def central_character(self):
"""
Returns the central character, i.e., determinant character
as a web character.
"""
if 'central_character' in self._data:
return self._data['central_character']
# Build it as a python function, id it, make a lmfdb character
# But, if the conductor is too large, this can stall because
# the function has to factor arbitrary integers modulo N
if Integer(self.conductor()) > 10**40:
return None
myfunc = self.central_char_function()
wc = id_dirichlet(myfunc, self.conductor(), 2 * self.character_field())
wc = WebSmallDirichletCharacter(modulus=wc[0], number=wc[1])
self._data['central_character'] = wc
return wc
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)