def elliptic_curve_search(info, query):
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_element_of(info,query,field='isodeg',qfield='isogeny_degrees',split_interval=1000)
#parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='maximal primes',
qfield='nonmax_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-maximal primes',
qfield='nonmax_primes',mode=mode, radical='nonmax_rad')
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
def artin_representation_search(info, query):
query['Hide'] = 0
info['sign_code'] = 0
parse_primes(info,
query,
"unramified",
name="Unramified primes",
qfield="BadPrimes",
mode="complement")
parse_primes(info,
query,
"ramified",
name="Ramified primes",
qfield="BadPrimes",
mode="append")
parse_element_of(info, query, "root_number", qfield="GalConjSigns")
parse_restricted(info,
query,
"frobenius_schur_indicator",
qfield="Indicator",
allowed=[1, 0, -1],
process=int)
parse_container(info,
query,
'container',
qfield='Container',
name="Smallest permutation representation")
parse_galgrp(info, query, "group", name="Group", qfield=("Galn", "Galt"))
parse_ints(info, query, 'dimension', qfield='Dim')
parse_ints(info, query, 'conductor', qfield='Conductor')
def common_parse(info, query):
parse_ints(info, query, 'weight', name="Weight")
if 'weight_parity' in info:
parity = info['weight_parity']
if parity == 'even':
query['odd_weight'] = False
elif parity == 'odd':
query['odd_weight'] = True
if 'char_parity' in info:
parity = info['char_parity']
if parity == 'even':
query['char_parity'] = 1
elif parity == 'odd':
query['char_parity'] = -1
parse_ints(info, query, 'level', name="Level")
parse_floats(info, query, 'analytic_conductor', name="Analytic conductor")
parse_character(info, query, 'char_label', qfield='char_orbit_index')
parse_character(info,
query,
'prim_label',
qfield='prim_orbit_index',
level_field='char_conductor',
conrey_field=None)
parse_ints(info, query, 'char_order', name="Character order")
prime_mode = info['prime_quantifier'] = info.get('prime_quantifier',
'exact')
parse_primes(info,
query,
'level_primes',
name='Primes dividing level',
mode=prime_mode,
radical='level_radical')
def artin_representation_search(**args):
info = to_dict(args)
if 'natural' in info:
label = info['natural']
# test if it is ok
try:
label = parse_artin_label(label)
except ValueError as err:
flash(Markup("Error: %s" % (err)), "error")
bread = get_bread([('Search results','')])
return search_input_error({'err':''}, bread)
return render_artin_representation_webpage(label)
title = 'Artin representation search results'
bread = [('Artin representation', url_for(".index")), ('Search results', ' ')]
sign_code = 0
query = {'Hide': 0}
try:
parse_primes(info,query,"unramified",name="Unramified primes",
qfield="BadPrimes",mode="complement",to_string=True)
parse_primes(info,query,"ramified",name="Ramified primes",
qfield="BadPrimes",mode="append",to_string=True)
parse_restricted(info,query,"root_number",qfield="GaloisConjugates.Sign",
allowed=[1,-1],process=int)
parse_restricted(info,query,"frobenius_schur_indicator",qfield="Indicator",
allowed=[1,0,-1],process=int)
parse_galgrp(info,query,"group",name="Group",qfield="Galois_nt",use_bson=False)
parse_ints(info,query,'dimension',qfield='Dim')
parse_ints(info,query,'conductor',qfield='Conductor_key', parse_singleton=make_cond_key)
#parse_paired_fields(info,query,field1='conductor',qfield1='Conductor_key',parse1=parse_ints,kwds1={'parse_singleton':make_cond_key},
#field2='dimension',qfield2='Dim', parse2=parse_ints)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info,10)
start = parse_start(info)
data = ArtinRepresentation.collection().find(query).sort([("Dim", ASC), ("Conductor_key", ASC)])
nres = data.count()
data = data.skip(start).limit(count)
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
if nres == 1:
report = 'unique match'
else:
if nres > count or start != 0:
report = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
report = 'displaying all %s matches' % nres
if nres == 0:
report = 'no matches'
initfunc = ArtinRepresentation
return render_template("artin-representation-search.html", req=info, data=data, title=title, bread=bread, query=query, start=start, report=report, nres=nres, initfunc=initfunc, sign_code=sign_code)
def elliptic_curve_search(info, query):
parse_rational(info, query, 'jinv', 'j-invariant')
parse_ints(info, query, 'conductor')
parse_ints(info, query, 'torsion', 'torsion order')
parse_ints(info, query, 'rank')
parse_ints(info, query, 'sha', 'analytic order of Ш')
parse_bracketed_posints(info,
query,
'torsion_structure',
maxlength=2,
check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne': 0}
parse_element_of(info,
query,
field='isodeg',
qfield='isogeny_degrees',
split_interval=1000)
#parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info,
query,
'surj_primes',
name='maximal primes',
qfield='nonmax_primes',
mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info,
query,
'nonsurj_primes',
name='non-maximal primes',
qfield='nonmax_primes',
mode=mode,
radical='nonmax_rad')
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['curve_url'] = lambda dbc: url_for(".by_triple_label",
conductor=dbc['conductor'],
iso_label=split_lmfdb_label(dbc[
'lmfdb_iso'])[1],
number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label",
conductor=dbc['conductor'],
iso_label=split_lmfdb_label(dbc[
'lmfdb_iso'])[1])
def artin_representation_search(info, query):
query['Hide'] = 0
info['sign_code'] = 0
parse_primes(info,query,"unramified",name="Unramified primes",
qfield="BadPrimes",mode="complement")
parse_primes(info,query,"ramified",name="Ramified primes",
qfield="BadPrimes",mode="append")
parse_element_of(info,query,"root_number",qfield="GalConjSigns")
parse_restricted(info,query,"frobenius_schur_indicator",qfield="Indicator",
allowed=[1,0,-1],process=int)
parse_container(info,query, 'container',qfield='Container', name="Smallest permutation representation")
parse_galgrp(info,query,"group",name="Group",qfield=("Galn","Galt"))
parse_ints(info,query,'dimension',qfield='Dim')
parse_ints(info,query,'conductor',qfield='Conductor')
def number_field_search(info, query):
parse_ints(info, query, 'degree')
parse_galgrp(info, query, qfield=('degree', 'galt'))
parse_bracketed_posints(info,
query,
'signature',
qfield=('degree', 'r2'),
exactlength=2,
extractor=lambda L: (L[0] + 2 * L[1], L[1]))
parse_signed_ints(info,
query,
'discriminant',
qfield=('disc_sign', 'disc_abs'))
parse_ints(info, query, 'class_number')
parse_bracketed_posints(info,
query,
'class_group',
check_divisibility='increasing',
process=int)
parse_primes(info,
query,
'ur_primes',
name='Unramified primes',
qfield='ramps',
mode='complement')
# modes are now contained (in), exactly, include
if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'include':
mode = 'append'
elif 'ram_quantifier' in info and str(
info['ram_quantifier']) == 'contained':
mode = 'subsets'
else:
mode = 'exact'
parse_primes(info,
query,
'ram_primes',
name='Ramified primes',
qfield='ramps',
mode=mode,
radical='disc_rad')
## This seems not to be used
#if 'lucky' in info:
# label = db.nf_fields.lucky(query, 0)
# if label:
# return redirect(url_for(".by_label", label=clean_input(label)))
info['wnf'] = WebNumberField.from_data
def number_field_search(info, query):
parse_ints(info,query,'degree')
parse_galgrp(info,query, qfield=('degree', 'galt'))
parse_bracketed_posints(info,query,'signature',qfield=('degree','r2'),exactlength=2,extractor=lambda L: (L[0]+2*L[1],L[1]))
parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs'))
parse_ints(info,query,'class_number')
parse_bracketed_posints(info,query,'class_group',check_divisibility='increasing',process=int)
parse_primes(info,query,'ur_primes',name='Unramified primes',
qfield='ramps',mode='complement')
# modes are now contained (in), exactly, include
if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'include':
mode='append'
elif 'ram_quantifier' in info and str(info['ram_quantifier']) == 'contained':
mode='subsets'
else:
mode='exact'
parse_primes(info,query,'ram_primes',name='Ramified primes',
qfield='ramps',mode=mode,radical='disc_rad')
## This seems not to be used
#if 'lucky' in info:
# label = db.nf_fields.lucky(query, 0)
# if label:
# return redirect(url_for(".by_label", label=clean_input(label)))
info['wnf'] = WebNumberField.from_data
def elliptic_curve_search(info):
if info.get('download') == '1' and info.get('Submit') and info.get('query'):
return download_search(info)
if 'SearchAgain' in info:
return rational_elliptic_curves()
query = {}
bread = info.get('bread',[('Elliptic Curves', url_for("ecnf.index")), ('$\Q$', url_for(".rational_elliptic_curves")), ('Search Results', '.')])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r'\s','',label)
lab = re.sub(r'^\[','',lab)
lab = re.sub(r']$','',lab)
try:
labvec = lab.split(',')
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec)
# Now we do have a valid curve over Q, but it might
# not be in the database.
ainvs = [str(c) for c in E.minimal_model().ainvs()]
xainvs = ''.join(['[',','.join(ainvs),']'])
data = db_ec().find_one({'xainvs': xainvs})
if data is None:
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
info['conductor'] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data['lmfdb_label'])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query['label'] = ''
try:
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,process=str,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
if 'torsion_structure' in query and not 'torsion' in query:
query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='surjective primes',
qfield='non-maximal_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-surjective primes',
qfield='non-maximal_primes',mode=mode)
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info,100)
start = parse_start(info)
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['query'] = query
cursor = db_ec().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING),
('lmfdb_number', ASCENDING)]).skip(start).limit(count)
info['curves'] = res
info['format_ainvs'] = format_ainvs
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
if nres == 1:
info['report'] = 'unique match'
elif nres == 2:
info['report'] = 'displaying both matches'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
#credit = 'John Cremona'
#if 'non-surjective_primes' in query or 'non-maximal_primes' in query:
# credit += ' and Andrew Sutherland'
t = info.get('title','Elliptic Curves search results')
return render_template("ec-search-results.html", info=info, credit=ec_credit(), bread=bread, title=t)
def number_field_search(info):
info['learnmore'] = [
('Global number field labels', url_for(".render_labels_page")),
('Galois group labels', url_for(".render_groups_page")),
(Completename, url_for(".render_discriminants_page")),
('Quadratic imaginary class groups',
url_for(".render_class_group_data"))
]
t = 'Global Number Field search results'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")),
('Search results', ' ')]
if 'natural' in info:
query = {'label_orig': info['natural']}
try:
parse_nf_string(info,
query,
'natural',
name="Label",
qfield='label')
return redirect(
url_for(".by_label", label=clean_input(query['label_orig'])))
except ValueError:
query['err'] = info['err']
return search_input_error(query, bread)
if 'algebra' in info:
fields = info['algebra'].split('_')
fields2 = [WebNumberField.from_coeffs(a) for a in fields]
for j in range(len(fields)):
if fields2[j] is None:
fields2[j] = WebNumberField.fakenf(fields[j])
t = 'Number field algebra'
info = {}
info = {'fields': fields2}
return render_template("number_field_algebra.html",
info=info,
title=t,
bread=bread)
query = {}
try:
parse_galgrp(info, query, qfield='galois')
parse_ints(info, query, 'degree')
parse_bracketed_posints(info,
query,
'signature',
split=False,
exactlength=2)
parse_signed_ints(info,
query,
'discriminant',
qfield=('disc_sign', 'disc_abs_key'),
parse_one=make_disc_key)
parse_ints(info, query, 'class_number')
parse_bracketed_posints(info,
query,
'class_group',
split=False,
check_divisibility='increasing')
parse_primes(info,
query,
'ur_primes',
name='Unramified primes',
qfield='ramps',
mode='complement',
to_string=True)
# modes are now contained (in), exactly, include
if 'ram_quantifier' in info and str(
info['ram_quantifier']) == 'include':
mode = 'append'
parse_primes(info,
query,
'ram_primes',
'ramified primes',
'ramps',
mode,
to_string=True)
elif 'ram_quantifier' in info and str(
info['ram_quantifier']) == 'contained':
parse_primes(info,
query,
'ram_primes',
'ramified primes',
'ramps_all',
'subsets',
to_string=False)
pass # build list
else:
mode = 'liststring'
parse_primes(info, query, 'ram_primes', 'ramified primes',
'ramps_all', mode)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info)
start = parse_start(info)
# nf_logger.debug(query)
info['query'] = dict(query)
if 'lucky' in info:
one = nfdb().find_one(query)
if one:
label = one['label']
return redirect(url_for(".by_label", label=clean_input(label)))
fields = nfdb()
res = fields.find(query)
res = res.sort([('degree', ASC), ('disc_abs_key', ASC),
('disc_sign', ASC)])
if 'download' in info and info['download'] != '0':
return download_search(info, res)
nres = res.count()
res = res.skip(start).limit(count)
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
info['fields'] = res
info['number'] = nres
info['start'] = start
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
info['wnf'] = WebNumberField.from_data
return render_template("number_field_search.html",
info=info,
title=t,
bread=bread)
def elliptic_curve_search(**args):
info = to_dict(args)
if 'download' in info and info['download'] != '0':
return download_search(info)
query = {}
bread = [('Elliptic Curves', url_for("ecnf.index")),
('$\Q$', url_for(".rational_elliptic_curves")),
('Search Results', '.')]
if 'SearchAgain' in args:
return rational_elliptic_curves()
if 'jump' in args:
label = info.get('label', '').replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r'\s','',label)
lab = re.sub(r'^\[','',lab)
lab = re.sub(r']$','',lab)
try:
labvec = lab.split(',')
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec)
# Now we do have a valid curve over Q, but it might
# not be in the database.
ainvs = [str(c) for c in E.minimal_model().ainvs()]
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
info['conductor'] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data['lmfdb_label'])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query['label'] = ''
try:
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,process=str,check_divisibility='increasing')
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_primes(info, query, 'surj_primes', name='surjective primes',
qfield='non-surjective_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-surjective primes',
qfield='non-surjective_primes',mode=mode)
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info,100)
start = parse_start(info)
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['query'] = query
cursor = db_ec().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING),
('lmfdb_number', ASCENDING)]).skip(start).limit(count)
info['curves'] = res
info['format_ainvs'] = format_ainvs
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
if nres == 1:
info['report'] = 'unique match'
elif nres == 2:
info['report'] = 'displaying both matches'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
credit = 'John Cremona'
if 'non-surjective_primes' in query:
credit += 'and Andrew Sutherland'
t = 'Elliptic Curves search results'
return render_template("search_results.html", info=info, credit=credit, bread=bread, title=t)
def number_field_search(info):
info['learnmore'] = [('Global number field labels', url_for(".render_labels_page")), ('Galois group labels', url_for(".render_groups_page")), (Completename, url_for(".render_discriminants_page")), ('Quadratic imaginary class groups', url_for(".render_class_group_data"))]
t = 'Global Number Field search results'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search Results', ' ')]
if 'natural' in info:
query = {'label_orig': info['natural']}
try:
parse_nf_string(info,query,'natural',name="Label",qfield='label')
return redirect(url_for(".by_label", label=query['label']))
except ValueError:
query['err'] = info['err']
return search_input_error(query, bread)
if 'algebra' in info:
fields=info['algebra'].split('_')
fields2=[WebNumberField.from_coeffs(a) for a in fields]
for j in range(len(fields)):
if fields2[j] is None:
fields2[j] = WebNumberField.fakenf(fields[j])
t = 'Number field algebra'
info = {}
info = {'fields': fields2}
return render_template("number_field_algebra.html", info=info, title=t, bread=bread)
query = {}
try:
parse_galgrp(info,query, qfield='galois')
parse_ints(info,query,'degree')
parse_bracketed_posints(info,query,'signature',split=False,exactlength=2)
parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs_key'),parse_one=make_disc_key)
parse_ints(info,query,'class_number')
parse_bracketed_posints(info,query,'class_group',split=False,check_divisibility='increasing')
parse_primes(info,query,'ur_primes',name='Unramified primes',qfield='ramps',mode='complement',to_string=True)
# modes are now contained (in), exactly, include
if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'include':
mode = 'append'
parse_primes(info,query,'ram_primes','ramified primes','ramps',mode,to_string=True)
elif 'ram_quantifier' in info and str(info['ram_quantifier']) == 'contained':
parse_primes(info,query,'ram_primes','ramified primes','ramps_all','subsets',to_string=False)
pass # build list
else:
mode = 'liststring'
parse_primes(info,query,'ram_primes','ramified primes','ramps_all',mode)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info)
start = parse_start(info)
# nf_logger.debug(query)
info['query'] = dict(query)
if 'lucky' in info:
one = nfdb().find_one(query)
if one:
label = one['label']
return redirect(url_for(".by_label", label=clean_input(label)))
fields = nfdb()
res = fields.find(query)
res = res.sort([('degree', ASC), ('disc_abs_key', ASC),('disc_sign', ASC)])
if 'download' in info and info['download'] != '0':
return download_search(info, res)
# equivalent to
# nres = res.count()
#if(start >= nres):
# start -= (1 + (start - nres) / count) * count
#if(start < 0):
# start = 0
# res = res.skip(start).limit(count)
try:
start, nres, res = search_cursor_timeout_decorator(res, start, count);
except ValueError as err:
info['err'] = err;
return search_input_error(info, bread)
info['fields'] = res
info['number'] = nres
info['start'] = start
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
info['wnf'] = WebNumberField.from_data
return render_template("number_field_search.html", info=info, title=t, bread=bread)
def number_field_search(**args):
info = to_dict(args)
info['learnmore'] = [('Global number field labels', url_for(".render_labels_page")), ('Galois group labels', url_for(".render_groups_page")), (Completename, url_for(".render_discriminants_page")), ('Quadratic imaginary class groups', url_for(".render_class_group_data"))]
t = 'Global Number Field search results'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search results', ' ')]
# for k in info.keys():
# nf_logger.debug(str(k) + ' ---> ' + str(info[k]))
# nf_logger.debug('******************* '+ str(info['search']))
if 'natural' in info:
query = {'label_orig': info['natural']}
try:
parse_nf_string(info,query,'natural',name="Label",qfield='label')
return redirect(url_for(".by_label", label= clean_input(query['label'])))
except ValueError:
query['err'] = info['err']
return search_input_error(query, bread)
query = {}
try:
parse_galgrp(info,query, qfield='galois')
parse_ints(info,query,'degree')
parse_bracketed_posints(info,query,'signature',split=False,exactlength=2)
parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs_key'),parse_one=make_disc_key)
parse_ints(info,query,'class_number')
parse_bracketed_posints(info,query,'class_group',split=False,check_divisibility='increasing')
parse_primes(info,query,'ur_primes',name='Unramified primes',qfield='ramps',mode='complement',to_string=True)
if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'some':
mode = 'append'
else:
mode = 'exact'
parse_primes(info,query,'ram_primes','ramified primes','ramps',mode,to_string=True)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info)
start = parse_start(info)
if info.get('paging'):
try:
paging = int(info['paging'])
if paging == 0:
start = 0
except:
pass
C = base.getDBConnection()
# nf_logger.debug(query)
info['query'] = dict(query)
if 'lucky' in args:
one = C.numberfields.fields.find_one(query)
if one:
label = one['label']
return redirect(url_for(".by_label", clean_input(label)))
fields = C.numberfields.fields
res = fields.find(query)
if 'download' in info and info['download'] != '0':
return download_search(info, res)
res = res.sort([('degree', ASC), ('disc_abs_key', ASC),('disc_sign', ASC)])
nres = res.count()
res = res.skip(start).limit(count)
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
info['fields'] = res
info['number'] = nres
info['start'] = start
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
info['wnf'] = WebNumberField.from_data
return render_template("number_field_search.html", info=info, title=t, bread=bread)
def number_field_search(**args):
info = to_dict(args)
info["learnmore"] = [
("Global number field labels", url_for(".render_labels_page")),
("Galois group labels", url_for(".render_groups_page")),
(Completename, url_for(".render_discriminants_page")),
("Quadratic imaginary class groups", url_for(".render_class_group_data")),
]
t = "Global Number Field search results"
bread = [("Global Number Fields", url_for(".number_field_render_webpage")), ("Search results", " ")]
# for k in info.keys():
# nf_logger.debug(str(k) + ' ---> ' + str(info[k]))
# nf_logger.debug('******************* '+ str(info['search']))
if "natural" in info:
query = {"label_orig": info["natural"]}
try:
parse_nf_string(info, query, "natural", name="Label", qfield="label")
return redirect(url_for(".by_label", label=clean_input(query["label"])))
except ValueError:
query["err"] = info["err"]
return search_input_error(query, bread)
query = {}
try:
parse_galgrp(info, query, qfield="galois")
parse_ints(info, query, "degree")
parse_bracketed_posints(info, query, "signature", split=False, exactlength=2)
parse_signed_ints(info, query, "discriminant", qfield=("disc_sign", "disc_abs_key"), parse_one=make_disc_key)
parse_ints(info, query, "class_number")
parse_bracketed_posints(info, query, "class_group", split=False, check_divisibility="increasing")
parse_primes(
info, query, "ur_primes", name="Unramified primes", qfield="ramps", mode="complement", to_string=True
)
if "ram_quantifier" in info and str(info["ram_quantifier"]) == "some":
mode = "append"
else:
mode = "exact"
parse_primes(info, query, "ram_primes", "ramified primes", "ramps", mode, to_string=True)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info)
start = parse_start(info)
if info.get("paging"):
try:
paging = int(info["paging"])
if paging == 0:
start = 0
except:
pass
C = base.getDBConnection()
# nf_logger.debug(query)
info["query"] = dict(query)
if "lucky" in args:
one = C.numberfields.fields.find_one(query)
if one:
label = one["label"]
return redirect(url_for(".by_label", clean_input(label)))
fields = C.numberfields.fields
res = fields.find(query)
if "download" in info and info["download"] != "0":
return download_search(info, res)
res = res.sort([("degree", ASC), ("disc_abs_key", ASC), ("disc_sign", ASC)])
nres = res.count()
res = res.skip(start).limit(count)
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
info["fields"] = res
info["number"] = nres
info["start"] = start
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
info["wnf"] = WebNumberField.from_data
return render_template("number_field_search.html", info=info, title=t, bread=bread)
def elliptic_curve_search(info):
if info.get('download') == '1' and info.get('Submit') and info.get('query'):
return download_search(info)
if 'SearchAgain' in info:
return rational_elliptic_curves()
query = {}
bread = info.get('bread',[('Elliptic Curves', url_for("ecnf.index")), ('$\Q$', url_for(".rational_elliptic_curves")), ('Search Results', '.')])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r'\s','',label)
lab = re.sub(r'^\[','',lab)
lab = re.sub(r']$','',lab)
try:
labvec = lab.split(',')
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec).minimal_model()
# Now we do have a valid curve over Q, but it might
# not be in the database.
data = db_ec().find_one({'xainvs': EC_ainvs(E)})
if data is None:
info['conductor'] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data['lmfdb_label'])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query['label'] = ''
try:
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,process=str,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
if 'torsion_structure' in query and not 'torsion' in query:
query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='surjective primes',
qfield='non-maximal_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-surjective primes',
qfield='non-maximal_primes',mode=mode)
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info,100)
start = parse_start(info)
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['query'] = query
cursor = db_ec().find(query);
cursor = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING),
('lmfdb_number', ASCENDING)]);
# equivalent to
# cursor = res
# nres = res.count()
# if(start >= nres):
# start -= (1 + (start - nres) / count) * count
# if(start < 0):
# start = 0
# res = res.skip(start).limit(count)
try:
start, nres, res = search_cursor_timeout_decorator(cursor, start, count);
except ValueError as err:
info['err'] = err;
return search_input_error(info, bread)
info['curves'] = res
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
if nres == 1:
info['report'] = 'unique match'
elif nres == 2:
info['report'] = 'displaying both matches'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = info.get('title','Elliptic Curves search results')
return render_template("ec-search-results.html", info=info, credit=ec_credit(), bread=bread, title=t)
def number_field_search(**args):
info = to_dict(args)
info['learnmore'] = [('Global number field labels', url_for(".render_labels_page")), ('Galois group labels', url_for(".render_groups_page")), (Completename, url_for(".render_discriminants_page")), ('Quadratic imaginary class groups', url_for(".render_class_group_data"))]
t = 'Global Number Field search results'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search results', ' ')]
# for k in info.keys():
# nf_logger.debug(str(k) + ' ---> ' + str(info[k]))
# nf_logger.debug('******************* '+ str(info['search']))
if 'natural' in info:
query = {'label_orig': info['natural']}
try:
parse_nf_string(info,query,'natural',name="Label",qfield='label')
return redirect(url_for(".by_label", label= clean_input(query['label_orig'])))
except ValueError:
query['err'] = info['err']
return search_input_error(query, bread)
query = {}
try:
parse_galgrp(info,query, qfield='galois')
parse_ints(info,query,'degree')
parse_bracketed_posints(info,query,'signature',split=False,exactlength=2)
parse_signed_ints(info,query,'discriminant',qfield=('disc_sign','disc_abs_key'),parse_one=make_disc_key)
parse_ints(info,query,'class_number')
parse_bracketed_posints(info,query,'class_group',split=False,check_divisibility='increasing')
parse_primes(info,query,'ur_primes',name='Unramified primes',qfield='ramps',mode='complement',to_string=True)
# modes are now contained (in), exactly, include
if 'ram_quantifier' in info and str(info['ram_quantifier']) == 'include':
mode = 'append'
parse_primes(info,query,'ram_primes','ramified primes','ramps',mode,to_string=True)
elif 'ram_quantifier' in info and str(info['ram_quantifier']) == 'contained':
parse_primes(info,query,'ram_primes','ramified primes','ramps_all','subsets',to_string=False)
pass # build list
else:
mode = 'liststring'
parse_primes(info,query,'ram_primes','ramified primes','ramps_all',mode)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info)
start = parse_start(info)
if info.get('paging'):
try:
paging = int(info['paging'])
if paging == 0:
start = 0
except:
pass
C = base.getDBConnection()
# nf_logger.debug(query)
info['query'] = dict(query)
if 'lucky' in args:
one = C.numberfields.fields.find_one(query)
if one:
label = one['label']
return redirect(url_for(".by_label", label=clean_input(label)))
fields = C.numberfields.fields
res = fields.find(query)
res = res.sort([('degree', ASC), ('disc_abs_key', ASC),('disc_sign', ASC)])
if 'download' in info and info['download'] != '0':
return download_search(info, res)
nres = res.count()
res = res.skip(start).limit(count)
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
info['fields'] = res
info['number'] = nres
info['start'] = start
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
info['wnf'] = WebNumberField.from_data
return render_template("number_field_search.html", info=info, title=t, bread=bread)
def artin_representation_search(**args):
info = to_dict(args)
if 'natural' in info:
label = info['natural']
# test if it is ok
try:
label = parse_artin_label(label)
except ValueError as err:
flash(Markup("Error: %s" % (err)), "error")
bread = get_bread([('Search results', '')])
return search_input_error({'err': ''}, bread)
return render_artin_representation_webpage(label)
title = 'Artin representation search results'
bread = [('Artin representation', url_for(".index")),
('Search results', ' ')]
sign_code = 0
query = {'Hide': 0}
try:
parse_primes(info,
query,
"unramified",
name="Unramified primes",
qfield="BadPrimes",
mode="complement",
to_string=True)
parse_primes(info,
query,
"ramified",
name="Ramified primes",
qfield="BadPrimes",
mode="append",
to_string=True)
parse_restricted(info,
query,
"root_number",
qfield="GaloisConjugates.Sign",
allowed=[1, -1],
process=int)
parse_restricted(info,
query,
"frobenius_schur_indicator",
qfield="Indicator",
allowed=[1, 0, -1],
process=int)
parse_galgrp(info,
query,
"group",
name="Group",
qfield="Galois_nt",
use_bson=False)
parse_ints(info, query, 'dimension', qfield='Dim')
parse_ints(info,
query,
'conductor',
qfield='Conductor_key',
parse_singleton=make_cond_key)
#parse_paired_fields(info,query,field1='conductor',qfield1='Conductor_key',parse1=parse_ints,kwds1={'parse_singleton':make_cond_key},
#field2='dimension',qfield2='Dim', parse2=parse_ints)
except ValueError:
return search_input_error(info, bread)
count = parse_count(info, 10)
start = parse_start(info)
data = ArtinRepresentation.collection().find(query).sort([("Dim", ASC),
("Conductor_key",
ASC)])
nres = data.count()
data = data.skip(start).limit(count)
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
if nres == 1:
report = 'unique match'
else:
if nres > count or start != 0:
report = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
report = 'displaying all %s matches' % nres
if nres == 0:
report = 'no matches'
initfunc = ArtinRepresentation
return render_template("artin-representation-search.html",
req=info,
data=data,
title=title,
bread=bread,
query=query,
start=start,
report=report,
nres=nres,
initfunc=initfunc,
sign_code=sign_code)
def elliptic_curve_search(**args):
info = to_dict(args)
if "download" in info and info["download"] != "0":
return download_search(info)
query = {}
bread = [
("Elliptic Curves", url_for("ecnf.index")),
("$\Q$", url_for(".rational_elliptic_curves")),
("Search Results", "."),
]
if "SearchAgain" in args:
return rational_elliptic_curves()
if "jump" in args:
label = info.get("label", "").replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r"\s", "", label)
lab = re.sub(r"^\[", "", lab)
lab = re.sub(r"]$", "", lab)
try:
labvec = lab.split(",")
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec)
# Now we do have a valid curve over Q, but it might
# not be in the database.
ainvs = [str(c) for c in E.minimal_model().ainvs()]
data = db_ec().find_one({"ainvs": ainvs})
if data is None:
info["conductor"] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data["lmfdb_label"])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query["label"] = ""
try:
parse_rational(info, query, "jinv", "j-invariant")
parse_ints(info, query, "conductor")
parse_ints(info, query, "torsion", "torsion order")
parse_ints(info, query, "rank")
parse_ints(info, query, "sha", "analytic order of Ш")
parse_bracketed_posints(
info, query, "torsion_structure", maxlength=2, process=str, check_divisibility="increasing"
)
parse_primes(
info, query, "surj_primes", name="surjective primes", qfield="non-surjective_primes", mode="complement"
)
if info.get("surj_quantifier") == "exactly":
mode = "exact"
else:
mode = "append"
parse_primes(
info, query, "nonsurj_primes", name="non-surjective primes", qfield="non-surjective_primes", mode=mode
)
except ValueError as err:
info["err"] = str(err)
return search_input_error(info, bread)
count = parse_count(info, 100)
start = parse_start(info)
if "optimal" in info and info["optimal"] == "on":
# fails on 990h3
query["number"] = 1
info["query"] = query
cursor = db_ec().find(query)
nres = cursor.count()
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
res = (
cursor.sort([("conductor", ASCENDING), ("iso_nlabel", ASCENDING), ("lmfdb_number", ASCENDING)])
.skip(start)
.limit(count)
)
info["curves"] = res
info["format_ainvs"] = format_ainvs
info["curve_url"] = lambda dbc: url_for(
".by_triple_label",
conductor=dbc["conductor"],
iso_label=split_lmfdb_label(dbc["lmfdb_iso"])[1],
number=dbc["lmfdb_number"],
)
info["iso_url"] = lambda dbc: url_for(
".by_double_iso_label", conductor=dbc["conductor"], iso_label=split_lmfdb_label(dbc["lmfdb_iso"])[1]
)
info["number"] = nres
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
if nres == 1:
info["report"] = "unique match"
elif nres == 2:
info["report"] = "displaying both matches"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
credit = "John Cremona"
if "non-surjective_primes" in query:
credit += "and Andrew Sutherland"
t = "Elliptic Curves search results"
return render_template("search_results.html", info=info, credit=credit, bread=bread, title=t)