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_coefficients(info):
r"""
Return a file with the Fourier coefficients in desired format.
"""
emf_logger.debug("IN GET_COEFFICIENTS!!!")
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
s = print_list_of_coefficients(info)
print "s=",s
if info['format']=="sage":
ending = "sobj"
else:
ending = "txt"
info['filename'] = str(weight) + '-' + str(
level) + '-' + str(character) + '-' + label + 'coefficients-0to' + info['number'] + "."+ending
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True)
def get_coefficients(info):
r"""
Return a file with the Fourier coefficients in desired format.
"""
emf_logger.debug("IN GET_COEFFICIENTS!!!")
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
s = print_list_of_coefficients(info)
print "s=", s
if info['format'] == "sage":
ending = "sobj"
else:
ending = "txt"
info['filename'] = str(weight) + '-' + str(level) + '-' + str(
character
) + '-' + label + 'coefficients-0to' + info['number'] + "." + ending
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True)
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 print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
bitprec = my_get(info, 'bitprec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
fmt = info.get("format", "q_expansion")
if character == '':
character = '1'
label = info.get('label', '')
if character.isalnum():
character = int(character)
else:
return "The character '{0}' is not well-defined!".format(character)
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
number = int(info['number']) + 1 if 'number' in info else 20
emf_logger.debug("number = {}".format(number))
F = WebNewForm(level=level,
weight=weight,
character=character,
label=label,
prec=number)
if not F.has_updated():
return ""
if not 'number' in info:
F.prec = number = max(F.parent.sturm_bound + 1, 20)
F.update_from_db()
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(
F.parent.group) + "\)"
s = ""
if ((character is not None) and (character > 0)):
shead = shead + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
if fmt == "sage":
res = []
if number > F.max_available_prec():
raise IndexError, "The database does not contain this many ({0}) coefficients for this modular form! We only have {1}".format(
number, F.max_available_prec())
if fmt == "sage":
qe = F.coefficients(range(number))
res.append(qe)
else:
coefs += print_coefficients_for_one_form(F,
number,
info['format'],
bitprec=bitprec)
if not fmt == "sage":
return s + "\n" + coefs
else:
if len(res) == 1:
res = res[0]
#print "res=",res
return dumps(res)
def get_coefficients(info):
r"""
Return a file with the Fourier coefficients in desired format.
"""
emf_logger.debug("IN GET_COEFFICIENTS!!!")
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
character = my_get(info, 'character', '', int) # int(info.get('weight',0))
number = my_get(info, 'number', 100, int)
label = my_get(info, 'label', '', str)
emf_logger.debug("info={0}".format(info))
if character == '':
character = 1
label = info.get('label', '')
if info['format'] == "sage":
ending = "sage"
f = WebNewForm(level, weight, character, label, prec=number)
s = f.download_to_sage(number)
elif info['format'] == "sobj":
ending = "sobj"
f = WebNewForm(level, weight, character, label, prec=number)
s = f.dump_coefficients(number)
else:
# we only want one form or one embedding
try:
s = print_list_of_coefficients(info)
except IndexError as e:
info['error'] = str(e)
flask.flash(str(e))
return redirect(url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character,
label=label),
code=301)
ending = "txt"
if info['format'] == 'q_expansion':
fmt = '-qexp'
elif info['format'] == "coefficients" or info['format'] == "sobj":
fmt = '-coef'
elif info['format'] == "embeddings":
fmt = '-emb'
else:
fmt = ''
info['filename'] = "{0}-{1}-{2}-{3}-coefficients-0-to-{4}{5}.{6}".format(
level, weight, character, label, number, fmt, ending)
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'], add_etags=False)
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True,
add_etags=False)
def get_coefficients(info):
r"""
Return a file with the Fourier coefficients in desired format.
"""
emf_logger.debug("IN GET_COEFFICIENTS!!!")
level = my_get(info, "level", -1, int)
weight = my_get(info, "weight", -1, int)
character = my_get(info, "character", "", int) # int(info.get('weight',0))
number = my_get(info, "number", 100, int)
label = my_get(info, "label", "", str)
emf_logger.debug("info={0}".format(info))
if character == "":
character = 1
label = info.get("label", "")
if info["format"] == "sage":
ending = "sage"
f = WebNewForm(level, weight, character, label, prec=number)
s = f.download_to_sage(number)
elif info["format"] == "sobj":
ending = "sobj"
f = WebNewForm(level, weight, character, label, prec=number)
s = f.dump_coefficients(number)
else:
# we only want one form or one embedding
try:
s = print_list_of_coefficients(info)
except IndexError as e:
info["error"] = str(e)
flask.flash(str(e))
return redirect(
url_for(
"emf.render_elliptic_modular_forms", level=level, weight=weight, character=character, label=label
),
code=301,
)
ending = "txt"
if info["format"] == "q_expansion":
fmt = "-qexp"
elif info["format"] == "coefficients" or info["format"] == "sobj":
fmt = "-coef"
elif info["format"] == "embeddings":
fmt = "-emb"
else:
fmt = ""
info["filename"] = "{0}-{1}-{2}-{3}-coefficients-0-to-{4}{5}.{6}".format(
level, weight, character, label, number, fmt, ending
)
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'], add_etags=False)
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO, attachment_filename=info["filename"], as_attachment=True, add_etags=False)
def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, "level", -1, int)
weight = my_get(info, "weight", -1, int)
bitprec = my_get(info, "bitprec", 12, int) # number of digits
character = my_get(info, "character", "", str) # int(info.get('weight',0))
fmt = info.get("format", "q_expansion")
if character == "":
character = "1"
label = info.get("label", "")
if character.isalnum():
character = int(character)
else:
return "The character '{0}' is not well-defined!".format(character)
print "--------------"
if label == "" or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
number = int(info["number"]) + 1 if "number" in info else 20
emf_logger.debug("number = {}".format(number))
F = WebNewForm(level=level, weight=weight, character=character, label=label, prec=number)
if not F.has_updated():
return ""
if not "number" in info:
F.prec = number = max(F.parent.sturm_bound + 1, 20)
F.update_from_db()
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(F.parent.group) + "\)"
s = ""
if (character is not None) and (character > 0):
shead = shead + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
if fmt == "sage":
res = []
if number > F.max_available_prec():
raise IndexError, "The database does not contain this many ({0}) coefficients for this modular form! We only have {1}".format(
number, F.max_available_prec()
)
if fmt == "sage":
qe = F.coefficients(range(number))
res.append(qe)
else:
coefs += print_coefficients_for_one_form(F, number, info["format"], bitprec=bitprec)
if not fmt == "sage":
return s + "\n" + coefs
else:
if len(res) == 1:
res = res[0]
# print "res=",res
return dumps(res)
def get_search_parameters(info):
ret = dict()
# if not info.has_key('search') or not info['search']:
# return ret
level = my_get(info, 'level', 0)
mwf_logger.debug("get_search param=%s" % info)
mwf_logger.debug("level=%s" % level)
if level > 0:
ret['l1'] = int(level)
ret['l2'] = int(level)
else:
level_range = my_get(info, 'level_range', '').split('..')
if len(level_range) == 0:
ret['l1'] = 0
ret['l2'] = 0
elif len(level_range) == 1:
ret['l1'] = level_range[0]
ret['l2'] = level_range[0]
else:
ret['l1'] = level_range[0]
ret['l2'] = level_range[1]
character = my_get(info, 'character', 1)
mwf_logger.info("character: %s" % character)
if character > 1:
ret['ch1'] = int(character)
ret['ch2'] = int(character)
weight = my_get(info, 'weight', -1)
if weight > -1:
ret['wt1'] = float(weight)
ret['wt2'] = float(weight)
else:
weight_range = my_get(info, 'weight_range', '').split('..')
if len(weight_range) == 0:
ret['wt1'] = 0
ret['wt2'] = 0
elif len(weight_range) == 1:
ret['wt1'] = weight_range[0]
ret['wt2'] = weight_range[0]
else:
ret['wt1'] = weight_range[0]
ret['wt2'] = weight_range[1]
ret['rec_start'] = my_get(info, 'rec_start', 1, int)
ret['limit'] = my_get(info, 'limit', 2000, int)
# ret['weight']=my_get(info,'weight',0,int)
ev_range = my_get(info, 'ev_range', '').split('..')
if len(ev_range) == 0:
ret['r1'] = 0
ret['r2'] = 0
elif len(ev_range) == 1:
mwf_logger.debug("ev_range=%s" % ev_range)
# ev_range[0]=float(ev_range[0]); ev_range[1]=float(ev_range[1])
ret['r1'] = ev_range[0]
ret['r2'] = ev_range[0]
else:
ev_range[0] = float(ev_range[0])
ev_range[1] = float(ev_range[1])
ret['r1'] = ev_range[0]
ret['r2'] = ev_range[1]
return ret
def get_search_parameters(info):
ret = dict()
# if not info.has_key('search') or not info['search']:
# return ret
level = my_get(info, 'level', 0)
mwf_logger.debug("get_search param=%s" % info)
mwf_logger.debug("level=%s" % level)
if level > 0:
ret['l1'] = int(level)
ret['l2'] = int(level)
else:
level_range = my_get(info, 'level_range', '').split('..')
if len(level_range) == 0:
ret['l1'] = 0
ret['l2'] = 0
elif len(level_range) == 1:
ret['l1'] = level_range[0]
ret['l2'] = level_range[0]
else:
ret['l1'] = level_range[0]
ret['l2'] = level_range[1]
character = my_get(info, 'character', 1)
mwf_logger.info("character: %s" % character)
if character > 1:
ret['ch1'] = int(character)
ret['ch2'] = int(character)
weight = my_get(info, 'weight', -1)
if weight > -1:
ret['wt1'] = float(weight)
ret['wt2'] = float(weight)
else:
weight_range = my_get(info, 'weight_range', '').split('..')
if len(weight_range) == 0:
ret['wt1'] = 0
ret['wt2'] = 0
elif len(weight_range) == 1:
ret['wt1'] = weight_range[0]
ret['wt2'] = weight_range[0]
else:
ret['wt1'] = weight_range[0]
ret['wt2'] = weight_range[1]
ret['rec_start'] = my_get(info, 'rec_start', 1, int)
ret['limit'] = my_get(info, 'limit', 2000, int)
# ret['weight']=my_get(info,'weight',0,int)
ev_range = my_get(info, 'ev_range', '').split('..')
if len(ev_range) == 0:
ret['r1'] = 0
ret['r2'] = 0
elif len(ev_range) == 1:
mwf_logger.debug("ev_range=%s" % ev_range)
# ev_range[0]=float(ev_range[0]); ev_range[1]=float(ev_range[1])
ret['r1'] = ev_range[0]
ret['r2'] = ev_range[0]
else:
ev_range[0] = float(ev_range[0])
ev_range[1] = float(ev_range[1])
ret['r1'] = ev_range[0]
ret['r2'] = ev_range[1]
return ret
def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
bitprec = my_get(info, 'bitprec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
if character == '':
character = 0
label = info.get('label', '')
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
WMFS = WebModFormSpace(N=level, k=weight, chi=character)
if not WMFS:
return ""
if ('number' in info):
number = int(info['number'])
else:
number = max(WMFS.sturm_bound() + 1, 20)
FS = list()
if (label is not None):
FS.append(WMFS.f(label))
else:
for a in WMFS.labels():
FS.append(WMFS.f(a))
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(
WMFS.group()) + "\)"
s = ""
if ((character is not None) and (character > 0)):
s = s + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
for F in FS:
if len(FS) > 1:
if info['format'] == 'html':
coefs += F.label()
else:
coefs += F.label()
coefs += print_coefficients_for_one_form(F,
number,
info['format'],
bitprec=bitprec)
ss = coefs
return ss
def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
if character == '':
character = 0
label = info.get('label', '')
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
WMFS = WebModFormSpace(N = level, k = weight, chi = character)
if not WMFS:
return ""
if('number' in info):
number = int(info['number'])
else:
number = max(WMFS.sturm_bound() + 1, 20)
if('prec' in info):
bprec = int(ceil(prec * 3.4))
else:
bprec = 53
FS = list()
if(label is not None):
FS.append(WMFS.f(label))
else:
for a in WMFS.labels():
FS.append(WMFS.f(a))
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(WMFS.group()) + "\)"
s = ""
if((character is not None) and (character > 0)):
s = s + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
for F in FS:
if len(FS) > 1:
if info['format'] == 'html':
coefs += F.label()
else:
coefs += F.label()
coefs += print_coefficients_for_one_form(F, number, info['format'])
ss = coefs
return ss
def get_args(request, level=0, weight=0, character=-1, label='', keys=[]):
r"""
Use default input of the same type as desired output.
"""
if request.method == 'GET':
dd = to_dict(request.args)
else:
dd = to_dict(request.form)
info = dict()
info['level'] = my_get(dd, 'level', level, int)
info['weight'] = my_get(dd, 'weight', weight, int)
info['character'] = my_get(dd, 'character', character, int)
info['label'] = my_get(dd, 'label', label, str)
for key in keys:
if key in dd:
info[key] = my_get(dd, key, '', str)
return info
def get_args(request, level=0, weight=0, character=-1, label='', keys=[]):
r"""
Use default input of the same type as desired output.
"""
if request.method == 'GET':
dd = to_dict(request.args)
else:
dd = to_dict(request.form)
info = dict()
info['level'] = my_get(dd, 'level', level, int)
info['weight'] = my_get(dd, 'weight', weight, int)
info['character'] = my_get(dd, 'character', character, int)
info['label'] = my_get(dd, 'label', label, str)
for key in keys:
if key in dd:
info[key] = my_get(dd, key, '', str)
return info
def render_elliptic_modular_forms(level=0,
weight=0,
character=None,
label='',
**kwds):
r"""
Default input of same type as required. Note that for holomorphic modular forms: level=0 or weight=0 are non-existent.
"""
if character is None and level == 0 and weight == 0:
character = 0
elif character is None:
character = -1
emf_logger.debug(
"In render: level={0},weight={1},character={2},label={3}".format(
level, weight, character, label))
emf_logger.debug("args={0}".format(request.args))
emf_logger.debug("args={0}".format(request.form))
emf_logger.debug("met={0}".format(request.method))
keys = ['download', 'jump_to']
info = get_args(request, level, weight, character, label, keys=keys)
level = info['level']
weight = info['weight']
character = info['character']
label = info['label']
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if 'download' in info:
return get_downloads(**info)
emf_logger.debug("info=%s" % info)
## Consistency of arguments>
# if level<=0: level=None
# if weight<=0: weight=None
if 'jump_to' in info: # try to find out which form we want to jump
s = my_get(info, 'jump_to', '', str)
emf_logger.info("info.keys1={0}".format(info.keys()))
info.pop('jump_to')
emf_logger.info("info.keys2={0}".format(info.keys()))
args = extract_data_from_jump_to(s)
emf_logger.debug("args=%s" % args)
return redirect(url_for("emf.render_elliptic_modular_forms", **args),
code=301)
# return render_elliptic_modular_forms(**args)
if level > 0 and weight > 0 and character > -1 and label != '':
emf_logger.debug("info=%s" % info)
return render_one_elliptic_modular_form(**info)
if level > 0 and weight > 0 and character > -1:
return render_elliptic_modular_form_space(**info)
if level > 0 and weight > 0:
return browse_elliptic_modular_forms(**info)
if (level > 0 and weight == 0) or (weight > 0 and level == 0):
emf_logger.debug("Have level or weight only!")
return browse_elliptic_modular_forms(**info)
# return render_elliptic_modular_form_navigation_wp(**info)
# Otherwise we go to the main navigation page
return render_elliptic_modular_form_navigation_wp(**info)
def get_coefficients(info):
r"""
Return a file with the Fourier coefficients in desired format.
"""
emf_logger.debug("IN GET_COEFFICIENTS!!!")
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))
number=my_get(info,'number',0,int) + 1
label=my_get(info,'label','',str)
emf_logger.debug("info={0}".format(info))
if character == '':
character = 0
label = info.get('label', '')
# we only want one form or one embedding
try:
s = print_list_of_coefficients(info)
except IndexError as e:
info['error']=str(e)
flask.flash(str(e))
return redirect(url_for("emf.render_elliptic_modular_forms", level=level,weight=weight,character=character,label=label), code=301)
if info['format']=="sage":
ending = "sobj"
else:
ending = "txt"
if info['format'] == 'q_expansion':
fmt = '-qexp'
elif info['format'] == "coefficients":
fmt = '-coef'
elif info['format'] == "embeddings":
fmt = '-emb'
else:
fmt=''
info['filename'] = "{0}-{1}-{2}-{3}-coefficients-0-to-{4}{5}.{6}".format(level,weight,character,label,number,fmt,ending)
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True)
def get_coefficients(info):
emf_logger.debug("IN GET_COEFFICIENTS!!!")
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
s = print_list_of_coefficients(info)
info['filename'] = str(weight) + '-' + str(level) + '-' + str(
character) + '-' + label + 'coefficients-0to' + info['number'] + '.txt'
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True)
def get_coefficients(info):
emf_logger.debug("IN GET_COEFFICIENTS!!!")
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
s = print_list_of_coefficients(info)
info['filename'] = str(weight) + '-' + str(
level) + '-' + str(character) + '-' + label + 'coefficients-0to' + info['number'] + '.txt'
# return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=info["filename"],
as_attachment=True)
def get_args(request,
level=0,
weight=0,
character=-1,
group=2,
label='',
keys=[]):
r"""
Use default input of the same type as desired output.
"""
if request.method == 'GET':
dd = to_dict(request.args)
else:
dd = to_dict(request.form)
emf_logger.debug("REQUEST:{0}".format(dd))
info = dict()
info['level'] = my_get(dd, 'level', level, int)
info['weight'] = my_get(dd, 'weight', weight, int)
info['character'] = my_get(dd, 'character', character, int)
emf_logger.debug("group={0}".format(group))
info['group'] = my_get(dd, 'group', group, int)
emf_logger.debug("info[group]={0}".format(info['group']))
info['label'] = my_get(dd, 'label', label, str)
for key in keys:
if key in dd:
info[key] = my_get(dd, key, '', str)
return info
def render_elliptic_modular_forms(level=0, weight=0, character=None, label='', **kwds):
r"""
Default input of same type as required. Note that for holomorphic modular forms: level=0 or weight=0 are non-existent.
"""
if character is None and level == 0 and weight == 0:
character = 0
elif character is None:
character = -1
emf_logger.debug(
"In render: level={0},weight={1},character={2},label={3}".format(level, weight, character, label))
emf_logger.debug("args={0}".format(request.args))
emf_logger.debug("args={0}".format(request.form))
emf_logger.debug("met={0}".format(request.method))
keys = ['download', 'jump_to']
info = get_args(request, level, weight, character, label, keys=keys)
level = info['level']
weight = info['weight']
character = info['character']
label = info['label']
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if 'download' in info:
return get_downloads(**info)
emf_logger.debug("info=%s" % info)
## Consistency of arguments>
# if level<=0: level=None
# if weight<=0: weight=None
if 'jump_to' in info: # try to find out which form we want to jump
s = my_get(info, 'jump_to', '', str)
emf_logger.info("info.keys1={0}".format(info.keys()))
info.pop('jump_to')
emf_logger.info("info.keys2={0}".format(info.keys()))
args = extract_data_from_jump_to(s)
emf_logger.debug("args=%s" % args)
return redirect(url_for("emf.render_elliptic_modular_forms", **args), code=301)
# return render_elliptic_modular_forms(**args)
if level > 0 and weight > 0 and character > -1 and label != '':
emf_logger.debug("info=%s" % info)
return render_one_elliptic_modular_form(**info)
if level > 0 and weight > 0 and character > -1:
return render_elliptic_modular_form_space(**info)
if level > 0 and weight > 0:
return browse_elliptic_modular_forms(**info)
if (level > 0 and weight == 0) or (weight > 0 and level == 0):
emf_logger.debug("Have level or weight only!")
return browse_elliptic_modular_forms(**info)
# return render_elliptic_modular_form_navigation_wp(**info)
# Otherwise we go to the main navigation page
return render_elliptic_modular_form_navigation_wp(**info)
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 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 get_args(request, level=0, weight=0, character=-1, group=2, label='', keys=[]):
r"""
Use default input of the same type as desired output.
"""
if request.method == 'GET':
dd = to_dict(request.args)
else:
dd = to_dict(request.form)
emf_logger.debug("REQUEST:{0}".format(dd))
info = dict()
info['level'] = my_get(dd, 'level', level, int)
info['weight'] = my_get(dd, 'weight', weight, int)
info['character'] = my_get(dd, 'character', character, int)
emf_logger.debug("group={0}".format(group))
info['group'] = my_get(dd, 'group', group, int)
emf_logger.debug("info[group]={0}".format(info['group']))
info['label'] = my_get(dd, 'label', label, str)
for key in keys:
if key in dd:
info[key] = my_get(dd, key, '', str)
return info
def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
bitprec = my_get(info, 'bitprec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
fmt = info.get("format", "q_expansion")
if character == '':
character = '1'
label = info.get('label', '')
if character.isalnum():
character = int(character)
else:
return "The character '{0}' is not well-defined!".format(character)
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
WMFS = WebModFormSpace(level=level,
weight=weight,
cuspidal=True,
character=character)
if not WMFS:
return ""
if ('number' in info):
number = int(info['number']) + 1
else:
number = max(WMFS.sturm_bound + 1, 20)
FS = list()
f = WMFS.hecke_orbits.get(label)
if f is not None:
FS.append(f)
else:
for label in WMFS.hecke_orbits:
FS.append(WMFS.f(label))
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(
WMFS.group) + "\)"
s = ""
if ((character is not None) and (character > 0)):
shead = shead + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
if fmt == "sage":
res = []
for F in FS:
if number > F.max_cn():
raise IndexError, "The database does not contain this many ({0}) coefficients for this modular form! We only have {1}".format(
number, F.max_cn())
if len(FS) > 1:
if info['format'] == 'html':
coefs += F.label()
else:
coefs += F.label()
if fmt == "sage":
qe = F.coefficients(range(number))
res.append(qe)
else:
coefs += print_coefficients_for_one_form(F,
number,
info['format'],
bitprec=bitprec)
if not fmt == "sage":
return s + "\n" + coefs
else:
if len(res) == 1:
res = res[0]
#print "res=",res
return dumps(res)
def render_elliptic_modular_form_navigation_wp1(**args):
r"""
Renders the webpage for the navigational page.
"""
from sage.all import is_even
info = to_dict(args)
args = to_dict(request.args)
info.update(args)
form = to_dict(request.form)
info.update(form)
emf_logger.debug("render_c_m_f_n_wp info={0}".format(info))
level = my_get(info, 'level', 0, int)
weight = my_get(info, 'weight', 0, int)
group = my_get(info, 'group', 1, int)
if group == int(0):
pass
character = my_get(info, 'character', 1, int)
label = info.get('label', '')
#disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
emf_logger.debug("group=%s, %s" % (group, type(group)))
if ('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
if isinstance(weight, int) and weight > 0:
is_set['weight'] = True
weight = int(weight)
else:
weight = None
info.pop('weight', None)
if isinstance(level, int) and level > 0:
is_set['level'] = True
level = int(level)
else:
level = None
info.pop('level', None)
## This is the list of weights we initially put on the form
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page')),
(title, url_for('.render_elliptic_modular_forms'))]
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
# Special case: if the range reduces to a singleton for both level
# and weight then we return a single page rather than a table:
if limits_weight[0] == limits_weight[1] and limits_level[
0] == limits_level[1]:
return render_elliptic_modular_form_space_list_chars(
limits_level[0], limits_weight[0])
if is_set['weight']:
limits_weight = (weight, weight)
elif limits_weight is None:
limits_weight = (2, 12) # default values
if is_set['level']:
limits_level = (level, level)
elif limits_level is None:
limits_level = (1, 24) # default values
try:
group = info.get('group', 0) # default group is gamma_0
group = int(group)
except ValueError:
group = 0
if group not in [0, 1]:
group = 0
if group == 0:
info['grouptype'] = 0
info['groupother'] = 1
else:
info['grouptype'] = 1
info['groupother'] = 0
emf_logger.debug("level:{0},level_range={1}".format(level, limits_level))
emf_logger.debug("weight:{0},weight_range={1}".format(
weight, limits_weight))
if limits_weight[0] == limits_weight[1] and limits_level[
0] == limits_level[1]:
return redirect(url_for("emf.render_elliptic_modular_forms",
level=limits_level[0],
weight=limits_weight[0],
group=group),
code=301)
info['show_switch'] = True
db = getDBConnection()['modularforms2']['webmodformspace_dimension']
table = {}
q = db.find_one({'group': 'gamma{0}'.format(group)})
if q:
table = q.get('data', {})
if table != {}:
table = json.loads(table)
info['table'] = {}
level_range = range(limits_level[0], limits_level[1] + 1)
# we don't have weight 1 in database
if limits_weight[0] == 1:
limits_weight = (2, limits_weight[1])
weight_range = range(limits_weight[0], limits_weight[1] + 1)
#print "levels=",level_range
#print "weights=",weight_range
if len(weight_range) > 1:
info['weight_range'] = "{0}-{1}".format(limits_weight[0],
limits_weight[1])
if len(level_range) > 1:
info['level_range'] = "{0}-{1}".format(limits_level[0],
limits_level[1])
if group == 0:
weight_range = filter(is_even, weight_range)
for n in level_range:
info['table'][n] = {}
sn = unicode(n)
for k in weight_range:
info['table'][n][k] = {}
sk = unicode(k)
if table.has_key(sn):
if table[sn].has_key(sk):
info['table'][n][k] = table[sn][
sk] #.get(str(n),{}).get(str(k),"n/a")
else:
emf_logger.debug("Set table for Gamma1")
for n in level_range:
info['table'][n] = {}
for k in weight_range:
info['table'][n][k] = table.get(str(n),
{}).get(str(k), {}).get(
str(-1), "n/a")
#print "table=\n",table
#print "info=\n",info
#info['table']=table
info['col_heads'] = level_range
info['row_heads'] = weight_range
return render_template("emf_browse_spaces.html",
info=info,
title=title,
bread=bread)
def render_elliptic_modular_form_navigation_wp(**args):
r"""
Renders the webpage for the navigational page.
"""
from sage.all import is_even
from lmfdb.modular_forms.elliptic_modular_forms import WebModFormSpace
dimension_table_name = WebModFormSpace._dimension_table_name
info = to_dict(args)
args = to_dict(request.args)
info.update(args)
form = to_dict(request.form)
info.update(form)
emf_logger.debug("render_c_m_f_n_wp info={0}".format(info))
level = my_get(info, 'level', None, int)
weight = my_get(info, 'weight', None, int)
character = my_get(info, 'character', 1, int)
label = info.get('label', '')
#disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if ('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
if isinstance(weight, int) and weight > 0:
is_set['weight'] = True
weight = int(weight)
else:
weight = None
info.pop('weight', None)
if isinstance(level, int) and level > 0:
is_set['level'] = True
level = int(level)
else:
level = None
info.pop('level', None)
## This is the list of weights we initially put on the form
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page'))]
bread.append((EMF_TOP, url_for('.render_elliptic_modular_forms')))
if is_set['weight']:
limits_weight = (weight, weight)
elif limits_weight is None:
limits_weight = (2, 12) # default values
if is_set['level']:
limits_level = (level, level)
elif limits_level is None:
limits_level = (1, 24) # default values
try:
group = info.get('group', 0) # default group is gamma_0
group = int(group)
except ValueError:
group = 0
if group not in [0, 1]:
group = 0
if group == 0:
info['grouptype'] = 0
info['groupother'] = 1
else:
info['grouptype'] = 1
info['groupother'] = 0
emf_logger.debug("group=%s, %s" % (group, type(group)))
emf_logger.debug("level:{0},level_range={1}".format(level, limits_level))
emf_logger.debug("weight:{0},weight_range={1}".format(
weight, limits_weight))
# Special case: if the range reduces to a singleton for both level
# and weight then we return a single page rather than a table:
if limits_weight[0] == limits_weight[1] and limits_level[
0] == limits_level[1]:
return redirect(url_for("emf.render_elliptic_modular_forms",
level=limits_level[0],
weight=limits_weight[0],
group=group),
code=301)
info['show_switch'] = True
emf_logger.debug("dimension table name={0}".format(dimension_table_name))
db_dim = getDBConnection()['modularforms2'][dimension_table_name]
s = {
'level': {
"$lt": int(limits_level[1] + 1),
"$gt": int(limits_level[0] - 1)
},
'weight': {
"$lt": int(limits_weight[1] + 1),
"$gt": int(limits_weight[0] - 1)
}
}
if group == 0:
s['cchi'] = int(1)
else:
s['gamma1_label'] = {"$exists": True}
g = db_dim.find(s).sort([('level', int(1)), ('weight', int(1))])
table = {}
info['table'] = {}
level_range = range(limits_level[0], limits_level[1] + 1)
# we don't have weight 1 in database
if limits_weight[0] == 1:
limits_weight = (2, limits_weight[1])
weight_range = range(limits_weight[0], limits_weight[1] + 1)
if group == 0:
weight_range = filter(is_even, weight_range)
if len(weight_range) > 1:
info['weight_range'] = "{0}-{1}".format(limits_weight[0],
limits_weight[1])
if len(level_range) > 1:
info['level_range'] = "{0}-{1}".format(limits_level[0],
limits_level[1])
for n in level_range:
info['table'][n] = {}
for k in weight_range:
info['table'][n][k] = {'dim_new': int(0), 'in_db': -1}
for r in db_dim.find(s):
N = r['level']
k = r['weight']
if group != 0 or k % 2 == 0:
#emf_logger.debug("Found:k={0},N={1}".format(k,N))
dim = r['d_newf'] # dimension of newforms
info['table'][N][k]['dim_new'] = dim
if group == 0:
indb = r['in_wdb'] # 1 if it is in the webmodforms db else 0
else:
indb = r.get('one_in_wdb',
0) # 1 if it is in the webmodforms db else 0
if dim == 0:
indb = 1
info['table'][N][k]['in_db'] = indb
info['col_heads'] = level_range
info['row_heads'] = weight_range
return render_template("emf_browse_spaces.html",
info=info,
title=title,
bread=bread)
def render_elliptic_modular_form_navigation_wp(**args):
r"""
Renders the webpage for the navigational page.
"""
from sage.all import is_even
from lmfdb.modular_forms.elliptic_modular_forms import WebModFormSpace
dimension_table_name = WebModFormSpace._dimension_table_name
info = to_dict(args)
args = to_dict(request.args)
info.update(args)
form = to_dict(request.form)
info.update(form)
emf_logger.debug("render_c_m_f_n_wp info={0}".format(info))
level = my_get(info, 'level', None, int)
weight = my_get(info, 'weight', None, int)
character = my_get(info, 'character', 1, int)
label = info.get('label', '')
#disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
if isinstance(weight,int) and weight > 0:
is_set['weight'] = True
weight = int(weight)
else:
weight = None
info.pop('weight',None)
if isinstance(level,int) and level > 0:
is_set['level'] = True
level = int(level)
else:
level = None
info.pop('level',None)
## This is the list of weights we initially put on the form
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page'))]
bread.append((EMF_TOP, url_for('.render_elliptic_modular_forms')))
if is_set['weight']:
limits_weight = (weight, weight)
elif limits_weight is None:
limits_weight = (2, 12) # default values
if is_set['level']:
limits_level = (level, level)
elif limits_level is None:
limits_level = (1, 24) # default values
try:
group = info.get('group',0) # default group is gamma_0
group = int(group)
except ValueError:
group = 0
if group not in [0,1]:
group = 0
if group == 0:
info['grouptype'] = 0; info['groupother'] = 1
else:
info['grouptype'] = 1; info['groupother'] = 0
emf_logger.debug("group=%s, %s" % (group, type(group)))
emf_logger.debug("level:{0},level_range={1}".format(level,limits_level))
emf_logger.debug("weight:{0},weight_range={1}".format(weight,limits_weight))
# Special case: if the range reduces to a singleton for both level
# and weight then we return a single page rather than a table:
if limits_weight[0] == limits_weight[1] and limits_level[0] == limits_level[1]:
return redirect(url_for("emf.render_elliptic_modular_forms",
level=limits_level[0],weight=limits_weight[0],group=group), code=301)
info['show_switch'] = True
emf_logger.debug("dimension table name={0}".format(dimension_table_name))
db_dim = getDBConnection()['modularforms2'][dimension_table_name]
s = {'level':{"$lt":int(limits_level[1]+1),"$gt":int(limits_level[0]-1)},
'weight' : {"$lt":int(limits_weight[1]+1),"$gt":int(limits_weight[0]-1)}}
if group == 0:
s['cchi']=int(1)
else:
s['gamma1_label']={"$exists":True}
g = db_dim.find(s).sort([('level',int(1)),('weight',int(1))])
table = {}
info['table'] = {}
level_range = range(limits_level[0],limits_level[1]+1)
# we don't have weight 1 in database
if limits_weight[0]==1:
limits_weight=(2,limits_weight[1])
weight_range = range(limits_weight[0],limits_weight[1]+1)
if group == 0:
weight_range = filter(is_even,weight_range)
if len(weight_range)>1:
info['weight_range']="{0}-{1}".format(limits_weight[0],limits_weight[1])
elif len(weight_range)==1:
info['weight_range']="{0}".format(limits_weight[0])
if len(level_range)>1:
info['level_range']="{0}-{1}".format(limits_level[0],limits_level[1])
if len(level_range)==1:
info['level_range']="{0}".format(limits_level[0])
for n in level_range:
info['table'][n]={}
for k in weight_range:
info['table'][n][k]={'dim_new':int(0), 'in_db':-1}
for r in db_dim.find(s):
N = r['level']
k = r['weight']
if group != 0 or k%2==0:
#emf_logger.debug("Found:k={0},N={1}".format(k,N))
dim = r['d_newf'] # dimension of newforms
info['table'][N][k]['dim_new'] = dim
if group == 0:
indb = r['in_wdb'] # 1 if it is in the webmodforms db else 0
else:
indb = r.get('one_in_wdb',0) # 1 if it is in the webmodforms db else 0
if dim == 0:
indb = 1
info['table'][N][k]['in_db'] = indb
info['col_heads'] = level_range
info['row_heads'] = weight_range
return render_template("emf_browse_spaces.html", info=info, title=title, bread=bread)
def set_info_for_web_newform(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_cached(level=level,
weight=weight,
character=character,
label=label)
if not WNF.has_updated():
raise IndexError(
"Unfortunately, we do not have this newform in the database.")
info['character_order'] = WNF.character.order
info['code'] = WNF.code
emf_logger.debug("defined webnewform for rendering!")
except IndexError as e:
info['error'] = e.message
url0 = url_for("mf.modular_form_main_page")
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character)
bread = [(MF_TOP, url0), (EMF_TOP, url1)]
bread.append(("Level %s" % level, url2))
bread.append(("Weight %s" % weight, url3))
bread.append(("Character \( %s \)" % (WNF.character.latex_name), url4))
bread.append(
("Newform %d.%d.%d.%s" % (level, weight, int(character), label), ''))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character)
friends.append(
('\( S_{%s}(%s, %s)\)' %
(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty,
WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)",
WNF.character.url()))
if WNF.dimension == 0 and not info.has_key('error'):
info['error'] = "This space is empty!"
info['title'] = 'Newform ' + WNF.hecke_orbit_label
info['learnmore'] = [('History of modular forms',
url_for('.holomorphic_mf_history'))]
if 'error' in info:
return info
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
## Example to illustrate the different cases
## base = CyclotomicField(n) -- of degree phi(n)
## coefficient_field = NumberField( p(x)) for some p in base['x'] of degree m
## we would then have cdeg = m*phi(n) and bdeg = phi(n)
## and rdeg = m
## Unfortunately, for e.g. base = coefficient_field = CyclotomicField(6)
## we get coefficient_field.relative_degree() == 2 although it should be 1
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
## just setting rdeg = WNF.coefficient_field.relative_degree() does not give correct result...
##
rdeg = QQ(cdeg) / QQ(bdeg)
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
if WNF.complexity_of_first_nonvanishing_coefficients(
) > default_max_height:
info['qexp'] = ""
info['qexp_display'] = ''
info['hide_qexp'] = True
n, c = WNF.first_nonvanishing_coefficient()
info['trace_nv'] = latex(WNF.first_nonvanishing_coefficient_trace())
info['norm_nv'] = '\\approx ' + latex(
WNF.first_nonvanishing_coefficient_norm().n())
info['index_nv'] = n
else:
if WNF.prec < prec:
#get WNF record at larger prec
WNF.prec = prec
WNF.update_from_db()
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex",
level=level,
weight=weight,
character=character,
label=label)
info["hide_qexp"] = False
info['max_cn_qexp'] = WNF.q_expansion.prec()
## All combinations should be tested...
## 13/4/4/a -> base ring = coefficient_field = QQ(zeta_6)
## 13/3/8/a -> base_ring = QQ(zeta_4), coefficient_field has poly x^2+(2\zeta_4+2x-3\zeta_$ over base_ring
## 13/4/3/a -> base_ring = coefficient_field = QQ(zeta_3)
## 13/4/1/a -> all rational
## 13/6/1/a/ -> base_ring = QQ, coefficient_field = Q(sqrt(17))
## These are variables which needs to be set properly below
info['polvars'] = {'base_ring': 'x', 'coefficient_field': '\\alpha'}
if not cf_is_QQ:
if rdeg > 1: # not WNF.coefficient_field == WNF.base_ring:
## Here WNF.base_ring should be some cyclotomic field and we have an extension over this.
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1,
'\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [
WNF.coefficient_field.absolute_polynomial_latex('x'),
c_pol_ltx_x, z1
]
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url,
WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_label
]
if z1 == 4:
info[
'polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(
c_pol_ltx)
info['polvars']['base_ring'] = 'i'
elif z1 <= 2:
info[
'polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(
c_pol_ltx)
else:
info[
'polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\) ' % (
c_pol_ltx, z1, z1)
info['polvars']['base_ring'] = '\zeta_{{ {0} }}'.format(z1)
if z1 == 3:
info[
'polynomial_st'] += 'is a primitive cube root of unity.'
else:
info[
'polynomial_st'] += 'is a primitive {0}-th root of unity.'.format(
z1)
elif not br_is_QQ:
## Now we have base and coefficient field being equal, meaning that since the coefficient field is not QQ it is some cyclotomic field
## generated by some \zeta_n
p1 = WNF.coefficient_field.absolute_polynomial()
z1 = WNF.coefficient_field.gens()[0].multiplicative_order()
c_pol_ltx = web_latex_poly(p1, '\\zeta_{{{0}}}'.format(z1))
c_pol_ltx_x = web_latex_poly(p1, 'x')
info['coeff_field'] = [
WNF.coefficient_field.absolute_polynomial_latex('x'),
c_pol_ltx_x
]
if hasattr(WNF.coefficient_field,
"lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url,
WNF.coefficient_field.lmfdb_pretty,
WNF.coefficient_field.lmfdb_label
]
if z1 == 4:
info[
'polynomial_st'] = '<div class="where">where \(\zeta_4=e^{{\\frac{{\\pi i}}{{ 2 }} }}=i \).</div>'.format(
c_pol_ltx)
info['polvars']['coefficient_field'] = 'i'
elif z1 <= 2:
info['polynomial_st'] = ''
else:
info[
'polynomial_st'] = '<div class="where">where \(\zeta_{{{0}}}=e^{{\\frac{{2\\pi i}}{{ {0} }} }}\) '.format(
z1)
info['polvars']['coefficient_field'] = '\zeta_{{{0}}}'.format(
z1)
if z1 == 3:
info[
'polynomial_st'] += 'is a primitive cube root of unity.</div>'
else:
info[
'polynomial_st'] += 'is a primitive {0}-th root of unity.</div>'.format(
z1)
else:
info['polynomial_st'] = ''
if info["hide_qexp"]:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg == 1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [
WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty
]
else:
info['is_rational'] = 0
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings[
'values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = [('Level', str(level)), ('Weight', str(weight)),
('Character', '$' + WNF.character.latex_name + '$'),
('Label', WNF.hecke_orbit_label),
('Dimension of Galois orbit', str(WNF.dimension))]
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'],
list) and len(info['twist_info']) > 0:
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})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm == 1:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(
info['cm_field'], getDBConnection(),
field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label",
label=info["cm_field"])
if WNF.is_cm is None or WNF.is_cm == -1:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm == 1:
s = 'Yes<br>'
else:
s = 'No<br>'
properties2.append(('CM', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if (level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6', '')
if poly != '':
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(
abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 1:
a = ""
if b == 1:
b = ""
if a == 0 and b != 0:
s += "E_6^{{ {0} }}(z)".format(b)
elif b == 0 and a != 0:
s += "E_4^{{ {0} }}(z)".format(a)
else:
s += "E_4^{{ {0} }}(z) \cdot E_6^{{ {1} }}(z)".format(a, b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
# cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + '&label=' + str(label) # never used
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if (label_other != label):
s = 'Modular form '
if character:
s += newform_label(level, weight, character, label_other)
else:
s += newform_label(level, weight, 1, 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 += newform_label(level, weight, character, label)
else:
s += newform_label(level, weight, 1, 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.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_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.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_available_prec()
return info
def render_elliptic_modular_form_navigation_wp(**args):
r"""
Renders the webpage for the navigational page.
"""
emf_logger.debug("render_c_m_f_n_wp")
info = to_dict(args)
level = my_get(info, 'level', 0, int)
weight = my_get(info, 'weight', 0, int)
character = my_get(info, 'character', 0, int)
label = info.get('label', '')
disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if ('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
if weight != 0:
is_set['weight'] = True
if level != 0:
is_set['level'] = True
if ('get_table' in info): # we want a table
info = set_table(info, is_set)
page = "emf_table.html"
title = "Table of spaces of elliptic modular forms"
return render_template(page, info=info, title=title)
## This is the list of weights we initially put on the form
weight = int(weight)
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page'))]
# fun = dimension_new_cusp_forms
# title = 'Newforms'
if is_set['weight']:
wt_range = (weight, weight)
else:
if character == 0:
wt_range = (2, 12)
else:
wt_range = (2, 12)
if is_set['level']:
level_range = (level, level)
else:
level_range = (1, 24)
if character == 0:
info['grouptype'] = 0
info['groupother'] = 1
else:
info['grouptype'] = 1
info['groupother'] = 0
info['show_switch'] = True
disp.set_table_browsing(limit=[wt_range, level_range],
keys=['Weight', 'Level'],
character=character,
dimension_table=DimensionTable(info['grouptype']),
title='Browse Holomorphic Modular Forms',
check_db=True)
info['browse_table'] = disp._table
return render_template("emf_navigation.html",
info=info,
title=title,
bread=bread)
def render_elliptic_modular_form_navigation_wp1(**args):
r"""
Renders the webpage for the navigational page.
"""
from sage.all import is_even
info = to_dict(args)
args = to_dict(request.args)
info.update(args)
form = to_dict(request.form)
info.update(form)
emf_logger.debug("render_c_m_f_n_wp info={0}".format(info))
level = my_get(info, 'level', 0, int)
weight = my_get(info, 'weight', 0, int)
group = my_get(info, 'group', 1, int)
if group == int(0):
pass
character = my_get(info, 'character', 1, int)
label = info.get('label', '')
#disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
emf_logger.debug("group=%s, %s" % (group, type(group)))
if('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
if isinstance(weight,int) and weight > 0:
is_set['weight'] = True
weight = int(weight)
else:
weight = None
info.pop('weight',None)
if isinstance(level,int) and level > 0:
is_set['level'] = True
level = int(level)
else:
level = None
info.pop('level',None)
## This is the list of weights we initially put on the form
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page')),
(title, url_for('.render_elliptic_modular_forms'))]
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
# Special case: if the range reduces to a singleton for both level
# and weight then we return a single page rather than a table:
if limits_weight[0] == limits_weight[1] and limits_level[0] == limits_level[1]:
return render_elliptic_modular_form_space_list_chars(limits_level[0], limits_weight[0])
if is_set['weight']:
limits_weight = (weight, weight)
elif limits_weight is None:
limits_weight = (2, 12) # default values
if is_set['level']:
limits_level = (level, level)
elif limits_level is None:
limits_level = (1, 24) # default values
try:
group = info.get('group',0) # default group is gamma_0
group = int(group)
except ValueError:
group = 0
if group not in [0,1]:
group = 0
if group == 0:
info['grouptype'] = 0; info['groupother'] = 1
else:
info['grouptype'] = 1; info['groupother'] = 0
emf_logger.debug("level:{0},level_range={1}".format(level,limits_level))
emf_logger.debug("weight:{0},weight_range={1}".format(weight,limits_weight))
if limits_weight[0] == limits_weight[1] and limits_level[0] == limits_level[1]:
return redirect(url_for("emf.render_elliptic_modular_forms",
level=limits_level[0],weight=limits_weight[0],group=group), code=301)
info['show_switch'] = True
db = getDBConnection()['modularforms2']['webmodformspace_dimension']
table = {}
q = db.find_one({'group':'gamma{0}'.format(group)})
if q:
table = q.get('data',{})
if table != {}:
table = json.loads(table)
info['table'] = {}
level_range = range(limits_level[0],limits_level[1]+1)
# we don't have weight 1 in database
if limits_weight[0]==1:
limits_weight=(2,limits_weight[1])
weight_range = range(limits_weight[0],limits_weight[1]+1)
#print "levels=",level_range
#print "weights=",weight_range
if len(weight_range)>1:
info['weight_range']="{0}-{1}".format(limits_weight[0],limits_weight[1])
if len(level_range)>1:
info['level_range']="{0}-{1}".format(limits_level[0],limits_level[1])
if group == 0:
weight_range = filter(is_even,weight_range)
for n in level_range:
info['table'][n]={}
sn = unicode(n)
for k in weight_range:
info['table'][n][k]={}
sk = unicode(k)
if table.has_key(sn):
if table[sn].has_key(sk):
info['table'][n][k] = table[sn][sk] #.get(str(n),{}).get(str(k),"n/a")
else:
emf_logger.debug("Set table for Gamma1")
for n in level_range:
info['table'][n]={}
for k in weight_range:
info['table'][n][k] = table.get(str(n),{}).get(str(k),{}).get(str(-1),"n/a")
#print "table=\n",table
#print "info=\n",info
#info['table']=table
info['col_heads'] = level_range
info['row_heads'] = weight_range
return render_template("emf_browse_spaces.html", info=info, title=title, bread=bread)
def set_info_for_web_newform(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_cached(level=level,
weight=weight,
character=character,
label=label)
emf_logger.critical("defined webnewform for rendering!")
# 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
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms",
level=level,
weight=weight,
character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',
level=level,
weight=weight,
character=character)
friends.append(
('\( S_{%s}(%s, %s)\)' %
(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if WNF.coefficient_field_label(check=True):
friends.append(('Number field ' + WNF.coefficient_field_label(),
WNF.coefficient_field_url()))
friends.append(
('Number field ' + WNF.base_field_label(), WNF.base_field_url()))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)",
WNF.character.url()))
if WNF.dimension == 0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
#info['name'] = name
info['title'] = 'Modular Form ' + WNF.hecke_orbit_label
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....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if WNF.coefficient_field.absolute_degree() == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
if cdeg == 1:
info['satake'] = WNF.satake
info['qexp'] = WNF.q_expansion_latex(prec=10, name='a')
info['qexp_display'] = url_for(".get_qexp_latex",
level=level,
weight=weight,
character=character,
label=label)
# info['qexp'] = WNF.q_expansion_latex(prec=prec)
#c_pol_st = str(WNF.absolute_polynomial)
#b_pol_st = str(WNF.polynomial(type='base_ring',format='str'))
#b_pol_ltx = str(WNF.polynomial(type='base_ring',format='latex'))
#print "c=",c_pol_ltx
#print "b=",b_pol_ltx
if cdeg > 1: ## Field is QQ
if bdeg > 1 and rdeg > 1:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = latex(p1)
lgc = p1.variables()[0]
c_pol_ltx = c_pol_ltx.replace(lgc, 'a')
z = p1.base_ring().gens()[0]
p2 = z.minpoly()
b_pol_ltx = latex(p2)
b_pol_ltx = b_pol_ltx.replace(latex(p2.variables()[0]), latex(z))
info['polynomial_st'] = 'where \({0}=0\) and \({1}=0\).'.format(
c_pol_ltx, b_pol_ltx)
else:
c_pol_ltx = latex(WNF.coefficient_field.relative_polynomial())
lgc = str(
latex(WNF.coefficient_field.relative_polynomial().variables()
[0]))
c_pol_ltx = c_pol_ltx.replace(lgc, 'a')
info['polynomial_st'] = 'where \({0}=0\)'.format(c_pol_ltx)
else:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg == 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._embeddings[
'values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'],
list) and len(info['twist_info']) > 0:
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})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm is None:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm is True:
s = '- Is a CM-form<br>'
else:
s = '- Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if (level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6', '')
if poly <> '':
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(d):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(
abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 0 and b <> 0:
s += "E_6^{{ {0} }}".format(b)
elif b == 0 and a <> 0:
s += "E_4^{{ {0} }}".format(a)
else:
s += "E_4^{{ {0} }}E_6^{{ {1} }}".format(a, b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
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.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_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.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def render_elliptic_modular_forms(level=None, weight=None, character=None, label=None,group=None, **kwds):
r"""
Default input of same type as required. Note that for holomorphic modular forms: level=0 or weight=0 are non-existent.
"""
emf_logger.debug(
"In render: level={0},weight={1},character={2},group={3},label={4}".format(level, weight, character, group, label))
emf_logger.debug("args={0}".format(request.args))
emf_logger.debug("args={0}".format(request.form))
emf_logger.debug("met={0}".format(request.method))
keys = ['download', 'jump_to']
info = get_args(request, level, weight, character, group, label, keys=keys)
valid = validate_parameters(level,weight,character,label,info)
if isinstance(valid,basestring):
return redirect(valid,code=301)
level = info['level']; weight = info['weight']; character = info['character']
#if info.has_key('error'):
# return render_elliptic_modular_form_navigation_wp(error=info['error'])
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
group = info.get('group',None)
emf_logger.debug("group=%s, %s" % (group, type(group)))
if group == 0:
info['character'] = character = 1 # only trivial character for Gamma_0(N)
try:
if 'download' in info:
return get_downloads(**info)
emf_logger.debug("info=%s" % info)
## Consistency of arguments>
# if level<=0: level=None
# if weight<=0: weight=None
if 'jump_to' in info: # try to find out which form we want to jump
s = my_get(info, 'jump_to', '', str)
emf_logger.info("info.keys1={0}".format(info.keys()))
info.pop('jump_to')
emf_logger.info("info.keys2={0}".format(info.keys()))
args = extract_data_from_jump_to(s)
emf_logger.debug("args=%s" % args)
return redirect(url_for("emf.render_elliptic_modular_forms", **args), code=301)
# return render_elliptic_modular_forms(**args)
emf_logger.debug("HERE! weight={0} level={1} char={2}".format(weight,level,character))
if level > 0 and weight > 0 and character > 0:
if label != '' and not label is None:
return render_web_newform(**info)
else:
return render_web_modform_space(**info)
if level > 0 and weight > 0 and (group != 0 or character == None):
return render_web_modform_space_gamma1(**info)
return render_elliptic_modular_form_navigation_wp(**info)
# Otherwise we go to the main navigation page
except IndexError as e: # catch everything here except KeyError below...
emf_logger.debug("catching exceptions. info={0}".format(info))
errst = str(e)
## Try to customise some of the error messages:
if 'Character' and 'not exist' in errst:
errst += " Please choose a character from the table below!"
flash(errst,'error')
return render_elliptic_modular_form_navigation_wp(**info)
if 'WebNewForm_computing' in errst:
errst = "The space {0}.{1}.{2} is not in the database!".format(level,weight,character)
flash(errst)
return render_elliptic_modular_form_navigation_wp()
except KeyError as e:
emf_logger.debug("catching exceptions. info={0}".format(info))
errst = "The space {0}.{1}.{2} is not in the database!".format(level,weight,character)
flash(errst)
return render_elliptic_modular_form_navigation_wp()
def render_elliptic_modular_form_navigation_wp(**args):
r"""
Renders the webpage for the navigational page.
"""
from sage.all import is_even
info = to_dict(args)
args = to_dict(request.args)
info.update(args)
form = to_dict(request.form)
info.update(form)
emf_logger.debug("render_c_m_f_n_wp info={0}".format(info))
level = my_get(info, 'level', 0, int)
weight = my_get(info, 'weight', 0, int)
character = my_get(info, 'character', 1, int)
label = info.get('label', '')
#disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
if weight != 0:
is_set['weight'] = True
if level != 0:
is_set['level'] = True
## This is the list of weights we initially put on the form
weight = int(weight)
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page')),
(title, url_for('emf.render_elliptic_modular_forms'))]
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
if limits_weight[0] == limits_weight[1] and limits_level[0] == limits_level[1]:
return render_elliptic_modular_form_space_list_chars(limits_level[0], limits_weight[0])
if is_set['weight']:
limits_weight = (weight, weight)
else:
if character == 1:
limits_weight = (2, 12)
else:
limits_weight = (2, 12)
if is_set['level']:
limits_level = (level, level)
else:
limits_level = (1, 24)
if character == 1:
info['grouptype'] = 0; info['groupother'] = 1
else:
info['grouptype'] = 1; info['groupother'] = 0
info['show_switch'] = True
db = getDBConnection()['modularforms2']['webmodformspace_dimension']
table = {}
if character == 1:
q = db.find_one({'group':'gamma0'})
if q:
table = q.get('data',{})
else:
q = db.find_one({'group':'gamma1'})
if q:
table = q.get('data',{})
if table != {}:
table = json.loads(table)
info['table'] = {}
level_range = range(limits_level[0],limits_level[1]+1)
weight_range = range(limits_weight[0],limits_weight[1]+1)
#print "levels=",level_range
#print "weights=",weight_range
if character == 1:
weight_range = filter(is_even,weight_range)
for n in level_range:
info['table'][n]={}
sn = unicode(n)
for k in weight_range:
info['table'][n][k]={}
sk = unicode(k)
if table.has_key(sn):
if table[sn].has_key(sk):
info['table'][n][k] = table[sn][sk] #.get(str(n),{}).get(str(k),"n/a")
else:
for n in level_range:
info['table'][n]={}
for k in weight_range:
info['table'][n][k] = table.get(str(n),{}).get(str(k),"{}").get(str(character),"n/a")
#print "table=\n",table
#print "info=\n",info
#info['table']=table
info['col_heads'] = level_range
info['row_heads'] = weight_range
return render_template("emf_browse_spaces.html", info=info, title=title, bread=bread)
def print_list_of_coefficients(info):
r"""
Print a table of Fourier coefficients in the requested format
"""
level = my_get(info, 'level', -1, int)
weight = my_get(info, 'weight', -1, int)
prec = my_get(info, 'prec', 12, int) # number of digits
bitprec = my_get(info, 'bitprec', 12, int) # number of digits
character = my_get(info, 'character', '', str) # int(info.get('weight',0))
fmt = info.get("format","q_expansion")
if character == '':
character = '1'
label = info.get('label', '')
if character.isalnum():
character = int(character)
else:
return "The character '{0}' is not well-defined!".format(character)
print "--------------"
if label == '' or level == -1 or weight == -1:
return "Need to specify a modular form completely!!"
WMFS = WebModFormSpace(level= level, weight = weight, cuspidal=True,character = character)
if not WMFS:
return ""
if('number' in info):
number = int(info['number']) + 1
else:
number = max(WMFS.sturm_bound + 1, 20)
FS = list()
f = WMFS.hecke_orbits.get(label)
if f is not None:
FS.append(f)
else:
for label in WMFS.hecke_orbits:
FS.append(WMFS.f(label))
shead = "Cusp forms of weight " + str(weight) + "on \(" + latex(WMFS.group) + "\)"
s = ""
if((character is not None) and (character > 0)):
shead = shead + " and character \( \chi_{" + str(character) + "}\)"
# s="<table><tr><td>"
coefs = ""
if fmt == "sage":
res = []
for F in FS:
if number > F.max_cn():
raise IndexError,"The database does not contain this many ({0}) coefficients for this modular form! We only have {1}".format(number,F.max_cn())
if len(FS) > 1:
if info['format'] == 'html':
coefs += F.label()
else:
coefs += F.label()
if fmt == "sage":
qe = F.coefficients(range(number))
res.append(qe)
else:
coefs += print_coefficients_for_one_form(F, number, info['format'],bitprec=bitprec)
if not fmt == "sage":
return s+"\n"+coefs
else:
if len(res)==1:
res = res[0]
#print "res=",res
return dumps(res)
def set_info_for_web_newform(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_cached(level=level, weight=weight, character=character, label=label)
emf_logger.critical("defined webnewform for rendering!")
# 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
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',level=level, weight=weight, character=character)
friends.append(('\( S_{%s}(%s, %s)\)'%(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty, WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension==0:
info['error'] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
#info['name'] = name
info['title'] = 'Modular Form ' + WNF.hecke_orbit_label
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....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
info['max_cn_qexp'] = WNF.q_expansion.prec()
if not cf_is_QQ:
if not br_is_QQ and rdeg>1: # not WNF.coefficient_field == WNF.base_ring:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'),c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(c_pol_ltx)
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\).'%(c_pol_ltx, z1,z1)
else:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha')
c_pol_ltx_x = web_latex_poly(p1, 'x')
z1 = p1.base_ring().gens()[0].multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'), c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).'.format(c_pol_ltx)
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\).'%(c_pol_ltx, z1,z1)
else:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg==1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty ]
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._embeddings['values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = []
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'], list) and len(info['twist_info'])>0:
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})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(info['cm_field'], getDBConnection(), field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label", label=info["cm_field"])
if WNF.is_cm is None:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm:
s = 'Is a CM-form<br>'
else:
s = 'Is not a CM-form<br>'
properties2.append(('CM info', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev,dict) and len(alev.keys())>0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if(level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6','')
if poly != '':
d,monom,coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d>1 and i >0 and c>0:
s="+"
if c<0:
s="-"
if c.denominator()>1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()),c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]; b = monom[i][1]
if a == 0 and b != 0:
s+="E_6^{{ {0} }}".format(b)
elif b ==0 and a != 0:
s+="E_4^{{ {0} }}".format(a)
else:
s+="E_4^{{ {0} }}E_6^{{ {1} }}".format(a,b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + \
'&label=' + str(label)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
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.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_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.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_cn()
return info
def set_info_for_web_newform(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_cached(level=level, weight=weight, character=character, label=label)
emf_logger.critical("defined webnewform for rendering!")
# 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
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(EMF_TOP, url1)]
bread.append(("of level %s" % level, url2))
bread.append(("weight %s" % weight, url3))
if int(character) == 0:
bread.append(("trivial character", url4))
else:
bread.append(("\( %s \)" % (WNF.character.latex_name), url4))
info["bread"] = bread
properties2 = list()
friends = list()
space_url = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
friends.append(("\( S_{%s}(%s, %s)\)" % (WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if WNF.coefficient_field_label(check=True):
friends.append(("Number field " + WNF.coefficient_field_label(), WNF.coefficient_field_url()))
friends.append(("Number field " + WNF.base_field_label(), WNF.base_field_url()))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension == 0:
info["error"] = "This space is empty!"
# emf_logger.debug("WNF={0}".format(WNF))
# info['name'] = name
info["title"] = "Modular Form " + WNF.hecke_orbit_label
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....
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if WNF.coefficient_field.absolute_degree() == 1:
rdeg = 1
else:
rdeg = WNF.coefficient_field.relative_degree()
if cdeg == 1:
info["satake"] = WNF.satake
info["qexp"] = WNF.q_expansion_latex(prec=10, name="a")
info["qexp_display"] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
# info['qexp'] = WNF.q_expansion_latex(prec=prec)
# c_pol_st = str(WNF.absolute_polynomial)
# b_pol_st = str(WNF.polynomial(type='base_ring',format='str'))
# b_pol_ltx = str(WNF.polynomial(type='base_ring',format='latex'))
# print "c=",c_pol_ltx
# print "b=",b_pol_ltx
if cdeg > 1: ## Field is QQ
if bdeg > 1 and rdeg > 1:
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = latex(p1)
lgc = p1.variables()[0]
c_pol_ltx = c_pol_ltx.replace(lgc, "a")
z = p1.base_ring().gens()[0]
p2 = z.minpoly()
b_pol_ltx = latex(p2)
b_pol_ltx = b_pol_ltx.replace(latex(p2.variables()[0]), latex(z))
info["polynomial_st"] = "where \({0}=0\) and \({1}=0\).".format(c_pol_ltx, b_pol_ltx)
else:
c_pol_ltx = latex(WNF.coefficient_field.relative_polynomial())
lgc = str(latex(WNF.coefficient_field.relative_polynomial().variables()[0]))
c_pol_ltx = c_pol_ltx.replace(lgc, "a")
info["polynomial_st"] = "where \({0}=0\)".format(c_pol_ltx)
else:
info["polynomial_st"] = ""
info["degree"] = int(cdeg)
if cdeg == 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._embeddings["values"] # q_expansion_embeddings(prec, bprec,format='latex')
info["embeddings_len"] = len(info["embeddings"])
properties2 = []
if (ZZ(level)).is_squarefree():
info["twist_info"] = WNF.twist_info
if isinstance(info["twist_info"], list) and len(info["twist_info"]) > 0:
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})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key("tau") and len(CM["tau"]) != 0:
info["CM_values"] = CM
info["is_cm"] = WNF.is_cm
if WNF.is_cm is None:
s = "- Unknown (insufficient data)<br>"
elif WNF.is_cm is True:
s = "- Is a CM-form<br>"
else:
s = "- Is not a CM-form<br>"
properties2.append(("CM info", s))
alev = WNF.atkin_lehner_eigenvalues()
info["atkinlehner"] = None
if isinstance(alev, dict) and len(alev.keys()) > 0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if level == 1:
poly = WNF.explicit_formulas.get("as_polynomial_in_E4_and_E6", "")
if poly != "":
d, monom, coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info["explicit_formulas"] = "\("
for i in range(d):
c = QQ(coeffs[i])
s = ""
if d > 1 and i > 0 and c > 0:
s = "+"
if c < 0:
s = "-"
if c.denominator() > 1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()), c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]
b = monom[i][1]
if a == 0 and b != 0:
s += "E_6^{{ {0} }}".format(b)
elif b == 0 and a != 0:
s += "E_4^{{ {0} }}".format(a)
else:
s += "E_4^{{ {0} }}E_6^{{ {1} }}".format(a, b)
info["explicit_formulas"] += s
info["explicit_formulas"] += " \)"
cur_url = (
"?&level=" + str(level) + "&weight=" + str(weight) + "&character=" + str(character) + "&label=" + str(label)
)
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
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.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_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.coefficient_field_degree == 1:
llabel = str(level) + "." + label
s = "Elliptic curve isogeny class " + llabel
url = "/EllipticCurve/Q/" + llabel
friends.append((s, url))
info["properties2"] = properties2
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, '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 render_elliptic_modular_form_navigation_wp(**args):
r"""
Renders the webpage for the navigational page.
"""
emf_logger.debug("render_c_m_f_n_wp")
info = to_dict(args)
level = my_get(info, 'level', 0, int)
weight = my_get(info, 'weight', 0, int)
character = my_get(info, 'character', 0, int)
label = info.get('label', '')
disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
if weight != 0:
is_set['weight'] = True
if level != 0:
is_set['level'] = True
if('get_table' in info): # we want a table
info = set_table(info, is_set)
page = "emf_table.html"
title = "Table of spaces of elliptic modular forms"
return render_template(page, info=info, title=title)
## This is the list of weights we initially put on the form
weight = int(weight)
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page'))]
# fun = dimension_new_cusp_forms
# title = 'Newforms'
if is_set['weight']:
wt_range = (weight, weight)
else:
if character == 0:
wt_range = (2, 12)
else:
wt_range = (2, 12)
if is_set['level']:
level_range = (level, level)
else:
level_range = (1, 24)
if character == 0:
info['grouptype'] = 0
info['groupother'] = 1
else:
info['grouptype'] = 1
info['groupother'] = 0
info['show_switch'] = True
disp.set_table_browsing(limit=[wt_range, level_range],
keys=['Weight', 'Level'], character=character,
dimension_table=DimensionTable(info['grouptype']), title='Browse Holomorphic Modular Forms', check_db=True)
info['browse_table'] = disp._table
return render_template("emf_navigation.html", info=info, title=title, bread=bread)
def render_elliptic_modular_form_navigation_wp(**args):
r"""
Renders the webpage for the navigational page.
"""
from sage.all import is_even
info = to_dict(args)
args = to_dict(request.args)
info.update(args)
form = to_dict(request.form)
info.update(form)
emf_logger.debug("render_c_m_f_n_wp info={0}".format(info))
level = my_get(info, 'level', 0, int)
weight = my_get(info, 'weight', 0, int)
character = my_get(info, 'character', 1, int)
label = info.get('label', '')
#disp = ClassicalMFDisplay('modularforms2')
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
emf_logger.debug("character=%s, %s" % (character, type(character)))
if ('plot' in info and level is not None):
return render_fd_plot(level, info)
is_set = dict()
is_set['weight'] = False
is_set['level'] = False
if weight != 0:
is_set['weight'] = True
if level != 0:
is_set['level'] = True
## This is the list of weights we initially put on the form
weight = int(weight)
title = "Holomorphic Cusp Forms"
bread = [(MF_TOP, url_for('mf.modular_form_main_page'))]
limits_weight = extract_limits_as_tuple(info, 'weight')
limits_level = extract_limits_as_tuple(info, 'level')
if limits_weight[0] == limits_weight[1] and limits_level[
0] == limits_level[1]:
return render_elliptic_modular_form_space_list_chars(
limits_level[0], limits_weight[0])
if is_set['weight']:
limits_weight = (weight, weight)
else:
if character == 1:
limits_weight = (2, 12)
else:
limits_weight = (2, 12)
if is_set['level']:
limits_level = (level, level)
else:
limits_level = (1, 24)
if character == 1:
info['grouptype'] = 0
info['groupother'] = 1
else:
info['grouptype'] = 1
info['groupother'] = 0
info['show_switch'] = True
db = getDBConnection()['modularforms2']['webmodformspace_dimension']
table = {}
if character == 1:
q = db.find_one({'group': 'gamma0'})
if q:
table = q.get('data', {})
else:
q = db.find_one({'group': 'gamma1'})
if q:
table = q.get('data', {})
if table <> {}:
table = json.loads(table)
info['table'] = {}
level_range = range(limits_level[0], limits_level[1] + 1)
weight_range = range(limits_weight[0], limits_weight[1] + 1)
#print "levels=",level_range
#print "weights=",weight_range
if character == 1:
weight_range = filter(is_even, weight_range)
for n in level_range:
info['table'][n] = {}
sn = unicode(n)
for k in weight_range:
info['table'][n][k] = {}
sk = unicode(k)
if table.has_key(sn):
if table[sn].has_key(sk):
info['table'][n][k] = table[sn][
sk] #.get(str(n),{}).get(str(k),"n/a")
else:
for n in level_range:
info['table'][n] = {}
for k in weight_range:
info['table'][n][k] = table.get(str(n),
{}).get(str(k), "{}").get(
str(character), "n/a")
#print "table=\n",table
#print "info=\n",info
#info['table']=table
info['col_heads'] = level_range
info['row_heads'] = weight_range
return render_template("emf_browse_spaces.html",
info=info,
title=title,
bread=bread)
def render_elliptic_modular_forms(level=None,
weight=None,
character=None,
label=None,
group=None,
**kwds):
r"""
Default input of same type as required. Note that for holomorphic modular forms: level=0 or weight=0 are non-existent.
"""
emf_logger.debug(
"In render: level={0},weight={1},character={2},group={3},label={4}".
format(level, weight, character, group, label))
emf_logger.debug("args={0}".format(request.args))
emf_logger.debug("args={0}".format(request.form))
emf_logger.debug("met={0}".format(request.method))
keys = ['download', 'jump_to']
info = get_args(request, level, weight, character, group, label, keys=keys)
valid = validate_parameters(level, weight, character, label, info)
if isinstance(valid, basestring):
return redirect(valid, code=301)
level = info['level']
weight = info['weight']
character = info['character']
#if info.has_key('error'):
# return render_elliptic_modular_form_navigation_wp(error=info['error'])
emf_logger.debug("info={0}".format(info))
emf_logger.debug("level=%s, %s" % (level, type(level)))
emf_logger.debug("label=%s, %s" % (label, type(label)))
emf_logger.debug("wt=%s, %s" % (weight, type(weight)))
group = info.get('group', None)
emf_logger.debug("group=%s, %s" % (group, type(group)))
if group == 0:
info[
'character'] = character = 1 # only trivial character for Gamma_0(N)
try:
if 'download' in info:
return get_downloads(**info)
emf_logger.debug("info=%s" % info)
## Consistency of arguments>
# if level<=0: level=None
# if weight<=0: weight=None
if 'jump_to' in info: # try to find out which form we want to jump
s = my_get(info, 'jump_to', '', str)
emf_logger.info("info.keys1={0}".format(info.keys()))
info.pop('jump_to')
emf_logger.info("info.keys2={0}".format(info.keys()))
args = extract_data_from_jump_to(s)
emf_logger.debug("args=%s" % args)
return redirect(url_for("emf.render_elliptic_modular_forms",
**args),
code=301)
# return render_elliptic_modular_forms(**args)
emf_logger.debug("HERE! weight={0} level={1} char={2}".format(
weight, level, character))
if level > 0 and weight > 0 and character > 0:
if label != '' and not label is None:
return render_web_newform(**info)
else:
return render_web_modform_space(**info)
if level > 0 and weight > 0 and (group != 0 or character == None):
return render_web_modform_space_gamma1(**info)
return render_elliptic_modular_form_navigation_wp(**info)
# Otherwise we go to the main navigation page
except IndexError as e: # catch everything here except KeyError below...
emf_logger.debug("catching exceptions. info={0} e={1}".format(info, e))
errst = str(e)
## Try to customise some of the error messages:
if 'Character' and 'not exist' in errst:
errst += " Please choose a character from the table below!"
flash(errst, 'error')
return render_elliptic_modular_form_navigation_wp(**info)
if 'WebNewForm_computing' in errst:
errst = "The space {0}.{1}.{2} is not in the database!".format(
level, weight, character)
flash(errst)
return render_elliptic_modular_form_navigation_wp()
except KeyError as e:
emf_logger.debug("catching exceptions. info={0} e={1}".format(info, e))
errst = "The orbit {0} is not in the database!".format(
newform_label(level, weight, character, label))
flash(errst)
return render_elliptic_modular_form_navigation_wp()
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
def set_info_for_web_newform(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_cached(level=level, weight=weight, character=character, label=label)
if not WNF.has_updated():
raise IndexError("Unfortunately, we do not have this newform in the database.")
info['character_order'] = WNF.character.order
info['code'] = WNF.code
emf_logger.debug("defined webnewform for rendering!")
except IndexError as e:
info['error'] = e.message
url0 = url_for("mf.modular_form_main_page")
url1 = url_for("emf.render_elliptic_modular_forms")
url2 = url_for("emf.render_elliptic_modular_forms", level=level)
url3 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight)
url4 = url_for("emf.render_elliptic_modular_forms", level=level, weight=weight, character=character)
bread = [(MF_TOP, url0), (EMF_TOP, url1)]
bread.append(("Level %s" % level, url2))
bread.append(("Weight %s" % weight, url3))
bread.append(("Character \( %s \)" % (WNF.character.latex_name), url4))
bread.append(("Newform %d.%d.%d.%s" % (level, weight, int(character), label),''))
info['bread'] = bread
properties2 = list()
friends = list()
space_url = url_for('emf.render_elliptic_modular_forms',level=level, weight=weight, character=character)
friends.append(('\( S_{%s}(%s, %s)\)'%(WNF.weight, WNF.level, WNF.character.latex_name), space_url))
if hasattr(WNF.base_ring, "lmfdb_url") and WNF.base_ring.lmfdb_url:
friends.append(('Number field ' + WNF.base_ring.lmfdb_pretty, WNF.base_ring.lmfdb_url))
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_label:
friends.append(('Number field ' + WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_url))
friends = uniq(friends)
friends.append(("Dirichlet character \(" + WNF.character.latex_name + "\)", WNF.character.url()))
if WNF.dimension==0 and not info.has_key('error'):
info['error'] = "This space is empty!"
info['title'] = 'Newform ' + WNF.hecke_orbit_label
info['learnmore'] = [('History of modular forms', url_for('.holomorphic_mf_history'))]
if 'error' in info:
return info
## Until we have figured out how to do the embeddings correctly we don't display the Satake
## parameters for non-trivial characters....
## Example to illustrate the different cases
## base = CyclotomicField(n) -- of degree phi(n)
## coefficient_field = NumberField( p(x)) for some p in base['x'] of degree m
## we would then have cdeg = m*phi(n) and bdeg = phi(n)
## and rdeg = m
## Unfortunately, for e.g. base = coefficient_field = CyclotomicField(6)
## we get coefficient_field.relative_degree() == 2 although it should be 1
cdeg = WNF.coefficient_field.absolute_degree()
bdeg = WNF.base_ring.absolute_degree()
if cdeg == 1:
rdeg = 1
else:
## just setting rdeg = WNF.coefficient_field.relative_degree() does not give correct result...
##
rdeg = QQ(cdeg)/QQ(bdeg)
cf_is_QQ = (cdeg == 1)
br_is_QQ = (bdeg == 1)
if cf_is_QQ:
info['satake'] = WNF.satake
if WNF.complexity_of_first_nonvanishing_coefficients() > default_max_height:
info['qexp'] = ""
info['qexp_display'] = ''
info['hide_qexp'] = True
n,c = WNF.first_nonvanishing_coefficient()
info['trace_nv'] = latex(WNF.first_nonvanishing_coefficient_trace())
info['norm_nv'] = '\\approx ' + latex(WNF.first_nonvanishing_coefficient_norm().n())
info['index_nv'] = n
else:
if WNF.prec < prec:
#get WNF record at larger prec
WNF.prec = prec
WNF.update_from_db()
info['qexp'] = WNF.q_expansion_latex(prec=10, name='\\alpha ')
info['qexp_display'] = url_for(".get_qexp_latex", level=level, weight=weight, character=character, label=label)
info["hide_qexp"] = False
info['max_cn_qexp'] = WNF.q_expansion.prec()
## All combinations should be tested...
## 13/4/4/a -> base ring = coefficient_field = QQ(zeta_6)
## 13/3/8/a -> base_ring = QQ(zeta_4), coefficient_field has poly x^2+(2\zeta_4+2x-3\zeta_$ over base_ring
## 13/4/3/a -> base_ring = coefficient_field = QQ(zeta_3)
## 13/4/1/a -> all rational
## 13/6/1/a/ -> base_ring = QQ, coefficient_field = Q(sqrt(17))
## These are variables which needs to be set properly below
info['polvars'] = {'base_ring':'x','coefficient_field':'\\alpha'}
if not cf_is_QQ:
if rdeg>1: # not WNF.coefficient_field == WNF.base_ring:
## Here WNF.base_ring should be some cyclotomic field and we have an extension over this.
p1 = WNF.coefficient_field.relative_polynomial()
c_pol_ltx = web_latex_poly(p1, '\\alpha') # make the variable \alpha
c_pol_ltx_x = web_latex_poly(p1, 'x')
zeta = p1.base_ring().gens()[0]
# p2 = zeta.minpoly() #this is not used anymore
# b_pol_ltx = web_latex_poly(p2, latex(zeta)) #this is not used anymore
z1 = zeta.multiplicative_order()
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'),c_pol_ltx_x, z1]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\) and \(\zeta_4=i\).</div><br/>'.format(c_pol_ltx)
info['polvars']['base_ring']='i'
elif z1<=2:
info['polynomial_st'] = '<div class="where">where</div> {0}\(\mathstrut=0\).</div><br/>'.format(c_pol_ltx)
else:
info['polynomial_st'] = '<div class="where">where</div> %s\(\mathstrut=0\) and \(\zeta_{%s}=e^{\\frac{2\\pi i}{%s}}\) '%(c_pol_ltx, z1,z1)
info['polvars']['base_ring']='\zeta_{{ {0} }}'.format(z1)
if z1==3:
info['polynomial_st'] += 'is a primitive cube root of unity.'
else:
info['polynomial_st'] += 'is a primitive {0}-th root of unity.'.format(z1)
elif not br_is_QQ:
## Now we have base and coefficient field being equal, meaning that since the coefficient field is not QQ it is some cyclotomic field
## generated by some \zeta_n
p1 = WNF.coefficient_field.absolute_polynomial()
z1 = WNF.coefficient_field.gens()[0].multiplicative_order()
c_pol_ltx = web_latex_poly(p1, '\\zeta_{{{0}}}'.format(z1))
c_pol_ltx_x = web_latex_poly(p1, 'x')
info['coeff_field'] = [ WNF.coefficient_field.absolute_polynomial_latex('x'), c_pol_ltx_x]
if hasattr(WNF.coefficient_field, "lmfdb_url") and WNF.coefficient_field.lmfdb_url:
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty, WNF.coefficient_field.lmfdb_label]
if z1==4:
info['polynomial_st'] = '<div class="where">where \(\zeta_4=e^{{\\frac{{\\pi i}}{{ 2 }} }}=i \).</div>'.format(c_pol_ltx)
info['polvars']['coefficient_field']='i'
elif z1<=2:
info['polynomial_st'] = ''
else:
info['polynomial_st'] = '<div class="where">where \(\zeta_{{{0}}}=e^{{\\frac{{2\\pi i}}{{ {0} }} }}\) '.format(z1)
info['polvars']['coefficient_field']='\zeta_{{{0}}}'.format(z1)
if z1==3:
info['polynomial_st'] += 'is a primitive cube root of unity.</div>'
else:
info['polynomial_st'] += 'is a primitive {0}-th root of unity.</div>'.format(z1)
else:
info['polynomial_st'] = ''
if info["hide_qexp"]:
info['polynomial_st'] = ''
info['degree'] = int(cdeg)
if cdeg==1:
info['is_rational'] = 1
info['coeff_field_pretty'] = [ WNF.coefficient_field.lmfdb_url, WNF.coefficient_field.lmfdb_pretty ]
else:
info['is_rational'] = 0
emf_logger.debug("PREC2: {0}".format(prec))
info['embeddings'] = WNF._embeddings['values'] #q_expansion_embeddings(prec, bprec,format='latex')
info['embeddings_len'] = len(info['embeddings'])
properties2 = [('Level', str(level)),
('Weight', str(weight)),
('Character', '$' + WNF.character.latex_name + '$'),
('Label', WNF.hecke_orbit_label),
('Dimension of Galois orbit', str(WNF.dimension))]
if (ZZ(level)).is_squarefree():
info['twist_info'] = WNF.twist_info
if isinstance(info['twist_info'], list) and len(info['twist_info'])>0:
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})
alev = None
CM = WNF._cm_values
if CM is not None:
if CM.has_key('tau') and len(CM['tau']) != 0:
info['CM_values'] = CM
info['is_cm'] = WNF.is_cm
if WNF.is_cm == 1:
info['cm_field'] = "2.0.{0}.1".format(-WNF.cm_disc)
info['cm_disc'] = WNF.cm_disc
info['cm_field_knowl'] = nf_display_knowl(info['cm_field'], getDBConnection(), field_pretty(info['cm_field']))
info['cm_field_url'] = url_for("number_fields.by_label", label=info["cm_field"])
if WNF.is_cm is None or WNF.is_cm==-1:
s = '- Unknown (insufficient data)<br>'
elif WNF.is_cm == 1:
s = 'Yes<br>'
else:
s = 'No<br>'
properties2.append(('CM', s))
alev = WNF.atkin_lehner_eigenvalues()
info['atkinlehner'] = None
if isinstance(alev,dict) and len(alev.keys())>0 and level != 1:
s1 = " Atkin-Lehner eigenvalues "
s2 = ""
for Q in alev.keys():
s2 += "\( \omega_{ %s } \) : %s <br>" % (Q, alev[Q])
properties2.append((s1, s2))
emf_logger.debug("properties={0}".format(properties2))
# alev = WNF.atkin_lehner_eigenvalues_for_all_cusps()
# if isinstance(alev,dict) and len(alev.keys())>0:
# emf_logger.debug("alev={0}".format(alev))
# info['atkinlehner'] = list()
# for Q in alev.keys():
# s = "\(" + latex(c) + "\)"
# Q = alev[c][0]
# ev = alev[c][1]
# info['atkinlehner'].append([Q, c, ev])
if(level == 1):
poly = WNF.explicit_formulas.get('as_polynomial_in_E4_and_E6','')
if poly != '':
d,monom,coeffs = poly
emf_logger.critical("poly={0}".format(poly))
info['explicit_formulas'] = '\('
for i in range(len(coeffs)):
c = QQ(coeffs[i])
s = ""
if d>1 and i >0 and c>0:
s="+"
if c<0:
s="-"
if c.denominator()>1:
cc = "\\frac{{ {0} }}{{ {1} }}".format(abs(c.numerator()),c.denominator())
else:
cc = str(abs(c))
s += "{0} \cdot ".format(cc)
a = monom[i][0]; b = monom[i][1]
if a == 0 and b != 0:
s+="E_6^{{ {0} }}".format(b)
elif b ==0 and a != 0:
s+="E_4^{{ {0} }}".format(a)
else:
s+="E_4^{{ {0} }}E_6^{{ {1} }}".format(a,b)
info['explicit_formulas'] += s
info['explicit_formulas'] += " \)"
# cur_url = '?&level=' + str(level) + '&weight=' + str(weight) + '&character=' + str(character) + '&label=' + str(label) # never used
if len(WNF.parent.hecke_orbits) > 1:
for label_other in WNF.parent.hecke_orbits.keys():
if(label_other != label):
s = 'Modular form '
if character:
s += newform_label(level,weight,character,label_other)
else:
s += newform_label(level,weight,1,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 += newform_label(level,weight,character,label)
else:
s += newform_label(level,weight,1,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.coefficient_field_degree > 1:
for h in range(WNF.coefficient_field_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.coefficient_field_degree == 1:
llabel = str(level) + '.' + label
s = 'Elliptic curve isogeny class ' + llabel
url = '/EllipticCurve/Q/' + llabel
friends.append((s, url))
info['properties2'] = properties2
info['friends'] = friends
info['max_cn'] = WNF.max_available_prec()
return info
def search_for_eigenvalues(search):
ev_l = float(search['ev_lower'])
ev_u = float(search['ev_upper'])
level_l = float(search['level_lower'])
level_u = float(search['level_upper'])
if level_l > 0 and level_u > 0:
level_range = {"$gte": level_l, "$lte": level_u}
elif level_u > 0:
level_range = {"$lte": level_u}
elif level_l > 0:
level_range = {"$gte": level_l}
if ev_l > 0 and ev_u > 0:
ev_range = {"$gte": ev_l, "$lte": ev_u}
elif ev_u > 0:
ev_range = {"$lte": ev_u}
elif ev_l > 0:
ev_range = {"$gte": ev_l}
# weight = float(search['weight']) # not used anywhere below
rec_start = search['rec_start']
limit = search['limit']
res = dict()
res['weights'] = []
# SearchLimit = limit_u
db = connect_db()
index = 0
searchp = {'fields': ['Eigenvalue', 'Symmetry', 'Level', 'Character', 'Weight', '_id'],
'sort': [('Eigenvalue', pymongo.ASCENDING), ('Level', pymongo.ASCENDING)],
'spec': {"Eigenvalue": ev_range}}
if level_range:
searchp['spec']["Level"] = level_range
if limit > 0:
searchp['limit'] = rec_start + limit
# the limit of number of records is 'global', for all collections.
# is this good?
print "searchp=", searchp
index = 0
search['more'] = 0
search['rec_start'] = rec_start
search['rec_stop'] = -1
for collection_name in db.collection_names():
if collection_name in ['system.indexes', 'contributors']:
continue
c = pymongo.collection.Collection(db, collection_name)
res[collection_name] = list()
print "c=", c
f = c.find(**searchp)
search['num_recs'] = f.count()
for rec in f:
print "rec=", rec
wt = my_get(rec, 'Weight', 0, float)
# print "index=",index
if index >= rec_start and index < limit + rec_start:
res[collection_name].append(rec)
if res['weights'].count(wt) == 0:
res['weights'].append(wt)
index = index + 1
if index > limit + rec_start:
search['rec_stop'] = index - 1
search['more'] = 1
# if len(res[collection_name])<f.count():
print "There are more to be displayed!"
exit
if search['rec_stop'] < 0:
search['rec_stop'] = limit + rec_start
return res
