def search(info, query):
parse_ints(info, query, 'level', name='Level')
parse_ints(info, query, 'weight', name='Weight')
parse_character(info, query, 'character', name='Character')
parse_floats(info, query, 'spectral_parameter', name='Spectral parameter')
if info.get('symmetry'):
query['symmetry'] = int(info['symmetry'])
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_floats(info, query, 'rd')
parse_floats(info, query, 'regulator')
parse_ints(info,query,'class_number')
parse_ints(info,query,'num_ram')
parse_bool(info,query,'cm_field',qfield='cm')
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
info['gg_display'] = group_pretty_and_nTj
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_floats(info, query, 'rd')
parse_ints(info,query,'class_number')
parse_bool(info,query,'cm_field',qfield='cm')
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
info['gg_display'] = group_pretty_and_nTj
def search(info, query):
parse_ints(info, query, 'level', name='Level')
parse_ints(info, query, 'weight', name='Weight')
parse_character(info, query, 'character', name='Character')
parse_floats(info, query, 'spectral_parameter', name='Spectral parameter', allow_singletons=True)
if info.get('symmetry'):
query['symmetry'] = int(info['symmetry'])
query['__sort__'] = ['level', 'weight', 'conrey_index', 'spectral_parameter']
def number_field_search(info, query):
parse_ints(info, query, 'degree')
parse_galgrp(info, query, qfield=('galois_label', 'degree'))
parse_bracketed_posints(info,
query,
'signature',
qfield=('degree', 'r2'),
exactlength=2,
allow0=True,
extractor=lambda L: (L[0] + 2 * L[1], L[1]))
parse_signed_ints(info,
query,
'discriminant',
qfield=('disc_sign', 'disc_abs'))
parse_floats(info, query, 'rd')
parse_floats(info, query, 'regulator')
parse_ints(info, query, 'class_number')
parse_ints(info, query, 'num_ram')
parse_bool(info, query, 'cm_field', qfield='cm')
parse_bool(info, query, 'is_galois')
parse_bracketed_posints(info,
query,
'class_group',
check_divisibility='increasing',
process=int)
parse_primes(info,
query,
'ur_primes',
name='Unramified primes',
qfield='ramps',
mode='exclude')
parse_primes(info,
query,
'ram_primes',
name='Ramified primes',
qfield='ramps',
mode=info.get('ram_quantifier'),
radical='disc_rad')
parse_subfield(info,
query,
'subfield',
qfield='subfields',
name='Intermediate field')
parse_padicfields(info,
query,
'completions',
qfield='local_algs',
name='$p$-adic completions')
info['wnf'] = WebNumberField.from_data
info['gg_display'] = group_pretty_and_nTj
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_ints(info,query,'num_int_pts','num_int_pts')
parse_floats(info,query,'regulator','regulator')
parse_bool(info,query,'semistable','semistable')
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'] = {'$ne' : 0}
#parse_ints(info,query,field='cm_disc',qfield='cm')
if 'cm_disc' in info:
query['cm'] = info['cm_disc']
parse_element_of(info,query,field='isodeg',qfield='isogeny_degrees',split_interval=1000)
#parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='maximal primes',
qfield='nonmax_primes', mode='exclude')
parse_primes(info, query, 'nonsurj_primes', name='non-maximal primes',
qfield='nonmax_primes',mode=info.get('surj_quantifier'), radical='nonmax_rad')
parse_primes(info, query, 'bad_primes', name='bad primes',
qfield='bad_primes',mode=info.get('bad_quantifier'))
# The button which used to be labelled Optimal only no/yes"
# (default no) has been renamed "Curves per isogeny class all/one"
# (default one) but the only change in behavious is that we no
# longer treat class 990h (where the optial curve is #3 not #1) as
# special: the "one" option just restricts to curves whose
# 'number' is 1.
if 'optimal' in info and info['optimal'] == 'on':
query.update({'number':1})
# Old behaviour was as follows:
# For all isogeny classes except 990h the optimal curve is number 1, while for class 990h it is number 3.
# So setting query['number'] = 1 is nearly correct, but fails on 990h3.
# Instead, we use this more complicated query:
# query.update({"$or":[{'iso':'990h', 'number':3}, {'iso':{'$ne':'990h'},'number':1}]})
info['curve_ainvs'] = lambda dbc: str([ZZ(ai) for ai in dbc['ainvs']])
info['curve_url_LMFDB'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url_LMFDB'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['curve_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['label'])
info['iso_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['iso'])
def elliptic_curve_search(info, query):
parse_rational_to_list(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_ints(info,query,'num_int_pts','num_int_pts')
parse_ints(info,query,'class_size','class_size')
parse_ints(info,query,'class_deg','class_deg')
parse_floats(info,query,'regulator','regulator')
parse_bool(info,query,'semistable','semistable')
parse_bool(info,query,'potential_good_reduction','potential_good_reduction')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_ints(info,query,field='cm_disc',qfield='cm')
parse_element_of(info,query,'isogeny_degrees',split_interval=1000,contained_in=get_stats().isogeny_degrees)
parse_primes(info, query, 'surj_primes', name='maximal primes',
qfield='nonmax_primes', mode='exclude')
parse_primes(info, query, 'nonsurj_primes', name='non-maximal primes',
qfield='nonmax_primes',mode=info.get('surj_quantifier'), radical='nonmax_rad')
parse_primes(info, query, 'bad_primes', name='bad primes',
qfield='bad_primes',mode=info.get('bad_quantifier'))
parse_primes(info, query, 'sha_primes', name='sha primes',
qfield='sha_primes',mode=info.get('sha_quantifier'))
# The button which used to be labelled Optimal only no/yes"
# (default: no) has been renamed "Curves per isogeny class
# all/one" (default: all). When this option is "one" we only list
# one curve in each class, currently choosing the curve with
# minimal Faltings heights, which is conjecturally the
# Gamma_1(N)-optimal curve.
if 'optimal' in info and info['optimal'] == 'on':
query.update({'lmfdb_number':1})
info['curve_ainvs'] = lambda dbc: str([ZZ(ai) for ai in dbc['ainvs']])
info['curve_url_LMFDB'] = 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_LMFDB'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['cremona_bound'] = CREMONA_BOUND
info['curve_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['Clabel'])
info['iso_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['Ciso'])
def elliptic_curve_search(info, query):
parse_nf_string(info,
query,
'field',
name="base number field",
qfield='field_label')
if query.get('field_label') == '1.1.1.1':
return redirect(url_for("ec.rational_elliptic_curves", **request.args),
301)
parse_ints(info, query, 'conductor_norm')
parse_noop(info, query, 'conductor_label')
parse_ints(info, query, 'rank')
parse_ints(info,
query,
'torsion',
name='Torsion order',
qfield='torsion_order')
parse_bracketed_posints(info, query, 'torsion_structure', maxlength=2)
if 'torsion_structure' in query and 'torsion_order' not in query:
t_o = 1
for n in query['torsion_structure']:
t_o *= int(n)
query['torsion_order'] = t_o
parse_element_of(info,
query,
'isodeg',
split_interval=1000,
contained_in=ECNF_stats().isogeny_degrees)
parse_bool(info, query, 'semistable', 'semistable')
parse_bool(info, query, 'potential_good_reduction',
'potential_good_reduction')
parse_ints(info, query, 'class_size', 'class_size')
parse_ints(info, query, 'class_deg', 'class_deg')
parse_ints(info, query, 'sha', 'analytic order of Ш')
parse_floats(info, query, 'reg', 'regulator')
parse_nf_jinv(info,
query,
'jinv',
'j-invariant',
field_label=query.get('field_label'))
if info.get('one') == "yes":
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info:
if info['include_base_change'] in [
'exclude', 'off'
]: # off for backward compat with urls
query['base_change'] = []
if info['include_base_change'] == 'only':
query['base_change'] = {'$ne': []}
else:
info['include_base_change'] = "on"
if 'include_Q_curves' in info:
if info['include_Q_curves'] == 'exclude':
query['q_curve'] = False
elif info['include_Q_curves'] == 'only':
query['q_curve'] = True
parse_cm_list(info,
query,
field='cm_disc',
qfield='cm',
name="CM discriminant")
if 'include_cm' in info:
if info['include_cm'] == 'PCM':
tmp = {'$ne': 0}
if 'cm' in query:
query['cm'] = {'$and': [tmp, query['cm']]}
else:
query['cm'] = tmp
elif info['include_cm'] == 'PCMnoCM':
tmp = {'$lt': 0}
if 'cm' in query:
query['cm'] = {'$and': [tmp, query['cm']]}
else:
query['cm'] = tmp
elif info['include_cm'] == 'CM':
tmp = {'$gt': 0}
if 'cm' in query:
query['cm'] = {'$and': [tmp, query['cm']]}
else:
query['cm'] = tmp
elif info['include_cm'] == 'noPCM':
tmp = 0
if 'cm' in query:
query['cm'] = {'$and': [tmp, query['cm']]}
else:
query['cm'] = tmp
parse_primes(info,
query,
'conductor_norm_factors',
name='bad primes',
qfield='conductor_norm_factors',
mode=info.get('bad_quantifier'))
info['field_pretty'] = field_pretty
parse_ints(info,
query,
'bf_deg',
name='Base field degree',
qfield='degree')
def elliptic_curve_search(info, query):
parse_nf_string(info,query,'field',name="base number field",qfield='field_label')
if query.get('field_label') == '1.1.1.1':
return redirect(url_for("ec.rational_elliptic_curves", **request.args), 301)
parse_ints(info,query,'conductor_norm')
parse_noop(info,query,'conductor_label')
parse_ints(info,query,'rank')
parse_ints(info,query,'torsion',name='Torsion order',qfield='torsion_order')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2)
if 'torsion_structure' in query and not 'torsion_order' in query:
t_o = 1
for n in query['torsion_structure']:
t_o *= int(n)
query['torsion_order'] = t_o
parse_element_of(info,query,'isodeg',split_interval=1000,contained_in=ECNF_stats().isogeny_degrees)
parse_bool(info,query,'semistable','semistable')
parse_bool(info,query,'potential_good_reduction','potential_good_reduction')
parse_ints(info,query,'class_size','class_size')
parse_ints(info,query,'class_deg','class_deg')
parse_ints(info,query,'sha','analytic order of Ш')
parse_floats(info,query,'reg','regulator')
if 'jinv' in info:
if info.get('field','').strip() == '2.2.5.1':
info['jinv'] = info['jinv'].replace('phi','a')
if info.get('field','').strip() == '2.0.4.1':
info['jinv'] = info['jinv'].replace('i','a')
if not 'a' in info['jinv'] and not info.get('field'): # rational j-invariant allowed for any field
parse_rational(info, query, 'jinv', name='j-invariant')
if query.get('jinv'):
query['jinv'] = {'$regex': '^' + query['jinv'] + '(,0)*$'} # nf elements like j,0,0,0
else: # j-invariant is a number field element
parse_nf_elt(info, query, 'jinv', name='j-invariant')
if query.get('jinv'):
query['jinv'] = ','.join(query['jinv'])
if info.get('one') == "yes":
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info:
if info['include_base_change'] in ['exclude', 'off']: # off for backward compat with urls
query['base_change'] = []
if info['include_base_change'] == 'only':
query['base_change'] = {'$ne':[]}
else:
info['include_base_change'] = "on"
if 'include_Q_curves' in info:
if info['include_Q_curves'] == 'exclude':
query['q_curve'] = False
elif info['include_Q_curves'] == 'only':
query['q_curve'] = True
if 'include_cm' in info:
if info['include_cm'] == 'PCM':
query['cm'] = {'$ne' : 0}
elif info['include_cm'] == 'PCMnoCM':
query['cm'] = {'$lt' : 0}
elif info['include_cm'] == 'CM':
query['cm'] = {'$gt' : 0}
elif info['include_cm'] == 'noPCM':
query['cm'] = 0
parse_ints(info,query,field='cm_disc',qfield='cm')
parse_primes(info, query, 'conductor_norm_factors', name='bad primes',
qfield='conductor_norm_factors',mode=info.get('bad_quantifier'))
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
parse_ints(info,query,'bf_deg',name='Base field degree',qfield='degree')
def elliptic_curve_search(info, query):
parse_rational_to_list(info, query, 'jinv', 'j-invariant')
parse_ints(info, query, 'conductor')
if info.get('conductor_type'):
if info['conductor_type'] == 'prime':
query['num_bad_primes'] = 1
query['semistable'] = True
elif info['conductor_type'] == 'prime_power':
query['num_bad_primes'] = 1
elif info['conductor_type'] == 'squarefree':
query['semistable'] = True
elif info['conductor_type'] == 'divides':
if not isinstance(query.get('conductor'), int):
err = "You must specify a single conductor"
flash_error(err)
raise ValueError(err)
else:
query['conductor'] = {'$in': integer_divisors(ZZ(query['conductor']))}
parse_signed_ints(info, query, 'discriminant', qfield=('signD', 'absD'))
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_ints(info,query,'num_int_pts','num_int_pts')
parse_ints(info,query,'class_size','class_size')
if info.get('class_deg'):
parse_ints(info,query,'class_deg','class_deg')
if not isinstance(query.get('class_deg'), int):
err = "You must specify a single isogeny class degree"
flash_error(err)
raise ValueError(err)
parse_floats(info,query,'regulator','regulator')
parse_floats(info, query, 'faltings_height', 'faltings_height')
if info.get('reduction'):
if info['reduction'] == 'semistable':
query['semistable'] = True
elif info['reduction'] == 'not semistable':
query['semistable'] = False
elif info['reduction'] == 'potentially good':
query['potential_good_reduction'] = True
elif info['reduction'] == 'not potentially good':
query['potential_good_reduction'] = False
if info.get('torsion'):
if info['torsion'][0] == '[':
parse_bracketed_posints(info,query,'torsion',qfield='torsion_structure',maxlength=2,check_divisibility='increasing')
else:
parse_ints(info,query,'torsion')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'cm' in info:
if info['cm'] == 'noCM':
query['cm'] = 0
elif info['cm'] == 'CM':
query['cm'] = {'$ne' : 0}
else:
parse_ints(info,query,field='cm',qfield='cm')
parse_element_of(info,query,'isogeny_degrees',split_interval=200,contained_in=get_stats().isogeny_degrees)
parse_primes(info, query, 'nonmax_primes', name='non-maximal primes',
qfield='nonmax_primes', mode=info.get('nonmax_quantifier'), radical='nonmax_rad')
parse_primes(info, query, 'bad_primes', name='bad primes',
qfield='bad_primes',mode=info.get('bad_quantifier'))
parse_primes(info, query, 'sha_primes', name='sha primes',
qfield='sha_primes',mode=info.get('sha_quantifier'))
if info.get('galois_image'):
labels = [a.strip() for a in info['galois_image'].split(',')]
elladic_labels = [a for a in labels if elladic_image_label_regex.fullmatch(a) and is_prime_power(elladic_image_label_regex.match(a)[1])]
modell_labels = [a for a in labels if modell_image_label_regex.fullmatch(a) and is_prime(modell_image_label_regex.match(a)[1])]
if len(elladic_labels)+len(modell_labels) != len(labels):
err = "Unrecognized Galois image label, it should be the label of a subgroup of GL(2,Z_ell), such as %s, or the label of a subgroup of GL(2,F_ell), such as %s, or a list of such labels"
flash_error(err, "13.91.3.2", "13S4")
raise ValueError(err)
if elladic_labels:
query['elladic_images'] = {'$contains': elladic_labels}
if modell_labels:
query['modell_images'] = {'$contains': modell_labels}
if 'cm' not in query:
query['cm'] = 0
info['cm'] = "noCM"
if query['cm']:
# try to help the user out if they specify the normalizer of a Cartan in the CM case (these are either maximal or impossible
if any(a.endswith("Nn") for a in modell_labels) or any(a.endswith("Ns") for a in modell_labels):
err = "To search for maximal images, exclude non-maximal primes"
flash_error(err)
raise ValueError(err)
else:
# if the user specifies full mod-ell image with ell > 3, automatically exclude nonmax primes (if possible)
max_labels = [a for a in modell_labels if a.endswith("G") and int(modell_image_label_regex.match(a)[1]) > 3]
if max_labels:
if info.get('nonmax_primes') and info['nonmax_quantifier'] != 'exclude':
err = "To search for maximal images, exclude non-maximal primes"
flash_error(err)
raise ValueError(err)
else:
modell_labels = [a for a in modell_labels if a not in max_labels]
max_primes = [modell_image_label_regex.match(a)[1] for a in max_labels]
if info.get('nonmax_primes'):
max_primes += [l.strip() for l in info['nonmax_primes'].split(',') if not l.strip() in max_primes]
max_primes.sort(key=int)
info['nonmax_primes'] = ','.join(max_primes)
info['nonmax_quantifier'] = 'exclude'
parse_primes(info, query, 'nonmax_primes', name='non-maximal primes',
qfield='nonmax_primes', mode=info.get('nonmax_quantifier'), radical='nonmax_rad')
info['galois_image'] = ','.join(modell_labels + elladic_labels)
query['modell_images'] = { '$contains': modell_labels }
# The button which used to be labelled Optimal only no/yes"
# (default: no) has been renamed "Curves per isogeny class
# all/one" (default: all). When this option is "one" we only list
# one curve in each class, currently choosing the curve with
# minimal Faltings heights, which is conjecturally the
# Gamma_1(N)-optimal curve.
if 'optimal' in info and info['optimal'] == 'on':
query["__one_per__"] = "lmfdb_iso"
info['curve_ainvs'] = lambda dbc: str([ZZ(ai) for ai in dbc['ainvs']])
info['curve_url_LMFDB'] = 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_LMFDB'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['cremona_bound'] = CREMONA_BOUND
info['curve_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['Clabel'])
info['iso_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['Ciso'])
info['FH'] = lambda dbc: RealField(20)(dbc['faltings_height'])
