def artin_postprocess(res, info, query):
gp_labels = list(
set([rec["GaloisLabel"]
for rec in res] + [rec["Container"].upper() for rec in res] +
["T".join(str(c) for c in rec["Proj_nTj"]) for rec in res]))
cache = knowl_cache(gp_labels)
return [ArtinRepresentation(data=x, knowl_cache=cache) for x in res]
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())
j += 1
return rts
# select the ones we want
#artargs = {'Dim': {'$gte': 2, '$lte': 9}}
#allarts=rep.find(artargs)
#arep = rep.find_one({'Dim': {'$gte': 2}})
#ar = ArtinRepresentation(str(arep['Baselabel'])+'c1')
#ar = ArtinRepresentation('2.2e3_3e2.6t5.1c1')
baselabel = label.split('c')
a = rep.find_one({'Baselabel': baselabel[0]})
ar = ArtinRepresentation(label)
outfile = open(label, 'w')
cf = a['CharacterField']
cfz = ZZ(cf)
nf = ar.nf()
nfcc = nf.conjugacy_classes()
nfcc = [int(z.order()) for z in nfcc]
nfcc = lcm(nfcc)
if not cfz.divides(nfcc):
print("Failure " + str(cfz) + " divides " + str(nfcc) + " from " + label)
sys.exit()
R, x = QQ['x'].objgen()
pol1 = R.cyclotomic_polynomial(nfcc)
K, z = NumberField(R.cyclotomic_polynomial(nfcc), 'z').objgen()
def render_artin_representation_webpage(label):
if re.compile(r'^\d+$').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", "$" + the_rep.factored_conductor_latex() + "$"),
#("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()))
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())))
info={}
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_list())
# Adds a field called field_len to objects in the_collection. It is based on the field called field
# It encodes the len of the string used
# This is kind of a hack for mongodb, see lmfdb.utils.len_val_fn for explanation
import sys
LMFDB_FOLDER = "../../../"
sys.path.append(LMFDB_FOLDER)
from lmfdb.artin_representations.math_classes import ArtinRepresentation
the_collection = ArtinRepresentation.collection()
print "Got", the_collection
field = "Conductor"
from lmfdb.utils import len_val_fn
new_field = field + "_plus"
print "Updating"
for x in the_collection.find():
val = x[field]
x[new_field] = len_val_fn(val)
the_collection.save(x)
def render_artin_representation_webpage(label):
if re.compile(r'^\d+$').match(label):
return artin_representation_search(**{'dimension': label})
bread = get_bread([(label, ' ')])
# label=dim.cond.nTt.indexcj, c is literal, j is index in conj class
# Should we have a big try around this to catch bad labels?
clean_label = clean_input(label)
if clean_label != label:
return redirect(
url_for('.render_artin_representation_webpage', label=clean_label),
301)
try:
the_rep = ArtinRepresentation(label)
except:
try:
newlabel = parse_artin_label(label)
flash_error("Artin representation %s is not in database", newlabel)
return redirect(url_for(".index"))
except ValueError:
flash_error(
"%s is not in a valid form for an Artin representation label",
label)
return redirect(url_for(".index"))
extra_data = {} # for testing?
extra_data['galois_knowl'] = group_display_knowl(5, 3) # for testing?
#artin_logger.info("Found %s" % (the_rep._data))
title = "Artin Representation %s" % label
the_nf = the_rep.number_field_galois_group()
if the_rep.sign() == 0:
processed_root_number = "not computed"
else:
processed_root_number = str(the_rep.sign())
properties = [
("Label", label),
("Dimension", str(the_rep.dimension())),
("Group", the_rep.group()),
("Conductor", "$" + 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()))
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())))
info = {}
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_list())
])
artin_columns.above_table = "<div>Galois conjugate representations are grouped into single lines.</div>"
artin_columns.dummy_download = True
@search_wrap(table=db.artin_reps,
title='Artin representation search results',
err_title='Artin representation search error',
per_page=50,
columns=artin_columns,
learnmore=learnmore_list,
url_for_label=url_for_label,
shortcuts={'jump': artin_representation_jump},
postprocess=lambda res, info, query:
[ArtinRepresentation(data=x) for x in res],
bread=lambda: [('Artin representations', url_for(".index")),
('Search results', ' ')])
def artin_representation_search(info, query):
query['Hide'] = 0
info['sign_code'] = 0
parse_primes(info,
query,
"unramified",
name="Unramified primes",
qfield="BadPrimes",
mode="exclude")
parse_primes(info,
query,
"ramified",
name="Ramified primes",
from lmfdb.artin_representations.math_classes import ArtinRepresentation
from lmfdb.website import dbport
import base
base._init(dbport, "")
# x is raw
# a is of type ArtinRepresentation
# all the artin reps that come out of this are safe to appear on the website
# their L functions need to be fixed however
# if you want to do complex queries, and sort using pymongo's interface:
for x in ArtinRepresentation.collection().find():
a = ArtinRepresentation(data=x)
print a
try:
print a.Lfunction()
except NotImplementedError or SyntaxError:
print "Need CYC types and sign"
# if you want to list them all, using a wrapper to directly convert to ArtinRepresentation
for a in ArtinRepresentation.find():
print a
try:
print a.Lfunction()
except NotImplementedError or SyntaxError:
print "Need CYC types"
return rts
# select the ones we want
#artargs = {'Dim': {'$gte': 2, '$lte': 9}}
#allarts=rep.find(artargs)
#arep = rep.find_one({'Dim': {'$gte': 2}})
#ar = ArtinRepresentation(str(arep['Baselabel'])+'c1')
#ar = ArtinRepresentation('2.2e3_3e2.6t5.1c1')
baselabel=label.split('c')
a = rep.find_one({'Baselabel': baselabel[0]})
ar=ArtinRepresentation(label)
outfile=open(label, 'w')
cf=a['CharacterField']
cfz = ZZ(cf)
nf = ar.nf()
nfcc = nf.conjugacy_classes()
nfcc = [int(z.order()) for z in nfcc]
nfcc = lcm(nfcc)
if not cfz.divides(nfcc):
print "Failure "+str(cfz)+" divides "+str(nfcc)+" from "+label
sys.exit()
R,x = QQ['x'].objgen()
pol1 = R.cyclotomic_polynomial(nfcc)
K,z=NumberField(R.cyclotomic_polynomial(nfcc),'z').objgen()
