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 general_webpagedata(self):
info = {}
try:
info['support'] = self.support
except AttributeError:
info['support'] = ''
info['Ltype'] = self.Ltype()
info['label'] = self.label
info['credit'] = self.credit
info['degree'] = int(self.degree)
info['conductor'] = self.level
if not is_prime(int(self.level)):
info['conductor_factored'] = latex(factor(int(self.level)))
info['sign'] = "$" + styleTheSign(self.sign) + "$"
info['algebraic'] = self.algebraic
if self.selfdual:
info['selfdual'] = 'yes'
else:
info['selfdual'] = 'no'
if self.primitive:
info['primitive'] = 'yes'
else:
info['primitive'] = 'no'
info['dirichlet'] = lfuncDShtml(self, "analytic")
# Hack, fix this more general?
info['dirichlet'] = info['dirichlet'].replace('*I','<em>i</em>')
info['eulerproduct'] = lfuncEPtex(self, "abstract")
info['functionalequation'] = lfuncFEtex(self, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(self, "selberg")
if hasattr(self, 'positive_zeros'):
info['positive_zeros'] = self.positive_zeros
info['negative_zeros'] = self.negative_zeros
if hasattr(self, 'plot'):
info['plot'] = self.plot
if hasattr(self, 'factorization'):
info['factorization'] = self.factorization
if self.fromDB and self.algebraic:
info['dirichlet_arithmetic'] = lfuncDShtml(self, "arithmetic")
info['eulerproduct_arithmetic'] = lfuncEPtex(self, "arithmetic")
info['functionalequation_arithmetic'] = lfuncFEtex(self, "arithmetic")
if self.motivic_weight % 2 == 0:
arith_center = "\\frac{" + str(1 + self.motivic_weight) + "}{2}"
else:
arith_center = str(ZZ(1)/2 + self.motivic_weight/2)
svt_crit = specialValueTriple(self, 0.5, '\\frac12',arith_center)
info['sv_critical'] = svt_crit[0] + "\\ =\\ " + svt_crit[2]
info['sv_critical_analytic'] = [svt_crit[0], svt_crit[2]]
info['sv_critical_arithmetic'] = [svt_crit[1], svt_crit[2]]
if self.motivic_weight % 2 == 1:
arith_edge = "\\frac{" + str(2 + self.motivic_weight) + "}{2}"
else:
arith_edge = str(ZZ(1) + self.motivic_weight/2)
svt_edge = specialValueTriple(self, 1, '1',arith_edge)
info['sv_edge'] = svt_edge[0] + "\\ =\\ " + svt_edge[2]
info['sv_edge_analytic'] = [svt_edge[0], svt_edge[2]]
info['sv_edge_arithmetic'] = [svt_edge[1], svt_edge[2]]
info['st_group'] = self.st_group
info['st_link'] = self.st_link
info['rank'] = self.order_of_vanishing
info['motivic_weight'] = self.motivic_weight
elif self.Ltype() != "artin" or (self.Ltype() == "artin" and self.sign != 0):
try:
info['sv_edge'] = specialValueString(self, 1, '1')
info['sv_critical'] = specialValueString(self, 0.5, '1/2')
except:
info['sv_critical'] = "L(1/2): not computed"
info['sv_edge'] = "L(1): not computed"
return info
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_for('render_Character', arg1=1, arg2=1))]
elif L.Ltype() == 'dirichlet':
info['navi'] = getPrevNextNavig(L.charactermodulus, L.characternumber, "L")
snum = str(L.characternumber)
smod = str(L.charactermodulus)
charname = '\(\\chi_{%s}({%s},\\cdot)\)' % (smod, snum)
info['bread'] = get_bread(1, [(charname, request.url)])
info['friends'] = [('Dirichlet Character ' + str(charname), friendlink)]
elif L.Ltype() == 'ellipticcurve':
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-function', 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"
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 general_webpagedata(self):
info = {}
try:
info['support'] = self.support
except AttributeError:
info['support'] = ''
info['Ltype'] = self.Ltype()
try:
info['label'] = self.label
except AttributeError:
info['label'] = ""
try:
info['credit'] = self.credit
except AttributeError:
info['credit'] = ""
info['degree'] = int(self.degree)
info['conductor'] = self.level
if not is_prime(int(self.level)):
info['conductor_factored'] = latex(factor(int(self.level)))
info['sign'] = "$" + styleTheSign(self.sign) + "$"
info['algebraic'] = self.algebraic
if self.selfdual:
info['selfdual'] = 'yes'
else:
info['selfdual'] = 'no'
if self.primitive:
info['primitive'] = 'yes'
else:
info['primitive'] = 'no'
info['dirichlet'] = lfuncDShtml(self, "analytic")
# Hack, fix this more general?
info['dirichlet'] = info['dirichlet'].replace('*I', '<em>i</em>')
info['eulerproduct'] = lfuncEPtex(self, "abstract")
info['functionalequation'] = lfuncFEtex(self, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(self, "selberg")
if hasattr(self, 'positive_zeros'):
info['positive_zeros'] = self.positive_zeros
info['negative_zeros'] = self.negative_zeros
if hasattr(self, 'plot'):
info['plot'] = self.plot
if hasattr(self, 'factorization'):
info['factorization'] = self.factorization
if self.fromDB and self.algebraic:
info['dirichlet_arithmetic'] = lfuncDShtml(self, "arithmetic")
info['eulerproduct_arithmetic'] = lfuncEPtex(self, "arithmetic")
info['functionalequation_arithmetic'] = lfuncFEtex(
self, "arithmetic")
if self.motivic_weight % 2 == 0:
arith_center = "\\frac{" + str(1 +
self.motivic_weight) + "}{2}"
else:
arith_center = str(ZZ(1) / 2 + self.motivic_weight / 2)
svt_crit = specialValueTriple(self, 0.5, '\\frac12', arith_center)
info['sv_critical'] = svt_crit[0] + "\\ =\\ " + svt_crit[2]
info['sv_critical_analytic'] = [svt_crit[0], svt_crit[2]]
info['sv_critical_arithmetic'] = [svt_crit[1], svt_crit[2]]
if self.motivic_weight % 2 == 1:
arith_edge = "\\frac{" + str(2 + self.motivic_weight) + "}{2}"
else:
arith_edge = str(ZZ(1) + self.motivic_weight / 2)
svt_edge = specialValueTriple(self, 1, '1', arith_edge)
info['sv_edge'] = svt_edge[0] + "\\ =\\ " + svt_edge[2]
info['sv_edge_analytic'] = [svt_edge[0], svt_edge[2]]
info['sv_edge_arithmetic'] = [svt_edge[1], svt_edge[2]]
chilatex = "$\chi_{" + str(self.charactermodulus) + "} (" + str(
self.characternumber) + ", \cdot )$"
info['chi'] = '<a href="' + url_for(
'characters.render_Dirichletwebpage',
modulus=self.charactermodulus,
number=self.characternumber)
info['chi'] += '">' + chilatex + '</a>'
info['st_group'] = self.st_group
info['st_link'] = self.st_link
info['rank'] = self.order_of_vanishing
info['motivic_weight'] = self.motivic_weight
elif self.Ltype() != "artin" or (self.Ltype() == "artin"
and self.sign != 0):
try:
info['sv_edge'] = specialValueString(self, 1, '1')
info['sv_critical'] = specialValueString(self, 0.5, '1/2')
except:
info['sv_critical'] = "L(1/2): not computed"
info['sv_edge'] = "L(1): not computed"
return info
def general_webpagedata(self):
info = {}
try:
info['support'] = self.support
except AttributeError:
info['support'] = ''
info['Ltype'] = self.Ltype()
try:
info['label'] = self.label
except AttributeError:
info['label'] = ""
try:
info['credit'] = self.credit
except AttributeError:
info['credit'] = ""
info['degree'] = int(self.degree)
info['conductor'] = self.level
if not is_prime(int(self.level)):
if self.level >= 10**8:
info['conductor'] = latex(self.level_factored)
else:
info['conductor_factored'] = latex(self.level_factored)
info['sign'] = "$" + styleTheSign(self.sign) + "$"
info['algebraic'] = self.algebraic
if self.selfdual:
info['selfdual'] = 'yes'
else:
info['selfdual'] = 'no'
if self.primitive:
info['primitive'] = 'yes'
else:
info['primitive'] = 'no'
info['dirichlet'] = lfuncDShtml(self, "analytic")
# Hack, fix this more general?
info['dirichlet'] = info['dirichlet'].replace('*I','<em>i</em>')
info['eulerproduct'] = lfuncEPtex(self, "abstract")
info['functionalequation'] = lfuncFEtex(self, "analytic")
info['functionalequationSelberg'] = lfuncFEtex(self, "selberg")
if hasattr(self, 'positive_zeros'):
info['positive_zeros'] = self.positive_zeros
info['negative_zeros'] = self.negative_zeros
if hasattr(self, 'plot'):
info['plot'] = self.plot
if hasattr(self, 'factorization'):
info['factorization'] = self.factorization
if self.fromDB and self.algebraic:
info['dirichlet_arithmetic'] = lfuncDShtml(self, "arithmetic")
info['eulerproduct_arithmetic'] = lfuncEPtex(self, "arithmetic")
info['functionalequation_arithmetic'] = lfuncFEtex(self, "arithmetic")
if self.motivic_weight % 2 == 0:
arith_center = "\\frac{" + str(1 + self.motivic_weight) + "}{2}"
else:
arith_center = str(ZZ(1)/2 + self.motivic_weight/2)
svt_crit = specialValueTriple(self, 0.5, '\\frac12',arith_center)
info['sv_critical'] = svt_crit[0] + "\\ =\\ " + svt_crit[2]
info['sv_critical_analytic'] = [svt_crit[0], svt_crit[2]]
info['sv_critical_arithmetic'] = [svt_crit[1], svt_crit[2]]
if self.motivic_weight % 2 == 1:
arith_edge = "\\frac{" + str(2 + self.motivic_weight) + "}{2}"
else:
arith_edge = str(ZZ(1) + self.motivic_weight/2)
svt_edge = specialValueTriple(self, 1, '1',arith_edge)
info['sv_edge'] = svt_edge[0] + "\\ =\\ " + svt_edge[2]
info['sv_edge_analytic'] = [svt_edge[0], svt_edge[2]]
info['sv_edge_arithmetic'] = [svt_edge[1], svt_edge[2]]
chilatex = "$\chi_{" + str(self.charactermodulus) + "} (" + str(self.characternumber) +", \cdot )$"
info['chi'] = ''
if self.charactermodulus != self.level:
info['chi'] += "induced by "
info['chi'] += '<a href="' + url_for('characters.render_Dirichletwebpage',
modulus=self.charactermodulus, number=self.characternumber)
info['chi'] += '">' + chilatex + '</a>'
info['st_group'] = self.st_group
info['st_link'] = self.st_link
info['rank'] = self.order_of_vanishing
info['motivic_weight'] = r'\(%d\)' % self.motivic_weight
elif self.Ltype() == "riemann":
info['sv_edge'] = r"\[\zeta(1) \approx $\infty$\]"
info['sv_critical'] = r"\[\zeta(1/2) \approx -1.460354508\]"
elif self.Ltype() != "artin" or (self.Ltype() == "artin" and self.sign != 0):
try:
info['sv_edge'] = specialValueString(self, 1, '1')
info['sv_critical'] = specialValueString(self, 0.5, '1/2')
except:
info['sv_critical'] = "L(1/2): not computed"
info['sv_edge'] = "L(1): not computed"
return info
