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'] = {'$ne' : 0}
parse_element_of(info,query,field='isodeg',qfield='isogeny_degrees',split_interval=1000)
#parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='maximal primes',
qfield='nonmax_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-maximal primes',
qfield='nonmax_primes',mode=mode, radical='nonmax_rad')
if 'optimal' in info and info['optimal'] == 'on':
# For all isogeny classes except 990h the optimal curve is number 1, while for class 990h it is number 3.
# So setting query['number'] = 1 is nearly correct, but fails on 990h3.
# Instead, we use this more complicated query:
query.update({"$or":[{'iso':'990h', 'number':3}, {'iso':{'$ne':'990h'},'number':1}]})
info['curve_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 galois_group_search(info, query):
def includes_composite(s):
s = s.replace(' ','').replace('..','-')
for interval in s.split(','):
if '-' in interval[1:]:
ix = interval.index('-',1)
a,b = int(interval[:ix]), int(interval[ix+1:])
if b == a:
if a != 1 and not a.is_prime():
return True
if b > a and b > 3:
return True
else:
a = ZZ(interval)
if a != 1 and not a.is_prime():
return True
parse_ints(info,query,'n','degree')
parse_ints(info,query,'t')
parse_ints(info,query,'order')
parse_bracketed_posints(info, query, qfield='gapidfull', split=False, exactlength=2, keepbrackets=True, name='GAP id', field='gapid')
for param in ('cyc', 'solv', 'prim'):
parse_bool(info, query, param, process=int, blank=['0','Any'])
parse_restricted(info,query,'parity',allowed=[1,-1],process=int,blank=['0','Any'])
if 'order' in query and 'n' not in query:
query['__sort__'] = ['order', 'gapid', 'n', 't']
degree_str = prep_ranges(info.get('n'))
info['show_subs'] = degree_str is None or (LIST_RE.match(degree_str) and includes_composite(degree_str))
info['group_display'] = group_display_pretty
info['yesno'] = yesno
info['wgg'] = WebGaloisGroup.from_data
def higher_genus_w_automorphisms_search(info, query):
if info.get('signature'):
# allow for ; in signature
info['signature'] = info['signature'].replace(';', ',')
parse_bracketed_posints(info,
query,
'signature',
split=False,
name='Signature',
keepbrackets=True)
if query.get('signature'):
query['signature'] = info['signature'] = str(
sort_sign(ast.literal_eval(query['signature']))).replace(
' ', '')
parse_gap_id(info, query, 'group', qfield='group')
parse_ints(info, query, 'g0')
parse_ints(info, query, 'genus')
parse_ints(info, query, 'dim')
parse_group_order(info, query, 'group_order')
if 'inc_hyper' in info:
if info['inc_hyper'] == 'exclude':
query['hyperelliptic'] = False
elif info['inc_hyper'] == 'only':
query['hyperelliptic'] = True
if 'inc_cyc_trig' in info:
if info['inc_cyc_trig'] == 'exclude':
query['cyclic_trigonal'] = False
elif info['inc_cyc_trig'] == 'only':
query['cyclic_trigonal'] = True
if 'inc_full' in info:
if info['inc_full'] == 'exclude':
query['full_auto'] = {'$exists': True}
elif info['inc_full'] == 'only':
query['full_auto'] = {'$exists': False}
query['cc.1'] = 1
info['group_display'] = group_display
info['sign_display'] = sign_display
if 'sort_order' in info:
if info['sort_order'] == '':
query['__sort__'] = ['genus', 'group_order', 'g0', 'dim']
elif info['sort_order'] == 'descgenus':
query['__sort__'] = [('genus', -1), 'group_order', 'g0', 'dim']
elif info['sort_order'] == 'g0':
query['__sort__'] = ['g0', 'genus', 'group_order', 'dim']
elif info['sort_order'] == 'descg0':
query['__sort__'] = [('g0', -1), 'genus', 'group_order', 'dim']
elif info.get('sort_order') == 'dim':
query['__sort__'] = ['dim', 'genus', 'group_order', 'g0']
elif info.get('sort_order') == 'descdim':
query['__sort__'] = [('dim', -1), 'genus', 'group_order', 'g0']
elif info.get('sort_order') == 'group_order':
query['__sort__'] = ['group_order', 'genus', 'g0', 'dim']
elif info.get('sort_order') == 'descgroup_order':
query['__sort__'] = [('group_order', -1), 'genus', 'g0', 'dim']
else:
query['__sort__'] = ['genus', 'group_order', 'g0', 'dim']
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 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 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 genus2_curve_search(info, query):
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type','is of GL2-type')
parse_bool(info,query,'has_square_sha','has square Sha')
parse_bool(info,query,'locally_solvable','is locally solvable')
parse_bool(info,query,'is_simple_geom','is geometrically simple')
parse_ints(info,query,'cond','conductor')
parse_ints(info,query,'num_rat_pts','rational points')
parse_ints(info,query,'num_rat_wpts','rational Weierstrass points')
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'torsion_order','torsion order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,[int(n) for n in query['torsion']],1)
if 'torsion' in query:
query['torsion_subgroup'] = str(query['torsion']).replace(" ","")
query.pop('torsion') # search using string key, not array of ints
parse_ints(info,query,'two_selmer_rank','2-Selmer rank')
parse_ints(info,query,'analytic_rank','analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2_inv'] = "['%s','%s','%s']"%(info['g20'], info['g21'], info['g22'])
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id', 'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
def galois_group_search(info, query):
def includes_composite(s):
s = s.replace(' ','').replace('..','-')
for interval in s.split(','):
if '-' in interval[1:]:
ix = interval.index('-',1)
a,b = int(interval[:ix]), int(interval[ix+1:])
if b == a:
if a != 1 and not a.is_prime():
return True
if b > a and b > 3:
return True
else:
a = ZZ(interval)
if a != 1 and not a.is_prime():
return True
parse_ints(info,query,'n','degree')
parse_ints(info,query,'t')
parse_ints(info,query,'order')
parse_ints(info,query,'nilpotency')
parse_bracketed_posints(info, query, qfield='gapidfull', split=False, exactlength=2, keepbrackets=True, name='GAP id', field='gapid')
for param in ('cyc', 'solv', 'prim'):
parse_bool(info, query, param, process=int, blank=['0','Any'])
parse_restricted(info,query,'parity',allowed=[1,-1],process=int,blank=['0','Any'])
if 'order' in query and 'n' not in query:
query['__sort__'] = ['order', 'gapid', 'n', 't']
degree_str = prep_ranges(info.get('n'))
info['show_subs'] = degree_str is None or (LIST_RE.match(degree_str) and includes_composite(degree_str))
info['group_display'] = group_display_short
info['yesno'] = yesno
info['wgg'] = WebGaloisGroup.from_data
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,
'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:
query['torsion_order'] = reduce(
mul, [int(n) for n in query['torsion_structure']], 1)
parse_ints(info, query, field='isodeg', qfield='isogeny_degrees')
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')
parse_nf_elt(info, query, 'jinv', name='j-invariant')
if query.get('jinv'):
query['jinv'] = ','.join(query['jinv'])
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info:
if info['include_base_change'] == 'off':
query['base_change'] = []
if info['include_base_change'] == 'only':
query['base_change'] = {'$ne': []}
else:
info['include_base_change'] = "on"
if 'include_Q_curves' in info:
if info['include_Q_curves'] == 'exclude':
query['q_curve'] = False
elif info['include_Q_curves'] == 'only':
query['q_curve'] = True
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne': 0}
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
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,'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,field='isodeg',qfield='isogeny_degrees',split_interval=1000)
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'] = {'$ne':[]}
else:
info['include_base_change'] = "on"
if 'include_Q_curves' in info:
if info['include_Q_curves'] == 'exclude':
query['q_curve'] = False
elif info['include_Q_curves'] == 'only':
query['q_curve'] = True
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_ints(info,query,field='cm_disc',qfield='cm')
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
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_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'] = {'$ne' : 0}
parse_element_of(info,query,field='isodeg',qfield='isogeny_degrees',split_interval=1000)
#parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='maximal primes',
qfield='nonmax_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-maximal primes',
qfield='nonmax_primes',mode=mode, radical='nonmax_rad')
if info.get('bad_quantifier') == 'exactly':
mode = 'exact'
elif info.get('bad_quantifier') == 'exclude':
mode = 'complement'
else:
mode = 'append'
parse_primes(info, query, 'bad_primes', name='bad primes',
qfield='bad_primes',mode=mode)
# The button which used to be labelled Optimal only no/yes"
# (default no) has been renamed "Curves per isogeny class all/one"
# (default one) but the only change in behavious is that we no
# longer treat class 990h (where the optial curve is #3 not #1) as
# special: the "one" option just restricts to curves whose
# 'number' is 1.
if 'optimal' in info and info['optimal'] == 'on':
query.update({'number':1})
# Old behaviour was as follows:
# For all isogeny classes except 990h the optimal curve is number 1, while for class 990h it is number 3.
# So setting query['number'] = 1 is nearly correct, but fails on 990h3.
# Instead, we use this more complicated query:
# query.update({"$or":[{'iso':'990h', 'number':3}, {'iso':{'$ne':'990h'},'number':1}]})
info['curve_ainvs'] = lambda dbc: str([ZZ(ai) for ai in dbc['ainvs']])
info['curve_url_LMFDB'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url_LMFDB'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['curve_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['label'])
info['iso_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['iso'])
def belyi_search(info, query):
if "group" in query:
info["group"] = query["group"]
parse_bracketed_posints(info, query, "abc_list", "a, b, c", maxlength=3)
if query.get("abc_list"):
if len(query["abc_list"]) == 3:
a, b, c = sorted(query["abc_list"])
query["a_s"] = a
query["b_s"] = b
query["c_s"] = c
elif len(query["abc_list"]) == 2:
a, b = sorted(query["abc_list"])
sub_query = []
sub_query.append({"a_s": a, "b_s": b})
sub_query.append({"b_s": a, "c_s": b})
query["$or"] = sub_query
elif len(query["abc_list"]) == 1:
a = query["abc_list"][0]
query["$or"] = [{"a_s": a}, {"b_s": a}, {"c_s": a}]
query.pop("abc_list")
# a naive hack
if info.get("abc"):
for elt in ["a_s", "b_s", "c_s"]:
info_hack = {}
info_hack[elt] = info["abc"]
parse_ints(info_hack, query, elt)
parse_ints(info, query, "g", "g")
parse_ints(info, query, "deg", "deg")
parse_ints(info, query, "orbit_size", "orbit_size")
parse_ints(info, query, "pass_size", "pass_size")
parse_nf_string(info,
query,
'field',
name="base number field",
qfield='base_field_label')
# invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
for fld in ["geomtype", "group"]:
if info.get(fld):
query[fld] = info[fld]
parse_bool(info, query, "is_primitive", name="is_primitive")
if info.get("primitivization"):
primitivization = info["primitivization"]
if re.match(GALMAP_RE, primitivization):
# 7T6-7_4.2.1_4.2.1-b
query["primitivization"] = primitivization
else:
raise ValueError("%s is not a valid Belyi map label",
primitivization)
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$-adic completions')
info['wnf'] = WebNumberField.from_data
info['gg_display'] = group_pretty_and_nTj
def belyi_search(info, query):
info["geometry_types_list"] = geometry_types_list
info["geometry_types_dict"] = geometry_types_dict
info["belyi_galmap_url"] = url_for_belyi_galmap_label
if "group" in query:
info["group"] = query["group"]
parse_bracketed_posints(info, query, "abc_list", "a, b, c", maxlength=3)
if query.get("abc_list"):
if len(query["abc_list"]) == 3:
a, b, c = sorted(query["abc_list"])
query["a_s"] = a
query["b_s"] = b
query["c_s"] = c
elif len(query["abc_list"]) == 2:
a, b = sorted(query["abc_list"])
sub_query = []
sub_query.append({"a_s": a, "b_s": b})
sub_query.append({"b_s": a, "c_s": b})
query["$or"] = sub_query
elif len(query["abc_list"]) == 1:
a = query["abc_list"][0]
query["$or"] = [{"a_s": a}, {"b_s": a}, {"c_s": a}]
query.pop("abc_list")
# a naive hack
if info.get("abc"):
for elt in ["a_s", "b_s", "c_s"]:
info_hack = {}
info_hack[elt] = info["abc"]
parse_ints(info_hack, query, elt)
parse_ints(info, query, "g", "g")
parse_ints(info, query, "deg", "deg")
parse_ints(info, query, "orbit_size", "orbit_size")
parse_ints(info, query, "pass_size", "pass_size")
parse_nf_string(info,
query,
'field',
name="base number field",
qfield='base_field_label')
# invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
for fld in ["geomtype", "group"]:
if info.get(fld):
query[fld] = info[fld]
info["nf_link"] = lambda elt: field_display_gen(
elt.get('base_field_label'), elt.get('base_field'), truncate=16)
parse_bool(info, query, "is_primitive", name="is_primitive")
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,'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:
query['torsion_order'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
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')
parse_nf_elt(info,query,'jinv',name='j-invariant')
if query.get('jinv'):
query['jinv'] =','.join(query['jinv'])
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info:
if info['include_base_change'] == 'off':
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'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
def elliptic_curve_search(info, query):
parse_rational_to_list(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_ints(info,query,'num_int_pts','num_int_pts')
parse_ints(info,query,'class_size','class_size')
parse_ints(info,query,'class_deg','class_deg')
parse_floats(info,query,'regulator','regulator')
parse_bool(info,query,'semistable','semistable')
parse_bool(info,query,'potential_good_reduction','potential_good_reduction')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$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 genus2_curve_search(info, query):
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
info["geom_end_alg_list"] = geom_end_alg_list
info["geom_end_alg_dict"] = geom_end_alg_dict
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type', 'is of GL2-type')
parse_bool(info, query, 'has_square_sha', 'has square Sha')
parse_bool(info, query, 'locally_solvable', 'is locally solvable')
parse_bool(info, query, 'is_simple_geom', 'is geometrically simple')
parse_ints(info, query, 'cond', 'conductor')
parse_ints(info, query, 'num_rat_pts', 'rational points')
parse_ints(info, query, 'num_rat_wpts', 'rational Weierstrass points')
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'torsion_order', 'torsion order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,
[int(n) for n in query['torsion']], 1)
if 'torsion' in query:
query['torsion_subgroup'] = str(query['torsion']).replace(" ", "")
query.pop('torsion') # search using string key, not array of ints
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2_inv'] = "['%s','%s','%s']" % (info['g20'], info['g21'],
info['g22'])
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id',
'geom_aut_grp_id', 'geom_end_alg'):
if info.get(fld): query[fld] = info[fld]
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
def belyi_search(info, query):
info['geometry_types_list'] = geometry_types_list
info['geometry_types_dict'] = geometry_types_dict
info["belyi_galmap_url"] = lambda label: url_for_belyi_galmap_label(label)
if 'group' in query:
info['group'] = query['group']
parse_bracketed_posints(info, query, 'abc_list', 'a, b, c', maxlength=3)
if query.get('abc_list'):
if len(query['abc_list']) == 3:
a, b, c = sorted(query['abc_list'])
query['a_s'] = a
query['b_s'] = b
query['c_s'] = c
elif len(query['abc_list']) == 2:
a, b = sorted(query['abc_list'])
sub_query = []
sub_query.append({'a_s': a, 'b_s': b})
sub_query.append({'b_s': a, 'c_s': b})
query['$or'] = sub_query
elif len(query['abc_list']) == 1:
a = query['abc_list'][0]
query['$or'] = [{'a_s': a}, {'b_s': a}, {'c_s': a}]
query.pop('abc_list')
# a naive hack
if info.get('abc'):
for elt in ['a_s', 'b_s', 'c_s']:
info_hack = {}
info_hack[elt] = info['abc']
parse_ints(info_hack, query, elt)
parse_ints(info, query, 'g', 'g')
parse_ints(info, query, 'deg', 'deg')
parse_ints(info, query, 'orbit_size', 'orbit_size')
# invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
for fld in ['geomtype', 'group']:
if info.get(fld):
query[fld] = info[fld]
def belyi_search(info, query):
info["geometry_types_list"] = geometry_types_list
info["geometry_types_dict"] = geometry_types_dict
info["belyi_galmap_url"] = lambda label: url_for_belyi_galmap_label(label)
if "group" in query:
info["group"] = query["group"]
parse_bracketed_posints(info, query, "abc_list", "a, b, c", maxlength=3)
if query.get("abc_list"):
if len(query["abc_list"]) == 3:
a, b, c = sorted(query["abc_list"])
query["a_s"] = a
query["b_s"] = b
query["c_s"] = c
elif len(query["abc_list"]) == 2:
a, b = sorted(query["abc_list"])
sub_query = []
sub_query.append({"a_s": a, "b_s": b})
sub_query.append({"b_s": a, "c_s": b})
query["$or"] = sub_query
elif len(query["abc_list"]) == 1:
a = query["abc_list"][0]
query["$or"] = [{"a_s": a}, {"b_s": a}, {"c_s": a}]
query.pop("abc_list")
# a naive hack
if info.get("abc"):
for elt in ["a_s", "b_s", "c_s"]:
info_hack = {}
info_hack[elt] = info["abc"]
parse_ints(info_hack, query, elt)
parse_ints(info, query, "g", "g")
parse_ints(info, query, "deg", "deg")
parse_ints(info, query, "orbit_size", "orbit_size")
# invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
for fld in ["geomtype", "group"]:
if info.get(fld):
query[fld] = info[fld]
def belyi_search(info, query):
info['geometry_types_list'] = geometry_types_list
info['geometry_types_dict'] = geometry_types_dict
info["belyi_galmap_url"] = lambda label: url_for_belyi_galmap_label(label)
if 'group' in query:
info['group'] = query['group']
parse_bracketed_posints(info, query, 'abc_list', 'a, b, c', maxlength=3)
if query.get('abc_list'):
if len(query['abc_list']) == 3:
a, b, c = sorted(query['abc_list'])
query['a_s'] = a
query['b_s'] = b
query['c_s'] = c
elif len(query['abc_list']) == 2:
a, b = sorted(query['abc_list'])
sub_query = []
sub_query.append( {'a_s': a, 'b_s': b} )
sub_query.append( {'b_s': a, 'c_s': b} )
query['$or'] = sub_query
elif len(query['abc_list']) == 1:
a = query['abc_list'][0]
query['$or'] = [{'a_s': a}, {'b_s': a}, {'c_s': a}]
query.pop('abc_list')
# a naive hack
if info.get('abc'):
for elt in ['a_s', 'b_s', 'c_s']:
info_hack = {}
info_hack[elt] = info['abc']
parse_ints(info_hack, query, elt)
parse_ints(info, query, 'g','g')
parse_ints(info, query, 'deg', 'deg')
parse_ints(info, query, 'orbit_size', 'orbit_size')
# invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
for fld in ['geomtype','group']:
if info.get(fld):
query[fld] = info[fld]
def hgm_search(info, query):
family_search = False
if info.get('Submit Family') or info.get('family'):
family_search = True
query['__title__'] = r'Hypergeometric Family over $\Q$ Search Result'
query[
'__err_title__'] = r'Hypergeometric Family over $\Q$ Search Input Error'
query['__table__'] = db.hgm_families
queryab = {}
for param in [
'A', 'B', 'A2', 'B2', 'A3', 'B3', 'A5', 'B5', 'A7', 'B7', 'Au2',
'Bu2', 'Au3', 'Bu3', 'Au5', 'Bu5', 'Au7', 'Bu7'
]:
parse_bracketed_posints(info,
queryab,
param,
split=False,
listprocess=lambda a: sorted(a, reverse=True))
# Combine the parts of the query if there are A,B parts
if queryab:
queryabrev = {}
for k in queryab.keys():
queryabrev[k + 'rev'] = queryab[k]
query['$or'] = [queryab, queryabrev]
# generic, irreducible not in DB yet
parse_ints(info, query, 'degree')
parse_ints(info, query, 'weight')
parse_bracketed_posints(info,
query,
'famhodge',
'family Hodge vector',
split=False)
parse_restricted(info, query, 'sign', allowed=['+1', 1, -1], process=int)
# Make a version to search reversed way
if not family_search:
parse_ints(info, query, 'conductor', 'Conductor', 'cond')
parse_rational(info, query, 't')
parse_bracketed_posints(info, query, 'hodge', 'Hodge vector')
info['make_label'] = make_abt_label
info['make_t_label'] = make_t_label
info['ab_label'] = ab_label
info['display_t'] = display_t
info['family'] = family_search
info['factorint'] = factorint
def hgm_search(info, query):
family_search = False
if info.get('Submit Family') or info.get('family'):
family_search = True
query['__title__'] = r'Hypergeometric Family over $\Q$ Search Result'
query['__err_title__'] = r'Hypergeometric Family over $\Q$ Search Input Error'
query['__table__'] = db.hgm_families
queryab = {}
for param in ['A', 'B', 'A2', 'B2', 'A3', 'B3', 'A5', 'B5', 'A7', 'B7',
'Au2', 'Bu2', 'Au3', 'Bu3', 'Au5', 'Bu5', 'Au7', 'Bu7']:
parse_bracketed_posints(info, queryab, param, split=False,
listprocess=lambda a: sorted(a, reverse=True))
# Combine the parts of the query if there are A,B parts
if queryab:
queryabrev = {}
for k in queryab.keys():
queryabrev[k+'rev'] = queryab[k]
query['$or'] = [queryab, queryabrev]
# generic, irreducible not in DB yet
parse_ints(info, query, 'degree')
parse_ints(info, query, 'weight')
parse_bracketed_posints(info, query, 'famhodge', 'family Hodge vector',split=False)
parse_restricted(info, query, 'sign', allowed=['+1',1,-1], process=int)
# Make a version to search reversed way
if not family_search:
parse_ints(info, query, 'conductor', 'Conductor' , 'cond')
parse_rational(info, query, 't')
parse_bracketed_posints(info, query, 'hodge', 'Hodge vector')
info['make_label'] = make_abt_label
info['make_t_label'] = make_t_label
info['ab_label'] = ab_label
info['display_t'] = display_t
info['family'] = family_search
info['factorint'] = factorint
def hgm_search(info, query):
info["search_type"] = search_type = info.get("search_type",
info.get("hst", "Motive"))
if search_type in ["Family", "RandomFamily"]:
query['__title__'] = r'Hypergeometric family over $\Q$ search result'
query[
'__err_title__'] = r'Hypergeometric family over $\Q$ search input error'
query['__table__'] = db.hgm_families
queryab = {}
p = info.get('p', '2')
for param in ['A', 'B']:
parse_bracketed_posints(info,
queryab,
param,
split=True,
keepbrackets=True,
listprocess=lambda a: sorted(a, reverse=True))
parse_bracketed_posints(info,
queryab,
'Ap',
qfield='A' + p,
split=True,
keepbrackets=True,
listprocess=lambda a: sorted(a, reverse=True))
parse_bracketed_posints(info,
queryab,
'Bp',
qfield='B' + p,
split=True,
keepbrackets=True,
listprocess=lambda a: sorted(a, reverse=True))
parse_bracketed_posints(info,
queryab,
'Apperp',
qfield='Au' + p,
split=True,
keepbrackets=True,
listprocess=lambda a: sorted(a, reverse=True))
parse_bracketed_posints(info,
queryab,
'Bpperp',
qfield='Bu' + p,
split=True,
keepbrackets=True,
listprocess=lambda a: sorted(a, reverse=True))
# Combine the parts of the query if there are A,B parts
if queryab:
queryabrev = {}
for k in queryab.keys():
queryabrev[k + 'rev'] = queryab[k]
query['$or'] = [queryab, queryabrev]
# generic, irreducible not in DB yet
parse_ints(info, query, 'degree')
parse_ints(info, query, 'weight')
parse_bracketed_posints(info,
query,
'famhodge',
'family Hodge vector',
split=True)
parse_restricted(info, query, 'sign', allowed=['+1', 1, -1], process=int)
# Make a version to search reversed way
if search_type not in ["Family", "RandomFamily"]:
parse_ints(info, query, 'conductor', 'Conductor', 'cond')
parse_rational(info, query, 't')
parse_bracketed_posints(info, query, 'hodge', 'Hodge vector')
query['__sort__'] = ['degree', 'weight', 'A', 'B', 'label']
# Should search on analytic conductor when available
# Sorts A and B first by length, then by the elements of the list; could go another way
info['make_label'] = make_abt_label
info['make_t_label'] = make_t_label
info['ab_label'] = ab_label
info['display_t'] = display_t
info['factorint'] = factorint
def genus2_curve_search(info, query):
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type', 'is of GL2-type')
parse_bool(info, query, 'has_square_sha', 'has square Sha')
parse_bool(info, query, 'locally_solvable', 'is locally solvable')
parse_bool(info, query, 'is_simple_geom', 'is geometrically simple')
parse_ints(info, query, 'cond', 'conductor')
if info.get('analytic_sha') == "None":
query['analytic_sha'] = None
else:
parse_ints(info, query, 'analytic_sha', 'analytic order of sha')
parse_ints(info, query, 'num_rat_pts', 'rational points')
parse_ints(info, query, 'num_rat_wpts', 'rational Weierstrass points')
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'torsion_order', 'torsion order')
if 'torsion' in query and not 'torsion_order' in query:
t_o = 1
for n in query['torsion']:
t_o *= int(n)
query['torsion_order'] = t_o
if 'torsion' in query:
query['torsion_subgroup'] = str(query['torsion']).replace(" ", "")
query.pop('torsion') # search using string key, not array of ints
geom_inv_type = info.get('geometric_invariants_type', 'igusa_clebsch_inv')
if geom_inv_type == 'igusa_clebsch_inv':
invlength = 4
elif geom_inv_type == 'igusa_inv':
invlength = 5
else:
invlength = 3
parse_bracketed_rats(info,
query,
'geometric_invariants',
qfield=geom_inv_type,
exactlength=invlength,
split=False,
keepbrackets=True)
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2_inv'] = "['%s','%s','%s']" % (info['g20'], info['g21'],
info['g22'])
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id',
'geom_aut_grp_id', 'end_alg', 'geom_end_alg'):
if info.get(fld): query[fld] = info[fld]
parse_primes(info,
query,
'bad_primes',
name='bad primes',
qfield='bad_primes',
mode=info.get('bad_quantifier'))
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
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'])
def genus2_curve_search(info, query):
parse_ints(info, query, "abs_disc", "absolute discriminant")
parse_bool(info, query, "is_gl2_type", "is of GL2-type")
parse_bool(info, query, "has_square_sha", "has square Sha")
parse_bool(info, query, "locally_solvable", "is locally solvable")
parse_bool(info, query, "is_simple_geom", "is geometrically simple")
parse_ints(info, query, "cond", "conductor")
if info.get("analytic_sha") == "None":
query["analytic_sha"] = None
else:
parse_ints(info, query, "analytic_sha", "analytic order of sha")
parse_ints(info, query, "num_rat_pts", "rational points")
parse_ints(info, query, "num_rat_wpts", "rational Weierstrass points")
parse_bracketed_posints(
info,
query,
"torsion",
"torsion structure",
maxlength=4,
check_divisibility="increasing",
)
parse_ints(info, query, "torsion_order", "torsion order")
if "torsion" in query and "torsion_order" not in query:
t_o = 1
for n in query["torsion"]:
t_o *= int(n)
query["torsion_order"] = t_o
if "torsion" in query:
query["torsion_subgroup"] = str(query["torsion"]).replace(" ", "")
query.pop("torsion") # search using string key, not array of ints
parse_bracketed_rats(
info,
query,
"geometric_invariants",
qfield="g2_inv",
minlength=3,
maxlength=5,
listprocess=geom_inv_to_G2,
split=False,
keepbrackets=True,
)
parse_ints(info, query, "two_selmer_rank", "2-Selmer rank")
parse_ints(info, query, "analytic_rank", "analytic rank")
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if "g20" in info and "g21" in info and "g22" in info:
query["g2_inv"] = "['%s','%s','%s']" % (info["g20"], info["g21"],
info["g22"])
if "class" in info:
query["class"] = info["class"]
# Support legacy aut_grp_id
if info.get("aut_grp_id"):
info["aut_grp_label"] = ".".join(
info.pop("aut_grp_id")[1:-1].split(","))
if info.get("geom_aut_grp_id"):
info["geom_aut_grp_label"] = ".".join(
info.pop("geom_aut_grp_id")[1:-1].split(","))
for fld in (
"st_group",
"real_geom_end_alg",
"aut_grp_label",
"geom_aut_grp_label",
"end_alg",
"geom_end_alg",
):
if info.get(fld):
query[fld] = info[fld]
parse_primes(
info,
query,
"bad_primes",
name="bad primes",
qfield="bad_primes",
mode=info.get("bad_quantifier"),
)
parse_sort(info, query)
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'] = {'$ne': 0}
parse_element_of(info,
query,
field='isodeg',
qfield='isogeny_degrees',
split_interval=1000)
#parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info,
query,
'surj_primes',
name='maximal primes',
qfield='nonmax_primes',
mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info,
query,
'nonsurj_primes',
name='non-maximal primes',
qfield='nonmax_primes',
mode=mode,
radical='nonmax_rad')
if 'optimal' in info and info['optimal'] == 'on':
# For all isogeny classes except 990h the optimal curve is number 1, while for class 990h it is number 3.
# So setting query['number'] = 1 is nearly correct, but fails on 990h3.
# Instead, we use this more complicated query:
query.update({
"$or": [{
'iso': '990h',
'number': 3
}, {
'iso': {
'$ne': '990h'
},
'number': 1
}]
})
info['curve_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'])