def init_g2c_stats(self):
if self._stats:
return
curves = g2c_db_curves()
counts = self._counts
total = counts["ncurves"]
stats = {}
dists = []
# TODO use aggregate $group to speed this up and/or just store these counts in the database
for attr in stats_attribute_list:
counts = attribute_value_counts(curves, attr['name'])
vcounts = []
rows = []
avg = 0
for value,n in counts:
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
def download_search(info):
lang = info.get('language','text').strip()
filename = 'genus2_curves' + download_file_suffix[lang]
mydate = time.strftime("%d %B %Y")
# reissue query here
try:
res = g2c_db_curves().find(literal_eval(info.get('query','{}')),{'_id':False,'eqn':True})
except Exception as err:
return "Unable to parse query: %s"%err
c = download_comment_prefix[lang]
s = '\n'
s += c + ' Genus 2 curves downloaded from the LMFDB downloaded on %s.\n'% mydate
s += c + ' Query "%s" returned %d curves.\n\n' %(str(info.get('query')), 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'
s += str(',\n'.join([str(r['eqn']) for r in res])) # list of curve equations
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, add_etags=False)
def by_url_isogeny_class_discriminant(cond, alpha, disc):
data = to_dict(request.args)
clabel = str(cond) + "." + alpha
# if the isogeny class is not present in the database, return a 404 (otherwise title and bread crumbs refer to a non-existent isogeny class)
if not g2c_db_curves().find_one({'class': clabel}, {'_id': True}):
return abort(
404, 'Genus 2 isogeny class %s not found in database.' % clabel)
data['title'] = 'Genus 2 curves in isogeny class %s of discriminant %s' % (
clabel, disc)
data['bread'] = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % cond, url_for(".by_conductor", cond=cond)),
('%s' % alpha,
url_for(".by_url_isogeny_class_label",
cond=cond,
alpha=alpha)),
('%s' % disc,
url_for(".by_url_isogeny_class_discriminant",
cond=cond,
alpha=alpha,
disc=disc))]
if len(request.args) > 0:
# if conductor or discriminant changed, fall back to a general search
if ('cond' in request.args and request.args['cond'] != str(cond)) or \
('abs_disc' in request.args and request.args['abs_disc'] != str(disc)):
return redirect(url_for(".index", **request.args), 307)
data['title'] += ' search results'
data['bread'].append(('search results', ''))
data['cond'] = cond
data['class'] = clabel
data['abs_disc'] = disc
return genus2_curve_search(data)
def download_search(info):
lang = info.get('language','text').strip()
filename = 'genus2_curves' + download_file_suffix[lang]
mydate = time.strftime("%d %B %Y")
# reissue query here
try:
res = g2c_db_curves().find(literal_eval(info.get('query','{}')),{'_id':False,'eqn':True})
except Exception as err:
return "Unable to parse query: %s"%err
c = download_comment_prefix[lang]
s = '\n'
s += c + ' Genus 2 curves downloaded from the LMFDB downloaded on %s.\n'% mydate
s += c + ' Query "%s" returned %d curves.\n\n' %(str(info.get('query')), 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'
s += str(',\n'.join([str(r['eqn']) for r in res])) # list of curve equations
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, add_etags=False)
def init_g2c_stats(self):
if self._stats:
return
curves = g2c_db_curves()
counts = self._counts
total = counts["ncurves"]
stats = {}
dists = []
# TODO use aggregate $group to speed this up and/or just store these counts in the database
for attr in stats_attribute_list:
counts = attribute_value_counts(curves, attr['name'])
vcounts = []
rows = []
avg = 0
for value,n in counts:
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
def init_g2c_count(self):
if self._counts:
return
curves = g2c_db_curves()
counts = {}
ncurves = curves.count()
counts['ncurves'] = ncurves
counts['ncurves_c'] = comma(ncurves)
nclasses = g2c_db_isogeny_classes_count()
counts['nclasses'] = nclasses
counts['nclasses_c'] = comma(nclasses)
max_D = 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
curves = g2c_db_curves()
counts = {}
ncurves = curves.count()
counts['ncurves'] = ncurves
counts['ncurves_c'] = comma(ncurves)
nclasses = g2c_db_isogeny_classes_count()
counts['nclasses'] = nclasses
counts['nclasses_c'] = comma(nclasses)
max_D = 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 by_url_isogeny_class_discriminant(cond, alpha, disc):
data = to_dict(request.args)
clabel = str(cond)+"."+alpha
# if the isogeny class is not present in the database, return a 404 (otherwise title and bread crumbs refer to a non-existent isogeny class)
if not g2c_db_curves().find_one({'class':clabel},{'_id':True}):
return abort(404, 'Genus 2 isogeny class %s not found in database.'%clabel)
data['title'] = 'Genus 2 curves in isogeny class %s of discriminant %s' % (clabel,disc)
data['bread'] = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % cond, url_for(".by_conductor", cond=cond)),
('%s' % alpha, url_for(".by_url_isogeny_class_label", cond=cond, alpha=alpha)),
('%s' % disc, url_for(".by_url_isogeny_class_discriminant", cond=cond, alpha=alpha, disc=disc))]
if len(request.args) > 0:
# if conductor or discriminant changed, fall back to a general search
if ('cond' in request.args and request.args['cond'] != str(cond)) or \
('abs_disc' in request.args and request.args['abs_disc'] != str(disc)):
return redirect (url_for(".index", **request.args), 307)
data['title'] += ' search results'
data['bread'].append(('search results',''))
data['cond'] = cond
data['class'] = clabel
data['abs_disc'] = disc
return genus2_curve_search(data)
def download_search(info):
lang = info.get('language','').strip()
if not lang in download_languages:
return "Please specify a language in %s"%download_languages
filename = 'genus2_curves' + download_file_suffix[lang]
mydate = time.strftime("%d %B %Y")
# reissue query here
try:
res = g2c_db_curves().find(literal_eval(info.get('query','{}')),{'_id':int(0),'eqn':int(1)})
except Exception as err:
return "Unable to parse query: %s"%err
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['eqn'])
entry = entry.replace('u','')
entry = entry.replace('\'','')
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 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 random_curve():
label = random_value_from_collection(g2c_db_curves(), 'label')
return redirect(url_for_curve_label(label), 307)
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 random_curve():
label = random_value_from_collection(g2c_db_curves(), 'label')
return redirect(url_for_curve_label(label), 307)