def bianchi_modular_form_search(info, query):
"""Function to handle requests from the top page, either jump to one
newform or do a search.
"""
parse_nf_string(info, query, 'field_label', name='base number field')
parse_noop(info, query, 'label')
parse_ints(info, query, 'dimension')
parse_ints(info, query, 'level_norm')
parse_primes(info, query, 'field_bad_primes', name='field bad primes',
qfield='field_bad_primes',mode=info.get('field_bad_quantifier'))
parse_primes(info, query, 'level_bad_primes', name='level bad primes',
qfield='level_bad_primes',mode=info.get('level_bad_quantifier'))
if 'sfe' not in info:
info['sfe'] = "any"
elif info['sfe'] != "any":
query['sfe'] = int(info['sfe'])
if 'include_cm' in info:
if info['include_cm'] in ['exclude', 'off']:
query['CM'] = 0 # will exclude NULL values
elif info['include_cm'] == 'only':
query['CM'] = {'$ne': 0} # will exclude NULL values
if info.get('include_base_change') =='exclude':
query['bc'] = 0
elif info.get('include_base_change') == 'only':
query['bc'] = {'$ne': 0}
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 number_field_jump(info):
query = {'label_orig': info['jump']}
try:
parse_nf_string(info, query, 'jump', name="Label", qfield='label')
return redirect(url_for(".by_label", label=query['label']))
except ValueError:
return redirect(url_for(".number_field_render_webpage"))
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 hilbert_modular_form_search(info, query):
parse_nf_string(info, query, 'field_label', name="Field")
parse_ints(info, query, 'deg', name='Field degree')
parse_ints(info, query, 'disc', name="Field discriminant")
parse_ints(info, query, 'dimension')
parse_ints(info, query, 'level_norm', name="Level norm")
parse_hmf_weight(info,
query,
'weight',
qfield=('parallel_weight', 'weight'))
parse_primes(info,
query,
'field_bad_primes',
name='field bad primes',
qfield='field_bad_primes',
mode=info.get('field_bad_quantifier'))
parse_primes(info,
query,
'level_bad_primes',
name='level bad primes',
qfield='level_bad_primes',
mode=info.get('level_bad_quantifier'))
if 'cm' in info:
if info['cm'] == 'exclude':
query['is_CM'] = 'no'
elif info['cm'] == 'only':
query['is_CM'] = 'yes'
if 'bc' in info:
if info['bc'] == 'exclude':
query['is_base_change'] = 'no'
elif info['bc'] == 'only':
query['is_base_change'] = 'yes'
def number_field_jump(info):
query = {'label_orig': info['natural']}
try:
parse_nf_string(info,query,'natural',name="Label",qfield='label')
return redirect(url_for(".by_label", label=query['label']))
except ValueError:
return redirect(url_for(".number_field_render_webpage"))
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 number_field_jump(info):
query = {'label_orig': info['jump']}
try:
parse_nf_string(info, query, 'jump', name="Label", qfield='label')
# we end up parsing the string twice, but that is okay
F1, _, _ = input_string_to_poly(info['jump'])
# we only use the output of input_string_to_poly with single-letter variable names
if F1 and len(str(F1.parent().gen())) == 1 and F1.list() != db.nf_fields.lookup(query['label'], 'coeffs'):
flash_info(r"The requested field $\Q[{}]/\langle {}\rangle$ is isomorphic to the field below, but uses a different defining polynomial.".format(str(F1.parent().gen()), latex(F1)))
return redirect(url_for(".by_label", label=query['label']))
except ValueError:
return redirect(url_for(".number_field_render_webpage"))
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 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 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 hilbert_modular_form_search(info, query):
parse_nf_string(info,query,'field_label',name="Field")
parse_ints(info,query,'deg', name='Field degree')
parse_ints(info,query,'disc',name="Field discriminant")
parse_ints(info,query,'dimension')
parse_ints(info,query,'level_norm', name="Level norm")
parse_hmf_weight(info,query,'weight',qfield=('parallel_weight','weight'))
if 'cm' in info:
if info['cm'] == 'exclude':
query['is_CM'] = 'no'
elif info['cm'] == 'only':
query['is_CM'] = 'yes'
if 'bc' in info:
if info['bc'] == 'exclude':
query['is_base_change'] = 'no'
elif info['bc'] == 'only':
query['is_base_change'] = 'yes'
def bianchi_modular_form_search(info, query):
"""Function to handle requests from the top page, either jump to one
newform or do a search.
"""
parse_nf_string(info, query, 'field_label', name='base number field')
parse_noop(info, query, 'label')
parse_ints(info, query, 'dimension')
parse_ints(info, query, 'level_norm')
if not 'sfe' in info:
info['sfe'] = "any"
elif info['sfe'] != "any":
query['sfe'] = int(info['sfe'])
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['CM'] = 0 # will exclude NULL values
elif info['include_cm'] == 'only':
query['CM'] = {'$ne': 0} # will exclude NULL values
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['bc'] = 0
else:
info['include_base_change'] = "on"
def bianchi_modular_form_search(info, query):
"""Function to handle requests from the top page, either jump to one
newform or do a search.
"""
parse_nf_string(info, query, 'field_label', name='base number field')
parse_noop(info, query, 'label')
parse_ints(info, query, 'dimension')
parse_ints(info, query, 'level_norm')
if not 'sfe' in info:
info['sfe'] = "any"
elif info['sfe'] != "any":
query['sfe'] = int(info['sfe'])
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['CM'] = 0 # will exclude NULL values
elif info['include_cm'] == 'only':
query['CM'] = {'$ne': 0} # will exclude NULL values
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['bc'] = 0
else:
info['include_base_change'] = "on"
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_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')