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':{'$ne':'990h'},'number':1}]})
info['curve_url_LMFDB'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url_LMFDB'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['curve_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['label'])
info['iso_url_Cremona'] = lambda dbc: url_for(".by_ec_label", label=dbc['iso'])
def elliptic_curve_search(info, query):
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
#if 'torsion_structure' in query and not 'torsion' in query:
# query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$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 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 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 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 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': [('Sato-Tate Groups', url_for('.index')),
('Search Results', '.')],
'credit': credit_string,
'learnmore': learnmore_list()
}
title = 'Sato-Tate Group Search Results'
err_title = 'Sato-Tate Groups 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')
if 'components' in query:
components_list = parse_ints_to_list_flash(info.get('components'),
'components')
parse_rational(info, query, 'trace_zero_density', 'trace zero density')
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')):
if not 'components' in query:
components_list = range(1, 3 if ratonly else start + count + 1)
elif ratonly:
components_list = [n for n in range(1, 3) if n in components_list]
nres = len(
components_list) if 'components' in query or ratonly else INFINITY
if search_type == "Random" and nres > 0:
# Need to return mu(1) and mu(2) 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 search(**args):
""" query processing for Sato-Tate groups -- returns rendered results page """
info = to_dict(args)
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)
template_kwds = {'bread':[('Sato-Tate Groups', url_for('.index')),('Search Results', '.')],
'credit':credit_string,
'learnmore':learnmore_list()}
title = 'Sato-Tate Group Search Results'
err_title = 'Sato-Tate Groups Search Input Error'
count = parse_count(info, 25)
start = parse_start(info)
# if user clicked refine search always restart at 0
if 'refine' in info:
start = 0
ratonly = True if info.get('rational_only','no').strip().lower() == 'yes' else False
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')
if 'components' in query:
components_list = parse_ints_to_list_flash(info.get('components'), 'components')
parse_rational(info,query,'trace_zero_density','trace zero density')
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'):
if not 'components' in query:
components_list = xrange(1,3 if ratonly else start+count+1)
elif ratonly:
components_list = [n for n in range(1,3) if n in components_list]
nres = len(components_list) if 'components' in query or ratonly else INFINITY
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)})
# 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 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 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 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'])
