def random_representation():
rep = db.artin_reps.random(projection=2)
num = random.randrange(len(rep['GaloisConjugates']))
label = rep['Baselabel'] + "." + num2letters(num + 1)
return redirect(
url_for(".render_artin_representation_webpage", label=label), 307)
def render_artin_representation_webpage(label):
if re.compile(r'^\d+$').match(label):
return artin_representation_search(**{
'dimension': label,
'search_array': ArtinSearchArray()
})
# label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
# Should we have a big try around this to catch bad labels?
clean_label = clean_input(label)
if clean_label != label:
return redirect(
url_for('.render_artin_representation_webpage', label=clean_label),
301)
# We could have a single representation or a Galois orbit
case = parse_any(label)
if case[0] == 'malformed':
try:
raise ValueError
except:
flash_error(
"%s is not in a valid form for the label for an Artin representation or a Galois orbit of Artin representations",
label)
return redirect(url_for(".index"))
# Do this twice to customize error messages
newlabel = case[1]
case = case[0]
if case == 'rep':
try:
the_rep = ArtinRepresentation(newlabel)
except:
newlabel = parse_artin_label(label)
flash_error("Artin representation %s is not in database", label)
return redirect(url_for(".index"))
else: # it is an orbit
try:
the_rep = ArtinRepresentation(newlabel + '.a')
except:
newlabel = parse_artin_orbit_label(newlabel)
flash_error(
"Galois orbit of Artin representations %s is not in database",
label)
return redirect(url_for(".index"))
# in this case we want all characters
num_conj = the_rep.galois_conjugacy_size()
allchars = [
ArtinRepresentation(newlabel + '.' +
num2letters(j)).character_formatted()
for j in range(1, num_conj + 1)
]
label = newlabel
bread = get_bread([(label, ' ')])
#artin_logger.info("Found %s" % (the_rep._data))
if case == 'rep':
title = "Artin representation %s" % label
else:
title = "Galois orbit of Artin representations %s" % label
the_nf = the_rep.number_field_galois_group()
if the_rep.sign() == 0:
processed_root_number = "not computed"
else:
processed_root_number = str(the_rep.sign())
properties = [("Label", label), ("Dimension", str(the_rep.dimension())),
("Group", the_rep.group()),
("Conductor", "$" + the_rep.factored_conductor_latex() + "$")
]
if case == 'rep':
properties.append(("Root number", processed_root_number))
properties.append(("Frobenius-Schur indicator", str(the_rep.indicator())))
friends = []
wnf = None
nf_url = the_nf.url_for()
if nf_url:
friends.append(("Artin field", nf_url))
wnf = the_nf.wnf()
proj_nf = WebNumberField.from_coeffs(the_rep._data['Proj_Polynomial'])
if proj_nf:
friends.append(
("Projective Artin field",
str(url_for("number_fields.by_label",
label=proj_nf.get_label()))))
if case == 'rep':
cc = the_rep.central_character()
if cc is not None:
if the_rep.dimension() == 1:
if cc.order == 2:
cc_name = cc.symbol
else:
cc_name = cc.texname
friends.append(("Dirichlet character " + cc_name,
url_for("characters.render_Dirichletwebpage",
modulus=cc.modulus,
number=cc.number)))
else:
detrep = the_rep.central_character_as_artin_rep()
friends.append(("Determinant representation " + detrep.label(),
detrep.url_for()))
add_lfunction_friends(friends, label)
# once the L-functions are in the database, the link can always be shown
#if the_rep.dimension() <= 6:
if the_rep.dimension() == 1:
# Zeta is loaded differently
if cc.modulus == 1 and cc.number == 1:
friends.append(
("L-function",
url_for("l_functions.l_function_dirichlet_page",
modulus=cc.modulus,
number=cc.number)))
else:
# looking for Lhash dirichlet_L_modulus.number
mylhash = 'dirichlet_L_%d.%d' % (cc.modulus, cc.number)
lres = db.lfunc_instances.lucky({'Lhash': mylhash})
if lres is not None:
friends.append(
("L-function",
url_for("l_functions.l_function_dirichlet_page",
modulus=cc.modulus,
number=cc.number)))
# Dimension > 1
elif int(the_rep.conductor())**the_rep.dimension() <= 729000000000000:
friends.append(("L-function",
url_for("l_functions.l_function_artin_page",
label=the_rep.label())))
orblabel = re.sub(r'\.[a-z]+$', '', label)
friends.append(("Galois orbit " + orblabel,
url_for(".render_artin_representation_webpage",
label=orblabel)))
else:
add_lfunction_friends(friends, label)
friends.append(("L-function",
url_for("l_functions.l_function_artin_page",
label=the_rep.label())))
for j in range(1, 1 + the_rep.galois_conjugacy_size()):
newlabel = label + '.' + num2letters(j)
friends.append(("Artin representation " + newlabel,
url_for(".render_artin_representation_webpage",
label=newlabel)))
info = {} # for testing
if case == 'rep':
return render_template("artin-representation-show.html",
credit=tim_credit,
support=support_credit,
title=title,
bread=bread,
friends=friends,
object=the_rep,
cycle_string=cycle_string,
wnf=wnf,
properties=properties,
info=info,
learnmore=learnmore_list())
# else we have an orbit
return render_template("artin-representation-galois-orbit.html",
credit=tim_credit,
support=support_credit,
title=title,
bread=bread,
allchars=allchars,
friends=friends,
object=the_rep,
cycle_string=cycle_string,
wnf=wnf,
properties=properties,
info=info,
learnmore=learnmore_list())