def render_Dirichletwebpage(modulus=None, number=None):
if modulus is None:
return render_DirichletNavigation()
modulus = modulus.replace(' ','')
if number is None and re.match('^[1-9][0-9]*\.([1-9][0-9]*|[a-z]+)$', modulus):
modulus, number = modulus.split('.')
return redirect(url_for(".render_Dirichletwebpage", modulus=modulus, number=number), 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 is 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)
number = label_to_number(modulus, number)
if number == 0:
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"))
args['number'] = number
webchar = make_webchar(args)
info = webchar.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)
def render_Dirichletwebpage(modulus=None, orbit_label=None, number=None):
if number is None and orbit_label is None and re.match(r'^[1-9][0-9]*\.[1-9][0-9]*$', modulus):
modulus, number = modulus.split('.')
return redirect(url_for(".render_Dirichletwebpage", modulus=modulus, number=number), 301)
args = {}
args['type'] = 'Dirichlet'
args['modulus'] = modulus
args['orbit_label'] = orbit_label
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_DirichletNavigation"))
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_DirichletNavigation"))
if number is None:
if orbit_label is None:
if modulus <= 10000:
info = WebDBDirichletGroup(**args).to_dict()
info['show_orbit_label'] = True
else:
info = WebSmallDirichletGroup(**args).to_dict()
info['title'] = 'Group of Dirichlet characters of modulus ' + str(modulus)
info['bread'] = bread([('%s' % 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)
else:
if modulus <= 10000:
try:
info = WebDBDirichletOrbit(**args).to_dict()
except ValueError:
flash_error(
"No Galois orbit of Dirichlet characters with label %s.%s was found in the database.", modulus, orbit_label
)
return redirect(url_for(".render_DirichletNavigation"))
info['show_orbit_label'] = True
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
info['bread'] = bread(
[('%s' % modulus, url_for(".render_Dirichletwebpage", modulus=modulus)),
('%s' % orbit_label, url_for(".render_Dirichletwebpage", modulus=modulus, orbit_label=orbit_label))])
return render_template('CharacterGaloisOrbit.html', **info)
else:
flash_error(
"Galois orbits have only been computed for modulus up to 10,000, but you entered %s", modulus)
return redirect(url_for(".render_DirichletNavigation"))
try:
number = label_to_number(modulus, number)
except ValueError:
flash_error(
"the value %s is invalid. It should either be a positive integer "
"coprime to and no greater than the modulus %s, or a letter that "
"corresponds to a valid orbit index.", args['number'], args['modulus']
)
return redirect(url_for(".render_DirichletNavigation"))
if modulus <= 10000:
db_orbit_label = db.char_dir_values.lookup("{}.{}".format(modulus, number), projection='orbit_label')
# The -1 in the line below is because labels index at 1, not 0
real_orbit_label = cremona_letter_code(int(db_orbit_label.partition('.')[-1]) - 1)
if orbit_label is not None:
if orbit_label != real_orbit_label:
flash_warning(
"The supplied character orbit label %s.%s was wrong. "
"The correct orbit label is %s.%s. The URL has been duly corrected.",
modulus, orbit_label, modulus, real_orbit_label)
return redirect(url_for("characters.render_Dirichletwebpage",
modulus=modulus,
orbit_label=real_orbit_label,
number=number))
args['orbit_label'] = real_orbit_label
else:
if orbit_label is not None:
flash_warning(
"You entered the character orbit label %s.%s. However, such labels "
"have not been computed for this modulus. The supplied orbit "
"label has therefore been ignored and expunged from the URL.",
modulus, orbit_label)
return redirect(url_for("characters.render_Dirichletwebpage",
modulus=modulus,
number=number))
args['number'] = number
webchar, bread_crumbs = make_webchar(args, get_bread=True)
info = webchar.to_dict()
info['bread'] = bread_crumbs
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
info['KNOWL_ID'] = 'character.dirichlet.%s.%s' % (modulus, number)
return render_template('Character.html', **info)