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 abelian_variety_search(info, query):
parse_ints(info,query,'q',name='base field')
parse_ints(info,query,'g',name='dimension')
parse_bool(info,query,'simple',qfield='is_simp')
parse_bool(info,query,'primitive',qfield='is_prim')
parse_bool_unknown(info, query, 'jacobian', qfield='is_jac')
parse_bool_unknown(info, query, 'polarizable', qfield='is_pp')
parse_ints(info,query,'p_rank')
parse_ints(info,query,'ang_rank')
parse_newton_polygon(info,query,'newton_polygon',qfield='slps')
parse_string_start(info,query,'initial_coefficients',qfield='poly_str',initial_segment=["1"])
parse_string_start(info,query,'abvar_point_count',qfield='A_cnts_str')
parse_string_start(info,query,'curve_point_count',qfield='C_cnts_str',first_field='pt_cnt')
if info.get('simple_quantifier') == 'contained':
parse_subset(info,query,'simple_factors',qfield='simple_distinct',mode='subsets')
elif info.get('simple_quantifier') == 'exactly':
parse_subset(info,query,'simple_factors',qfield='simple_distinct',mode='exact')
elif info.get('simple_quantifier') == 'include':
parse_submultiset(info,query,'simple_factors',mode='append')
for n in range(1,6):
parse_ints(info,query,'dim%s_factors'%n)
for n in range(1,4):
parse_ints(info,query,'dim%s_distinct'%n)
parse_nf_string(info,query,'number_field',qfield='nf')
parse_galgrp(info,query,qfield=('galois_n','galois_t'))
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 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')
parse_bool(info, query, 'Is_Even')
def abelian_variety_search(info, query):
parse_ints(info,query,'q',name='base field')
parse_ints(info,query,'g',name='dimension')
parse_bool(info,query,'simple',qfield='is_simp')
parse_bool(info,query,'primitive',qfield='is_prim')
parse_bool_unknown(info, query, 'jacobian', qfield='is_jac')
parse_bool_unknown(info, query, 'polarizable', qfield='is_pp')
parse_ints(info,query,'p_rank')
parse_ints(info,query,'ang_rank')
parse_newton_polygon(info,query,'newton_polygon',qfield='slps')
parse_string_start(info,query,'initial_coefficients',qfield='poly_str',initial_segment=["1"])
parse_string_start(info,query,'abvar_point_count',qfield='A_cnts_str')
parse_string_start(info,query,'curve_point_count',qfield='C_cnts_str',first_field='pt_cnt')
if info.get('simple_quantifier') == 'contained':
parse_subset(info,query,'simple_factors',qfield='simple_distinct',mode='subsets')
elif info.get('simple_quantifier') == 'exactly':
parse_subset(info,query,'simple_factors',qfield='simple_distinct',mode='exact')
elif info.get('simple_quantifier') == 'include':
parse_submultiset(info,query,'simple_factors',mode='append')
for n in range(1,6):
parse_ints(info,query,'dim%s_factors'%n)
for n in range(1,4):
parse_ints(info,query,'dim%s_distinct'%n)
parse_nf_string(info,query,'number_field',qfield='nf')
parse_galgrp(info,query,qfield=('galois_n','galois_t'))
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 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 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 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 artin_representation_search(info, query):
query['Hide'] = 0
info['sign_code'] = 0
parse_primes(info,
query,
"unramified",
name="Unramified primes",
qfield="BadPrimes",
mode="exclude")
parse_primes(info,
query,
"ramified",
name="Ramified primes",
qfield="BadPrimes",
mode=info.get("ram_quantifier"))
parse_restricted(info,
query,
"root_number",
qfield="GalConjSigns",
allowed=[-1, 1],
process=lambda x: {"$contains": [int(x)]})
parse_restricted(info,
query,
"frobenius_schur_indicator",
qfield="Indicator",
allowed=[1, 0, -1],
process=int)
parse_container(info,
query,
'container',
qfield='Container',
name="Smallest permutation representation")
parse_galgrp(info,
query,
"group",
name="Group",
qfield=("GaloisLabel", None))
parse_ints(info, query, 'dimension', qfield='Dim')
parse_ints(info, query, 'conductor', qfield='Conductor')
parse_ints(info, query, 'num_ram', qfield='NumBadPrimes')
parse_projective_group(info, query, 'projective_image', qfield='Proj_GAP')
parse_projective_type(info,
query,
'projective_image_type',
qfield='Proj_GAP')
# Backward support for old URLs
if 'Is_Even' in info:
info['parity'] = info.pop('Is_Even')
parse_bool(info, query, 'parity', qfield='Is_Even')
def elliptic_curve_search(info, query):
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_ints(info,query,'num_int_pts','num_int_pts')
parse_floats(info,query,'regulator','regulator')
parse_bool(info,query,'semistable','semistable')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$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 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_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 common_parse(info, query):
parse_ints(info, query, "q", name="base field")
parse_ints(info, query, "p", name="base cardinality")
parse_ints(info, query, "g", name="dimension")
parse_ints(info, query, "geom_deg", qfield="geometric_extension_degree")
parse_bool(info, query, "simple", qfield="is_simple")
parse_bool(info, query, "geom_simple", qfield="is_geometrically_simple")
parse_bool(info, query, "primitive", qfield="is_primitive")
parse_bool_unknown(info, query, "jacobian", qfield="has_jacobian")
parse_bool_unknown(info, query, "polarizable", qfield="has_principal_polarization")
parse_ints(info, query, "p_rank")
parse_ints(info, query, "p_rank_deficit")
parse_ints(info, query, "angle_rank")
parse_ints(info, query, "jac_cnt", qfield="jacobian_count", name="Number of Jacobians")
parse_ints(info, query, "hyp_cnt", qfield="hyp_count", name="Number of Hyperelliptic Jacobians")
parse_ints(info, query, "twist_count")
parse_ints(info, query, "max_twist_degree")
parse_ints(info, query, "size")
parse_newton_polygon(info, query, "newton_polygon", qfield="slopes")
parse_string_start(info, query, "initial_coefficients", qfield="poly_str", initial_segment=["1"])
parse_string_start(info, query, "abvar_point_count", qfield="abvar_counts_str", first_field="abvar_count")
parse_string_start(info, query, "curve_point_count", qfield="curve_counts_str", first_field="curve_count")
if info.get("simple_quantifier") in ["subset", "exactly"]:
parse_subset(info, query, "simple_factors", qfield="simple_distinct", mode=info.get("simple_quantifier"))
else:
parse_submultiset(info, query, "simple_factors")
if info.get("use_geom_decomp") == "on":
dimstr = "geom_dim"
nf_qfield = "geometric_number_fields"
gal_qfield = "geometric_galois_groups"
else:
dimstr = "dim"
nf_qfield = "number_fields"
gal_qfield = "galois_groups"
for n in range(1, 6):
parse_ints(info, query, "dim%s_factors" % n, qfield="%s%s_factors" % (dimstr, n))
for n in range(1, 4):
parse_ints(info, query, "dim%s_distinct" % n, qfield="%s%s_distinct" % (dimstr, n))
parse_nf_string(info, query, "number_field", qfield=nf_qfield)
parse_galgrp(info, query, "galois_group", qfield=gal_qfield)
if 'geom_squarefree' in info:
if info['geom_squarefree'] == 'Yes':
query['is_squarefree'] = True
elif info['geom_squarefree'] == 'YesAndGeom':
query['is_squarefree'] = True
query['is_geometrically_squarefree'] = True
elif info['geom_squarefree'] == 'YesNotGeom':
query['is_squarefree'] = True
query['is_geometrically_squarefree'] = False
elif info['geom_squarefree'] == 'No':
query['is_squarefree'] = False
elif info['geom_squarefree'] == 'NotGeom':
query['is_geometrically_squarefree'] = False
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 common_parse(info, query):
parse_ints(info, query, "modulus", name="modulus")
parse_ints(info, query, "conductor", name="conductor")
parse_ints(info, query, "order", name="order")
if 'parity' in info:
parity = info['parity']
if parity == 'even':
query['parity'] = 1
elif parity == 'odd':
query['parity'] = -1
parse_bool(info, query, "is_primitive", name="is_primitive")
parse_bool(info, query, "is_real", name="is_real")
parse_bool(info, query, "is_minimal", name="is_minimal")
def search(info):
""" query processing for Sato-Tate groups -- returns rendered results page """
if 'jump' in info:
return redirect(url_for('.by_label', label=info['jump']), 301)
if 'label' in info:
return redirect(url_for('.by_label', label=info['label']), 301)
search_type = info.get("search_type", info.get("hst", "List"))
template_kwds = {
'bread': get_bread("Search results"),
'credit': credit_string,
'learnmore': learnmore_list()
}
title = 'Sato-Tate group search results'
err_title = 'Sato-Tate group search input error'
count = parse_count(info, 50)
start = parse_start(info)
# if user clicked refine search always restart at 0
if 'refine' in info:
start = 0
ratonly = (info.get('include_irrational', 'no').strip().lower() == 'no')
if search_type == "Random" and not ratonly:
info['err'] = err = 'Cannot select random irrational Sato-Tate group'
flash_error(err)
return render_template('st_results.html',
info=info,
title=err_title,
**template_kwds)
query = {'rational': True} if ratonly else {}
try:
parse_ints(info, query, 'weight', 'weight')
if 'weight' in query:
weight_list = parse_ints_to_list_flash(info.get('weight'),
'weight')
parse_ints(info, query, 'degree', 'degree')
if 'degree' in query:
degree_list = parse_ints_to_list_flash(info.get('degree'),
'degree')
if info.get('identity_component'):
query['identity_component'] = info['identity_component']
parse_ints(info, query, 'components', 'components')
def refine_components(current, condition):
if current is None:
return condition
return [x for x in condition if x in current]
# The following are used to constraint which mu(n) will show up in search results
components_list = None
ommitted = set()
if 'components' in query:
components_list = parse_ints_to_list_flash(info.get('components'),
'components')
parse_component_group(info, query)
gps = query.get("component_group")
if gps:
if isinstance(gps, dict):
gps = gps["$in"]
else:
gps = [gps]
if not ratonly:
cyclic_labels = set(
db.gps_small.search({"cyclic": True}, "label"))
irrat = []
for code in gps:
if code in cyclics:
irrat.append(cyclics[code])
elif re.match(cyclicre, code):
irrat.append(int(code[1:]))
elif not ratonly and code in cyclic_labels:
irrat.append(int(code.split(".")[0]))
components_list = refine_components(components_list, irrat)
parse_rational(info, query, 'trace_zero_density', 'trace zero density')
parse_ints(info, query, 'second_trace_moment')
parse_ints(info, query, 'fourth_trace_moment')
for name, ones in [('second_trace_moment', [1, 2]),
('fourth_trace_moment', [1, 2, 4])]:
if name in query:
# E(x^2) for mu(1) and mu(2) are 1; others are 0
# E(x^4) for mu(1), mu(2) and mu(4) are 1; others are 0
E = parse_ints_to_list_flash(info.get(name),
name.replace("_", " "))
if 0 not in E:
components_list = refine_components(components_list, ones)
if 1 not in E:
ommitted.update(ones)
parse_ints(info, query, 'first_a2_moment')
parse_bool(info, query, 'maximal')
if "first_a2_moment" in query or query.get("maximal"):
# mu(n) do not have a2 moments and none are maximal
components_list = []
except ValueError as err:
info['err'] = str(err)
return render_template('st_results.html',
info=info,
title=err_title,
**template_kwds)
# Check mu(n) groups first (these are not stored in the database)
results = []
if ((not 'weight' in query or 0 in weight_list)
and (not 'degree' in query or 1 in degree_list)
and (not 'identity_component' in query
or query['identity_component'] == 'SO(1)')
and (not 'trace_zero_density' in query
or query['trace_zero_density'] == '0')):
nres = None
if components_list is None:
components_list = range(
1, 3 if ratonly else (start + count + 1 + len(ommitted)))
nres = None if ratonly else INFINITY
elif ratonly:
components_list = [n for n in range(1, 3) if n in components_list]
components_list = [n for n in components_list if n not in ommitted]
if nres is None:
nres = len(components_list)
if search_type == "Random" and nres > 0:
# Need to return mu(1), mu(2) or mu(4) sometimes
otherlen = db.gps_sato_tate.count(query)
r = ZZ.random_element(nres + otherlen)
if r < nres:
return redirect(
url_for(".by_label", label="0.1.%d" % components_list[r]),
307)
for n in itertools.islice(components_list, start, start + count):
results.append(mu_info(n))
else:
nres = 0
if 'result_count' in info:
nres += db.gps_sato_tate.count(query)
return jsonify({"nres": str(nres)})
if search_type == "Random":
label = db.gps_sato_tate.random(query, "label")
if label is not None:
return redirect(url_for(".by_label", label=label), 307)
# Now lookup other (rational) ST groups in database
if nres != INFINITY:
start2 = start - nres if start > nres else 0
proj = [
'label', 'weight', 'degree', 'real_dimension',
'identity_component', 'name', 'pretty', 'components',
'component_group', 'trace_zero_density', 'moments'
]
try:
res = db.gps_sato_tate.search(query,
proj,
limit=max(count - len(results), 0),
offset=start2,
info=info)
except QueryCanceledError as err:
ctx = ctx_proc_userdata()
flash_error(
'The search query took longer than expected! Please help us improve by reporting this error <a href="%s" target=_blank>here</a>.'
% ctx['feedbackpage'])
info['err'] = str(err)
return render_template('st_results.html',
info=info,
title=err_title,
**template_kwds)
info['number'] += nres
if start < info['number'] and len(results) < count:
for v in res:
v['identity_component'] = st0_pretty(v['identity_component'])
v['component_group'] = sg_pretty(v['component_group'])
v['trace_moments'] = trace_moments(v['moments'])
results.append(v)
else:
info['number'] = 'infinity'
info['start'] = start
info['count'] = count
info['st0_list'] = st0_list
info['st0_dict'] = st0_dict
info['results'] = results
info['stgroup_url'] = lambda dbc: url_for('.by_label', label=dbc['label'])
return render_template('st_results.html',
info=info,
title=title,
**template_kwds)
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 group_search(info, query):
info['group_url'] = get_url
parse_ints(info, query, 'order', 'order')
parse_ints(info, query, 'dim', 'dim')
parse_bool(info, query, 'irreducible', 'irreducible')
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
if info.get('jump', '').strip():
jump_list = [
"1T1", "2T1", "3T1", "4T1", "4T2", "5T1", "6T1", "7T1", "8T1",
"8T2", "8T3", "8T5", "9T1", "9T2", "10T1", "11T1", "12T1", "12T2",
"12T5", "13T1", "14T1", "15T1", "16T1", "16T2", "16T3", "16T4",
"16T5", "16T7", "16T8", "16T14", "17T1", "18T1", "18T2", "19T1",
"20T1", "20T2", "20T3", "21T1", "22T1", "23T1", "24T1", "24T2",
"24T3", "24T4", "24T5", "24T6", "24T8", "25T1", "25T2", "26T1",
"27T1", "27T2", "27T4", "28T1", "28T2", "28T3", "29T1", "30T1",
"31T1", "32T32", "32T33", "32T34", "32T35", "32T36", "32T37",
"32T38", "32T39", "32T40", "32T41", "32T42", "32T43", "32T44",
"32T45", "32T46", "32T47", "32T48", "32T49", "32T50", "32T51",
"33T1", "34T1", "35T1", "36T1", "36T2", "36T3", "36T4", "36T7",
"36T9", "37T1", "38T1", "39T1", "40T1", "40T2", "40T3", "40T4",
"40T5", "40T7", "40T8", "40T13", "41T1", "42T1", "43T1", "44T1",
"44T2", "44T3", "45T1", "45T2", "46T1", "47T1"
]
strip_label = info.get('jump', '').strip().upper()
# If the user entered a simple label
if re.match(r'^\d+T\d+$', strip_label):
return redirect(url_for('.by_label', label=strip_label), 301)
try:
parse_galgrp(
info,
query,
qfield=['label', 'n'],
name='a Galois group label',
field='jump',
list_ok=False,
err_msg=
"It needs to be a transitive group in nTj notation, such as 5T1, a GAP id, such as [4,1], or a <a title = 'Galois group labels' knowl='nf.galois_group.name'>group label</a>"
)
except ValueError:
return redirect(url_for('.index'))
if query.get('label', '') in jump_list:
return redirect(url_for('.by_label', label=query['label']), 301)
else: # convert this to a regular search
info['gal'] = info['jump']
parse_ints(info, query, 'n', 'degree')
parse_ints(info, query, 't')
parse_ints(info, query, 'order')
parse_ints(info, query, 'arith_equiv')
parse_ints(info, query, 'nilpotency')
parse_galgrp(info,
query,
qfield=['label', 'n'],
name='Galois group',
field='gal')
for param in ('cyc', 'solv', 'prim'):
parse_bool(info, query, param, process=int, blank=['0', 'Any'])
if info.get("parity") == "even":
query["parity"] = 1
elif info.get("parity") == "odd":
query["parity"] = -1
#parse_restricted(info,query,'parity',allowed=[1,-1],process=int,blank=['0','Any'])
if 'order' in query and 'n' not in query:
query['__sort__'] = ['order', 'gapid', 'n', 't']
degree_str = prep_ranges(info.get('n'))
info['show_subs'] = degree_str is None or (LIST_RE.match(degree_str) and
includes_composite(degree_str))
info['group_display'] = group_display_short
info['yesno'] = yesno
info['wgg'] = WebGaloisGroup.from_data
def group_search(info, query):
info['group_url'] = get_url
info['getname'] = lambda xx: '$' + group_names_pretty(xx) + '$'
parse_ints(info, query, 'order', 'order')
parse_ints(info, query, 'dim', 'dim')
parse_bool(info, query, 'irreducible', 'irreducible')
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)
