def render_maass_waveforms(level=0, weight=-1, character=-1, r1=0, r2=0, **kwds):
info = get_args_mwf(level=level, weight=weight, character=character, r1=r1, r2=r2, **kwds)
info["credit"] = ""
info["learnmore"] = learnmore_list()
mwf_logger.debug("args=%s" % request.args)
mwf_logger.debug("method=%s" % request.method)
mwf_logger.debug("req.form=%s" % request.form)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("level,weight,char={0},{1},{2}".format(level, weight, character))
if info.get('maass_id', None) and info.get('db', None):
return render_one_maass_waveform_wp(**info)
if info['search'] or (info['browse'] and int(info['weight']) != 0):
search = get_search_parameters(info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
if info['browse']:
mwf_logger.debug("browse info=%s" % info)
return render_browse_all_eigenvalues(**info)
info['cur_character'] = character
if level > 0:
info['maass_weight'] = maass_db.weights(int(level))
info['cur_level'] = level
if weight > -1:
info['cur_weight'] = weight
if level > 0:
info['maass_character'] = maass_db.characters(int(level), float(weight))
if character > - 1:
info['cur_character'] = character
if level > 0 or weight > -1 or character > -1:
search = get_search_parameters(info)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
title = 'Maass Forms'
info['list_of_levels'] = maass_db.levels()
if info['list_of_levels']:
info['max_level'] = max(info['list_of_levels'])
else:
info['max_level'] = 0
mwf_logger.debug("info3=%s" % info)
bread = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Forms', url_for('.render_maass_waveforms'))]
info['bread'] = bread
info['title'] = title
maass_db.set_table()
maass_db.table['ncols'] = 10
info['DB'] = maass_db
info['dbcount'] = maass_db.count()
info['limit'] = maxNumberOfResultsToShow
return render_template("mwf_navigate.html", **info)
def __init__(self, skip=[0, 0], limit=[6, 10], keys=['Level', 'Eigenvalue'], weight=0):
r"""
Skip tells you how many chunks of data you want to skip (from the beginning) and limit tells you how large each chunk is.
"""
self.keys = keys
if not isinstance(skip, list):
self.skip = [skip, skip]
if not isinstance(limit, list):
self.limit = [limit, limit]
mwf_logger.debug("count={0}".format(maass_db.count()))
self.title = ''
self.table = []
self.wt = weight
self.paging = []
def __init__(self, skip=[0, 0], limit=[6, 10], keys=['Level', 'Eigenvalue'], weight=0):
r"""
Skip tells you how many chunks of data you want to skip (from the beginning) and limit tells you how large each chunk is.
"""
self.keys = keys
if not isinstance(skip, list):
self.skip = [skip, skip]
if not isinstance(limit, list):
self.limit = [limit, limit]
mwf_logger.debug("count={0}".format(maass_db.count()))
self.title = ''
self.table = []
self.wt = weight
self.paging = []
def render_maass_waveforms(level=0,
weight=-1,
character=-1,
r1=0,
r2=0,
**kwds):
info = get_args_mwf(level=level,
weight=weight,
character=character,
r1=r1,
r2=r2,
**kwds)
info[
"credit"] = u"Data computed by Stefan Lemurell and Fredrik Str\u00f6mberg."
info["bread"] = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Forms', url_for('.render_maass_waveforms'))]
info["learnmore"] = learnmore_list()
mwf_logger.debug("args=%s" % request.args)
mwf_logger.debug("method=%s" % request.method)
mwf_logger.debug("req.form=%s" % request.form)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("level,weight,char={0},{1},{2}".format(
level, weight, character))
if info.get('maass_id', None) and info.get('db', None):
return render_one_maass_waveform_wp(**info)
if info['search'] or (info['browse'] and int(info['weight']) != 0):
# This isn't the right place to do input validation, but it is easier to flash errors here (this is a hack to address issue #1820)
if info.get('level_range'):
if not re.match(POSINT_RE, info['level_range']):
if "-" in info['level_range']:
info['level_range'] = "..".join(
info['level_range'].split("-"))
if not re.match(POSINT_RANGE_RE, info['level_range']):
flash_error(
"%s is not a level, please specify a positive integer <span style='color:black'>n</span> or postivie integer range <span style='color:black'>m..n</span>.",
info['level_range'])
return render_template('mwf_navigate.html', **info)
if info['character'] != -1:
if info['character'] == '1' or info['character'] == '1.1':
info['character'] = '1'
else:
try:
N = int(info.get('level_range', '0'))
except:
flash_error(
"Only the trivial character can be specified in combination with a range of levels.",
info['character'])
return render_template('mwf_navigate.html', **info)
if re.match(POSINT_RE, info['character']):
if N == 0:
flash_error(
"Character %s is ambiguous. Please either specify a level or use a character label of the form <span style='color:black'>q.n</span>, where q specifies the level.",
info['character'])
return render_template('mwf_navigate.html', **info)
n = int(info['character'])
if gcd(N, n) != 1:
flash_error(
"Character %s is not coprime to the level %s.",
info['character'], str(N))
return render_template('mwf_navigate.html', **info)
else:
if not re.match(r'^[1-9][0-9]*\.[1-9][0-9]*$',
info['character']):
flash_error(
"%s is not a valid label for a Dirichlet character. It should be either be 1 (for the trivial character) or of the form <span style='color:black'>q.n</span>, where q and n are coprime positive integers with n < q, or q=n=1.",
info['character'])
return render_template('mwf_navigate.html', **info)
s = info['character'].split('.')
q, n = int(s[0]), int(s[1])
if n > q or gcd(q, n) != 1:
flash_error(
"%s is not a valid label for a Dirichlet character. It should be of the form <span style='color:black'>q.n</span>, where q and n are coprime positive integers with n < q, or q=n=1.",
info['character'])
return render_template('mwf_navigate.html', **info)
if N > 0 and q != N:
flash_error(
"The specified character %s is not compatible with the level %s.",
info['character'], info['level'])
return render_template('mwf_navigate.html', **info)
info['level_range'] = str(q)
info['character'] = str(n)
if info['weight'] != -1:
if not re.match(INT_RE, info['weight']):
flash_error(
"%s is not a valid weight. It should be a nonnegative integer.",
info['weight'])
return render_template('mwf_navigate.html', **info)
if info.get('ev_range'):
if not re.match(FLOAT_RE, info['ev_range']):
if "-" in info['ev_range']:
info['ev_range'] = "..".join(info['ev_range'].split("-"))
s = info['ev_range'].split("..")
if len(s) != 2:
flash_error(
"%s is not a valid eigenvalue range. It should be postive real interval.",
info['ev_range'])
return render_template('mwf_navigate.html', **info)
if not re.match(FLOAT_RE, s[0]) or not re.match(
FLOAT_RE, s[1]):
flash_error(
"%s is not a valid eigenvalue range. It should be postive real interval.",
info['ev_range'])
return render_template('mwf_navigate.html', **info)
search = get_search_parameters(info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
if info['browse']:
mwf_logger.debug("browse info=%s" % info)
return render_browse_all_eigenvalues(**info)
info['cur_character'] = character
if level > 0:
info['maass_weight'] = maass_db.weights(int(level))
info['cur_level'] = level
if weight > -1:
info['cur_weight'] = weight
if level > 0:
info['maass_character'] = maass_db.characters(
int(level), float(weight))
if character > -1:
info['cur_character'] = character
if level > 0 or weight > -1 or character > -1:
search = get_search_parameters(info)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
title = 'Maass Forms'
info['list_of_levels'] = maass_db.levels()
if info['list_of_levels']:
info['max_level'] = max(info['list_of_levels'])
else:
info['max_level'] = 0
mwf_logger.debug("info3=%s" % info)
bread = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Forms', url_for('.render_maass_waveforms'))]
info['bread'] = bread
info['title'] = title
maass_db.set_table()
maass_db.table['ncols'] = 10
info['DB'] = maass_db
info['dbcount'] = maass_db.count()
info['limit'] = maxNumberOfResultsToShow
return render_template("mwf_navigate.html", **info)
def evs_table2(search, twodarray=False, limit=50, offset=0):
r"""
Returns an object containing the results of a search for Maass forms.
"""
table = []
nrows = 0
fs = maass_db.get_Maass_forms(search, limit=limit, offset=offset)
mwf_logger.debug("numrec:{0}".format(len(fs)))
for f in fs: # indices:
row = {}
R = f.get('Eigenvalue', None)
N = f.get('Level', None)
k = f.get('Weight', None)
if R is None or N is None or k is None:
continue
row['R'] = R
row['N'] = N
if k == 0 or k == 1:
row['k'] = int(k)
else:
row['k'] = k
##
chi = f.get('Character', 0)
## Now get the COnrey number.
## First the character
if k == 0:
url = url_for('characters.render_Dirichletwebpage',
modulus=N,
number=chi)
s = "<a href={0}>{1}</a>".format(url, chi)
row['ch'] = s
else:
row['ch'] = "eta"
st = f.get('Symmetry', -1)
if st == 1:
st = "odd"
elif st == 0:
st = "even"
else:
st = "n/a"
row['symmetry'] = st
er = f.get('Error', 0)
if er > 0:
er = "{0:1.0e}".format(float(er))
else:
er = "unknown"
row['err'] = er
dim = f.get('Dim', 0)
if dim is None:
dim = 1 # "undefined"
row['dim'] = dim
numc = f.get('Numc', 0)
row['numc'] = numc
cev = f.get('Cusp_evs', [])
row['fricke'] = 'n/a'
row['cuspevs'] = 'n/a'
if row['k'] == 0 and isinstance(cev, list):
if len(cev) > 1:
fricke = cev[1]
row['fricke'] = fricke
s = '{0}'.format(cev[0])
for j in range(1, len(cev)):
s += ",{0}".format(cev[j])
elif len(cev) == 1:
s = str(cev[0])
elif len(cev) == 0:
s = 'n/a'
row['cuspevs'] = s
url = url_for('mwf.render_one_maass_waveform',
maass_id=f.get('maass_id'))
row['url'] = url
nrows += 1
if twodarray:
s = '<a href="{0}">{1}</a>'.format(row['url'], row['R'])
rowr = [
row['N'], row['k'], row['ch'], s, row['symmetry'], row['err'],
row['dim'], row['numc'], row['fricke'], row['cuspevs']
]
table.append(rowr)
else:
# row=row.values()
table.append(row)
mwf_logger.debug("nrows:".format(nrows))
evs = {'table': {}}
evs['table']['data'] = table
evs['table']['nrows'] = nrows
evs['table']['ncols'] = 10
evs['table']['colheads'] = []
knowls = [
'mf.maass.mwf.level', 'mf.maass.mwf.weight', 'mf.maass.mwf.character',
'mf.maass.mwf.eigenvalue', 'mf.maass.mwf.symmetry',
'mf.maass.mwf.precision', 'mf.maass.mwf.dimension',
'mf.maass.mwf.ncoefficients', 'cmf.fricke', 'cmf.atkin-lehner'
]
titles = [
'Level', 'Weight', 'Char', 'Eigenvalue', 'Symmetry', 'Precision',
'Mult.', 'Coeff.', 'Fricke', 'Atkin-Lehner'
]
for i in range(10):
evs['table']['colheads'].append((knowls[i], titles[i]))
if 'limit' in search:
search.pop('limit')
if 'skip' in search:
search.pop('skip')
evs['totalrecords'] = maass_db.count(search)
evs['totalrecords_filtered'] = len(fs)
return evs
def render_one_maass_waveform_wp(info, prec=9):
r"""
Render the webpage of one Maass waveform.
The precision kwarg `prec` is passed to the coefficient table, and
indicates to round to 0 when the difference is less than 1e-`prec`.
"""
info["check"] = []
maass_id = info['maass_id']
mwf_logger.debug("id1={0}".format(maass_id))
try:
MF = WebMaassForm(maass_id)
except KeyError:
return flask.abort(404)
info['MF'] = MF
info['title'] = "Maass Form"
info['bread'] = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Forms', url_for('.render_maass_waveforms'))]
if hasattr(MF, 'level'):
info['bread'].append(('Level {0}'.format(MF.level),
url_for('.render_maass_waveforms',
level=MF.level)))
info['title'] += r" on \(\Gamma_{0}( %s )\)" % info['MF'].level
if hasattr(MF, 'R') and MF.R:
info['title'] += r" with \(R=%s\)" % info['MF'].R
# make sure all the expected attributes of a WebMaassForm are actually present
missing = [
attr for attr in ['level', 'dim', 'num_coeff', 'R', 'character']
if not hasattr(MF, attr)
]
if missing:
mwf_logger.critical(
"Unable to render Maass form {0}; required attributes {1} missing from database record."
.format(maass_id, missing))
info['explain'] = "Unable to render Maass form {0} because the following required attributes were missing from the database record:".format(maass_id) \
+ "<ul>" + "".join(["<li>"+attr+"</li>" for attr in missing]) + "</ul>"
return render_template("problem.html", **info)
level = info['MF'].level
dim = info['MF'].dim
# numc = info['MF'].num_coeff # never used
# if info['MF'].has_plot(): # and level == 1: # Bara level = 1 har rätt format för tillfället //Lemurell
# info['plotlink'] = url_for('mwf.plot_maassform', maass_id=maass_id)
# Create the link to the L-function (put in '/L' at the beginning and '/' before '?'
Llink = "/L" + url_for('mwf.render_one_maass_waveform',
maass_id=maass_id) # + '/?db=' + info['db']
if dim == 1:
info["friends"] = [("L-function", Llink)]
# Navigation to previous and next form
# next_form_id = info['MF'].next_maassform_id()
# if next_form_id:
# next_data = ('next', r"$f_{\text next}$", url_for('mwf.render_one_maass_waveform', maass_id = next_form_id) )
# else:
# next_data = ('','','')
# prev_form_id = info['MF'].prev_maassform_id()
# if prev_form_id:
# prev_data = ('previous', r"$f_{\text prev}$", url_for('mwf.render_one_maass_waveform', maass_id = prev_form_id) )
# else:
# prev_data = ('','','')
# info['navi'] = ( prev_data, next_data )
info["downloads"] = [('All stored data of the form',
url_for('mwf.render_one_maass_waveform',
maass_id=maass_id,
download='all')),
('All coefficients of the form',
url_for('mwf.render_one_maass_waveform',
maass_id=maass_id,
download='coefficients'))]
mwf_logger.debug("count={0}".format(maass_db.count()))
ch = info['MF'].character
s = r"\( \chi_{" + str(level) + "}(" + str(ch) + r",\cdot) \)"
# Q: Is it possible to get the knowls into the properties?
# A: Not in a nice way and this is not done elsewhere in the LMFDB; the knowls should appear on labels in the template
# knowls = {'level': 'mf.maass.mwf.level',
# 'weight': 'mf.maass.mwf.weight',
# 'char': 'mf.maass.mwf.character',
# 'R': 'mf.maass.mwf.eigenvalue',
# 'sym': 'mf.maass.mwf.symmetry',
# 'prec': 'mf.maass.mwf.precision',
# 'mult': 'mf.maass.mwf.dimension',
# 'ncoeff': 'mf.maass.mwf.ncoefficients',
# 'fricke': 'cmf.fricke',
# 'atkinlehner': 'cmf.atkin-lehner'}
properties = [
('Level', [info['MF'].level]),
('Symmetry', [info['MF'].even_odd()]),
('Weight', [info['MF'].the_weight()]),
('Character', [s]),
('Multiplicity', [dim]),
('Precision', [info['MF'].precision()]),
('Fricke Eigenvalue', [info['MF'].fricke()]),
('Atkin-Lehner Eigenvalues', [info['MF'].atkinlehner()]),
]
if dim > 1 and info['MF'].the_character() == "trivial":
properties.append(("Possibly oldform", []))
info['properties'] = properties
# The precision in set_table indicates which coefficients to set to zero.
# For instance, if the imaginary part is less than the precision in
# absolute value, then it is set to 0 in set_table.
# The value 1e-9 is chosen arbitrarily, as recommended in issue #2076.
info['MF'].set_table(prec=prec)
cols = [{
"aaSorting": "asc",
"sWidth": "10%",
"bSortable": "true",
"bSearchable": "false",
"sType": "numeric"
}]
negc = info['MF'].table.get('negc', 0)
for j in range(dim):
if not negc:
col = {
"bSortable": "false",
"bSearchable": "true",
"sClass": "alignLeft",
"fnRender": "text-align:left",
"sType": "numeric"
}
cols.append(col)
else:
col1 = {
"bSortable": "false",
"bSearchable": "true",
"sClass": "alignLeft",
"fnRender": "text-align:left",
"sType": "numeric"
}
col2 = {
"bSortable": "false",
"bSearchable": "true",
"sClass": "alignLeft",
"fnRender": "text-align:left",
"sType": "numeric"
}
cols.append(col1)
cols.append(col2)
info['credit'] = info['MF'].contributor_name
info['coeff_aoColumns'] = cols # json.dumps(cols)
mwf_logger.debug("col={0}".format(cols))
return render_template("mwf_one_form.html", **info)
def render_maass_waveforms(level=0,
weight=-1,
character=-1,
r1=0,
r2=0,
**kwds):
info = get_args_mwf(level=level,
weight=weight,
character=character,
r1=r1,
r2=r2,
**kwds)
info["credit"] = ""
info["learnmore"] = []
mwf_logger.debug("args=%s" % request.args)
mwf_logger.debug("method=%s" % request.method)
mwf_logger.debug("req.form=%s" % request.form)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("level,weight,char={0},{1},{2}".format(
level, weight, character))
if info.get('maass_id', None) and info.get('db', None):
return render_one_maass_waveform_wp(**info)
if info['search'] or (info['browse'] and int(info['weight']) != 0):
search = get_search_parameters(info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
if info['browse']:
mwf_logger.debug("browse info=%s" % info)
return render_browse_all_eigenvalues(**info)
info['cur_character'] = character
if level > 0:
info['maass_weight'] = maass_db.weights(int(level))
info['cur_level'] = level
if weight > -1:
info['cur_weight'] = weight
if level > 0:
info['maass_character'] = maass_db.characters(
int(level), float(weight))
if character > -1:
info['cur_character'] = character
if level > 0 or weight > -1 or character > -1:
search = get_search_parameters(info)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
title = 'Maass Forms'
info['list_of_levels'] = maass_db.levels()
if info['list_of_levels']:
info['max_level'] = max(info['list_of_levels'])
else:
info['max_level'] = 0
mwf_logger.debug("info3=%s" % info)
bread = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Forms', url_for('.render_maass_waveforms'))]
info['bread'] = bread
info['title'] = title
maass_db.set_table()
maass_db.table['ncols'] = 10
info['DB'] = maass_db
info['dbcount'] = maass_db.count()
info['limit'] = maxNumberOfResultsToShow
return render_template("mwf_navigate.html", **info)
def set_table(self, data={}):
# data = maass_db.get_search_parameters(data,kwds
mwf_logger.debug("set table, data = {0}".format(data))
mwf_logger.debug("skip= {0}".format(self.skip))
mwf_logger.debug("limit= {0}".format(self.limit))
self.table = []
data['skip'] = self.skip
data['limit'] = self.limit
l1 = self.keys.index('Level')
level_ll = (self.skip[l1]) * self.limit[l1]
level_ul = (self.skip[l1] + 1) * self.limit[l1]
ev_limit = self.limit[self.keys.index('Eigenvalue')]
ev_skip = self.skip[self.keys.index('Eigenvalue')] * ev_limit
new_cols = []
levels = maass_db.levels()
mwf_logger.debug("levels= {0}".format(levels))
cur_level = data.get('level', None)
cur_wt = data.get('weight', None)
print("cur_level=", cur_level)
print("cur_wt=", cur_wt)
for N in levels:
if cur_level and cur_level != N:
continue
N = int(N)
if N < level_ll or N > level_ul:
continue
print("N=", N)
weights = maass_db.weights(N)
print("weights=", weights)
self.wt = weights
for k in weights:
if cur_wt is not None and cur_wt != k:
continue
print("k=", k)
k = int(k)
evs = []
query = {'Level': N, 'Weight': k}
totalc = maass_db.count(query)
finds = maass_db.get_Maass_forms(query,
limit=ev_limit,
offset=ev_skip)
for rec in finds:
row = {}
maass_id = rec.get('_id', None)
row['R'] = rec.get('Eigenvalue', None)
row['st'] = rec.get("Symmetry")
row['cusp_evs'] = rec.get("Cusp_evs")
row['err'] = rec.get('Error', 0)
row['url'] = url_for('mwf.render_one_maass_waveform',
maass_id=maass_id)
row['numc'] = rec.get('Numc', 0)
evs.append(row)
kmax = int(totalc / ev_limit)
paging = []
for j in range(ev_skip, kmax):
k0 = (j) * ev_limit
k1 = (j + 1) * ev_limit
url = url_for('mwf.render_maass_waveforms',
level=N,
weight=k,
skip=ev_skip + j,
limit=ev_limit)
skip = {
'url': url,
'k0': k0,
'k1': k1,
'cur_skip': ev_skip,
'cur_limit': ev_limit,
"skip": j
}
paging.append(skip)
# s+="]"
self.paging = paging
smalltbl = {'N': N, 'k': k, 'evs': evs, 'paging': paging}
if len(evs) > 0:
self.table.append(smalltbl)
print("table=", self.table)
self.cols = new_cols
def set_table(self, data={}):
# data = maass_db.get_search_parameters(data,kwds
mwf_logger.debug("set table, data = {0}".format(data))
mwf_logger.debug("skip= {0}".format(self.skip))
mwf_logger.debug("limit= {0}".format(self.limit))
self.table = []
data['skip'] = self.skip
data['limit'] = self.limit
l1 = self.keys.index('Level')
level_ll = (self.skip[l1]) * self.limit[l1]
level_ul = (self.skip[l1] + 1) * self.limit[l1]
ev_limit = self.limit[self.keys.index('Eigenvalue')]
ev_skip = self.skip[self.keys.index('Eigenvalue')] * ev_limit
new_cols = []
levels = maass_db.levels()
mwf_logger.debug("levels= {0}".format(levels))
cur_level = data.get('level', None)
cur_wt = data.get('weight', None)
print "cur_level=", cur_level
print "cur_wt=", cur_wt
for N in levels:
if cur_level and cur_level != N:
continue
N = int(N)
if N < level_ll or N > level_ul:
continue
print "N=", N
weights = maass_db.weights(N)
print "weights=", weights
self.wt = weights
for k in weights:
if cur_wt is not None and cur_wt != k:
continue
print "k=", k
k = int(k)
evs = []
query = {'Level': N, 'Weight': k}
totalc = maass_db.count(query)
finds = maass_db.get_Maass_forms(query, limit=ev_limit, offset=ev_skip)
for rec in finds:
row = {}
maass_id = rec.get('_id', None)
row['R'] = rec.get('Eigenvalue', None)
row['st'] = rec.get("Symmetry")
row['cusp_evs'] = rec.get("Cusp_evs")
row['err'] = rec.get('Error', 0)
row['url'] = url_for('mwf.render_one_maass_waveform', maass_id=maass_id)
row['numc'] = rec.get('Numc', 0)
evs.append(row)
kmax = int(totalc / ev_limit)
paging = []
for j in range(ev_skip, kmax):
k0 = (j) * ev_limit
k1 = (j + 1) * ev_limit
url = url_for(
'mwf.render_maass_waveforms', level=N, weight=k, skip=ev_skip + j, limit=ev_limit)
skip = {'url': url, 'k0': k0, 'k1': k1, 'cur_skip': ev_skip,
'cur_limit': ev_limit, "skip": j}
paging.append(skip)
# s+="]"
self.paging = paging
smalltbl = {'N': N, 'k': k, 'evs': evs, 'paging': paging}
if len(evs) > 0:
self.table.append(smalltbl)
print "table=", self.table
self.cols = new_cols
def evs_table2(search, twodarray=False, limit=50, offset=0):
r"""
Returns an object containing the results of a search for Maass forms.
"""
table = []
nrows = 0
fs = maass_db.get_Maass_forms(search, limit=limit, offset=offset)
mwf_logger.debug("numrec:{0}".format(len(fs)))
for f in fs: # indices:
row = {}
R = f.get('Eigenvalue', None)
N = f.get('Level', None)
k = f.get('Weight', None)
if R is None or N is None or k is None:
continue
row['R'] = R
row['N'] = N
if k == 0 or k == 1:
row['k'] = int(k)
else:
row['k'] = k
##
chi = f.get('Character', 0)
## Now get the COnrey number.
## First the character
if k == 0:
url = url_for('characters.render_Dirichletwebpage', modulus=N, number=chi)
s = "<a href={0}>{1}</a>".format(url, chi)
row['ch'] = s
else:
row['ch'] = "eta"
st = f.get('Symmetry', -1)
if st == 1:
st = "odd"
elif st == 0:
st = "even"
else:
st = "n/a"
row['symmetry'] = st
er = f.get('Error', 0)
if er > 0:
er = "{0:1.0e}".format(float(er))
else:
er = "unknown"
row['err'] = er
dim = f.get('Dim', 0)
if dim is None:
dim = 1 # "undefined"
row['dim'] = dim
numc = f.get('Numc', 0)
row['numc'] = numc
cev = f.get('Cusp_evs', [])
row['fricke'] = 'n/a'
row['cuspevs'] = 'n/a'
if row['k'] == 0 and isinstance(cev, list):
if len(cev) > 1:
fricke = cev[1]
row['fricke'] = fricke
s = '{0}'.format(cev[0])
for j in range(1, len(cev)):
s += ",{0}".format(cev[j])
elif len(cev) == 1:
s = str(cev[0])
elif len(cev) == 0:
s = 'n/a'
row['cuspevs'] = s
url = url_for('mwf.render_one_maass_waveform', maass_id=f.get('maass_id'))
row['url'] = url
nrows += 1
if twodarray:
s = '<a href="{0}">{1}</a>'.format(row['url'], row['R'])
rowr = [row['N'], row['k'], row['ch'], s,
row['symmetry'], row['err'], row['dim'], row['numc'],
row['fricke'], row['cuspevs']]
table.append(rowr)
else:
# row=row.values()
table.append(row)
mwf_logger.debug("nrows:".format(nrows))
evs = {'table': {}}
evs['table']['data'] = table
evs['table']['nrows'] = nrows
evs['table']['ncols'] = 10
evs['table']['colheads'] = []
knowls = ['mf.maass.mwf.level', 'mf.maass.mwf.weight', 'mf.maass.mwf.character',
'mf.maass.mwf.eigenvalue', 'mf.maass.mwf.symmetry',
'mf.maass.mwf.precision', 'mf.maass.mwf.dimension',
'mf.maass.mwf.ncoefficients', 'mf.maass.mwf.fricke',
'mf.maass.mwf.atkinlehner']
titles = ['Level', 'Weight', 'Char',
'Eigenvalue', 'Symmetry',
'Precision', 'Mult.',
'Coeff.', 'Fricke', 'Atkin-Lehner']
for i in range(10):
evs['table']['colheads'].append((knowls[i], titles[i]))
if 'limit' in search:
search.pop('limit')
if 'skip' in search:
search.pop('skip')
evs['totalrecords'] = maass_db.count(search)
evs['totalrecords_filtered'] = len(fs)
return evs
def render_one_maass_waveform_wp(info, prec=9):
r"""
Render the webpage of one Maass waveform.
The precision kwarg `prec` is passed to the coefficient table, and
indicates to round to 0 when the difference is less than 1e-`prec`.
"""
info["check"] = []
maass_id = info['maass_id']
mwf_logger.debug("id1={0}".format(maass_id))
try:
MF = WebMaassForm(maass_id)
except KeyError:
return flask.abort(404)
info['MF'] = MF
info['title'] = "Maass Form"
info['bread'] = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Waveforms', url_for('.render_maass_waveforms'))]
if hasattr(MF,'level'):
info['bread'].append(('Level {0}'.format(MF.level), url_for('.render_maass_waveforms', level=MF.level)))
info['title'] += " on \(\Gamma_{0}( %s )\)" % info['MF'].level
if hasattr(MF, 'R') and MF.R:
info['title'] += " with \(R=%s\)" % info['MF'].R
# make sure all the expected attributes of a WebMaassForm are actually present
missing = [attr for attr in ['level', 'dim', 'num_coeff', 'R', 'character'] if not hasattr(MF, attr)]
if missing:
mwf_logger.critical("Unable to render Maass form {0}; required attributes {1} missing from database record.".format(maass_id,missing))
info['explain'] = "Unable to render Maass form {0} because the following required attributes were missing from the database record:".format(maass_id) \
+ "<ul>" + "".join(["<li>"+attr+"</li>" for attr in missing]) + "</ul>"
return render_template("problem.html", **info)
level = info['MF'].level
dim = info['MF'].dim
# numc = info['MF'].num_coeff # never used
# if info['MF'].has_plot(): # and level == 1: # Bara level = 1 har rätt format för tillfället //Lemurell
# info['plotlink'] = url_for('mwf.plot_maassform', maass_id=maass_id)
# Create the link to the L-function (put in '/L' at the beginning and '/' before '?'
Llink = "/L" + url_for('mwf.render_one_maass_waveform', maass_id=maass_id) # + '/?db=' + info['db']
if dim == 1:
info["friends"] = [("L-function", Llink)]
# Navigation to previous and next form
next_form_id = info['MF'].next_maassform_id()
if next_form_id:
next_data = ('next', r"$f_{\text next}$", url_for('mwf.render_one_maass_waveform',
maass_id = next_form_id) )
else:
next_data = ('','','')
prev_form_id = info['MF'].prev_maassform_id()
if prev_form_id:
prev_data = ('previous', r"$f_{\text prev}$", url_for('mwf.render_one_maass_waveform',
maass_id = prev_form_id) )
else:
prev_data = ('','','')
info['navi'] = ( prev_data, next_data )
info["downloads"] = [ ('All stored data of the form',
url_for('mwf.render_one_maass_waveform', maass_id=maass_id,
download='all')),
('All coefficients of the form',
url_for('mwf.render_one_maass_waveform', maass_id=maass_id,
download='coefficients')) ]
mwf_logger.debug("count={0}".format(maass_db.count()))
ch = info['MF'].character
s = "\( \chi_{" + str(level) + "}(" + str(ch) + ",\cdot) \)"
# Q: Is it possible to get the knowls into the properties?
# A: Not in a nice way and this is not done elsewhere in the LMFDB; the knowls should appear on labels in the template
# knowls = {'level': 'mf.maass.mwf.level',
# 'weight': 'mf.maass.mwf.weight',
# 'char': 'mf.maass.mwf.character',
# 'R': 'mf.maass.mwf.eigenvalue',
# 'sym': 'mf.maass.mwf.symmetry',
# 'prec': 'mf.maass.mwf.precision',
# 'mult': 'mf.maass.mwf.dimension',
# 'ncoeff': 'mf.maass.mwf.ncoefficients',
# 'fricke': 'mf.maass.mwf.fricke',
# 'atkinlehner': 'mf.maass.mwf.atkinlehner'}
properties = [('Level', [info['MF'].level]),
('Symmetry', [info['MF'].even_odd()]),
('Weight', [info['MF'].the_weight()]),
('Character', [s]),
('Multiplicity', [dim]),
('Precision', [info['MF'].precision()]),
('Fricke Eigenvalue', [info['MF'].fricke()]),
('Atkin-Lehner Eigenvalues', [info['MF'].atkinlehner()]),
]
if dim > 1 and info['MF'].the_character() == "trivial":
properties.append(("Possibly oldform", []))
info['properties2'] = properties
# The precision in set_table indicates which coefficients to set to zero.
# For instance, if the imaginary part is less than the precision in
# absolute value, then it is set to 0 in set_table.
# The value 1e-9 is chosen arbitrarily, as recommended in issue #2076.
info['MF'].set_table(prec=prec)
cols = [{"aaSorting": "asc", "sWidth": "10%", "bSortable": "true", "bSearchable": "false",
"sType": "numeric"}]
negc = info['MF'].table.get('negc', 0)
for j in range(dim):
if not negc:
col = {"bSortable": "false", "bSearchable": "true", "sClass": "alignLeft",
"fnRender": "text-align:left", "sType": "numeric"}
cols.append(col)
else:
col1 = {"bSortable": "false", "bSearchable": "true", "sClass": "alignLeft",
"fnRender": "text-align:left", "sType": "numeric"}
col2 = {"bSortable": "false", "bSearchable": "true", "sClass": "alignLeft",
"fnRender": "text-align:left", "sType": "numeric"}
cols.append(col1)
cols.append(col2)
info['credit'] = info['MF'].contributor_name
info['coeff_aoColumns'] = cols # json.dumps(cols)
mwf_logger.debug("col={0}".format(cols))
return render_template("mwf_one_form.html", **info)
def render_maass_waveforms(level=0, weight=-1, character=-1, r1=0, r2=0, **kwds):
info = get_args_mwf(level=level, weight=weight, character=character, r1=r1, r2=r2, **kwds)
info["credit"] = ""
info["learnmore"] = learnmore_list()
mwf_logger.debug("args=%s" % request.args)
mwf_logger.debug("method=%s" % request.method)
mwf_logger.debug("req.form=%s" % request.form)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("level,weight,char={0},{1},{2}".format(level, weight, character))
if info.get('maass_id', None) and info.get('db', None):
return render_one_maass_waveform_wp(**info)
if info['search'] or (info['browse'] and int(info['weight']) != 0):
# This isn't the right place to do input validation, but it is easier to flash errors here (this is a hack to address issue #1820)
if info.get('level_range'):
if not re.match(POSINT_RE, info['level_range']):
if "-" in info['level_range']:
info['level_range'] = "..".join(info['level_range'].split("-"))
if not re.match(POSINT_RANGE_RE, info['level_range']):
flash_error("%s is not a level, please specify a positive integer <span style='color:black'>n</span> or postivie integer range <span style='color:black'>m..n</span>.", info['level_range'])
return render_template('mwf_navigate.html', **info)
if info['character'] != -1:
try:
N = int(info.get('level_range','0'))
except:
flash_error("Character %s cannot be specified in combination with a range of levels.", info['character'])
return render_template('mwf_navigate.html', **info)
if not re.match(r'^[1-9][0-9]*\.[1-9][0-9]*$', info['character']):
flash_error("%s is not a valid label for a Dirichlet character. It should be of the form <span style='color:black'>q.n</span>, where q and n are coprime positive integers with n < q, or q=n=1.", info['character'])
return render_template('mwf_navigate.html', **info)
s = info['character'].split('.')
q,n = int(s[0]), int(s[1])
if n > q or gcd(q,n) != 1 or (N > 0 and q != N):
flash_error("%s is not a valid label for a Dirichlet character. It should be of the form <span style='color:black'>q.n</span>, where q and n are coprime positive integers with n < q, or q=n=1.", info['character'])
return render_template('mwf_navigate.html', **info)
info['level_range'] = str(q)
info['character'] = str(n)
if info['weight'] != -1:
if not re.match(INT_RE, info['weight']):
flash_error("%s is not a valid weight. It should be a nonnegative integer.", info['weight'])
return render_template('mwf_navigate.html', **info)
if info.get('ev_range'):
if not re.match(FLOAT_RE,info['ev_range']):
if "-" in info['ev_range']:
info['ev_range'] = "..".join(info['ev_range'].split("-"))
s = info['ev_range'].split("..")
if len(s) != 2:
flash_error("%s is not a valid eigenvalue range. It should be postive real interval.", info['ev_range'])
return render_template('mwf_navigate.html', **info)
if not re.match(FLOAT_RE,s[0]) or not re.match(FLOAT_RE,s[1]):
flash_error("%s is not a valid eigenvalue range. It should be postive real interval.", info['ev_range'])
return render_template('mwf_navigate.html', **info)
search = get_search_parameters(info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
if info['browse']:
mwf_logger.debug("browse info=%s" % info)
return render_browse_all_eigenvalues(**info)
info['cur_character'] = character
if level > 0:
info['maass_weight'] = maass_db.weights(int(level))
info['cur_level'] = level
if weight > -1:
info['cur_weight'] = weight
if level > 0:
info['maass_character'] = maass_db.characters(int(level), float(weight))
if character > - 1:
info['cur_character'] = character
if level > 0 or weight > -1 or character > -1:
search = get_search_parameters(info)
mwf_logger.debug("info=%s" % info)
mwf_logger.debug("search=%s" % search)
return render_search_results_wp(info, search)
title = 'Maass Forms'
info['list_of_levels'] = maass_db.levels()
if info['list_of_levels']:
info['max_level'] = max(info['list_of_levels'])
else:
info['max_level'] = 0
mwf_logger.debug("info3=%s" % info)
bread = [('Modular Forms', url_for('mf.modular_form_main_page')),
('Maass Forms', url_for('.render_maass_waveforms'))]
info['bread'] = bread
info['title'] = title
maass_db.set_table()
maass_db.table['ncols'] = 10
info['DB'] = maass_db
info['dbcount'] = maass_db.count()
info['limit'] = maxNumberOfResultsToShow
return render_template("mwf_navigate.html", **info)
