def render_artin_representation_webpage(label):
if re.compile(r'^\d+$').match(label):
return artin_representation_search(**{'dimension': label})
bread = get_bread([(label, ' ')])
# label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
# Should we have a big try around this to catch bad labels?
clean_label = clean_input(label)
if clean_label != label:
return redirect(
url_for('.render_artin_representation_webpage', label=clean_label),
301)
try:
the_rep = ArtinRepresentation(label)
except:
flash(
Markup(
"Error: <span style='color:black'>%s</span> is not the label of an Artin representation in the database."
% (label)), "error")
return search_input_error({'err': ''}, bread)
extra_data = {} # for testing?
extra_data['galois_knowl'] = group_display_knowl(5, 3) # for testing?
#artin_logger.info("Found %s" % (the_rep._data))
title = "Artin Representation %s" % label
the_nf = the_rep.number_field_galois_group()
if the_rep.sign() == 0:
processed_root_number = "not computed"
else:
processed_root_number = str(the_rep.sign())
properties = [
("Label", label),
("Dimension", str(the_rep.dimension())),
("Group", the_rep.group()),
#("Conductor", str(the_rep.conductor())),
("Conductor", "$" + the_rep.factored_conductor_latex() + "$"),
#("Bad primes", str(the_rep.bad_primes())),
("Root number", processed_root_number),
("Frobenius-Schur indicator", str(the_rep.indicator()))
]
friends = []
nf_url = the_nf.url_for()
if nf_url:
friends.append(("Artin Field", nf_url))
cc = the_rep.central_character()
if cc is not None:
if the_rep.dimension() == 1:
if cc.order == 2:
cc_name = cc.symbol
else:
cc_name = cc.texname
friends.append(("Dirichlet character " + cc_name,
url_for("characters.render_Dirichletwebpage",
modulus=cc.modulus,
number=cc.number)))
else:
detrep = the_rep.central_character_as_artin_rep()
friends.append(("Determinant representation " + detrep.label(),
detrep.url_for()))
# once the L-functions are in the database, the link can always be shown
#if the_rep.dimension() <= 6:
if the_rep.dimension() == 1:
# Zeta is loaded differently
if cc.modulus == 1 and cc.number == 1:
friends.append(("L-function",
url_for("l_functions.l_function_dirichlet_page",
modulus=cc.modulus,
number=cc.number)))
else:
# looking for Lhash dirichlet_L_modulus.number
mylhash = 'dirichlet_L_%d.%d' % (cc.modulus, cc.number)
lres = db.lfunc_instances.lucky({'Lhash': mylhash})
if lres is not None:
friends.append(
("L-function",
url_for("l_functions.l_function_dirichlet_page",
modulus=cc.modulus,
number=cc.number)))
# Dimension > 1
elif int(the_rep.conductor())**the_rep.dimension() <= 729000000000000:
friends.append(("L-function",
url_for("l_functions.l_function_artin_page",
label=the_rep.label())))
info = {}
#mychar = the_rep.central_char()
#info['pol2']= str([((j+1),mychar(j+1, 2*the_rep.character_field())) for j in range(50)])
#info['pol3']=str(the_rep.central_character())
#info['pol3']=str(the_rep.central_char(3))
#info['pol5']=str(the_rep.central_char(5))
#info['pol7']=str(the_rep.central_char(7))
#info['pol11']=str(the_rep.central_char(11))
learnmore = [('Artin representations labels', url_for(".labels_page"))]
return render_template("artin-representation-show.html",
credit=tim_credit,
support=support_credit,
title=title,
bread=bread,
friends=friends,
object=the_rep,
properties2=properties,
extra_data=extra_data,
info=info,
learnmore=learnmore)
