def init_g2c_stats(self):
if self._stats:
return
g2c_logger.debug("Computing genus 2 curve stats...")
counts = self._counts
total = counts["ncurves"]
stats = {}
dists = []
for attr in stats_attribute_list:
values = g2cdb().curves.distinct(attr['name'])
values.sort()
vcounts = []
rows = []
colcount = 0
avg = 0
for value in values:
n = g2cdb().curves.find({attr['name']:value}).count()
prop = format_percentage(n,total)
if 'avg' in attr and attr['avg']:
avg += n*value
value_string = attr['format'](value) if 'format' in attr else value
vcounts.append({'value': value_string, 'curves': n, 'query':url_for(".index_Q")+'?'+attr['name']+'='+str(value),'proportion': prop})
if len(vcounts) == 10:
rows.append(vcounts)
vcounts = []
if len(vcounts):
rows.append(vcounts)
if 'avg' in attr and attr['avg']:
vcounts.append({'value':'\\mathrm{avg}\\ %.2f'%(float(avg)/total), 'curves':total, 'query':url_for(".index_Q") +'?'+attr['name'],'proportion':format_percentage(1,1)})
dists.append({'attribute':attr,'rows':rows})
stats["distributions"] = dists
self._stats = stats
g2c_logger.debug("... finished computing genus 2 curve stats.")
def index_Q():
if len(request.args) != 0:
return genus2_curve_search(**request.args)
info = {'counts' : g2cstats().counts()}
info["stats_url"] = url_for(".statistics")
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["browse_curves"] = [
g2cdb().curves.find_one({"label":"169.a.169.1"}),
g2cdb().curves.find_one({"label":"1116.a.214272.1"}),
g2cdb().curves.find_one({"label":"1152.a.147456.1"}),
g2cdb().curves.find_one({"label":"1369.a.50653.1"}),
g2cdb().curves.find_one({"label":"12500.a.12500.1"}),
]
info["conductor_list"] = ['1-499', '500-999', '1000-99999','100000-1000000' ]
info["discriminant_list"] = ['1-499', '500-999', '1000-99999','100000-1000000' ]
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
title = 'Genus 2 curves over $\Q$'
bread = [('Genus 2 Curves', url_for(".index")), ('$\Q$', ' ')]
return render_template("browse_search_g2.html", info=info, credit=credit_string, title=title, learnmore=learnmore_list(), bread=bread)
def init_g2c_stats(self):
if self._stats:
return
g2c_logger.debug("Computing genus 2 curve stats...")
counts = self._counts
total = counts["ncurves"]
stats = {}
dists = []
for attr in stats_attribute_list:
values = g2cdb().curves.distinct(attr['name'])
values.sort()
vcounts = []
rows = []
colcount = 0
avg = 0
for value in values:
n = g2cdb().curves.find({attr['name']: value}).count()
prop = format_percentage(n, total)
if 'avg' in attr and attr['avg']:
avg += n * value
value_string = attr['format'](
value) if 'format' in attr else value
vcounts.append({
'value':
value_string,
'curves':
n,
'query':
url_for(".index_Q") + '?' + attr['name'] + '=' +
str(value),
'proportion':
prop
})
if len(vcounts) == 10:
rows.append(vcounts)
vcounts = []
if len(vcounts):
rows.append(vcounts)
if 'avg' in attr and attr['avg']:
vcounts.append({
'value':
'\\mathrm{avg}\\ %.2f' % (float(avg) / total),
'curves':
total,
'query':
url_for(".index_Q") + '?' + attr['name'],
'proportion':
format_percentage(1, 1)
})
dists.append({'attribute': attr, 'rows': rows})
stats["distributions"] = dists
self._stats = stats
g2c_logger.debug("... finished computing genus 2 curve stats.")
def init_g2c_count(self):
if self._counts:
return
counts = {}
ncurves = g2cdb().curves.count()
counts['ncurves'] = ncurves
counts['ncurves_c'] = comma(ncurves)
nclasses = g2cdb().isogeny_classes.count()
counts['nclasses'] = nclasses
counts['nclasses_c'] = comma(nclasses)
max_D = g2cdb().curves.find().sort('abs_disc', DESCENDING).limit(1)[0]['abs_disc']
counts['max_D'] = max_D
counts['max_D_c'] = comma(max_D)
self._counts = counts
def init_g2c_count(self):
if self._counts:
return
counts = {}
ncurves = g2cdb().curves.count()
counts['ncurves'] = ncurves
counts['ncurves_c'] = comma(ncurves)
nclasses = g2cdb().isogeny_classes.count()
counts['nclasses'] = nclasses
counts['nclasses_c'] = comma(nclasses)
max_D = g2cdb().curves.find().sort('abs_disc',
DESCENDING).limit(1)[0]['abs_disc']
counts['max_D'] = max_D
counts['max_D_c'] = comma(max_D)
self._counts = counts
def download_search(info):
lang = info["submit"]
filename = 'genus2_curves' + download_file_suffix[lang]
mydate = time.strftime("%d %B %Y")
# reissue saved query here
res = g2cdb().curves.find(ast.literal_eval(info["query"]))
c = download_comment_prefix[lang]
s = '\n'
s += c + ' Genus 2 curves downloaded from the LMFDB downloaded on %s. Found %s curves.\n'%(mydate, res.count())
s += c + ' Below is a list called data. Each entry has the form:\n'
s += c + ' [[f coeffs],[h coeffs]]\n'
s += c + ' defining the hyperelliptic curve y^2+h(x)y=f(x)\n'
s += c + '\n'
s += c + ' ' + download_make_data_comment[lang] + '\n'
s += '\n'
s += download_assignment_start[lang] + '\\\n'
# loop through all search results and grab the curve equations
for r in res:
entry = str(r['min_eqn'])
entry = entry.replace('u','')
entry = entry.replace('\'','')
s += entry + ',\\\n'
s = s[:-3]
s += download_assignment_end[lang]
s += '\n\n'
s += download_make_data[lang]
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO, attachment_filename=filename, as_attachment=True)
def download_search(info):
lang = info["submit"]
filename = 'genus2_curves' + download_file_suffix[lang]
mydate = time.strftime("%d %B %Y")
# reissue saved query here
res = g2cdb().curves.find(literal_eval(info["query"]), {
'_id': int(0),
'min_eqn': int(1)
})
c = download_comment_prefix[lang]
s = '\n'
s += c + ' Genus 2 curves downloaded from the LMFDB downloaded on %s. Found %s curves.\n' % (
mydate, res.count())
s += c + ' Below is a list called data. Each entry has the form:\n'
s += c + ' [[f coeffs],[h coeffs]]\n'
s += c + ' defining the hyperelliptic curve y^2+h(x)y=f(x)\n'
s += c + '\n'
s += c + ' ' + download_make_data_comment[lang] + '\n'
s += '\n'
s += download_assignment_start[lang] + '\\\n'
# loop through all search results and grab the curve equations
for r in res:
entry = str(r['min_eqn'])
entry = entry.replace('u', '')
entry = entry.replace('\'', '')
s += entry + ',\\\n'
s = s[:-3]
s += download_assignment_end[lang]
s += '\n\n'
s += download_make_data[lang]
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO, attachment_filename=filename, as_attachment=True)
def by_label(label):
"""
Searches for a specific genus 2 curve isogeny class in the
curves collection by its label.
"""
try:
data = g2cdb().isogeny_classes.find_one({"label" : label})
except AttributeError:
return "Invalid isogeny class label" # caller must catch this and raise an error
if data:
return G2Cisogeny_class(data)
return "No isogeny class with this label currently in the database" # caller must catch this and raise an error
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 random_curve():
label = random_object_from_collection(g2cdb().curves)['label']
# This version leaves the word 'random' in the URL:
#return render_curve_webpage_by_label(label)
# This version uses the curve's own URL:
return redirect(url_for(".by_g2c_label", label=label), 301)
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 random_curve():
label = random_value_from_collection(g2cdb().curves, 'label')
return redirect(url_for_curve_label(label), 301)
def make_class(self):
from lmfdb.genus2_curves.genus2_curve import url_for_curve_label
# Data
curves_data = g2cdb().curves.find({"class" : self.label},{'_id':int(0),'label':int(1),'min_eqn':int(1),'disc_key':int(1)}).sort([("disc_key", ASCENDING), ("label", ASCENDING)])
assert curves_data
self.curves = [ {"label" : c['label'], "equation_formatted" : list_to_min_eqn(c['min_eqn']),
"url": url_for_curve_label(c['label'])} for c in curves_data ]
self.ncurves = curves_data.count()
self.bad_lfactors = [ [c[0], list_to_factored_poly_otherorder(c[1])]
for c in self.bad_lfactors]
# Data derived from Sato-Tate group
self.st_group_name = st_group_name(self.st_group)
self.st_group_href = st_group_href(self.st_group)
self.st0_group_name = st0_group_name(self.real_geom_end_alg)
# Later used in Lady Gaga box:
self.real_geom_end_alg_disp = [r'\End(J_{\overline{\Q}}) \otimes \R',
end_alg_name(self.real_geom_end_alg)]
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
# Endomorphism data
endodata = g2cdb().endomorphisms.find_one({"label" :
self.curves[0]['label']})
self.gl2_statement_base = \
gl2_statement_base(endodata['factorsRR_base'], r'\(\Q\)')
self.endo_statement_base = \
"""Endomorphism algebra over \(\Q\):<br>""" + \
endo_statement_isog(endodata['factorsQQ_base'],
endodata['factorsRR_base'], r'')
endodata['fod_poly'] = intlist_to_poly(endodata['fod_coeffs'])
self.fod_statement = fod_statement(endodata['fod_label'],
endodata['fod_poly'])
if endodata['fod_label'] != '1.1.1.1':
self.endo_statement_geom = \
"""Endomorphism algebra over \(\overline{\Q}\):<br>""" + \
endo_statement_isog(endodata['factorsQQ_geom'],
endodata['factorsRR_geom'], r'\overline{\Q}')
else:
self.endo_statement_geom = ''
# Title
self.title = "Genus 2 Isogeny Class %s" % (self.label)
# Lady Gaga box
self.properties = (
('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor','%s' % self.cond),
('Sato-Tate group', self.st_group_href),
('\(%s\)' % self.real_geom_end_alg_disp[0],
'\(%s\)' % self.real_geom_end_alg_disp[1]),
('\(\mathrm{GL}_2\)-type','%s' % self.is_gl2_type_name)
)
x = self.label.split('.')[1]
self.friends = [('L-function', url_for("l_functions.l_function_genus2_page", cond=self.cond,x=x))]
#self.downloads = [('Download Euler factors', ".")]
#self.downloads = [
# ('Download Euler factors', "."),
# url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves',
# url_for(".download_g2c_all", label=self.label))
# ]
# Breadcrumbs
self.bread = (
('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond, url_for(".by_conductor", cond=self.cond)),
('%s' % self.label, ' ')
)
# More friends (NOTE: to be improved)
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) != 1:
self.friends.append(('Elliptic curve ' + curve_label,
crv_url))
self.ecproduct_wurl.append({'label' : curve_label, 'url' :
crv_url})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass", nf = crv_spl[0],
conductor_label = crv_spl[1], class_label = crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({'label' : curve_label, 'url' :
crv_url, 'nf' : crv_spl[0]})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms",
level=mf_spl[0], weight=mf_spl[1], character=mf_spl[2],
label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage",
field_label=mf_spl[0], label=mf_label)
self.friends.append(('Hilbert modular form ' + mf_label, mf_url))
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 random_curve():
label = random_value_from_collection(g2cdb().curves, 'label')
return redirect(url_for_curve_label(label), 301)
