def init_ecdb_stats(self):
if self._stats:
return
logger.debug("Computing elliptic curve stats...")
ecdb = db.ec_curves
counts = self._counts
stats = {}
# rank distribution
rank_counts = []
ranks = range(counts['max_rank']+1)
for r in ranks:
ncu = ecdb.count({'rank':r})
ncl = ecdb.count({'rank':r, 'number':1})
prop = format_percentage(ncl,counts['nclasses'])
rank_counts.append({'r': r, 'ncurves': ncu, 'nclasses': ncl, 'prop': prop})
stats['rank_counts'] = rank_counts
# torsion distribution
tor_counts = []
tor_counts2 = []
ncurves = counts['ncurves']
for t in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16]:
ncu = ecdb.count({'torsion':t})
if t in [4,8,12]: # two possible structures
ncyc = ecdb.count({'torsion_structure':[t]})
gp = "\(C_{%s}\)"%t
prop = format_percentage(ncyc,ncurves)
tor_counts.append({'t': t, 'gp': gp, 'ncurves': ncyc, 'prop': prop})
nncyc = ncu-ncyc
gp = "\(C_{2}\\times C_{%s}\)"%(t//2)
prop = format_percentage(nncyc,ncurves)
tor_counts2.append({'t': t, 'gp': gp, 'ncurves': nncyc, 'prop': prop})
elif t==16: # all C_2 x C_8
gp = "\(C_{2}\\times C_{8}\)"
prop = format_percentage(ncu,ncurves)
tor_counts2.append({'t': t, 'gp': gp, 'ncurves': ncu, 'prop': prop})
else: # all cyclic
gp = "\(C_{%s}\)"%t
prop = format_percentage(ncu,ncurves)
tor_counts.append({'t': t, 'gp': gp, 'ncurves': ncu, 'prop': prop})
stats['tor_counts'] = tor_counts+tor_counts2
# Sha distribution
max_sha = ecdb.max('sha')
stats['max_sha'] = max_sha
max_sqrt_sha = max_sha.sqrt() # exact!
sha_counts = [{'s':s,'ncurves':ecdb.count({'sha':s**2})} for s in range(1,1+max_sqrt_sha)]
# remove values with a count of 0
sha_counts = [sc for sc in sha_counts if sc['ncurves']]
stats['sha_counts'] = sha_counts
self._stats = stats
logger.debug("... finished computing elliptic curve stats.")
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'])
counts = [c for c in counts if c[0] != None]
if len(counts) == 0:
continue
vcounts = []
rows = []
avg = 0
total = sum([c[1] for c in counts])
for value, n in counts:
prop = format_percentage(n, total)
if 'avg' in attr and attr['avg'] and (type(value) == int
or type(value) == float):
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_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'])
counts = [c for c in counts if c[0] != None]
if len(counts) == 0:
continue
vcounts = []
rows = []
avg = 0
total = sum([c[1] for c in counts])
for value,n in counts:
prop = format_percentage(n,total)
if 'avg' in attr and attr['avg'] and (type(value) == int or type(value) == float):
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 galstatdict(li, tots, t):
return [{
'cnt':
comma(li[nn]),
'prop':
format_percentage(li[nn], tots[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&galois_group=%s' % (nn + 1, "%dt%d" % (nn + 1, t[nn]))
} for nn in range(len(li))]
def statistics():
t = 'Global Number Field Statistics'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")),
('Number Field Statistics', '')]
init_nf_count()
n = db.nf_fields.stats.get_oldstat('degree')['counts']
nsig = db.nf_fields.stats.get_oldstat('nsig')['counts']
# Galois groups
nt_all = db.nf_fields.stats.get_oldstat('nt')['counts']
nt = [nt_all[j] for j in range(7)]
# Galois group families
cn = galstatdict([u[0] for u in nt_all], n, [1 for u in nt_all])
sn = galstatdict([u[max(len(u) - 1, 0)] for u in nt_all], n,
[len(u) for u in nt_all])
an = galstatdict([u[max(len(u) - 2, 0)] for u in nt_all], n,
[len(u) - 1 for u in nt_all])
# t-numbers for D_n
dn_tlist = [
1, 1, 2, 3, 2, 3, 2, 6, 3, 3, 2, 12, 2, 3, 2, 56, 2, 13, 2, 10, 5, 3, 2
]
dn = galstatdict(
db.nf_fields.stats.get_oldstat('dn')['counts'], n, dn_tlist)
h = db.nf_fields.stats.get_oldstat('h_range')['counts']
has_h = db.nf_fields.stats.get_oldstat('has_h')['val']
hdeg = db.nf_fields.stats.get_oldstat('hdeg')['counts']
has_hdeg = db.nf_fields.stats.get_oldstat('has_hdeg')['counts']
hdeg = [[{
'cnt':
comma(hdeg[nn][j]),
'prop':
format_percentage(hdeg[nn][j], has_hdeg[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&class_number=%s' %
(nn + 1, str(1 + 10**(j - 1)) + '-' + str(10**j))
} for j in range(len(h))] for nn in range(len(hdeg))]
has_hdeg = [{
'cnt':
comma(has_hdeg[nn]),
'prop':
format_percentage(has_hdeg[nn], n[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&class_number=1-10000000000000' % (nn + 1)
} for nn in range(len(has_hdeg))]
maxt = 1 + max([len(entry) for entry in nt])
nt = [[{
'cnt':
comma(nt[nn][tt]),
'prop':
format_percentage(nt[nn][tt], n[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&galois_group=%s' % (nn + 1, "%dt%d" % (nn + 1, tt + 1))
} for tt in range(len(nt[nn]))] for nn in range(len(nt))]
# Totals for signature table
sigtotals = [
comma(sum([nsig[nn][r2] for nn in range(max(r2 * 2 - 1, 0), 23)]))
for r2 in range(12)
]
nsig = [[{
'cnt':
comma(nsig[nn][r2]),
'prop':
format_percentage(nsig[nn][r2], n[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&signature=[%d,%d]' % (nn + 1, nn + 1 - 2 * r2, r2)
} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
h = [{
'cnt':
comma(h[j]),
'prop':
format_percentage(h[j], has_h),
'label':
'$10^{' + str(j - 1) + '}<h\leq 10^{' + str(j) + '}$',
'query':
url_for(".number_field_render_webpage") + '?class_number=%s' %
(str(1 + 10**(j - 1)) + '-' + str(10**j))
} for j in range(len(h))]
h[0]['label'] = '$h=1$'
h[1]['label'] = '$1<h\leq 10$'
h[2]['label'] = '$10<h\leq 10^2$'
h[0]['query'] = url_for(".number_field_render_webpage") + '?class_number=1'
# Class number 1 by signature
sigclass1 = db.nf_fields.stats.get_oldstat('sigclass1')['counts']
sighasclass = db.nf_fields.stats.get_oldstat('sighasclass')['counts']
sigclass1 = [[{
'cnt':
comma(sigclass1[nn][r2]),
'prop':
format_percentage(sigclass1[nn][r2], sighasclass[nn][r2])
if sighasclass[nn][r2] > 0 else 0,
'show':
sighasclass[nn][r2] > 0,
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&signature=[%d,%d]&class_number=1' %
(nn + 1, nn + 1 - 2 * r2, r2)
} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
n = [{
'cnt':
comma(n[nn]),
'prop':
format_percentage(n[nn], nfields),
'query':
url_for(".number_field_render_webpage") + '?degree=%d' % (nn + 1)
} for nn in range(len(n))]
info = {
'degree': n,
'nt': nt,
'nsig': nsig,
'sigtotals': sigtotals,
'h': h,
'has_h': comma(has_h),
'has_h_pct': format_percentage(has_h, nfields),
'hdeg': hdeg,
'has_hdeg': has_hdeg,
'sigclass1': sigclass1,
'total': comma(nfields),
'maxt': maxt,
'cn': cn,
'dn': dn,
'an': an,
'sn': sn,
'maxdeg': max_deg
}
return render_template("nf-statistics.html",
info=info,
credit=NF_credit,
title=t,
bread=bread)
def statistics():
fields = db.nf_fields
nfstatdb = fields.stats
title = 'Number field statistics'
bread = bread_prefix() + [('Statistics', '')]
init_nf_count()
ntrans = [
0, 1, 1, 2, 5, 5, 16, 7, 50, 34, 45, 8, 301, 9, 63, 104, 1954, 10, 983,
8, 1117, 164, 59, 7, 25000, 211, 96, 2392, 1854, 8, 5712
]
degree_stats = nfstatdb.column_counts('degree')
n = [degree_stats[elt + 1] for elt in range(23)]
degree_r2_stats = nfstatdb.column_counts(['degree', 'r2'])
# if a count is missing it is because it is zero
nsig = [[
degree_r2_stats.get((deg + 1, s), 0) for s in range((deg + 3) // 2)
] for deg in range(23)]
# Galois groups
nt_stats = nfstatdb.column_counts(['degree', 'galois_label'])
nt_stats = {(key[0], int(key[1].split('T')[1])): value
for (key, value) in nt_stats.items()}
# if a count is missing it is because it is zero
nt_all = [[
nt_stats.get((deg + 1, t + 1), 0) for t in range(ntrans[deg + 1])
] for deg in range(23)]
nt = [nt_all[j] for j in range(7)]
# Galois group families
cn = galstatdict([u[0] for u in nt_all], n, [1 for u in nt_all])
sn = galstatdict([u[max(len(u) - 1, 0)] for u in nt_all], n,
[len(u) for u in nt_all])
an = galstatdict([u[max(len(u) - 2, 0)] for u in nt_all], n,
[len(u) - 1 for u in nt_all])
# t-numbers for D_n
dn_tlist = [
1, 1, 2, 3, 2, 3, 2, 6, 3, 3, 2, 12, 2, 3, 2, 56, 2, 13, 2, 10, 5, 3, 2
]
dn = galstatdict(
[nt_stats[(j + 1, dn_tlist[j])] for j in range(len(dn_tlist))], n,
dn_tlist)
hdeg_stats = {
j: nfstatdb.column_counts(
'degree', {'class_number': {
'$lt': 1 + 10**j,
'$gt': 10**(j - 1)
}})
for j in range(1, 12)
}
hdeg_stats[0] = nfstatdb.column_counts('degree', {'class_number': 1})
h = [
sum(hdeg_stats[j].get(k + 1, 0) for k in range(max_deg))
for j in range(12)
]
# if a count is missing it is because it is zero
hdeg = [[hdeg_stats[j].get(deg + 1, 0) for j in range(12)]
for deg in range(23)]
has_hdeg_stats = nfstatdb.column_counts(
'degree', {'class_number': {
'$exists': True
}})
has_hdeg = [has_hdeg_stats[deg + 1] for deg in range(23)]
has_h = sum(has_hdeg[j] for j in range(len(has_hdeg)))
hdeg = [[{
'cnt':
comma(hdeg[nn][j]),
'prop':
format_percentage(hdeg[nn][j], has_hdeg[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&class_number=%s' %
(nn + 1, str(1 + 10**(j - 1)) + '-' + str(10**j))
} for j in range(len(h))] for nn in range(len(hdeg))]
has_hdeg = [{
'cnt':
comma(has_hdeg[nn]),
'prop':
format_percentage(has_hdeg[nn], n[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&class_number=1-10000000000000' % (nn + 1)
} for nn in range(len(has_hdeg))]
maxt = 1 + max([len(entry) for entry in nt])
nt = [[{
'cnt':
comma(nt[nn][tt]),
'prop':
format_percentage(nt[nn][tt], n[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&galois_group=%s' % (nn + 1, "%dt%d" % (nn + 1, tt + 1))
} for tt in range(len(nt[nn]))] for nn in range(len(nt))]
# Totals for signature table
sigtotals = [
comma(sum([nsig[nn][r2] for nn in range(max(r2 * 2 - 1, 0), 23)]))
for r2 in range(12)
]
nsig = [[{
'cnt':
comma(nsig[nn][r2]),
'prop':
format_percentage(nsig[nn][r2], n[nn]),
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&signature=[%d,%d]' % (nn + 1, nn + 1 - 2 * r2, r2)
} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
h = [{
'cnt':
comma(h[j]),
'prop':
format_percentage(h[j], has_h),
'label':
'$10^{' + str(j - 1) + r'}<h\leq 10^{' + str(j) + '}$',
'query':
url_for(".number_field_render_webpage") + '?class_number=%s' %
(str(1 + 10**(j - 1)) + '-' + str(10**j))
} for j in range(len(h))]
h[0]['label'] = '$h=1$'
h[1]['label'] = r'$1<h\leq 10$'
h[2]['label'] = r'$10<h\leq 10^2$'
h[0]['query'] = url_for(".number_field_render_webpage") + '?class_number=1'
# Class number 1 by signature
sigclass1 = nfstatdb.column_counts(['degree', 'r2'], {'class_number': 1})
sighasclass = nfstatdb.column_counts(['degree', 'r2'],
{'class_number': {
'$exists': True
}})
sigclass1 = [[{
'cnt':
comma(sigclass1.get((nn + 1, r2), 0)),
'prop':
format_percentage(sigclass1.get(
(nn + 1, r2), 0), sighasclass.get(
(nn + 1, r2), 0)) if sighasclass.get(
(nn + 1, r2), 0) > 0 else 0,
'show':
sighasclass.get((nn + 1, r2), 0) > 0,
'query':
url_for(".number_field_render_webpage") +
'?degree=%d&signature=[%d,%d]&class_number=1' %
(nn + 1, nn + 1 - 2 * r2, r2)
} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
n = [{
'cnt':
comma(n[nn]),
'prop':
format_percentage(n[nn], nfields),
'query':
url_for(".number_field_render_webpage") + '?degree=%d' % (nn + 1)
} for nn in range(len(n))]
info = {
'degree': n,
'nt': nt,
'nsig': nsig,
'sigtotals': sigtotals,
'h': h,
'has_h': comma(has_h),
'has_h_pct': format_percentage(has_h, nfields),
'hdeg': hdeg,
'has_hdeg': has_hdeg,
'sigclass1': sigclass1,
'total': comma(nfields),
'maxt': maxt,
'cn': cn,
'dn': dn,
'an': an,
'sn': sn,
'maxdeg': max_deg
}
return render_template("nf-statistics.html",
info=info,
credit=NF_credit,
title=title,
bread=bread)
def init_ecdb_stats(self):
if self._stats:
return
logger.debug("Computing elliptic curve stats...")
ecdbstats = db.ec_curves.stats
counts = self._counts
stats = {}
rank_counts = []
rdict = dict(ecdbstats.get_oldstat('rank')['counts'])
crdict = dict(ecdbstats.get_oldstat('class/rank')['counts'])
for r in range(counts['max_rank'] + 1):
try:
ncu = rdict[str(r)]
ncl = crdict[str(r)]
except KeyError:
ncu = rdict[r]
ncl = crdict[r]
prop = format_percentage(ncl, counts['nclasses'])
rank_counts.append({
'r': r,
'ncurves': ncu,
'nclasses': ncl,
'prop': prop
})
stats['rank_counts'] = rank_counts
tor_counts = []
tor_counts2 = []
ncurves = counts['ncurves']
tdict = dict(ecdbstats.get_oldstat('torsion')['counts'])
tsdict = dict(ecdbstats.get_oldstat('torsion_structure')['counts'])
for t in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16]:
try:
ncu = tdict[t]
except KeyError:
ncu = tdict[str(t)]
if t in [4, 8, 12]: # two possible structures
ncyc = tsdict[str(t)]
gp = "\(C_{%s}\)" % t
prop = format_percentage(ncyc, ncurves)
tor_counts.append({
't': t,
'gp': gp,
'ncurves': ncyc,
'prop': prop
})
nncyc = ncu - ncyc
gp = "\(C_{2}\\times C_{%s}\)" % (t // 2)
prop = format_percentage(nncyc, ncurves)
tor_counts2.append({
't': t,
'gp': gp,
'ncurves': nncyc,
'prop': prop
})
elif t == 16: # all C_2 x C_8
gp = "\(C_{2}\\times C_{8}\)"
prop = format_percentage(ncu, ncurves)
tor_counts2.append({
't': t,
'gp': gp,
'ncurves': ncu,
'prop': prop
})
else: # all cyclic
gp = "\(C_{%s}\)" % t
prop = format_percentage(ncu, ncurves)
tor_counts.append({
't': t,
'gp': gp,
'ncurves': ncu,
'prop': prop
})
stats['tor_counts'] = tor_counts + tor_counts2
shadict = dict(ecdbstats.get_oldstat('sha')['counts'])
stats['max_sha'] = max([int(s) for s in shadict])
sha_counts = []
from sage.misc.functional import isqrt
sha_is_int = True
try:
nc = shadict[1]
except KeyError:
sha_is_int = False
for s in range(1, 1 + isqrt(stats['max_sha'])):
s2 = s * s
if sha_is_int:
nc = shadict.get(s2, 0)
else:
nc = shadict.get(str(s2), 0)
if nc:
sha_counts.append({'s': s, 'ncurves': nc})
stats['sha_counts'] = sha_counts
self._stats = stats
logger.debug("... finished computing elliptic curve stats.")
def statistics():
t = 'Global Number Field Statistics'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Number Field Statistics', '')]
init_nf_count()
n = db.nf_fields.stats.get_oldstat('degree')['counts']
nsig = db.nf_fields.stats.get_oldstat('nsig')['counts']
# Galois groups
nt_all = db.nf_fields.stats.get_oldstat('nt')['counts']
nt = [nt_all[j] for j in range(7)]
# Galois group families
cn = galstatdict([u[0] for u in nt_all], n, [1 for u in nt_all])
sn = galstatdict([u[max(len(u)-1,0)] for u in nt_all], n, [len(u) for u in nt_all])
an = galstatdict([u[max(len(u)-2,0)] for u in nt_all], n, [len(u)-1 for u in nt_all])
# t-numbers for D_n
dn_tlist = [1,1,2,3,2,3,2,6,3,3,2,12,2,3,2,56,2,13,2,10,5,3,2]
dn = galstatdict(db.nf_fields.stats.get_oldstat('dn')['counts'], n, dn_tlist)
h = db.nf_fields.stats.get_oldstat('h_range')['counts']
has_h = db.nf_fields.stats.get_oldstat('has_h')['val']
hdeg = db.nf_fields.stats.get_oldstat('hdeg')['counts']
has_hdeg = db.nf_fields.stats.get_oldstat('has_hdeg')['counts']
hdeg = [ [ {'cnt': comma(hdeg[nn][j]),
'prop': format_percentage(hdeg[nn][j], has_hdeg[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&class_number=%s'%(nn+1,str(1+10**(j-1))+'-'+str(10**j))} for j in range(len(h))] for nn in range(len(hdeg))]
has_hdeg = [{'cnt': comma(has_hdeg[nn]),
'prop': format_percentage(has_hdeg[nn], n[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&class_number=1-10000000000000'%(nn+1)} for nn in range(len(has_hdeg))]
maxt = 1+max([len(entry) for entry in nt])
nt = [ [ {'cnt': comma(nt[nn][tt]),
'prop': format_percentage(nt[nn][tt], n[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&galois_group=%s'%(nn+1,"%dt%d"%(nn+1,tt+1))} for tt in range(len(nt[nn]))] for nn in range(len(nt))]
# Totals for signature table
sigtotals = [ comma(sum([nsig[nn][r2] for nn in range(max(r2*2-1,0),23)])) for r2 in range(12)]
nsig = [ [ {'cnt': comma(nsig[nn][r2]),
'prop': format_percentage(nsig[nn][r2], n[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&signature=[%d,%d]'%(nn+1,nn+1-2*r2,r2)} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
h = [ {'cnt': comma(h[j]),
'prop': format_percentage(h[j], has_h),
'label': '$10^{'+str(j-1)+'}<h\leq 10^{'+str(j)+'}$',
'query': url_for(".number_field_render_webpage")+'?class_number=%s'%(str(1+10**(j-1))+'-'+str(10**j))} for j in range(len(h))]
h[0]['label'] = '$h=1$'
h[1]['label'] = '$1<h\leq 10$'
h[2]['label'] = '$10<h\leq 10^2$'
h[0]['query'] = url_for(".number_field_render_webpage")+'?class_number=1'
# Class number 1 by signature
sigclass1 = db.nf_fields.stats.get_oldstat('sigclass1')['counts']
sighasclass = db.nf_fields.stats.get_oldstat('sighasclass')['counts']
sigclass1 = [ [ {'cnt': comma(sigclass1[nn][r2]),
'prop': format_percentage(sigclass1[nn][r2], sighasclass[nn][r2]) if sighasclass[nn][r2]>0 else 0,
'show': sighasclass[nn][r2]>0,
'query': url_for(".number_field_render_webpage")+'?degree=%d&signature=[%d,%d]&class_number=1'%(nn+1,nn+1-2*r2,r2)} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
n = [ {'cnt': comma(n[nn]),
'prop': format_percentage(n[nn], nfields),
'query': url_for(".number_field_render_webpage")+'?degree=%d'%(nn+1)} for nn in range(len(n))]
info = {'degree': n,
'nt': nt,
'nsig': nsig,
'sigtotals': sigtotals,
'h': h,
'has_h': comma(has_h),
'has_h_pct': format_percentage(has_h, nfields),
'hdeg': hdeg,
'has_hdeg': has_hdeg,
'sigclass1': sigclass1,
'total': comma(nfields),
'maxt': maxt,
'cn': cn, 'dn': dn, 'an': an, 'sn': sn,
'maxdeg': max_deg}
return render_template("nf-statistics.html", info=info, credit=NF_credit, title=t, bread=bread)
def galstatdict(li, tots, t):
return [ {'cnt': comma(li[nn]),
'prop': format_percentage(li[nn], tots[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&galois_group=%s'%(nn+1,"%dt%d"%(nn+1,t[nn]))} for nn in range(len(li))]
def test_format_percentage(self):
r"""
Checking utility: format_percentage
"""
self.assertEqual(format_percentage(12, 31), ' 38.71')
self.assertEqual(format_percentage(12, 37), ' 32.43')
def test_format_percentage(self):
r"""
Checking utility: format_percentage
"""
self.assertEqual(format_percentage(12,31), ' 38.71')
self.assertEqual(format_percentage(12,37), ' 32.43')
def init_ecdb_stats(self):
if self._stats:
return
logger.debug("Computing elliptic curve stats...")
ecdbstats = db.ec_curves.stats
counts = self._counts
stats = {}
rank_counts = []
rdict = dict(ecdbstats.get_oldstat('rank')['counts'])
crdict = dict(ecdbstats.get_oldstat('class/rank')['counts'])
for r in range(counts['max_rank']+1):
try:
ncu = rdict[str(r)]
ncl = crdict[str(r)]
except KeyError:
ncu = rdict[r]
ncl = crdict[r]
prop = format_percentage(ncl,counts['nclasses'])
rank_counts.append({'r': r, 'ncurves': ncu, 'nclasses': ncl, 'prop': prop})
stats['rank_counts'] = rank_counts
tor_counts = []
tor_counts2 = []
ncurves = counts['ncurves']
tdict = dict(ecdbstats.get_oldstat('torsion')['counts'])
tsdict = dict(ecdbstats.get_oldstat('torsion_structure')['counts'])
for t in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16]:
try:
ncu = tdict[t]
except KeyError:
ncu = tdict[str(t)]
if t in [4,8,12]: # two possible structures
ncyc = tsdict[str(t)]
gp = "\(C_{%s}\)"%t
prop = format_percentage(ncyc,ncurves)
tor_counts.append({'t': t, 'gp': gp, 'ncurves': ncyc, 'prop': prop})
nncyc = ncu-ncyc
gp = "\(C_{2}\\times C_{%s}\)"%(t//2)
prop = format_percentage(nncyc,ncurves)
tor_counts2.append({'t': t, 'gp': gp, 'ncurves': nncyc, 'prop': prop})
elif t==16: # all C_2 x C_8
gp = "\(C_{2}\\times C_{8}\)"
prop = format_percentage(ncu,ncurves)
tor_counts2.append({'t': t, 'gp': gp, 'ncurves': ncu, 'prop': prop})
else: # all cyclic
gp = "\(C_{%s}\)"%t
prop = format_percentage(ncu,ncurves)
tor_counts.append({'t': t, 'gp': gp, 'ncurves': ncu, 'prop': prop})
stats['tor_counts'] = tor_counts+tor_counts2
shadict = dict(ecdbstats.get_oldstat('sha')['counts'])
stats['max_sha'] = max([int(s) for s in shadict])
sha_counts = []
from sage.misc.functional import isqrt
sha_is_int = True
try:
nc = shadict[1]
except KeyError:
sha_is_int = False
for s in range(1,1+isqrt(stats['max_sha'])):
s2 = s*s
if sha_is_int:
nc = shadict.get(s2,0)
else:
nc = shadict.get(str(s2),0)
if nc:
sha_counts.append({'s': s, 'ncurves': nc})
stats['sha_counts'] = sha_counts
self._stats = stats
logger.debug("... finished computing elliptic curve stats.")
def init_ecdb_stats(self):
if self._stats:
return
logger.debug("Computing elliptic curve stats...")
ecdb = db.ec_curves
counts = self._counts
stats = {}
# rank distribution
rank_counts = []
ranks = range(counts['max_rank'] + 1)
for r in ranks:
ncu = ecdb.count({'rank': r})
ncl = ecdb.count({'rank': r, 'number': 1})
prop = format_percentage(ncl, counts['nclasses'])
rank_counts.append({
'r': r,
'ncurves': ncu,
'nclasses': ncl,
'prop': prop
})
stats['rank_counts'] = rank_counts
# torsion distribution
tor_counts = []
tor_counts2 = []
ncurves = counts['ncurves']
for t in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16]:
ncu = ecdb.count({'torsion': t})
if t in [4, 8, 12]: # two possible structures
ncyc = ecdb.count({'torsion_structure': [t]})
gp = "\(C_{%s}\)" % t
prop = format_percentage(ncyc, ncurves)
tor_counts.append({
't': t,
'gp': gp,
'ncurves': ncyc,
'prop': prop
})
nncyc = ncu - ncyc
gp = "\(C_{2}\\times C_{%s}\)" % (t // 2)
prop = format_percentage(nncyc, ncurves)
tor_counts2.append({
't': t,
'gp': gp,
'ncurves': nncyc,
'prop': prop
})
elif t == 16: # all C_2 x C_8
gp = "\(C_{2}\\times C_{8}\)"
prop = format_percentage(ncu, ncurves)
tor_counts2.append({
't': t,
'gp': gp,
'ncurves': ncu,
'prop': prop
})
else: # all cyclic
gp = "\(C_{%s}\)" % t
prop = format_percentage(ncu, ncurves)
tor_counts.append({
't': t,
'gp': gp,
'ncurves': ncu,
'prop': prop
})
stats['tor_counts'] = tor_counts + tor_counts2
# Sha distribution
max_sha = ecdb.max('sha')
stats['max_sha'] = max_sha
max_sqrt_sha = Integer(
max_sha).sqrt() # exact since all sha values are squares!
sha_counts = [{
's': s,
'ncurves': ecdb.count({'sha': s**2})
} for s in range(1, 1 + max_sqrt_sha)]
# remove values with a count of 0
sha_counts = [sc for sc in sha_counts if sc['ncurves']]
stats['sha_counts'] = sha_counts
self._stats = stats
logger.debug("... finished computing elliptic curve stats.")
def statistics():
# FIXME use StatsDisplay
fields = db.nf_fields
title = 'Global Number Field Statistics'
bread = [('Global Number Fields', url_for(".number_field_render_webpage")),
('Number Field Statistics', '')]
init_nf_count()
ntrans = [0, 1, 1, 2, 5, 5, 16, 7, 50, 34, 45, 8, 301, 9, 63, 104, 1954,
10, 983, 8, 1117, 164, 59, 7, 25000, 211, 96, 2392, 1854, 8, 5712]
degree_stats = fields.stats.column_counts('degree')
n = [degree_stats[elt + 1] for elt in range(23)]
degree_r2_stats = fields.stats.column_counts(['degree', 'r2'])
# if a count is missing it is because it is zero
nsig = [[degree_r2_stats.get((deg+1, s), 0) for s in range((deg+3)/2)]
for deg in range(23)]
# Galois groups
nt_stats = fields.stats.column_counts(['degree', 'galt'])
# if a count is missing it is because it is zero
nt_all = [[nt_stats.get((deg+1, t+1), 0) for t in range(ntrans[deg+1])]
for deg in range(23)]
nt = [nt_all[j] for j in range(7)]
# Galois group families
cn = galstatdict([u[0] for u in nt_all], n, [1 for u in nt_all])
sn = galstatdict([u[max(len(u)-1,0)] for u in nt_all], n, [len(u) for u in nt_all])
an = galstatdict([u[max(len(u)-2,0)] for u in nt_all], n, [len(u)-1 for u in nt_all])
# t-numbers for D_n
dn_tlist = [1, 1, 2, 3, 2, 3, 2, 6, 3, 3, 2, 12, 2, 3, 2, 56, 2, 13, 2, 10,
5, 3, 2]
dn = galstatdict([nt_stats[(j+1,dn_tlist[j])] for j in range(len(dn_tlist))], n, dn_tlist)
h = [fields.count({'class_number': {'$lt': 1+10**j, '$gt': 10**(j-1)}}) for j in range(12)]
has_h = fields.count({'class_number': {'$exists': True}})
hdeg_stats = {j: fields.stats.column_counts('degree', {'class_number': {'$lt': 1+10**j, '$gt': 10**(j-1)}}) for j in range(1, 12)}
hdeg_stats[0] = fields.stats.column_counts('degree', {'class_number': 1})
# if a count is missing it is because it is zero
hdeg = [[hdeg_stats[j].get(deg+1, 0) for j in range(12)] for deg in range(23)]
has_hdeg_stats = fields.stats.column_counts('degree', {'class_number': {'$exists': True}})
has_hdeg = [has_hdeg_stats[deg+1] for deg in range(23)]
hdeg = [[{'cnt': comma(hdeg[nn][j]),
'prop': format_percentage(hdeg[nn][j], has_hdeg[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&class_number=%s' % (nn + 1, str(1 + 10**(j - 1)) + '-' + str(10**j))}
for j in range(len(h))]
for nn in range(len(hdeg))]
has_hdeg = [{'cnt': comma(has_hdeg[nn]),
'prop': format_percentage(has_hdeg[nn], n[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&class_number=1-10000000000000' % (nn + 1)} for nn in range(len(has_hdeg))]
maxt = 1+max([len(entry) for entry in nt])
nt = [[{'cnt': comma(nt[nn][tt]),
'prop': format_percentage(nt[nn][tt], n[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&galois_group=%s' % (nn + 1, "%dt%d" % (nn + 1, tt + 1))}
for tt in range(len(nt[nn]))]
for nn in range(len(nt))]
# Totals for signature table
sigtotals = [comma(
sum([nsig[nn][r2]
for nn in range(max(r2*2 - 1, 0), 23)]))
for r2 in range(12)]
nsig = [[{'cnt': comma(nsig[nn][r2]),
'prop': format_percentage(nsig[nn][r2], n[nn]),
'query': url_for(".number_field_render_webpage")+'?degree=%d&signature=[%d,%d]'%(nn+1,nn+1-2*r2,r2)} for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
h = [{'cnt': comma(h[j]),
'prop': format_percentage(h[j], has_h),
'label': '$10^{' + str(j - 1) + '}<h\leq 10^{' + str(j) + '}$',
'query': url_for(".number_field_render_webpage")+'?class_number=%s' % (str(1 + 10**(j - 1)) + '-' + str(10**j))} for j in range(len(h))]
h[0]['label'] = '$h=1$'
h[1]['label'] = '$1<h\leq 10$'
h[2]['label'] = '$10<h\leq 10^2$'
h[0]['query'] = url_for(".number_field_render_webpage")+'?class_number=1'
# Class number 1 by signature
sigclass1 = fields.stats.get_oldstat('sigclass1')['counts']
sighasclass = fields.stats.get_oldstat('sighasclass')['counts']
sigclass1 = [[{'cnt': comma(sigclass1[nn][r2]),
'prop': format_percentage(sigclass1[nn][r2], sighasclass[nn][r2]) if sighasclass[nn][r2] > 0 else 0,
'show': sighasclass[nn][r2] > 0,
'query': url_for(".number_field_render_webpage")+'?degree=%d&signature=[%d,%d]&class_number=1' % (nn + 1, nn + 1 - 2*r2, r2)}
for r2 in range(len(nsig[nn]))] for nn in range(len(nsig))]
n = [{'cnt': comma(n[nn]),
'prop': format_percentage(n[nn], nfields),
'query': url_for(".number_field_render_webpage")+'?degree=%d' % (nn + 1)}
for nn in range(len(n))]
info = {'degree': n,
'nt': nt,
'nsig': nsig,
'sigtotals': sigtotals,
'h': h,
'has_h': comma(has_h),
'has_h_pct': format_percentage(has_h, nfields),
'hdeg': hdeg,
'has_hdeg': has_hdeg,
'sigclass1': sigclass1,
'total': comma(nfields),
'maxt': maxt,
'cn': cn, 'dn': dn, 'an': an, 'sn': sn,
'maxdeg': max_deg}
return render_template("nf-statistics.html",
info=info,
credit=NF_credit,
title=title,
bread=bread)
