':
minNumberOfCoefficients = 100 # TODO: Fix this to take level into account
if len(L.dirichlet_coefficients) < minNumberOfCoefficients:
info['zeroeslink'] = ''
info['plotlink'] = ''
info['bread'] = get_bread(
2, [('Maass Form', url_for('.l_function_maass_browse_page')),
('\(' + L.texname + '\)', request.url)])
info['friends'] = [('Maass Form ', friendlink)]
else:
info['bread'] = get_bread(
L.degree, [('Maass Form',
url_for('.l_function_maass_gln_browse_page',
degree='degree' + str(L.degree))),
(L.dbid, request.url)])
elif L.Ltype() == 'riemann':
info['bread'] = get_bread(1, [('Riemann Zeta', request.url)])
info['friends'] = [('\(\mathbb Q\)',
url_for('number_fields.by_label',
label='1.1.1.1')),
('Dirichlet Character \(\\chi_{1}(1,\\cdot)\)',
url_character(type='Dirichlet',
modulus=1,
number=1))]
elif L.Ltype() == 'dirichlet':
mod, num = L.charactermodulus, L.characternumber
Lpattern = r"\(L(s,\chi_{%s}(%s,·))\)"
if mod > 1:
pmod, pnum = WebDirichlet.prevprimchar(mod, num)
Lprev = (Lpattern % (pmod, pnum),
url_for('.l_function_dirichlet_page',
modulus=pmod,
number=pnum))
else:
Lprev = ('', '')
nmod, nnum = WebDirichlet.nextprimchar(mod, num)
Lnext = (Lpattern % (nmod, nnum),
url_for('.l_function_dirichlet_page',
modulus=nmod,
number=nnum))
info['navi'] = (Lprev, Lnext)
snum = str(L.characternumber)
smod = str(L.charactermodulus)
charname = WebDirichlet.char2tex(smod, snum)
info['bread'] = get_bread(1, [(charname, request.url)])
info['friends'] = [('Dirichlet Character ' + str(charname), friendlink)
]
elif L.Ltype() == 'ellipticcurveQ':
label = L.label
while friendlink[len(friendlink) - 1].isdigit(
): # Remove any number at the end to get isogeny class url
friendlink = friendlink[0:len(friendlink) - 1]
info['friends'] = [('Isogeny class ' + label, friendlink)]
for i in range(1, L.nr_of_curves_in_class + 1):
info['friends'].append(
('Elliptic curve ' + label + str(i), friendlink + str(i)))
if L.modform:
info['friends'].append(
('Modular form ' + label.replace('.', '.2'),
url_for("emf.render_elliptic_modular_forms",
level=L.modform['level'],
weight=2,
character=0,
label=L.modform['iso'])))
info['friends'].append(('L-function ' + label.replace('.', '.2'),
url_for('.l_function_emf_page',
level=L.modform['level'],
weight=2,
character=0,
label=L.modform['iso'],
number=0)))
info['friends'].append(('Symmetric square L-function',
url_for(".l_function_ec_sym_page",
power='2',
label=label)))
info['friends'].append(('Symmetric cube L-function',
url_for(".l_function_ec_sym_page",
power='3',
label=label)))
info['bread'] = get_bread(
2, [('Elliptic curve', url_for('.l_function_ec_browse_page')),
(label, url_for('.l_function_ec_page', label=label))])
elif L.Ltype() == 'ellipticmodularform':
friendlink = friendlink + L.addToLink # Strips off the embedding
friendlink = friendlink.rpartition('/')[0] # number for the L-function
if L.character:
info['friends'] = [
('Modular form ' + str(L.level) + '.' + str(L.weight) + '.' +
str(L.character) + str(L.label), friendlink)
]
else:
info['friends'] = [('Modular form ' + str(L.level) + '.' +
str(L.weight) + str(L.label), friendlink)]
if L.ellipticcurve:
info['friends'].append(('EC isogeny class ' + L.ellipticcurve,
url_for("by_ec_label",
label=L.ellipticcurve)))
info['friends'].append(
('L-function ' + str(L.level) + '.' + str(L.label),
url_for('.l_function_ec_page', label=L.ellipticcurve)))
for i in range(1, L.nr_of_curves_in_class + 1):
info['friends'].append(
('Elliptic curve ' + L.ellipticcurve + str(i),
url_for("by_ec_label", label=L.ellipticcurve + str(i))))
info['friends'].append(('Symmetric square L-function',
url_for(".l_function_ec_sym_page",
power='2',
label=label)))
info['friends'].append(('Symmetric cube L-function',
url_for(".l_function_ec_sym_page",
power='3',
label=label)))
elif L.Ltype() == 'hilbertmodularform':
friendlink = '/'.join(friendlink.split('/')[:-1])
info['friends'] = [('Hilbert Modular Form',
friendlink.rpartition('/')[0])]
elif L.Ltype() == 'dedekindzeta':
info['friends'] = [('Number Field', friendlink)]
elif L.Ltype() in ['lcalcurl', 'lcalcfile']:
info['bread'] = [('L-functions', url_for('.l_function_top_page'))]
elif L.Ltype() == 'SymmetricPower':
def ordinal(n):
if n == 2:
return "Square"
elif n == 3:
return "Cube"
elif 10 <= n % 100 < 20:
return str(n) + "th Power"
else:
return str(n) + {
1: 'st',
2: 'nd',
3: 'rd'
}.get(n % 10, "th") + " Power"
if L.m == 2:
info['bread'] = get_bread(3, [
("Symmetric square of Elliptic curve",
url_for('.l_function_ec_sym2_browse_page')),
(L.label,
url_for('.l_function_ec_sym_page', label=L.label, power=L.m))
])
elif L.m == 3:
info['bread'] = get_bread(4, [
("Symmetric cube of Elliptic curve",
url_for('.l_function_ec_sym3_browse_page')),
(L.label,
url_for('.l_function_ec_sym_page', label=L.label, power=L.m))
])
else:
info['bread'] = [
('L-functions', url_for('.l_function_top_page')),
('Symmetric %s of Elliptic curve ' % ordinal(L.m) +
str(L.label),
url_for('.l_function_ec_sym_page', label=L.label, power=L.m))
]
friendlink = request.url.replace('/L/SymmetricPower/%d/' % L.m, '/')
splitlink = friendlink.rpartition('/')
friendlink = splitlink[0] + splitlink[2]
friendlink2 = request.url.replace('/L/SymmetricPower/%d/' % L.m, '/L/')
splitlink = friendlink2.rpartition('/')
friendlink2 = splitlink[0] + splitlink[2]
info['friends'] = [('Isogeny class ' + L.label, friendlink),
('Symmetric 1st Power', friendlink2)]
for j in range(2, L.m + 2):
if j != L.m:
friendlink3 = request.url.replace(
'/L/SymmetricPower/%d/' % L.m, '/L/SymmetricPower/%d/' % j)
info['friends'].append(
('Symmetric %s' % ordinal(j), friendlink3))
elif L.Ltype() == 'siegelnonlift' or L.Ltype(
) == 'siegeleisenstein' or L.Ltype(
) == 'siegelklingeneisenstein' or L.Ltype() == 'siegelmaasslift':
weight = str(L.weight)
number = str(L.number)
info['friends'] = [('Siegel Modular Form', friendlink)]
elif L.Ltype() == "artin":
# info['zeroeslink'] = ''
# info['plotlink'] = ''
info['friends'] = [('Artin representation', L.artin.url_for())]
if L.sign == 0: # The root number is now unknown
info['zeroeslink'] = ''
info['plotlink'] = ''
info['dirichlet'] = lfuncDStex(L, "analytic")
info['eulerproduct'] = lfuncEPtex(L, "abstract")
info['functionalequation'] = lfuncFEtex(L, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(L, "selberg")
if len(request.args) == 0:
lcalcUrl = request.url + '?download=lcalcfile'
else:
lcalcUrl = request.url + '&download=lcalcfile'
info['downloads'] = [('Lcalcfile', lcalcUrl)]
return info
