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 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 parse_self_twist(info, query):
# self_twist_values = [('', 'unrestricted'), ('yes', 'has self-twist'), ('cm', 'has CM'), ('rm', 'has RM'), ('cm_and_rm', 'has CM and RM'), ('no', 'no self-twists') ]
translate = {'cm': '1', 'rm': '2', 'cm_and_rm': '3'}
inp = info.get('has_self_twist')
if inp:
if inp in ['no', 'yes']:
info['is_self_twist'] = inp
parse_bool(info, query, 'is_self_twist', name='Has self-twist')
else:
try:
info['self_twist_type'] = translate[inp]
parse_ints(info,
query,
'self_twist_type',
name='Has self-twist')
except KeyError:
raise ValueError('%s not in %s' % (inp, translate.keys()))
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 newform_parse(info, query):
common_parse(info, query)
parse_ints(info, query, 'dim', name="Dimension")
parse_nf_string(info, query, 'nf_label', name="Coefficient field")
parse_self_twist(info, query)
parse_subset(info,
query,
'cm_discs',
name="CM discriminant",
parse_singleton=lambda d: parse_discriminant(d, -1))
parse_subset(info,
query,
'rm_discs',
name="RM discriminant",
parse_singleton=lambda d: parse_discriminant(d, 1))
parse_bool(info, query, 'is_twist_minimal')
parse_bool_unknown(info, query, 'has_inner_twist')
parse_ints(info, query, 'analytic_rank')
parse_noop(info, query, 'atkin_lehner_string')
parse_ints(info, query, 'fricke_eigenval')
parse_bool_unknown(info, query, 'is_self_dual')
parse_noop(info, query, 'projective_image')
parse_noop(info, query, 'projective_image_type')
parse_ints(info, query, 'artin_degree', name="Artin degree")
def genus2_curve_search(info, query):
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type', 'is of GL2-type')
parse_bool(info, query, 'has_square_sha', 'has square Sha')
parse_bool(info, query, 'locally_solvable', 'is locally solvable')
parse_bool(info, query, 'is_simple_geom', 'is geometrically simple')
parse_ints(info, query, 'cond', 'conductor')
parse_ints(info, query, 'num_rat_pts', 'rational points')
parse_ints(info, query, 'num_rat_wpts', 'rational Weierstrass points')
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'torsion_order', 'torsion order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,
[int(n) for n in query['torsion']], 1)
if 'torsion' in query:
query['torsion_subgroup'] = str(query['torsion']).replace(" ", "")
query.pop('torsion') # search using string key, not array of ints
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2_inv'] = "['%s','%s','%s']" % (info['g20'], info['g21'],
info['g22'])
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id',
'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
def galois_group_search(**args):
info = to_dict(args)
bread = get_bread([("Search results", url_for('.search'))])
C = base.getDBConnection()
query = {}
if 'jump_to' in info:
return render_group_webpage({'label': info['jump_to']})
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
try:
parse_ints(info, query, 'n', 'degree')
parse_ints(info, query, 't')
for param in ('cyc', 'solv', 'prim', 'parity'):
parse_bool(info,
query,
param,
minus_one_to_zero=(param != 'parity'))
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))
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info, 50)
start = parse_start(info)
res = C.transitivegroups.groups.find(query).sort([('n', pymongo.ASCENDING),
('t', pymongo.ASCENDING)
])
nres = res.count()
res = res.skip(start).limit(count)
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
info['groups'] = res
info['group_display'] = group_display_prettyC(C)
info['report'] = "found %s groups" % nres
info['yesno'] = yesno
info['wgg'] = WebGaloisGroup.from_data
info['start'] = start
info['number'] = nres
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
return render_template("gg-search.html",
info=info,
title="Galois Group Search Result",
bread=bread,
credit=GG_credit)
def genus2_curve_search(**args):
info = to_dict(args)
if 'download' in info and info['download'] == '1':
return download_search(info)
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
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
curve_label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+$')
if curve_label_regex.match(info["jump"].strip()):
data = render_curve_webpage_by_label(info["jump"].strip())
else:
class_label_regex = re.compile(r'\d+\.[a-z]+$')
if class_label_regex.match(info["jump"].strip()):
data = render_isogeny_class(info["jump"].strip())
else:
class_label_regex = re.compile(r'#\d+$')
if class_label_regex.match(info["jump"].strip()) and ZZ(info["jump"][1:]) < 2**61:
c = g2cdb().isogeny_classes.find_one({'hash':int(info["jump"][1:])})
if c:
data = render_isogeny_class(c["label"])
else:
data = "Hash not found"
else:
data = "Invalid label"
if isinstance(data,str):
flash(Markup(data + " <span style='color:black'>%s</span>"%(info["jump"])),"error")
return redirect(url_for(".index"))
return data
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type')
parse_bool(info,query,'has_square_sha')
parse_bool(info,query,'locally_solvable')
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'cond','conductor')
parse_ints(info,query,'num_rat_wpts','Weierstrass points')
parse_ints(info,query,'torsion_order')
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 info.get('g20') and info.get('g21') and info.get('g22'):
query['g2inv'] = [ info['g20'], info['g21'], info['g22'] ]
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id', 'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
info["query"] = dict(query)
count = parse_count(info, 50)
start = parse_start(info)
cursor = g2cdb().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING), ("class", pymongo.ASCENDING), ("disc_key", pymongo.ASCENDING), ("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = g2cdb().isogeny_classes.find_one({'label' :
isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
v_clean["st_group_href"] = st_group_href(isogeny_class['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit,learnmore=learnmore_list(), bread=bread, title=title)
def galois_group_search(**args):
info = to_dict(args)
bread = get_bread([("Search results", url_for(".search"))])
C = base.getDBConnection()
query = {}
if "jump_to" in info:
return render_group_webpage({"label": info["jump_to"]})
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
try:
parse_ints(info, query, "n", "degree")
parse_ints(info, query, "t")
for param in ("cyc", "solv", "prim", "parity"):
parse_bool(info, query, param, minus_one_to_zero=(param != "parity"))
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))
except ValueError as err:
info["err"] = str(err)
return search_input_error(info, bread)
count = parse_count(info, 50)
start = parse_start(info)
res = C.transitivegroups.groups.find(query).sort([("n", pymongo.ASCENDING), ("t", pymongo.ASCENDING)])
nres = res.count()
res = res.skip(start).limit(count)
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
info["groups"] = res
info["group_display"] = group_display_prettyC(C)
info["report"] = "found %s groups" % nres
info["yesno"] = yesno
info["wgg"] = WebGaloisGroup.from_data
info["start"] = start
info["number"] = nres
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
return render_template(
"gg-search.html", info=info, title="Galois Group Search Result", bread=bread, credit=GG_credit
)
def genus2_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
jump = info["jump"].strip()
curve_label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+$')
if curve_label_regex.match(jump):
return redirect(url_for_curve_label(jump), 301)
else:
class_label_regex = re.compile(r'\d+\.[a-z]+$')
if class_label_regex.match(jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
class_label_regex = re.compile(r'#\d+$')
if class_label_regex.match(jump) and ZZ(jump[1:]) < 2**61:
c = g2cdb().isogeny_classes.find_one({'Lhash': jump[1:].strip()})
if c:
return redirect(url_for_isogeny_class_label(c["label"]), 301)
else:
errmsg = "Hash not found"
else:
errmsg = "Invalid label"
flash(Markup(errmsg + " <span style='color:black'>%s</span>"%(jump)),"error")
return redirect(url_for(".index"))
if 'download' in info and info['download'] == '1':
return download_search(info)
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
bread = info.get('bread',(('Genus 2 Curves', url_for(".index")), ('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type')
parse_bool(info,query,'has_square_sha')
parse_bool(info,query,'locally_solvable')
parse_bool(info,query,'is_simple_geom')
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'cond')
parse_ints(info,query,'num_rat_wpts','Weierstrass points')
parse_ints(info,query,'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)
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['g2inv'] = [ 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]
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
info["query"] = dict(query)
# Database query happens here
cursor = g2cdb().curves.find(query,{'_id':int(0),'label':int(1),'min_eqn':int(1),'st_group':int(1),'is_gl2_type':int(1),'analytic_rank':int(1)})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING), ("disc_key", ASCENDING), ("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_gl2_type_display"] = '✔' if v["is_gl2_type"] else '' # display checkmark if true, blank otherwise
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(v['st_group'])
v_clean["st_group_href"] = st_group_href(v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
title = info.get('title','Genus 2 Curve search results')
credit = credit_string
return render_template("search_results_g2.html", info=info, credit=credit,learnmore=learnmore_list(), bread=bread, title=title)
def genus2_curve_search(info):
if 'jump' in info:
jump = info["jump"].strip()
if re.match(r'^\d+\.[a-z]+\.\d+\.\d+$',jump):
return redirect(url_for_curve_label(jump), 301)
else:
if re.match(r'^\d+\.[a-z]+$', jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
if re.match(r'^\#\d+$',jump) and ZZ(jump[1:]) < 2**61:
c = g2c_db_curves().find_one({'Lhash': jump[1:].strip()})
if c:
return redirect(url_for_isogeny_class_label(c["class"]), 301)
else:
errmsg = "hash %s not found"
else:
errmsg = "%s is not a valid genus 2 curve or isogeny class label"
flash_error (errmsg, jump)
return redirect(url_for(".index"))
if info.get('download','').strip() == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
bread = info.get('bread',(('Genus 2 Curves', url_for(".index")), ('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
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_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]
except ValueError as err:
info['err'] = str(err)
return render_template("g2c_search_results.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
# Database query happens here
info["query"] = query # save query for reuse in download_search
cursor = g2c_db_curves().find(query, {'_id':False, 'label':True, 'eqn':True, 'st_group':True, 'is_gl2_type':True, 'is_simple_geom':True, 'analytic_rank':True})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING), ("disc_key", ASCENDING), ("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_simple_geom"] = v["is_simple_geom"]
v_clean["equation_formatted"] = list_to_min_eqn(literal_eval(v["eqn"]))
v_clean["st_group_link"] = st_link_by_name(1,4,v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
title = info.get('title','Genus 2 Curve search results')
credit = credit_string
return render_template("g2c_search_results.html", info=info, credit=credit,learnmore=learnmore_list(), bread=bread, title=title)
def galois_group_search(**args):
info = to_dict(args)
if info.get('jump_to'):
return redirect(url_for('.by_label', label=info['jump_to']).strip(), 301)
bread = get_bread([("Search Results", ' ')])
C = base.getDBConnection()
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
try:
parse_ints(info,query,'n','degree')
parse_ints(info,query,'t')
parse_ints(info,query,'order', qfield='orderkey', parse_singleton=make_order_key)
parse_bracketed_posints(info, query, qfield='gapidfull', split=False, exactlength=2, keepbrackets=True, name='Gap id', field='gapid')
for param in ('cyc', 'solv', 'prim', 'parity'):
parse_bool(info,query,param,minus_one_to_zero=(param != 'parity'))
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))
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info, 50)
start = parse_start(info)
if 'orderkey' in query and not ('n' in query):
res = C.transitivegroups.groups.find(query).sort([('orderkey', pymongo.ASCENDING), ('gapid', pymongo.ASCENDING), ('n', pymongo.ASCENDING), ('t', pymongo.ASCENDING)])
else:
res = C.transitivegroups.groups.find(query).sort([('n', pymongo.ASCENDING), ('t', pymongo.ASCENDING)])
nres = res.count()
res = res.skip(start).limit(count)
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
info['groups'] = res
info['group_display'] = group_display_prettyC(C)
info['report'] = "found %s groups" % nres
info['yesno'] = yesno
info['wgg'] = WebGaloisGroup.from_data
info['start'] = start
info['number'] = nres
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
return render_template("gg-search.html", info=info, title="Galois Group Search Result", bread=bread, credit=GG_credit)
def genus2_curve_search(**args):
info = to_dict(args)
if 'download' in info and info['download'] == '1':
return download_search(info)
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
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+')
if label_regex.match(info["jump"].strip()):
data = render_curve_webpage_by_label(info["jump"].strip())
else:
data = "Invalid label"
if data == "Invalid label":
flash(
Markup(
"The label <span style='color:black'>%s</span> is invalid."
% (info["jump"])), "error")
return redirect(url_for(".index"))
if data == "Data for curve not found":
flash(
Markup(
"No genus 2 curve with label <span style='color:black'>%s</span> was found in the database."
% (info["jump"])), "error")
return redirect(url_for(".index"))
return data
try:
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type')
parse_bool(info, query, 'has_square_sha')
parse_bool(info, query, 'locally_solvable')
for fld in ('st_group', 'real_geom_end_alg'):
if info.get(fld): query[fld] = info[fld]
for fld in ('aut_grp', 'geom_aut_grp'):
parse_bracketed_posints(info, query, fld,
exactlength=2) #Encoded into a GAP ID.
# igusa and igusa_clebsch invariants not currently searchable
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'cond', 'conductor')
parse_ints(info, query, 'num_rat_wpts', 'Weierstrass points')
parse_ints(info, query, 'torsion_order')
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html",
info=info,
title='Genus 2 Curves Search Input Error',
bread=bread,
credit=credit_string)
info["query"] = dict(query)
count = parse_count(info, 50)
start = parse_start(info)
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one(
{'label': isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html",
info=info,
credit=credit,
learnmore=learnmore_list(),
bread=bread,
title=title)
def genus2_curve_search(**args):
info = to_dict(args)
print "info", info
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
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+')
if label_regex.match(info["jump"].strip()):
data = render_curve_webpage_by_label(info["jump"].strip())
else:
data = "Invalid label"
print data
if data == "Invalid label":
flash(Markup("The label <span style='color:black'>%s</span> is invalid."%(info["jump"])),"error")
return redirect(url_for(".index"))
if data == "Data for curve not found":
flash(Markup("No genus 2 curve with label <span style='color:black'>%s</span> was found in the database."%(info["jump"])),"error")
return redirect(url_for(".index"))
return data
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type')
parse_bool(info,query,'has_square_sha')
parse_bool(info,query,'locally_solvable')
for fld in ('st_group', 'real_geom_end_alg'):
if info.get(fld): query[fld] = info[fld]
for fld in ('aut_grp', 'geom_aut_grp'):
#Encoded into a GAP ID.
parse_bracketed_posints(info,query,fld,exactlength=2)
# igusa and igusa_clebsch invariants not currently searchable
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'cond','conductor')
parse_ints(info,query,'num_rat_wpts','Weierstrass points')
parse_ints(info,query,'torsion_order')
parse_ints(info,query,'two_selmer_rank','2-Selmer rank')
parse_ints(info,query,'analytic_rank','analytic rank')
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
info["query"] = dict(query)
print "query", info["query"]
print "info", info
count = parse_count(info, 50)
start = parse_start(info)
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1,
min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one({'label' :
isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit,learnmore=learnmore_list(),
bread=bread, title=title)
credit = credit_string
title = 'Genus 2 curves over $\Q$'
bread = [('Genus 2 Curves', url_for(".index")), ('$\Q$', ' ')]
def genus2_curve_search(info):
if 'jump' in info:
jump = info["jump"].strip()
if re.match(r'^\d+\.[a-z]+\.\d+\.\d+$', jump):
return redirect(url_for_curve_label(jump), 301)
else:
if re.match(r'^\d+\.[a-z]+$', jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
if re.match(r'^\#\d+$', jump) and ZZ(jump[1:]) < 2**61:
c = g2c_db_curves().find_one({'Lhash': jump[1:].strip()})
if c:
return redirect(
url_for_isogeny_class_label(c["class"]), 301)
else:
errmsg = "hash %s not found"
else:
errmsg = "%s is not a valid genus 2 curve or isogeny class label"
flash_error(errmsg, jump)
return redirect(url_for(".index"))
if info.get('download', '').strip() == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
bread = info.get('bread',
(('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
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_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]
except ValueError as err:
info['err'] = str(err)
return render_template("g2c_search_results.html",
info=info,
title='Genus 2 Curves Search Input Error',
bread=bread,
credit=credit_string)
# Database query happens here
info["query"] = query # save query for reuse in download_search
cursor = g2c_db_curves().find(
query, {
'_id': False,
'label': True,
'eqn': True,
'st_group': True,
'is_gl2_type': True,
'is_simple_geom': True,
'analytic_rank': True
})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING),
("disc_key", ASCENDING),
("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_simple_geom"] = v["is_simple_geom"]
v_clean["equation_formatted"] = list_to_min_eqn(literal_eval(v["eqn"]))
v_clean["st_group_link"] = st_link_by_name(1, 4, v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
title = info.get('title', 'Genus 2 Curve search results')
credit = credit_string
return render_template("g2c_search_results.html",
info=info,
credit=credit,
learnmore=learnmore_list(),
bread=bread,
title=title)
def genus2_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
jump = info["jump"].strip()
curve_label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+$')
if curve_label_regex.match(jump):
return redirect(url_for_curve_label(jump), 301)
else:
class_label_regex = re.compile(r'\d+\.[a-z]+$')
if class_label_regex.match(jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
class_label_regex = re.compile(r'#\d+$')
if class_label_regex.match(jump) and ZZ(jump[1:]) < 2**61:
c = g2cdb().isogeny_classes.find_one(
{'Lhash': jump[1:].strip()})
if c:
return redirect(
url_for_isogeny_class_label(c["label"]), 301)
else:
errmsg = "Hash not found"
else:
errmsg = "Invalid label"
flash(Markup(errmsg + " <span style='color:black'>%s</span>" % (jump)),
"error")
return redirect(url_for(".index"))
if 'download' in info and info['download'] == '1':
return download_search(info)
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
bread = info.get('bread',
(('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type')
parse_bool(info, query, 'has_square_sha')
parse_bool(info, query, 'locally_solvable')
parse_bool(info, query, 'is_simple_geom')
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'cond')
parse_ints(info, query, 'num_rat_wpts', 'Weierstrass points')
parse_ints(info, query, '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)
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['g2inv'] = [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]
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html",
info=info,
title='Genus 2 Curves Search Input Error',
bread=bread,
credit=credit_string)
info["query"] = dict(query)
# Database query happens here
cursor = g2cdb().curves.find(
query, {
'_id': int(0),
'label': int(1),
'min_eqn': int(1),
'st_group': int(1),
'is_gl2_type': int(1),
'analytic_rank': int(1)
})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING),
("disc_key", ASCENDING),
("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_gl2_type_display"] = '✔' if v[
"is_gl2_type"] else '' # display checkmark if true, blank otherwise
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(v['st_group'])
v_clean["st_group_href"] = st_group_href(v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
title = info.get('title', 'Genus 2 Curve search results')
credit = credit_string
return render_template("search_results_g2.html",
info=info,
credit=credit,
learnmore=learnmore_list(),
bread=bread,
title=title)