def get_qexp(level, weight, character, label, **kwds):
emf_logger.debug(
"get_qexp for: level={0},weight={1},character={2},label={3}".format(level, weight, character, label))
prec = my_get(request.args, "prec", default_prec, int)
if not arg:
return flask.abort(404)
try:
WNF = WebNewForm(weight, level, chi=character, label=label, prec=prec, verbose=2)
nc = max(prec, 5)
c = WNF.print_q_expansion(nc)
return c
except Exception, e:
return "<span style='color:red;'>ERROR: %s</span>" % e
def download_web_modform(info):
emf_logger.debug("IN GET_WEB_MODFORM!!! info={0}".format(info))
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
emf_logger.debug("info={0}".format(info))
if character == '':
character = 0
label = info.get('label', '')
# we only want one form or one embedding
if label != '':
if format == 'sage':
if character != 0:
D = DirichletGroup(level)
x = D[character]
X = Newforms(x, weight, names='a')
else:
X = Newforms(level, weight, names='a')
else: # format=='web_new':
X = WebNewForm(N=level, k=weight, chi=character, label=label)
s = dumps(X)
name = "{0}-{1}-{2}-{3}-web_newform.sobj".format(weight, level, character,
label)
emf_logger.debug("name={0}".format(name))
info['filename'] = name
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
try:
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True)
except IOError:
info['error'] = "Could not send file!"
def get_qexp(level, weight, character, label, **kwds):
emf_logger.debug(
"get_qexp for: level={0},weight={1},character={2},label={3}".format(
level, weight, character, label))
prec = my_get(request.args, "prec", default_prec, int)
if not arg:
return flask.abort(404)
try:
WNF = WebNewForm(level,
weight,
chi=character,
label=label,
prec=prec,
verbose=2)
nc = max(prec, 5)
c = WNF.print_q_expansion(nc)
return c
except Exception as e:
return "<span style='color:red;'>ERROR: %s</span>" % e.message
def set_info_for_one_modular_form(level=None,
weight=None,
character=None,
label=None,
**kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(
level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'bprec', default_display_bprec, int)
emf_logger.debug("PREC: {0}".format(prec))
emf_logger.debug("BITPREC: {0}".format(bprec))
try:
WNF = WebNewForm(N=level,
k=weight,
chi=character,
label=label,
verbose=1)
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError as e:
WNF = None
info['error'] = e.message
properties2 = list()
parents = list()
siblings = list()
friends = list()
if hasattr(WNF, "dimension") and WNF.dimension() == 0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
name = "Cuspidal newform %s of weight %s for " % (label, weight)
if level == 1:
name += "\(\mathrm{SL}_{2}(\mathbb{Z})\)"
else:
name += "\(\Gamma_0(%s)\)" % (level)
if int(character) != 0 and hasattr(WNF, "conrey_character"):
conrey_char = WNF.conrey_character()
conrey_char_name = WNF.conrey_character_name()
name += " with character \(%s\)" % (conrey_char_name)
else:
name += " with trivial character"
info['name'] = name
info['title'] = 'Modular Form ' + info['name']
if 'error' in info:
return info
# info['name']=WNF._name
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
if WNF.degree() == 1:
info['satake'] = WNF.satake_parameters(prec, bprec)
# br = 60
# info['qexp'] =
# ajax_more(WNF.print_q_expansion,{'prec':5,'br':br},{'prec':10,'br':br},{'prec':20,'br':br},{'prec':100,'br':br},{'prec':200,'br':br})
#K = WNF.base_ring()
#L = WNF.coefficient_field()
info['qexp'] = WNF.print_q_expansion(prec=prec, br=120)
# c = list(WNF.q_expansion(prec))
# c = map(lambda x: str(x).replace("*",""), c)
# info['c'] = map(lambda x: x.replace(, c)
# emf_logger.debug("c={0}".format(info['c']))
# info['maxc']=len(c)
# emf_logger.debug("maxc={0}".format(info['maxc']))
c_pol_st = str(WNF.polynomial(type='coefficient_field', format='str'))
b_pol_st = str(WNF.polynomial(type='base_ring', format='str'))
c_pol_ltx = str(WNF.polynomial(type='coefficient_field', format='latex'))
b_pol_ltx = str(WNF.polynomial(type='base_ring', format='latex'))
#print "c=",c_pol_ltx
#print "b=",b_pol_ltx
if c_pol_st <> 'x': ## Field is QQ
if b_pol_st <> 'x' and WNF.relative_degree() > 1:
info['polynomial_st'] = 'where \({0}=0\) and \({1}=0\).'.format(
c_pol_ltx, b_pol_ltx)
else:
info['polynomial_st'] = 'where \({0}=0\).'.format(c_pol_ltx)
else:
info['polynomial_st'] = ''
info['degree'] = int(WNF.degree())
if WNF.degree() == 1:
info['is_rational'] = 1
else:
info['is_rational'] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF.q_expansion_embeddings(prec,
bprec,
format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.print_twist_info()
info['is_minimal'] = info['twist_info'][0]
if (info['twist_info'][0]):
s = '- Is minimal<br>'
else:
s = '- Is a twist of lower level<br>'
properties2 = [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 = [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
digits = 7
alev = None
if level < N_max_extra_comp:
info['is_cm'] = WNF.is_CM()
info['CM'] = WNF.print_is_CM()
info['CM_values'] = WNF.cm_values(digits=digits)
if len(info['CM_values']['tau']) == 0:
info.pop('CM_values')
if (WNF.is_CM()[0]) == None:
s = '- Unknown (insufficient data)<br>'
elif (WNF.is_CM()[0]):
s = '- Is a CM-form<br>'
else:
s = '- Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
if len(alev.keys()) > 0:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
# properties.append(s)
emf_logger.debug("properties={0}".format(properties2))
else:
properties2.append(("CM info", "not available"))
if level != 1:
properties2.append(("Atkin-Lehner eigenvalues", "not available"))
info['atkinlehner'] = None
if alev and level != 1:
alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
info['atkinlehner'] = list()
# info['atkin_lehner_cusps']=list()
for c in alev.keys():
if (c == Cusp(Infinity)):
continue
s = "\(" + latex(c) + "\)"
Q = alev[c][0]
ev = alev[c][1]
info['atkinlehner'].append([Q, c, ev])
if (level == 1):
info['explicit_formulas'] = WNF.print_as_polynomial_in_E4_and_E6()
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if (len(WNF.parent().galois_decomposition()) > 1):
for label_other in WNF.parent()._galois_orbits_labels:
if (label_other != label):
s = 'Modular form '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(
character) + str(label_other)
else:
s = s + str(level) + '.' + str(weight) + str(label_other)
url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(
label)
else:
s = s + str(level) + '.' + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character,
label=label)
if WNF.degree() > 1:
for h in range(WNF.degree()):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight() == 2 and WNF.degree() == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
space_url = '?&level=' + str(level) + '&weight=' + str(
weight) + '&character=' + str(character)
parents.append(
('\( S_{k} (\Gamma_0(' + str(level) + '),\chi )\)', space_url))
info['properties2'] = properties2
info['parents'] = parents
info['siblings'] = siblings
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def set_info_for_one_modular_form(level=None, weight=None, character=None, label=None, **kwds):
r"""
Set the info for on modular form.
"""
info = to_dict(kwds)
info['level'] = level
info['weight'] = weight
info['character'] = character
info['label'] = label
if level is None or weight is None or character is None or label is None:
s = "In set info for one form but do not have enough args!"
s += "level={0},weight={1},character={2},label={3}".format(level, weight, character, label)
emf_logger.critical(s)
emf_logger.debug("In set_info_for_one_mf: info={0}".format(info))
prec = my_get(info, 'prec', default_prec, int)
bprec = my_get(info, 'prec', default_bprec, int)
try:
WNF = WebNewForm(weight, level, character, label, verbose=1)
# if info.has_key('download') and info.has_key('tempfile'):
# WNF._save_to_file(info['tempfile'])
# info['filename']=str(weight)+'-'+str(level)+'-'+str(character)+'-'+label+'.sobj'
# return info
except IndexError:
WNF = None
emf_logger.debug("Could not compute the desired function!")
emf_logger.debug("{0},{1},{2}".format(level,weight,character))
print level, weight, character, label
info['error'] = "Could not compute the desired function!"
properties2 = list()
parents = list()
siblings = list()
friends = list()
if WNF is None or WNF._f is None:
info['error'] = "This space is empty!"
emf_logger.debug("WNF={0}".format(WNF))
name = "Cuspidal newform %s of weight %s for " % (label, weight)
if level == 1:
name += "\(\mathrm{SL}_{2}(\mathbb{Z})\)"
else:
name += "\(\Gamma_0(%s)\)" % (level)
if int(character) != 0 and hasattr(WNF,"conrey_character"):
conrey_char = WNF.conrey_character()
conrey_char_name = WNF.conrey_character_name()
name += " with character \(%s\)" % (conrey_char_name)
else:
name += " with trivial character"
info['name'] = name
info['title'] = 'Modular Form ' + info['name']
if 'error' in info:
return info
# info['name']=WNF._name
info['satake'] = WNF.satake_parameters(prec, bprec)
# br = 60
# info['qexp'] =
# ajax_more(WNF.print_q_expansion,{'prec':5,'br':br},{'prec':10,'br':br},{'prec':20,'br':br},{'prec':100,'br':br},{'prec':200,'br':br})
K = WNF.base_ring()
info['qexp'] = WNF.print_q_expansion(prec, 120)
# c = list(WNF.q_expansion(prec))
# c = map(lambda x: str(x).replace("*",""), c)
# info['c'] = map(lambda x: x.replace(, c)
# emf_logger.debug("c={0}".format(info['c']))
# info['maxc']=len(c)
# emf_logger.debug("maxc={0}".format(info['maxc']))
info['polynomial'] = str(WNF.polynomial()).replace('x', str(latex(K.gen())))
if(K != QQ):
info['polynomial_st'] = 'where ' + r'\(' + info['polynomial'] + r'=0\)'
else:
info['polynomial_st'] = ''
info['degree'] = int(WNF.degree())
if K == QQ:
info['is_rational'] = 1
else:
info['is_rational'] = 0
# info['q_exp_embeddings'] = WNF.print_q_expansion_embeddings()
# if(int(info['degree'])>1 and WNF.dimension()>1):
# s = 'One can embed it into \( \mathbb{C} \) as:'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# elif(int(info['degree'])>1):
# s = 'There are '+str(info['degree'])+' embeddings into \( \mathbb{C} \):'
# bprec = 26
# print s
# info['embeddings'] = ajax_more2(WNF.print_q_expansion_embeddings,{'prec':[5,10,25,50],'bprec':[26,53,106]},text=['more coeffs.','higher precision'])
# else:
# info['embeddings'] = ''
info['embeddings'] = WNF.q_expansion_embeddings(prec, bprec)
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.print_twist_info()
info['is_minimal'] = info['twist_info'][0]
if(info['twist_info'][0]):
s = '- Is minimal<br>'
else:
s = '- Is a twist of lower level<br>'
properties2 = [('Twist info', s)]
else:
info['twist_info'] = 'Twist info currently not available.'
properties2 = [('Twist info', 'not available')]
args = list()
for x in range(5, 200, 10):
args.append({'digits': x})
digits = 7
alev = None
if level < N_max_extra_comp:
info['is_cm'] = WNF.is_CM()
info['CM'] = WNF.print_is_CM()
info['CM_values'] = WNF.cm_values(digits=digits)
if(WNF.is_CM()[0]):
s = '- Is a CM-form<br>'
else:
s = '- Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
if len(alev.keys()) > 0:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
# properties.append(s)
emf_logger.debug("properties={0}".format(properties2))
else:
properties2.append(("CM info", "not available"))
if level != 1:
properties2.append(("Atkin-Lehner eigenvalues", "not available"))
info['atkinlehner'] = None
if alev and level != 1:
alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
info['atkinlehner'] = list()
# info['atkin_lehner_cusps']=list()
for c in alev.keys():
if(c == Cusp(Infinity)):
continue
s = "\(" + latex(c) + "\)"
Q = alev[c][0]
ev = alev[c][1]
info['atkinlehner'].append([Q, c, ev])
if(level == 1):
info['explicit_formulas'] = WNF.print_as_polynomial_in_E4_and_E6()
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if(len(WNF.parent().galois_decomposition()) > 1):
for label_other in WNF.parent()._galois_orbits_labels:
if(label_other != label):
s = 'Modular form '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(label_other)
else:
s = s + str(level) + '.' + str(weight) + str(label_other)
url = url_for('emf.render_elliptic_modular_forms', level=level,
weight=weight, character=character, label=label_other)
friends.append((s, url))
s = 'L-Function '
if character:
s = s + str(level) + '.' + str(weight) + '.' + str(character) + str(label)
else:
s = s + str(level) + '.' + str(weight) + str(label)
# url =
# "/L/ModularForm/GL2/Q/holomorphic?level=%s&weight=%s&character=%s&label=%s&number=%s"
# %(level,weight,character,label,0)
url = '/L' + url_for(
'emf.render_elliptic_modular_forms', level=level, weight=weight, character=character, label=label)
if WNF.degree() > 1:
for h in range(WNF.degree()):
s0 = s + ".{0}".format(h)
url0 = url + "{0}/".format(h)
friends.append((s0, url0))
else:
friends.append((s, url))
# if there is an elliptic curve over Q associated to self we also list that
if WNF.weight() == 2 and WNF.degree() == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
space_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character)
parents.append(('\( S_{k} (\Gamma_0(' + str(level) + '),\chi )\)', space_url))
info['properties2'] = properties2
info['parents'] = parents
info['siblings'] = siblings
info['friends'] = friends
return info
