def processMaassNavigation(numrecs=35):
"""
Produces a table of numrecs Maassforms with Fourier coefficients in the database
"""
s = '<h5>The L-functions attached to the first 4 weight 0 Maass newforms with trivial character on Hecke congruence groups $\Gamma_0(N)$</h5>'
s += '<table>\n'
i = 0
maxinlevel = 4
for level in [1, 2, 3, 4, 5, 6, 7, 9]:
j = 0
s += '<tr>\n'
s += '<td><bold>N={0}:</bold></td>\n'.format(level)
finds = maass_db.get_Maass_forms({'Level': int(level),
'char': 1,
'Newform' : None})
for f in finds:
nc = f.get('Numc', 0)
if nc <= 0:
continue
R = f.get('Eigenvalue', 0)
if R == 0:
continue
if f.get('Symmetry',0) == 1:
T = 'o'
else:
T = 'e'
_until = min(12, len(str(R)))
Rst = str(R)[:_until]
idd = f.get('maass_id', None)
if idd is None:
continue
idd = str(idd)
url = url_for('.l_function_maass_page', maass_id=idd)
s += '<td><a href="{0}">{1}</a>{2}'.format(url, Rst, T)
i += 1
j += 1
if i >= numrecs or j >= maxinlevel:
break
s += '</tr>\n'
if i > numrecs:
break
s += '</table>\n'
return s
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 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 paintSvgMaass(min_level,
max_level,
min_R,
max_R,
weight=0,
char=1,
width=1000,
heightfactor=20,
L=""):
''' Returns the contents (as a string) of the svg-file for
all Maass forms in the database.
Takes all levels from min_level to max_level
Spectral parameter in [min_R, max_R]
Set L="/L" to make link go to the L-function
'''
xMax = int(max_R)
yMax = int(max_level)
xMin = int(min_R)
yMin = int(min_level)
extraSpace = 40
length_R = xMax - xMin
length_level = yMax - yMin + 1
if length_level < 15:
heightfactor = heightfactor * 2
height = length_level * heightfactor + extraSpace
xfactor = (width - extraSpace) / length_R
yfactor = (height - extraSpace) / length_level
ticlength = 4
radius = 3
xshift = extraSpace
# Start of file and add coordinate system
ans = "<svg xmlns='http://www.w3.org/2000/svg'"
ans += " xmlns:xlink='http://www.w3.org/1999/xlink'"
ans += " height='{0}' width='{1}'>\n".format(height + 20, width + 20)
ans += paintCSMaass(width, height, xMin, xMax, yMin, yMax, xfactor,
yfactor, ticlength, xshift)
# Fetch Maass forms from database
search = {
'level1': yMin,
'level2': yMax,
'char': char,
'R1': xMin,
'R2': xMax,
'Newform': None,
'weight': weight
}
projection = ['maass_id', 'Eigenvalue', 'Level', 'Symmetry']
forms = maass_db.get_Maass_forms(search, projection, sort=[], limit=10000)
# Loop through all forms and add a clickable dot for each
for f in forms:
linkurl = L + "/ModularForm/GL2/Q/Maass/{0}".format(f['maass_id'])
x = (f['Eigenvalue'] - xMin) * xfactor + xshift
y = (f['Level'] - yMin + 1) * yfactor
try: # Shifting even slightly up and odd slightly down
if f['Symmetry'] == 0 or f['Symmetry'] == 'even':
y -= 1
color = signtocolour(1)
elif f['Symmetry'] == 1 or f['Symmetry'] == 'odd':
y += 1
color = signtocolour(-1)
else:
color = signtocolour(0)
except Exception:
color = signtocolour(0)
ans += "<a xlink:href='{0}' target='_top'>".format(linkurl)
ans += "<circle cx='{0}' cy='{1}' ".format(str(x)[0:6], str(y))
ans += "r='{0}' style='fill:{1}'>".format(str(radius), color)
ans += "<title>{0}</title></circle></a>\n".format(f['Eigenvalue'])
ans += "</svg>"
return ans
