本文整理汇总了Python中lmfdb.WebNumberField.WebNumberField.poly方法的典型用法代码示例。如果您正苦于以下问题：Python WebNumberField.poly方法的具体用法？Python WebNumberField.poly怎么用？Python WebNumberField.poly使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类lmfdb.WebNumberField.WebNumberField的用法示例。
在下文中一共展示了WebNumberField.poly方法的9个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: render_hmf_webpage
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
def render_hmf_webpage(**args):
C = getDBConnection()
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such form"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
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()))
info.update(data)
info['downloads'] = [
('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
if hmf_field['narrow_class_no'] == 1 and nf.disc()**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]
bread = [('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")), ('%s' % data[
'label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = C.hmfs.forms.search.find(
{'field_label': data['field_label'], 'level_ideal': data['level_ideal']},{'dimension':True})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])
if 'AL_eigenvalues_fixed' in data:
if data['AL_eigenvalues_fixed'] == 'done':
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
info['AL_eigs_count'] = len(info['AL_eigs']) != 0
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len<=300)
#.........这里部分代码省略.........
示例2: render_field_webpage
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
def render_field_webpage(args):
data = None
C = base.getDBConnection()
info = {}
bread = [('Global Number Fields', url_for(".number_field_render_webpage"))]
# This function should not be called unless label is set.
label = clean_input(args['label'])
nf = WebNumberField(label)
data = {}
if nf.is_null():
bread.append(('Search results', ' '))
info['err'] = 'There is no field with label %s in the database' % label
info['label'] = args['label_orig'] if 'label_orig' in args else args['label']
return search_input_error(info, bread)
info['wnf'] = nf
data['degree'] = nf.degree()
data['class_number'] = nf.class_number()
t = nf.galois_t()
n = nf.degree()
data['is_galois'] = nf.is_galois()
data['is_abelian'] = nf.is_abelian()
if nf.is_abelian():
conductor = nf.conductor()
data['conductor'] = conductor
dirichlet_chars = nf.dirichlet_group()
if len(dirichlet_chars)>0:
data['dirichlet_group'] = ['<a href = "%s">$\chi_{%s}(%s,·)$</a>' % (url_for('characters.render_Dirichletwebpage',modulus=data['conductor'], number=j), data['conductor'], j) for j in dirichlet_chars]
data['dirichlet_group'] = r'$\lbrace$' + ', '.join(data['dirichlet_group']) + r'$\rbrace$'
if data['conductor'].is_prime() or data['conductor'] == 1:
data['conductor'] = "\(%s\)" % str(data['conductor'])
else:
data['conductor'] = "\(%s=%s\)" % (str(data['conductor']), latex(data['conductor'].factor()))
data['galois_group'] = group_display_knowl(n, t, C)
data['cclasses'] = cclasses_display_knowl(n, t, C)
data['character_table'] = character_table_display_knowl(n, t, C)
data['class_group'] = nf.class_group()
data['class_group_invs'] = nf.class_group_invariants()
data['signature'] = nf.signature()
data['coefficients'] = nf.coeffs()
nf.make_code_snippets()
D = nf.disc()
ram_primes = D.prime_factors()
data['disc_factor'] = nf.disc_factored_latex()
if D.abs().is_prime() or D == 1:
data['discriminant'] = "\(%s\)" % str(D)
else:
data['discriminant'] = "\(%s=%s\)" % (str(D), data['disc_factor'])
npr = len(ram_primes)
ram_primes = str(ram_primes)[1:-1]
if ram_primes == '':
ram_primes = r'\textrm{None}'
data['frob_data'], data['seeram'] = frobs(nf)
data['phrase'] = group_phrase(n, t, C)
zk = nf.zk()
Ra = PolynomialRing(QQ, 'a')
zk = [latex(Ra(x)) for x in zk]
zk = ['$%s$' % x for x in zk]
zk = ', '.join(zk)
grh_label = '<small>(<a title="assuming GRH" knowl="nf.assuming_grh">assuming GRH</a>)</small>' if nf.used_grh() else ''
# Short version for properties
grh_lab = nf.short_grh_string()
if 'Not' in str(data['class_number']):
grh_lab=''
grh_label=''
pretty_label = field_pretty(label)
if label != pretty_label:
pretty_label = "%s: %s" % (label, pretty_label)
info.update(data)
if nf.degree() > 1:
gpK = nf.gpK()
rootof1coeff = gpK.nfrootsof1()[2]
rootofunity = Ra(str(pari("lift(%s)" % gpK.nfbasistoalg(rootof1coeff))).replace('x','a'))
else:
rootofunity = Ra('-1')
info.update({
'label': pretty_label,
'label_raw': label,
'polynomial': web_latex_split_on_pm(nf.poly()),
'ram_primes': ram_primes,
'integral_basis': zk,
'regulator': web_latex(nf.regulator()),
'unit_rank': nf.unit_rank(),
'root_of_unity': web_latex(rootofunity),
'fund_units': nf.units(),
'grh_label': grh_label
})
bread.append(('%s' % info['label_raw'], ' '))
info['downloads_visible'] = True
info['downloads'] = [('worksheet', '/')]
info['friends'] = []
if nf.can_class_number():
# hide ones that take a lond time to compute on the fly
# note that the first degree 4 number field missed the zero of the zeta function
if abs(D**n) < 50000000:
info['friends'].append(('L-function', "/L/NumberField/%s" % label))
#.........这里部分代码省略.........
示例3: FIELD
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
def FIELD(label):
nf = WebNumberField(label, gen_name=special_names.get(label, 'a'))
nf.parse_NFelt = lambda s: nf.K()([QQ(c.encode()) for c in s.split(",")])
nf.latex_poly = web_latex(nf.poly())
return nf示例4: render_field_webpage
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
#.........这里部分代码省略.........
ram_primes = str(ram_primes)[1:-1]
if ram_primes == '':
ram_primes = r'\textrm{None}'
data['phrase'] = group_phrase(n, t)
zk = nf.zk()
Ra = PolynomialRing(QQ, 'a')
zk = [latex(Ra(x)) for x in zk]
zk = ['$%s$' % x for x in zk]
zk = ', '.join(zk)
grh_label = '<small>(<a title="assuming GRH" knowl="nf.assuming_grh">assuming GRH</a>)</small>' if nf.used_grh() else ''
# Short version for properties
grh_lab = nf.short_grh_string()
if 'Not' in str(data['class_number']):
grh_lab=''
grh_label=''
pretty_label = field_pretty(label)
if label != pretty_label:
pretty_label = "%s: %s" % (label, pretty_label)
info.update(data)
if nf.degree() > 1:
gpK = nf.gpK()
rootof1coeff = gpK.nfrootsof1()
rootofunityorder = int(rootof1coeff[1])
rootof1coeff = rootof1coeff[2]
rootofunity = web_latex(Ra(str(pari("lift(%s)" % gpK.nfbasistoalg(rootof1coeff))).replace('x','a')))
rootofunity += ' (order $%d$)' % rootofunityorder
else:
rootofunity = web_latex(Ra('-1'))+ ' (order $2$)'
info.update({
'label': pretty_label,
'label_raw': label,
'polynomial': web_latex_split_on_pm(nf.poly()),
'ram_primes': ram_primes,
'integral_basis': zk,
'regulator': web_latex(nf.regulator()),
'unit_rank': nf.unit_rank(),
'root_of_unity': rootofunity,
'fund_units': nf.units(),
'grh_label': grh_label,
'loc_alg': loc_alg
})
bread.append(('%s' % info['label_raw'], ' '))
info['downloads_visible'] = True
info['downloads'] = [('worksheet', '/')]
info['friends'] = []
if nf.can_class_number():
# hide ones that take a lond time to compute on the fly
# note that the first degree 4 number field missed the zero of the zeta function
if abs(D**n) < 50000000:
info['friends'].append(('L-function', "/L/NumberField/%s" % label))
info['friends'].append(('Galois group', "/GaloisGroup/%dT%d" % (n, t)))
if 'dirichlet_group' in info:
info['friends'].append(('Dirichlet character group', url_for("characters.dirichlet_group_table",
modulus=int(conductor),
char_number_list=','.join(
[str(a) for a in dirichlet_chars]),
poly=info['polynomial'])))
resinfo=[]
galois_closure = nf.galois_closure()
if galois_closure[0]>0:
if len(galois_closure[1])>0:
resinfo.append(('gc', galois_closure[1]))
if len(galois_closure[2]) > 0:示例5: bmf_field_dim_table
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
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)示例6: FIELD
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
def FIELD(label):
nf = WebNumberField(label, gen_name=special_names.get(label, "a"))
nf.parse_NFelt = lambda s: nf.K()([QQ(str(c)) for c in s])
nf.latex_poly = web_latex(nf.poly())
return nf示例7: render_hmf_webpage
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
def render_hmf_webpage(**args):
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = get_hmf(label)
if data is None:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a" % args['label']), "error")
return search_input_error()
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
hmf_field = get_hmf_field(data['field_label'])
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
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()))
info.update(data)
info['downloads'] = [
('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
if hmf_field['narrow_class_no'] == 1 and nf.disc()**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]
bread = [("Modular Forms", url_for('mf.modular_form_main_page')), ('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = db_forms().find(
{'field_label': data['field_label'], 'level_ideal': data['level_ideal']},{'dimension':True})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
# Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
info['numeigs'] = numeigs
hecke_pol = data['hecke_polynomial']
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
AL_eigs = data['AL_eigenvalues']
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': add_space_if_positive(teXify_pol(eigs[i])),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = web_latex_split_on_pm(teXify_pol(hecke_pol))
if not AL_eigs: # empty list
if data['level_norm']==1: # OK, no bad primes
info['AL_eigs'] = 'none'
else: # not OK, AL eigs are missing
info['AL_eigs'] = 'missing'
else:
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
#.........这里部分代码省略.........
示例8: render_bmf_space_webpage
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
def render_bmf_space_webpage(field_label, level_label):
info = {}
t = "Bianchi modular forms of level %s over %s" % (level_label, field_label)
credit = bianchi_credit
bread = [('Bianchi modular forms', url_for(".index")),
(field_pretty(field_label), url_for(".render_bmf_field_dim_table_gl2", field_label=field_label)),
(level_label, '')]
friends = []
properties2 = []
if not field_label_regex.match(field_label):
info['err'] = "%s is not a valid label for an imaginary quadratic field" % field_label
else:
pretty_field_label = field_pretty(field_label)
if not db_dims().find({'field_label': field_label}):
info['err'] = "no dimension information exists in the database for field %s" % pretty_field_label
else:
t = "Bianchi Modular Forms of level %s over %s" % (level_label, pretty_field_label)
data = db_dims().find({'field_label': field_label, 'level_label': level_label})
nres = data.count()
if nres==0:
info['err'] = "no dimension information exists in the database for level %s and field %s" % (level_label, pretty_field_label)
else:
data = data.next()
info['label'] = data['label']
nf = WebNumberField(field_label)
info['base_galois_group'] = nf.galois_string()
info['field_label'] = field_label
info['pretty_field_label'] = pretty_field_label
info['level_label'] = level_label
info['level_norm'] = data['level_norm']
info['field_degree'] = nf.degree()
info['field_classno'] = nf.class_number()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info['field_knowl'] = nf_display_knowl(field_label, getDBConnection(), pretty_field_label)
w = 'i' if nf.disc()==-4 else 'a'
L = nf.K().change_names(w)
alpha = L.gen()
info['field_gen'] = latex(alpha)
I = ideal_from_label(L,level_label)
info['level_gen'] = latex(I.gens_reduced()[0])
info['level_fact'] = latex(I.factor())
dim_data = data['gl2_dims']
weights = dim_data.keys()
weights.sort(key=lambda w: int(w))
for w in weights:
dim_data[w]['dim']=dim_data[w]['cuspidal_dim']
info['dim_data'] = dim_data
info['weights'] = weights
info['nweights'] = len(weights)
newdim = data['gl2_dims']['2']['new_dim']
newforms = db_forms().find({'field_label':field_label, 'level_label':level_label}).sort('label_suffix', ASCENDING)
info['nfdata'] = [{
'label': f['short_label'],
'url': url_for(".render_bmf_webpage",field_label=f['field_label'], level_label=f['level_label'], label_suffix=f['label_suffix']),
'wt': f['weight'],
'dim': f['dimension'],
'sfe': "+1" if f['sfe']==1 else "-1",
'bc': bc_info(f['bc']),
'cm': cm_info(f['CM']),
} for f in newforms]
info['nnewforms'] = len(info['nfdata'])
properties2 = [('Base field', pretty_field_label), ('Level',info['level_label']), ('Norm',str(info['level_norm'])), ('New dimension',str(newdim))]
friends = [('Newform {}'.format(f['label']), f['url']) for f in info['nfdata'] ]
return render_template("bmf-space.html", info=info, credit=credit, title=t, bread=bread, properties2=properties2, friends=friends)示例9: bmf_field_dim_table
# 需要导入模块: from lmfdb.WebNumberField import WebNumberField [as 别名]
# 或者: from lmfdb.WebNumberField.WebNumberField import poly [as 别名]
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)