def by_label(label):
try:
nflabel = nf_string_to_label(clean_input(label))
if label != nflabel:
return redirect(url_for(".by_label", label=nflabel), 301)
return render_field_webpage({'label': nf_string_to_label(label)})
except ValueError as err:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid number field. %s" % (label,err)), "error")
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search Results', ' ')]
return search_input_error({'err':''}, bread)
def by_label(label):
try:
nflabel = nf_string_to_label(clean_input(label))
if label != nflabel:
return redirect(url_for(".by_label", label=nflabel), 301)
return render_field_webpage({'label': nf_string_to_label(label)})
except ValueError as err:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid number field. %s" % (label,err)), "error")
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search Results', ' ')]
return search_input_error({'err':''}, bread)
def show_ecnf(nf, conductor_label, class_label, number):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {"query": {}}
info["err"] = "No elliptic curve in the database has label %s." % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls["field"]))
bread.append((ec.conductor_label, ec.urls["conductor"]))
bread.append((ec.iso_label, ec.urls["class"]))
bread.append((ec.number, ec.urls["curve"]))
info = {}
return render_template(
"show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list(),
)
def show_ecnf_isoclass(nf, conductor_label, class_label):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
conductor_label = unquote(conductor_label)
label = "-".join([nf_label, conductor_label, class_label])
full_class_label = "-".join([conductor_label, class_label])
cl = ECNF_isoclass.by_label(label)
title = "Elliptic Curve isogeny class %s over Number Field %s" % (full_class_label, cl.field)
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((cl.field, url_for(".show_ecnf1", nf=nf_label)))
bread.append((conductor_label, url_for(".show_ecnf_conductor", nf=nf_label, conductor_label=conductor_label)))
bread.append(
(
class_label,
url_for(
".show_ecnf_isoclass", nf=nf_label, conductor_label=quote(conductor_label), class_label=class_label
),
)
)
info = {}
return render_template(
"show-ecnf-isoclass.html",
credit=ecnf_credit,
title=title,
bread=bread,
cl=cl,
properties2=cl.properties,
friends=cl.friends,
learnmore=learnmore_list(),
)
def show_ecnf(nf, conductor_label, class_label, number):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {'query':{}}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
code = ec.code()
code['show'] = {'magma':'','pari':'','sage':''} # use default show names
info = {}
return render_template("show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
code = code,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list())
def show_ecnf_isoclass(nf, conductor_label, class_label):
conductor_label = unquote(conductor_label)
if re.match(OLD_COND_RE, conductor_label):
conductor_label = '.'.join(conductor_label[1:-1].split(','))
return redirect(url_for('.show_ecnf_isoclass',nf=nf,conductor_label=conductor_label,class_label=class_label),301)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "-".join([nf_label, conductor_label, class_label])
full_class_label = "-".join([conductor_label, class_label])
cl = ECNF_isoclass.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not isinstance(cl, ECNF_isoclass):
info = {'query':{}, 'err':'No elliptic curve isogeny class in the database has label %s.' % label}
return search_input_error(info, bread)
title = "Elliptic Curve isogeny class %s over Number Field %s" % (full_class_label, cl.field)
bread.append((cl.field, url_for(".show_ecnf1", nf=nf_label)))
bread.append((conductor_label, url_for(".show_ecnf_conductor", nf=nf_label, conductor_label=conductor_label)))
bread.append((class_label, url_for(".show_ecnf_isoclass", nf=nf_label, conductor_label=quote(conductor_label), class_label=class_label)))
return render_template("ecnf-isoclass.html",
credit=ecnf_credit,
title=title,
bread=bread,
cl=cl,
properties2=cl.properties,
friends=cl.friends,
learnmore=learnmore_list())
def show_ecnf(nf, conductor_label, class_label, number):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(
["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {'query': {}}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (
ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
info = {}
return render_template(
"show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list())
def show_ecnf_isoclass(nf, conductor_label, class_label):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
conductor_label = unquote(conductor_label)
label = "-".join([nf_label, conductor_label, class_label])
full_class_label = "-".join([conductor_label, class_label])
cl = ECNF_isoclass.by_label(label)
title = "Elliptic Curve isogeny class %s over Number Field %s" % (
full_class_label, cl.field)
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((cl.field, url_for(".show_ecnf1", nf=nf_label)))
bread.append((conductor_label,
url_for(".show_ecnf_conductor",
nf=nf_label,
conductor_label=conductor_label)))
bread.append((class_label,
url_for(".show_ecnf_isoclass",
nf=nf_label,
conductor_label=quote(conductor_label),
class_label=class_label)))
info = {}
return render_template("show-ecnf-isoclass.html",
credit=ecnf_credit,
title=title,
bread=bread,
cl=cl,
properties2=cl.properties,
friends=cl.friends,
learnmore=learnmore_list())
def show_ecnf_isoclass(nf, conductor_label, class_label):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "-".join([nf_label, conductor_label, class_label])
full_class_label = "-".join([conductor_label, class_label])
cl = ECNF_isoclass.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not isinstance(cl, ECNF_isoclass):
info = {'query':{}, 'err':'No elliptic curve isogeny class in the database has label %s.' % label}
return search_input_error(info, bread)
title = "Elliptic Curve isogeny class %s over Number Field %s" % (full_class_label, cl.field)
bread.append((cl.field, url_for(".show_ecnf1", nf=nf_label)))
bread.append((conductor_label, url_for(".show_ecnf_conductor", nf=nf_label, conductor_label=conductor_label)))
bread.append((class_label, url_for(".show_ecnf_isoclass", nf=nf_label, conductor_label=quote(conductor_label), class_label=class_label)))
return render_template("ecnf-isoclass.html",
credit=ecnf_credit,
title=title,
bread=bread,
cl=cl,
properties2=cl.properties,
friends=cl.friends,
learnmore=learnmore_list())
def show_ecnf1(nf):
if nf == "1.1.1.1":
return redirect(url_for("ec.rational_elliptic_curves", **request.args))
if request.args:
return elliptic_curve_search(data=request.args)
start = 0
count = 50
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
query = {'field_label': nf_label}
cursor = db_ecnf().find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC),
('conductor_label', ASC), ('iso_nlabel', ASC),
('number', ASC)]).skip(start).limit(count)
bread = [('Elliptic Curves', url_for(".index")),
(nf_label, url_for('.show_ecnf1', nf=nf_label))]
res = list(res)
for e in res:
e['field_knowl'] = nf_display_knowl(e['field_label'],
getDBConnection(),
field_pretty(e['field_label']))
info = {}
info['field'] = nf_label
info['query'] = query
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
#don't risk recomputing all the ecnf stats just to show curves for a single number field
#if nf_label:
#info['stats'] = ecnf_field_summary(nf_label)
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
t = 'Elliptic Curves over %s' % field_pretty(nf_label)
return render_template("ecnf-search-results.html",
info=info,
credit=ecnf_credit,
bread=bread,
title=t,
learnmore=learnmore_list())
def by_label(label):
try:
return render_field_webpage({'label': nf_string_to_label(label)})
except ValueError:
bread = [('Global Number Fields',
url_for(".number_field_render_webpage")),
('Search results', ' ')]
return search_input_error({'err': ''}, bread)
def get_nf_info(lab):
r""" extract number field label from string and pretty"""
try:
label = nf_string_to_label(lab)
pretty = field_pretty (label)
except ValueError as err:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid number field. %s" % (lab,err)), "error")
raise ValueError
return label, pretty
def get_nf_info(lab):
r""" extract number field label from string and pretty"""
try:
label = nf_string_to_label(lab)
pretty = field_pretty (label)
except ValueError as err:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid number field. %s" % (lab,err)), "error")
raise ValueError
return label, pretty
def show_ecnf_conductor(nf, conductor_label):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
return elliptic_curve_search(data={
'nf_label': nf_label,
'conductor_label': quote(conductor_label)
},
**request.args)
def show_ecnf(nf, conductor_label, class_label, number):
conductor_label = unquote(conductor_label)
if re.match(OLD_COND_RE, conductor_label):
conductor_label = '.'.join(conductor_label[1:-1].split(','))
return redirect(
url_for('.show_ecnf',
nf=nf,
conductor_label=conductor_label,
class_label=class_label,
number=number), 301)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(
["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {'query': {}}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (
ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
code = ec.code()
code['show'] = {
'magma': '',
'pari': '',
'sage': ''
} # use default show names
info = {}
return render_template(
"ecnf-curve.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
code=code,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list())
def show_ecnf1(nf):
if nf == "1.1.1.1":
return redirect(url_for("ec.rational_elliptic_curves", **request.args))
if request.args:
return elliptic_curve_search(data=request.args)
start = 0
count = 50
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
query = {'field_label': nf_label}
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count)
bread = [('Elliptic Curves', url_for(".index")),
(nf_label, url_for('.show_ecnf1', nf=nf_label))]
res = list(res)
for e in res:
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), field_pretty(e['field_label']))
info = {}
info['field'] = nf_label
info['query'] = query
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
#don't risk recomputing all the ecnf stats just to show curves for a single number field
#if nf_label:
#info['stats'] = ecnf_field_summary(nf_label)
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
t = 'Elliptic Curves over %s' % field_pretty(nf_label)
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t, learnmore=learnmore_list())
def download_ECNF_all(nf,conductor_label,class_label,number):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
data = db.ec_nfcurves.lookup(label)
if data is None:
return search_input_error()
response = make_response(Json.dumps(data))
response.headers['Content-type'] = 'text/plain'
return response
def download_ECNF_all(nf,conductor_label,class_label,number):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
data = db.ec_nfcurves.lookup(label)
if data is None:
return search_input_error()
response = make_response(Json.dumps(data))
response.headers['Content-type'] = 'text/plain'
return response
def download_ECNF_all(nf,conductor_label,class_label,number):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
data = db_ecnf().find_one({'label':label}, {'_id':False})
if data is None:
return search_input_error()
import json
response = make_response(json.dumps(data))
response.headers['Content-type'] = 'text/plain'
return response
def download_ECNF_all(nf,conductor_label,class_label,number):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
data = db_ecnf().find_one({'label':label}, {'_id':False})
if data is None:
return search_input_error()
import json
response = make_response(json.dumps(data))
response.headers['Content-type'] = 'text/plain'
return response
def ecnf_simple_label_search(search, baseurl, label):
label_bits = label.split('/')
try:
nf = label_bits[0]
conductor_label = label_bits[1]
class_label = label_bits[2]
number = label_bits[3]
except IndexError:
search['query'] = {'label': 'dummy'}
return
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf, conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
search['query'] = {'label': 'dummy'}
return
label = "".join(
["-".join([nf_label, conductor_label, class_label]), number])
search['query'] = {'label': label}
def bmf_field_dim_table(**args):
argsdict = to_dict(args)
argsdict.update(to_dict(request.args))
gl_or_sl = argsdict['gl_or_sl']
field_label = argsdict['field_label']
field_label = nf_string_to_label(field_label)
start = 0
if 'start' in argsdict:
start = int(argsdict['start'])
info = {}
info['gl_or_sl'] = gl_or_sl
# level_flag controls whether to list all levels ('all'), only
# those with positive cuspidal dimension ('cusp'), or only those
# with positive new dimension ('new'). Default is 'cusp'.
level_flag = argsdict.get('level_flag', 'cusp')
info['level_flag'] = level_flag
count = 50
if 'count' in argsdict:
count = int(argsdict['count'])
pretty_field_label = field_pretty(field_label)
bread = [('Bianchi Modular Forms', url_for(".index")),
(pretty_field_label, ' ')]
properties = []
if gl_or_sl == 'gl2_dims':
info['group'] = 'GL(2)'
info['bgroup'] = '\GL(2,\mathcal{O}_K)'
else:
info['group'] = 'SL(2)'
info['bgroup'] = '\SL(2,\mathcal{O}_K)'
t = ' '.join([
'Dimensions of spaces of {} Bianchi modular forms over'.format(
info['group']), pretty_field_label
])
query = {}
query['field_label'] = field_label
query[gl_or_sl] = {'$exists': True}
if level_flag != 'all':
# find which weights are present (TODO: get this from a stats collection)
wts = list(
sum((Set(d.keys()) for d in db_dims().distinct(gl_or_sl)), Set()))
if level_flag == 'cusp':
# restrict the query to only return levels where at least one
# cuspidal dimension is positive:
query.update({
'$or': [{
gl_or_sl + '.{}.cuspidal_dim'.format(w): {
'$gt': 0
}
} for w in wts]
})
if level_flag == 'new':
# restrict the query to only return levels where at least one
# new dimension is positive:
query.update({
'$or': [{
gl_or_sl + '.{}.new_dim'.format(w): {
'$gt': 0
}
} for w in wts]
})
data = db_dims().find(query)
data = data.sort([('level_norm', ASCENDING)])
info['number'] = nres = data.count()
if nres > count or start != 0:
info['report'] = 'Displaying items %s-%s of %s levels,' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'Displaying all %s levels,' % nres
data = list(data.skip(start).limit(count))
info['field'] = field_label
info['field_pretty'] = pretty_field_label
nf = WebNumberField(field_label)
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
weights = set()
for dat in data:
weights = weights.union(set(dat[gl_or_sl].keys()))
weights = list([int(w) for w in weights])
weights.sort()
info['weights'] = weights
info['nweights'] = len(weights)
info['count'] = count
info['start'] = start
info['more'] = int(start + count < nres)
dims = {}
for dat in data:
dims[dat['level_label']] = d = {}
for w in weights:
sw = str(w)
if sw in dat[gl_or_sl]:
d[w] = {
'd': dat[gl_or_sl][sw]['cuspidal_dim'],
'n': dat[gl_or_sl][sw]['new_dim']
}
else:
d[w] = {'d': '?', 'n': '?'}
info['nlevels'] = len(data)
dimtable = [{
'level_label':
dat['level_label'],
'level_norm':
dat['level_norm'],
'level_space':
url_for(".render_bmf_space_webpage",
field_label=field_label,
level_label=dat['level_label'])
if gl_or_sl == 'gl2_dims' else "",
'dims':
dims[dat['level_label']]
} for dat in data]
print("Length of dimtable = {}".format(len(dimtable)))
info['dimtable'] = dimtable
return render_template("bmf-field_dim_table.html",
info=info,
title=t,
properties=properties,
bread=bread)
def bmf_field_dim_table(**args):
argsdict = to_dict(args)
argsdict.update(to_dict(request.args))
gl_or_sl = argsdict['gl_or_sl']
field_label=argsdict['field_label']
field_label = nf_string_to_label(field_label)
start = 0
if 'start' in argsdict:
start = int(argsdict['start'])
info={}
info['gl_or_sl'] = gl_or_sl
# level_flag controls whether to list all levels ('all'), only
# those with positive cuspidal dimension ('cusp'), or only those
# with positive new dimension ('new'). Default is 'cusp'.
level_flag = argsdict.get('level_flag', 'cusp')
info['level_flag'] = level_flag
count = 50
if 'count' in argsdict:
count = int(argsdict['count'])
pretty_field_label = field_pretty(field_label)
bread = [('Bianchi Modular Forms', url_for(".index")), (
pretty_field_label, ' ')]
properties = []
if gl_or_sl=='gl2_dims':
info['group'] = 'GL(2)'
info['bgroup'] = '\GL(2,\mathcal{O}_K)'
else:
info['group'] = 'SL(2)'
info['bgroup'] = '\SL(2,\mathcal{O}_K)'
t = ' '.join(['Dimensions of Spaces of {} Bianchi Modular Forms over'.format(info['group']), pretty_field_label])
query = {}
query['field_label'] = field_label
query[gl_or_sl] = {'$exists': True}
data = db_dims().find(query)
data = data.sort([('level_norm', ASCENDING)])
info['number'] = nres = data.count()
if nres > count or start != 0:
info['report'] = 'Displaying items %s-%s of %s levels,' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'Displaying all %s levels,' % nres
# convert data to a list and eliminate levels where all
# new/cuspidal dimensions are 0. (This could be done at the
# search stage, but that requires adding new fields to each
# record.)
def filter(dat, flag):
dat1 = dat[gl_or_sl]
return any([int(dat1[w][flag])>0 for w in dat1])
flag = 'cuspidal_dim' if level_flag=='cusp' else 'new_dim'
data = [dat for dat in data if level_flag == 'all' or filter(dat, flag)]
data = data[start:start+count]
info['field'] = field_label
info['field_pretty'] = pretty_field_label
nf = WebNumberField(field_label)
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
weights = set()
for dat in data:
weights = weights.union(set(dat[gl_or_sl].keys()))
weights = list([int(w) for w in weights])
weights.sort()
info['weights'] = weights
info['nweights'] = len(weights)
info['count'] = count
info['start'] = start
info['more'] = int(start + count < nres)
data.sort(key = lambda x: [int(y) for y in x['level_label'].split(".")])
dims = {}
for dat in data:
dims[dat['level_label']] = d = {}
for w in weights:
sw = str(w)
if sw in dat[gl_or_sl]:
d[w] = {'d': dat[gl_or_sl][sw]['cuspidal_dim'],
'n': dat[gl_or_sl][sw]['new_dim']}
else:
d[w] = {'d': '?', 'n': '?'}
info['nlevels'] = len(data)
dimtable = [{'level_label': dat['level_label'],
'level_norm': dat['level_norm'],
'level_space': url_for(".render_bmf_space_webpage", field_label=field_label, level_label=dat['level_label']) if gl_or_sl=='gl2_dims' else "",
'dims': dims[dat['level_label']]} for dat in data]
info['dimtable'] = dimtable
return render_template("bmf-field_dim_table.html", info=info, title=t, properties=properties, bread=bread)
def by_label(label):
try:
return render_field_webpage({'label': nf_string_to_label(label)})
except ValueError:
bread = [('Global Number Fields', url_for(".number_field_render_webpage")), ('Search results', ' ')]
return search_input_error({'err':''}, bread)
def bmf_field_dim_table(**args):
argsdict = to_dict(args)
argsdict.update(to_dict(request.args))
gl_or_sl = argsdict['gl_or_sl']
field_label=argsdict['field_label']
field_label = nf_string_to_label(field_label)
start = 0
if 'start' in argsdict:
start = int(argsdict['start'])
info={}
info['gl_or_sl'] = gl_or_sl
# level_flag controls whether to list all levels ('all'), only
# those with positive cuspidal dimension ('cusp'), or only those
# with positive new dimension ('new'). Default is 'cusp'.
level_flag = argsdict.get('level_flag', 'cusp')
info['level_flag'] = level_flag
count = 50
if 'count' in argsdict:
count = int(argsdict['count'])
pretty_field_label = field_pretty(field_label)
bread = [('Bianchi Modular Forms', url_for(".index")), (
pretty_field_label, ' ')]
properties = []
if gl_or_sl=='gl2_dims':
info['group'] = 'GL(2)'
info['bgroup'] = '\GL(2,\mathcal{O}_K)'
else:
info['group'] = 'SL(2)'
info['bgroup'] = '\SL(2,\mathcal{O}_K)'
t = ' '.join(['Dimensions of spaces of {} Bianchi modular forms over'.format(info['group']), pretty_field_label])
query = {}
query['field_label'] = field_label
query[gl_or_sl] = {'$exists': True}
if level_flag != 'all':
# find which weights are present (TODO: get this from a stats collection)
wts = list(sum((Set(d.keys()) for d in db_dims().distinct(gl_or_sl)),Set()))
if level_flag == 'cusp':
# restrict the query to only return levels where at least one
# cuspidal dimension is positive:
query.update(
{'$or':[{gl_or_sl+'.{}.cuspidal_dim'.format(w):{'$gt':0}} for w in wts]}
)
if level_flag == 'new':
# restrict the query to only return levels where at least one
# new dimension is positive:
query.update(
{'$or':[{gl_or_sl+'.{}.new_dim'.format(w):{'$gt':0}} for w in wts]}
)
data = db_dims().find(query)
data = data.sort([('level_norm', ASCENDING)])
info['number'] = nres = data.count()
if nres > count or start != 0:
info['report'] = 'Displaying items %s-%s of %s levels,' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'Displaying all %s levels,' % nres
data = list(data.skip(start).limit(count))
info['field'] = field_label
info['field_pretty'] = pretty_field_label
nf = WebNumberField(field_label)
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
weights = set()
for dat in data:
weights = weights.union(set(dat[gl_or_sl].keys()))
weights = list([int(w) for w in weights])
weights.sort()
info['weights'] = weights
info['nweights'] = len(weights)
info['count'] = count
info['start'] = start
info['more'] = int(start + count < nres)
dims = {}
for dat in data:
dims[dat['level_label']] = d = {}
for w in weights:
sw = str(w)
if sw in dat[gl_or_sl]:
d[w] = {'d': dat[gl_or_sl][sw]['cuspidal_dim'],
'n': dat[gl_or_sl][sw]['new_dim']}
else:
d[w] = {'d': '?', 'n': '?'}
info['nlevels'] = len(data)
dimtable = [{'level_label': dat['level_label'],
'level_norm': dat['level_norm'],
'level_space': url_for(".render_bmf_space_webpage", field_label=field_label, level_label=dat['level_label']) if gl_or_sl=='gl2_dims' else "",
'dims': dims[dat['level_label']]} for dat in data]
print("Length of dimtable = {}".format(len(dimtable)))
info['dimtable'] = dimtable
return render_template("bmf-field_dim_table.html", info=info, title=t, properties=properties, bread=bread)
def show_ecnf_conductor(nf, conductor_label):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
return elliptic_curve_search(data={'nf_label': nf_label, 'conductor_label': quote(conductor_label)}, **request.args)
def by_label(label):
try:
return render_field_webpage({"label": nf_string_to_label(label)})
except ValueError:
bread = [("Global Number Fields", url_for(".number_field_render_webpage")), ("Search results", " ")]
return search_input_error({"err": ""}, bread)
def bmf_field_dim_table(**args):
argsdict = to_dict(args)
argsdict.update(to_dict(request.args))
gl_or_sl = argsdict['gl_or_sl']
field_label=argsdict['field_label']
field_label = nf_string_to_label(field_label)
start = 0
if 'start' in argsdict:
start = int(argsdict['start'])
info={}
info['gl_or_sl'] = gl_or_sl
# level_flag controls whether to list all levels ('all'), only
# those with positive cuspidal dimension ('cusp'), or only those
# with positive new dimension ('new'). Default is 'cusp'.
level_flag = argsdict.get('level_flag', 'cusp')
info['level_flag'] = level_flag
count = 50
if 'count' in argsdict:
count = int(argsdict['count'])
pretty_field_label = field_pretty(field_label)
bread = [('Bianchi Modular Forms', url_for(".index")), (
pretty_field_label, ' ')]
properties = []
if gl_or_sl=='gl2_dims':
info['group'] = 'GL(2)'
info['bgroup'] = '\GL(2,\mathcal{O}_K)'
else:
info['group'] = 'SL(2)'
info['bgroup'] = '\SL(2,\mathcal{O}_K)'
t = ' '.join(['Dimensions of spaces of {} Bianchi modular forms over'.format(info['group']), pretty_field_label])
query = {}
query['field_label'] = field_label
query[gl_or_sl] = {'$exists': True}
data = db_dims().find(query)
data = data.sort([('level_norm', ASCENDING)])
info['number'] = nres = data.count()
if nres > count or start != 0:
info['report'] = 'Displaying items %s-%s of %s levels,' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'Displaying all %s levels,' % nres
# convert data to a list and eliminate levels where all
# new/cuspidal dimensions are 0. (This could be done at the
# search stage, but that requires adding new fields to each
# record.)
def filter(dat, flag):
dat1 = dat[gl_or_sl]
return any([int(dat1[w][flag])>0 for w in dat1])
flag = 'cuspidal_dim' if level_flag=='cusp' else 'new_dim'
data = [dat for dat in data if level_flag == 'all' or filter(dat, flag)]
data = data[start:start+count]
info['field'] = field_label
info['field_pretty'] = pretty_field_label
nf = WebNumberField(field_label)
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
weights = set()
for dat in data:
weights = weights.union(set(dat[gl_or_sl].keys()))
weights = list([int(w) for w in weights])
weights.sort()
info['weights'] = weights
info['nweights'] = len(weights)
info['count'] = count
info['start'] = start
info['more'] = int(start + count < nres)
data.sort(key = lambda x: [int(y) for y in x['level_label'].split(".")])
dims = {}
for dat in data:
dims[dat['level_label']] = d = {}
for w in weights:
sw = str(w)
if sw in dat[gl_or_sl]:
d[w] = {'d': dat[gl_or_sl][sw]['cuspidal_dim'],
'n': dat[gl_or_sl][sw]['new_dim']}
else:
d[w] = {'d': '?', 'n': '?'}
info['nlevels'] = len(data)
dimtable = [{'level_label': dat['level_label'],
'level_norm': dat['level_norm'],
'level_space': url_for(".render_bmf_space_webpage", field_label=field_label, level_label=dat['level_label']) if gl_or_sl=='gl2_dims' else "",
'dims': dims[dat['level_label']]} for dat in data]
info['dimtable'] = dimtable
return render_template("bmf-field_dim_table.html", info=info, title=t, properties=properties, bread=bread)
