def len_as_printed(s,format='latex'):
r"""
Returns the length of s, as it will appear after being math_jax'ed
"""
lenq=1
lendig=1
lenpm=1.5
lenpar=0.5
lenexp=0.75
lensub=0.75
## remove all html first since it is not displayed
ss = re.sub("<[^>]*>","",s)
logger.debug("ss=%s" % ss)
ss = re.sub(" ","",ss) # remove white-space
ss = re.sub("\*","",ss) # remove *
num_exp = s.count("^") # count number of exponents
exps = re.findall("\^{?(\d*)",s) # a list of all exponents
sexps = "".join(exps)
num_subs = s.count("_") # count number of exponents
subs = re.findall("_{?(\d*)",s) # a list of all subscripts
ssubs = "".join(subs)
ss = re.sub("\^{?(\d*)}?","",ss) # remove exponenents
logger.debug(join([ss,ssubs,sexps]))
tot_len=(ss.count(")")+ss.count("("))*lenpar
tot_len+=ss.count("q")*lenq
tot_len+=len(re.findall("\d",s))*lendig
tot_len+=len(re.findall("\w",s))*lenq
tot_len+=(s.count("+")+s.count("-"))*lenpm
tot_len+=num_subs*lensub
tot_len+=num_exp*lenexp
#
#tot_len = len(ss)+ceil((len(ssubs)+len(sexps))*0.67)
return tot_len
def len_as_printed(s, format='latex'):
r"""
Returns the length of s, as it will appear after being math_jax'ed
"""
lenq = 1
lendig = 1
lenpm = 1.5
lenpar = 0.5
lenexp = 0.75
lensub = 0.75
## remove all html first since it is not displayed
ss = re.sub("<[^>]*>", "", s)
logger.debug("ss=%s" % ss)
ss = re.sub(" ", "", ss) # remove white-space
ss = re.sub("\*", "", ss) # remove *
num_exp = s.count("^") # count number of exponents
exps = re.findall("\^{?(\d*)", s) # a list of all exponents
sexps = "".join(exps)
num_subs = s.count("_") # count number of exponents
subs = re.findall("_{?(\d*)", s) # a list of all subscripts
ssubs = "".join(subs)
ss = re.sub("\^{?(\d*)}?", "", ss) # remove exponenents
logger.debug(join([ss, ssubs, sexps]))
tot_len = (ss.count(")") + ss.count("(")) * lenpar
tot_len += ss.count("q") * lenq
tot_len += len(re.findall("\d", s)) * lendig
tot_len += len(re.findall("\w", s)) * lenq
tot_len += (s.count("+") + s.count("-")) * lenpm
tot_len += num_subs * lensub
tot_len += num_exp * lenexp
#
#tot_len = len(ss)+ceil((len(ssubs)+len(sexps))*0.67)
return tot_len
def render_elliptic_modular_form_space(info):
r"""
Render the webpage for a elliptic modular forms space.
"""
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))
label = my_get(info, 'label', 'a', str)
if character == '':
character = 0
properties = list()
parents = list()
friends = list()
lifts = list()
siblings = list()
sbar = (properties, parents, friends, siblings, lifts)
if character == 0:
dimtbl = DimensionTable()
else:
dimtbl = DimensionTable(1)
emf_logger.debug("Created dimension table in render_elliptic_modular_form_space")
if 'character' in info and info['character'] == '*':
return render_elliptic_modular_form_space_list_chars(level, weight)
if not dimtbl.is_in_db(level, weight, character):
emf_logger.debug("Data not available")
return render_template("not_available.html")
info = set_info_for_modular_form_space(info)
emf_logger.debug("keys={0}".format(info.keys()))
if 'download' in info and 'error' not in info:
return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
if 'dimension_newspace' in info and info['dimension_newspace'] == 1: # if there is only one orbit we list it
emf_logger.debug("Dimension of newforms is one!")
info = dict()
info['level'] = level
info['weight'] = weight
info['label'] = 'a'
info['character'] = character
return redirect(url_for('emf.render_elliptic_modular_forms', **info))
info['title'] = "Holomorphic Cusp Forms of weight %s on \(\Gamma_{0}(%s)\)" % (weight, level)
bread = [(MF_TOP, url_for('mf.modular_form_main_page'))]
bread.append((EMF_TOP, url_for('emf.render_elliptic_modular_forms')))
bread.append(("Level %s" % level, url_for('emf.render_elliptic_modular_forms', level=level)))
bread.append(
("Weight %s" % weight, url_for('emf.render_elliptic_modular_forms', level=level, weight=weight)))
emf_logger.debug("friends={0}".format(friends))
info['bread'] = bread
if info['dimension_newspace'] == 0:
return render_template("emf_space.html", **info)
else:
return render_template("emf_space.html", **info)
def ajax_once(callback,*arglist,**kwds):
r"""
"""
text = kwds.get('text', 'more')
emf_logger.debug("text={0}".format(text))
emf_logger.debug("arglist={0}".format(arglist))
emf_logger.debug("kwds={0}".format(kwds))
#emf_logger.debug("req={0}".format(request.args
nonce = hex(random.randint(0, 1<<128))
res = callback()
url = ajax_url(ajax_once,arglist,kwds,inline=True)
s0 = """<span id='%(nonce)s'>%(res)s """ % locals()
# s1 = """[<a onclick="$('#%(nonce)s').load('%(url)s', {'level':22,'weight':4},function() { MathJax.Hub.Queue(['Typeset',MathJax.Hub,'%(nonce)s']);}); return false;" href="#">%(text)s</a>""" % locals()
s1 = """[<a onclick="$('#%(nonce)s').load('%(url)s', {a:1},function() { MathJax.Hub.Queue(['Typeset',MathJax.Hub,'%(nonce)s']);}); return false;" href="#">%(text)s</a>""" % locals()
return s0+s1
def set_table_browsing(self,skip=[0,0],limit=[(2,16),(1,50)],keys=['Weight','Level'],character=0,dimension_fun=dimension_new_cusp_forms,title='Dimension of newforms'):
r"""
Table of Holomorphic modular forms spaces.
Skip tells you how many chunks of data you want to skip (from the geginning) and limit tells you how large each chunk is.
INPUT:
- dimension_fun should be a function which gives you the desired dimensions, as functions of level N and weight k
- character = 0 for trivial character and 1 for Kronecker symbol.
set to 'all' for all characters.
"""
self._keys=keys
self._skip=skip
self._limit=limit
self._metadata=[]
self._title=''
self._cols=[]
self.table={}
self._character = character
emf_logger.debug("skip= {0}".format(self._skip))
emf_logger.debug("limit= {0}".format(self._limit))
il = self._keys.index('Level')
iwt = self._keys.index('Weight')
level_len = self._limit[il][1]-self._limit[il][0]+1
level_ll=self._skip[il]*level_len+self._limit[il][0]; level_ul=self._skip[il]*level_len+self._limit[il][1]
wt_len = self._limit[iwt][1]-self._limit[iwt][0]+1
wt_ll=self._skip[iwt]*wt_len+self._limit[iwt][0]; wt_ul=self._skip[iwt]*wt_len+self._limit[iwt][1]
if level_ll<1: level_l=1
self._table={}
self._table['rows']=[]
self._table['col_heads']=[] #range(wt_ll,wt_ul+1)
self._table['row_heads']=[] #range(level_ll,level_ul+1)
emf_logger.debug("wt_range: {0} -- {1}".format(wt_ll,wt_ul))
emf_logger.debug("level_range: {0} -- {1}".format(level_ll,level_ul))
if character in [0,1]:
if level_ll == level_ul:
N=level_ll
self._table['rowhead']='Weight'
if character==0:
self._table['row_heads']=['Trivial character']
else:
self._table['row_heads']=['\( \\( \frac{\cdot}{N} \\)\)']
row=[]
for k in range(wt_ll,wt_ul+1):
if character == 0 and is_odd(k):
continue
try:
if character==0:
d = dimension_fun(N,k)
elif character==1:
x = kronecker_character_upside_down(N)
d = dimension_fun(x,k)
except Exception as ex:
emf_logger.critical("Exception: {0}. \n Could not compute the dimension with function {0}".format(ex,dimension_fun))
url = url_for('emf.render_elliptic_modular_form_browsing',level=N,weight=k)
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
row.append({'N':N,'k':k,'url':url,'dim':d})
self._table['rows'].append(row)
else:
for N in range(level_ll,level_ul+1):
if not N in self._table['row_heads']:
self._table['row_heads'].append(N)
row=[]
for k in range(wt_ll,wt_ul+1):
if character == 0 and is_odd(k):
continue
try:
if character==0:
d = dimension_fun(N,k)
elif character==1:
x = kronecker_character_upside_down(N)
d = dimension_fun(x,k)
except Exception as ex:
emf_logger.critical("Exception: {0}. \n Could not compute the dimension with function {0}".format(ex,dimension_fun))
url = url_for('emf.render_elliptic_modular_form_browsing',level=N,weight=k)
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
row.append({'N':N,'k':k,'url':url,'dim':d})
self._table['rows'].append(row)
elif character=='all':
# make table with all characters.
self._table['characters']=dict()
if level_ll == level_ul:
N = level_ll
D = DirichletGroup(N)
emf_logger.debug("I am here!")
self._table['rowhead']='Character \ Weight'
for x in D:
xi = D.list().index(x)
row=[]
self._table['row_heads'].append(xi)
for k in range(wt_ll,wt_ul+1):
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
try:
d = dimension_fun(x,k)
except Exception as ex:
emf_logger.critical("Exception: {0} \n Could not compute the dimension with function {0}".format(ex,dimension_fun))
d = -1
url = url_for('emf.render_elliptic_modular_form_space',level=N,weight=k,character=xi)
row.append({'N':N,'k':k,'chi':xi,'url':url,'dim':d})
self._table['rows'].append(row)
else:
for N in range(level_ll,level_ul+1):
self._table['row_heads'].append(N)
self._table['characters'][N]=list()
row=[]
if N==0: continue
D = DirichletGroup(N)
for k in range(wt_ll,wt_ul+1):
tbl=[]
for x in D:
xi = D.list().index(x)
if not N in self._table['characters'][N]:
self._table['characters'][N].append(xi)
if x.is_even() and is_odd(k):
continue
if x.is_odd() and is_even(k):
continue
try:
d = dimension_fun(x,k)
except Exception as ex:
emf_logger.critical("Exception: {0} \n Could not compute the dimension with function {0}".format(ex,dimension_fun))
url = url_for('emf.render_elliptic_modular_form_browsing',level=N,weight=k)
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
tbl.append({'N':N,'k':k,'chi':xi,'url':url,'dim':d})
row.append(tbl)
self._table['rows'].append(row)
def find_inverse_images_of_twists(k, N=1, chi=0, fi=0, prec=10, verbose=0):
r"""
Checks if f is minimal and if not, returns the associated
minimal form to precision prec.
INPUT:
- ''k'' -- positive integer : the weight
- ''N'' -- positive integer (default 1) : level
- ''chi'' -- non-neg. integer (default 0) use character nr. chi
- ''fi'' -- non-neg. integer (default 0) We want to use the element nr. fi f=Newforms(N,k)[fi]
- ''prec'' -- integer (the number of coefficients to get)
- ''verbose'' -- integer
OUTPUT:
-''[t,l]'' -- tuple of a Bool t and a list l. The list l contains all tuples of forms which twists to the given form.
The actual minimal one is the first element of this list.
EXAMPLES::
"""
(t, f) = _get_newform(k, N, chi, fi)
if (not t):
return f
if (is_squarefree(ZZ(N))):
return [True, f]
# We need to check all square factors of N
logger.info("investigating: %s" % f)
N_sqfree = squarefree_part(ZZ(N))
Nsq = ZZ(N / N_sqfree)
twist_candidates = list()
KF = f.base_ring()
# check how many Hecke eigenvalues we need to check
max_nump = number_of_hecke_to_check(f)
maxp = max(primes_first_n(max_nump))
for d in divisors(N):
# we look at all d such that d^2 divdes N
if (not ZZ(d**2).divides(ZZ(N))):
continue
D = DirichletGroup(d)
# check possible candidates to twist into f
# g in S_k(M,chi) wit M=N/d^2
M = ZZ(N / d**2)
logger.info("Checking level %s" % M)
for xig in range(euler_phi(M)):
(t, glist) = _get_newform(k, M, xig)
if (not t):
return glist
for g in glist:
logger.debug("Comparing to function %s" % g)
KG = g.base_ring()
# we now see if twisting of g by xi in D gives us f
for xi in D:
try:
for p in primes_first_n(max_nump):
if (ZZ(p).divides(ZZ(N))):
continue
bf = f.q_expansion(maxp + 1)[p]
bg = g.q_expansion(maxp + 1)[p]
if (bf == 0 and bg == 0):
continue
elif (bf == 0 and bg <> 0 or bg == 0 and bf <> 0):
raise StopIteration()
if (ZZ(p).divides(xi.conductor())):
raise ArithmeticError, ""
xip = xi(p)
# make a preliminary check that the base rings match with respect to being real or not
try:
QQ(xip)
XF = QQ
if (KF <> QQ or KG <> QQ):
raise StopIteration
except TypeError:
# we have a non-rational (i.e. complex) value of the character
XF = xip.parent()
if ((KF == QQ or KF.is_totally_real()) and
(KG == QQ or KG.is_totally_real())):
raise StopIteration
## it is diffcult to compare elements from diferent rings in general but we make some checcks
## is it possible to see if there is a larger ring which everything can be coerced into?
ok = False
try:
a = KF(bg / xip)
b = KF(bf)
ok = True
if (a <> b):
raise StopIteration()
except TypeError:
pass
try:
a = KG(bg)
b = KG(xip * bf)
ok = True
if (a <> b):
raise StopIteration()
except TypeError:
pass
if (
not ok
): # we could coerce and the coefficients were equal
return "Could not compare against possible candidates!"
# otherwise if we are here we are ok and found a candidate
twist_candidates.append([dd, g.q_expansion(prec), xi])
except StopIteration:
# they are not equal
pass
#logger.debug("Candidates=%s" % twist_candidates)
if (len(twist_candidates) == 0):
return (True, None)
else:
return (False, twist_candidates)
def get_values_at_CM_points(k, N=1, chi=0, fi=0, digits=12, verbose=0):
r""" Computes and returns a list of values of f at a collection of CM points as complex floating point numbers.
INPUT:
- ''k'' -- positive integer : the weight
- ''N'' -- positive integer (default 1) : level
- ''chi'' -- non-neg. integer (default 0) use character nr. chi - ''fi'' -- non-neg. integer (default 0) We want to use the element nr. fi f=Newforms(N,k)[fi]
-''digits'' -- we want this number of corrrect digits in the value
OUTPUT:
-''s'' string representation of a dictionary {I:f(I):rho:f(rho)}.
TODO: Get explicit, algebraic values if possible!
"""
(t, f) = _get_newform(k, N, chi, fi)
if (not t):
return f
bits = max(53, ceil(digits * 4))
CF = ComplexField(bits)
RF = ComplexField(bits)
eps = RF(10**-(digits + 1))
logger.debug("eps=" % eps)
K = f.base_ring()
cm_vals = dict()
# the points we want are i and rho. More can be added later...
rho = CyclotomicField(3).gen()
zi = CyclotomicField(4).gen()
points = [rho, zi]
maxprec = 1000 # max size of q-expansion
minprec = 10 # max size of q-expansion
for tau in points:
q = CF(exp(2 * pi * I * tau))
fexp = dict()
if (K == QQ):
v1 = CF(0)
v2 = CF(1)
try:
for prec in range(minprec, maxprec, 10):
logger.debug("prec=%s" % prec)
v2 = f.q_expansion(prec)(q)
err = abs(v2 - v1)
logger.debug("err=%s" % err)
if (err < eps):
raise StopIteration()
v1 = v2
cm_vals[tau] = ""
except StopIteration:
cm_vals[tau] = str(fq)
else:
v1 = dict()
v2 = dict()
err = dict()
cm_vals[tau] = dict()
for h in range(K.degree()):
v1[h] = 1
v2[h] = 0
try:
for prec in range(minprec, maxprec, 10):
logger.debug("prec=%s" % prec)
for h in range(K.degree()):
fexp[h] = list()
v2[h] = 0
for n in range(prec):
c = f.coefficients(ZZ(prec))[n]
cc = c.complex_embeddings(CF.prec())[h]
v2[h] = v2[h] + cc * q**n
err[h] = abs(v2[h] - v1[h])
logger.debug("v1[%s]=%s" % (h, v1[h]))
logger.debug("v2[%s]=%s" % (h, v2[h]))
logger.debug("err[%s]=%s" % (h, err[h]))
if (max(err.values()) < eps):
raise StopIteration()
v1[h] = v2[h]
except StopIteration:
pass
for h in range(K.degree()):
if (err[h] < eps):
cm_vals[tau][h] = v2[h]
else:
cm_vals[tau][h] = ""
logger.debug("vals=%s" % cm_vals)
logger.debug("errs=%s" % err)
tbl = dict()
tbl['corner_label'] = ['$\tau$']
tbl['headersh'] = ['$\\rho=\zeta_{3}$', '$i$']
if (K == QQ):
tbl['headersv'] = ['$f(\\tau)$']
tbl['data'] = [cm_vals]
else:
tbl['data'] = list()
tbl['headersv'] = list()
for h in range(K.degree()):
tbl['headersv'].append("$\sigma_{%s}(f(\\tau))$" % h)
row = list()
for tau in points:
row.append(cm_vals[tau][h])
tbl['data'].append(row)
s = html_table(tbl)
#s=html.table([cm_vals.keys(),cm_vals.values()])
return s
def find_inverse_images_of_twists(k,N=1,chi=0,fi=0,prec=10,verbose=0):
r"""
Checks if f is minimal and if not, returns the associated
minimal form to precision prec.
INPUT:
- ''k'' -- positive integer : the weight
- ''N'' -- positive integer (default 1) : level
- ''chi'' -- non-neg. integer (default 0) use character nr. chi
- ''fi'' -- non-neg. integer (default 0) We want to use the element nr. fi f=Newforms(N,k)[fi]
- ''prec'' -- integer (the number of coefficients to get)
- ''verbose'' -- integer
OUTPUT:
-''[t,l]'' -- tuple of a Bool t and a list l. The list l contains all tuples of forms which twists to the given form.
The actual minimal one is the first element of this list.
EXAMPLES::
"""
(t,f) = _get_newform(k,N,chi,fi)
if(not t):
return f
if(is_squarefree(ZZ(N))):
return [True,f]
# We need to check all square factors of N
logger.info("investigating: %s" % f)
N_sqfree=squarefree_part(ZZ(N))
Nsq=ZZ(N/N_sqfree)
twist_candidates=list()
KF=f.base_ring()
# check how many Hecke eigenvalues we need to check
max_nump=number_of_hecke_to_check(f)
maxp=max(primes_first_n(max_nump))
for d in divisors(N):
# we look at all d such that d^2 divdes N
if(not ZZ(d**2).divides(ZZ(N))):
continue
D=DirichletGroup(d)
# check possible candidates to twist into f
# g in S_k(M,chi) wit M=N/d^2
M=ZZ(N/d**2)
logger.info("Checking level %s"%M)
for xig in range(euler_phi(M)):
(t,glist) = _get_newform(k,M,xig)
if(not t):
return glist
for g in glist:
logger.debug("Comparing to function %s" %g)
KG=g.base_ring()
# we now see if twisting of g by xi in D gives us f
for xi in D:
try:
for p in primes_first_n(max_nump):
if(ZZ(p).divides(ZZ(N))):
continue
bf=f.q_expansion(maxp+1)[p]
bg=g.q_expansion(maxp+1)[p]
if(bf == 0 and bg == 0):
continue
elif(bf==0 and bg<>0 or bg==0 and bf<>0):
raise StopIteration()
if(ZZ(p).divides(xi.conductor())):
raise ArithmeticError,""
xip=xi(p)
# make a preliminary check that the base rings match with respect to being real or not
try:
QQ(xip)
XF=QQ
if( KF<>QQ or KG<>QQ):
raise StopIteration
except TypeError:
# we have a non-rational (i.e. complex) value of the character
XF=xip.parent()
if( (KF == QQ or KF.is_totally_real()) and (KG == QQ or KG.is_totally_real())):
raise StopIteration
## it is diffcult to compare elements from diferent rings in general but we make some checcks
## is it possible to see if there is a larger ring which everything can be coerced into?
ok=False
try:
a=KF(bg/xip); b=KF(bf)
ok=True
if(a<>b):
raise StopIteration()
except TypeError:
pass
try:
a=KG(bg); b=KG(xip*bf)
ok=True
if(a<>b):
raise StopIteration()
except TypeError:
pass
if(not ok): # we could coerce and the coefficients were equal
return "Could not compare against possible candidates!"
# otherwise if we are here we are ok and found a candidate
twist_candidates.append([dd,g.q_expansion(prec),xi])
except StopIteration:
# they are not equal
pass
#logger.debug("Candidates=%s" % twist_candidates)
if(len(twist_candidates)==0):
return (True,None)
else:
return (False,twist_candidates)
def get_values_at_CM_points(k,N=1,chi=0,fi=0,digits=12,verbose=0):
r""" Computes and returns a list of values of f at a collection of CM points as complex floating point numbers.
INPUT:
- ''k'' -- positive integer : the weight
- ''N'' -- positive integer (default 1) : level
- ''chi'' -- non-neg. integer (default 0) use character nr. chi - ''fi'' -- non-neg. integer (default 0) We want to use the element nr. fi f=Newforms(N,k)[fi]
-''digits'' -- we want this number of corrrect digits in the value
OUTPUT:
-''s'' string representation of a dictionary {I:f(I):rho:f(rho)}.
TODO: Get explicit, algebraic values if possible!
"""
(t,f) = _get_newform(k,N,chi,fi)
if(not t):
return f
bits=max(53,ceil(digits*4))
CF=ComplexField(bits)
RF=ComplexField(bits)
eps=RF(10**-(digits+1))
logger.debug("eps=" % eps)
K=f.base_ring()
cm_vals=dict()
# the points we want are i and rho. More can be added later...
rho=CyclotomicField(3).gen()
zi=CyclotomicField(4).gen()
points=[rho,zi]
maxprec=1000 # max size of q-expansion
minprec=10 # max size of q-expansion
for tau in points:
q=CF(exp(2*pi*I*tau))
fexp=dict()
if(K==QQ):
v1=CF(0); v2=CF(1)
try:
for prec in range(minprec,maxprec,10):
logger.debug("prec=%s" % prec)
v2=f.q_expansion(prec)(q)
err=abs(v2-v1)
logger.debug("err=%s"%err)
if(err< eps):
raise StopIteration()
v1=v2
cm_vals[tau]=""
except StopIteration:
cm_vals[tau]=str(fq)
else:
v1=dict()
v2=dict()
err=dict()
cm_vals[tau]=dict()
for h in range(K.degree()):
v1[h]=1
v2[h]=0
try:
for prec in range(minprec,maxprec,10):
logger.debug("prec=%s"%prec)
for h in range(K.degree()):
fexp[h]=list()
v2[h]=0
for n in range(prec):
c=f.coefficients(ZZ(prec))[n]
cc=c.complex_embeddings(CF.prec())[h]
v2[h]=v2[h]+cc*q**n
err[h]=abs(v2[h]-v1[h])
logger.debug("v1[%s]=%s"% (h,v1[h]))
logger.debug("v2[%s]=%s"% (h,v2[h]))
logger.debug("err[%s]=%s"% (h,err[h]))
if(max(err.values()) < eps):
raise StopIteration()
v1[h]=v2[h]
except StopIteration:
pass
for h in range(K.degree()):
if(err[h] < eps):
cm_vals[tau][h]=v2[h]
else:
cm_vals[tau][h]=""
logger.debug("vals=%s"%cm_vals)
logger.debug("errs=%s"%err)
tbl=dict()
tbl['corner_label']=['$\tau$']
tbl['headersh']=['$\\rho=\zeta_{3}$','$i$']
if(K==QQ):
tbl['headersv']=['$f(\\tau)$']
tbl['data']=[cm_vals]
else:
tbl['data']=list()
tbl['headersv']=list()
for h in range(K.degree()):
tbl['headersv'].append("$\sigma_{%s}(f(\\tau))$" % h)
row=list()
for tau in points:
row.append(cm_vals[tau][h])
tbl['data'].append(row)
s=html_table(tbl)
#s=html.table([cm_vals.keys(),cm_vals.values()])
return s
def set_table_browsing(self,
skip=[0, 0],
limit=[(2, 16), (1, 50)],
keys=['Weight', 'Level'],
character=0,
dimension_fun=dimension_new_cusp_forms,
title='Dimension of newforms'):
r"""
Table of Holomorphic modular forms spaces.
Skip tells you how many chunks of data you want to skip (from the geginning) and limit tells you how large each chunk is.
INPUT:
- dimension_fun should be a function which gives you the desired dimensions, as functions of level N and weight k
- character = 0 for trivial character and 1 for Kronecker symbol.
set to 'all' for all characters.
"""
self._keys = keys
self._skip = skip
self._limit = limit
self._metadata = []
self._title = ''
self._cols = []
self.table = {}
self._character = character
emf_logger.debug("skip= {0}".format(self._skip))
emf_logger.debug("limit= {0}".format(self._limit))
il = self._keys.index('Level')
iwt = self._keys.index('Weight')
level_len = self._limit[il][1] - self._limit[il][0] + 1
level_ll = self._skip[il] * level_len + self._limit[il][0]
level_ul = self._skip[il] * level_len + self._limit[il][1]
wt_len = self._limit[iwt][1] - self._limit[iwt][0] + 1
wt_ll = self._skip[iwt] * wt_len + self._limit[iwt][0]
wt_ul = self._skip[iwt] * wt_len + self._limit[iwt][1]
if level_ll < 1: level_l = 1
self._table = {}
self._table['rows'] = []
self._table['col_heads'] = [] #range(wt_ll,wt_ul+1)
self._table['row_heads'] = [] #range(level_ll,level_ul+1)
emf_logger.debug("wt_range: {0} -- {1}".format(wt_ll, wt_ul))
emf_logger.debug("level_range: {0} -- {1}".format(level_ll, level_ul))
if character in [0, 1]:
if level_ll == level_ul:
N = level_ll
self._table['rowhead'] = 'Weight'
if character == 0:
self._table['row_heads'] = ['Trivial character']
else:
self._table['row_heads'] = ['\( \\( \frac{\cdot}{N} \\)\)']
row = []
for k in range(wt_ll, wt_ul + 1):
if character == 0 and is_odd(k):
continue
try:
if character == 0:
d = dimension_fun(N, k)
elif character == 1:
x = kronecker_character_upside_down(N)
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0}. \n Could not compute the dimension with function {0}"
.format(ex, dimension_fun))
url = url_for('emf.render_elliptic_modular_form_browsing',
level=N,
weight=k)
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
row.append({'N': N, 'k': k, 'url': url, 'dim': d})
self._table['rows'].append(row)
else:
for N in range(level_ll, level_ul + 1):
if not N in self._table['row_heads']:
self._table['row_heads'].append(N)
row = []
for k in range(wt_ll, wt_ul + 1):
if character == 0 and is_odd(k):
continue
try:
if character == 0:
d = dimension_fun(N, k)
elif character == 1:
x = kronecker_character_upside_down(N)
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0}. \n Could not compute the dimension with function {0}"
.format(ex, dimension_fun))
url = url_for(
'emf.render_elliptic_modular_form_browsing',
level=N,
weight=k)
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
row.append({'N': N, 'k': k, 'url': url, 'dim': d})
self._table['rows'].append(row)
elif character == 'all':
# make table with all characters.
self._table['characters'] = dict()
if level_ll == level_ul:
N = level_ll
D = DirichletGroup(N)
emf_logger.debug("I am here!")
self._table['rowhead'] = 'Character \ Weight'
for x in D:
xi = D.list().index(x)
row = []
self._table['row_heads'].append(xi)
for k in range(wt_ll, wt_ul + 1):
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
try:
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0} \n Could not compute the dimension with function {0}"
.format(ex, dimension_fun))
d = -1
url = url_for('emf.render_elliptic_modular_form_space',
level=N,
weight=k,
character=xi)
row.append({
'N': N,
'k': k,
'chi': xi,
'url': url,
'dim': d
})
self._table['rows'].append(row)
else:
for N in range(level_ll, level_ul + 1):
self._table['row_heads'].append(N)
self._table['characters'][N] = list()
row = []
if N == 0: continue
D = DirichletGroup(N)
for k in range(wt_ll, wt_ul + 1):
tbl = []
for x in D:
xi = D.list().index(x)
if not N in self._table['characters'][N]:
self._table['characters'][N].append(xi)
if x.is_even() and is_odd(k):
continue
if x.is_odd() and is_even(k):
continue
try:
d = dimension_fun(x, k)
except Exception as ex:
emf_logger.critical(
"Exception: {0} \n Could not compute the dimension with function {0}"
.format(ex, dimension_fun))
url = url_for(
'emf.render_elliptic_modular_form_browsing',
level=N,
weight=k)
if not k in self._table['col_heads']:
self._table['col_heads'].append(k)
tbl.append({
'N': N,
'k': k,
'chi': xi,
'url': url,
'dim': d
})
row.append(tbl)
self._table['rows'].append(row)
def ajax_more2(callback, *arg_list, **kwds):
r"""
Like ajax_more but accepts increase in two directions.
Call with
ajax_more2(function,{'arg1':[x1,x2,...,],'arg2':[y1,y2,...]},'text1','text2')
where function takes two named argument 'arg1' and 'arg2'
"""
inline = kwds.get('inline', True)
text = kwds.get('text', 'more')
emf_logger.debug("inline={0}".format(inline))
emf_logger.debug("text={0}".format(text))
text0 = text[0]
text1 = text[1]
emf_logger.debug("arglist={0}".format(arg_list))
nonce = hex(random.randint(0, 1<<128))
if inline:
args = arg_list[0]
emf_logger.debug("args={0}".format(args))
key1,key2=args.keys()
l1=args[key1]
l2=args[key2]
emf_logger.debug("key1={0}".format(key1))
emf_logger.debug("key2={0}".format(key2))
emf_logger.debug("l1={0}".format(l1))
emf_logger.debug("l2={0}".format(l2))
args={key1:l1[0],key2:l2[0]}
l11=l1[1:]; l21=l2[1:]
#arg_list = arg_list[1:]
arg_list1 = {key1:l1,key2:l21}
arg_list2 = {key1:l11,key2:l2}
#emf_logger.debug("arglist1={0}".format(arg_list))
if isinstance(args, tuple):
res = callback(*arg_list)
elif isinstance(args, dict):
res = callback(**args)
else:
res = callback(args)
res = web_latex(res)
else:
res = ''
emf_logger.debug("arg_list1={0}".format(arg_list1))
emf_logger.debug("arg_list2={0}".format(arg_list2))
arg_list1=(arg_list1,)
arg_list2=(arg_list2,)
if arg_list1 or arg_list2:
url1 = ajax_url(ajax_more2, callback, *arg_list1, inline=True, text=text)
url2 = ajax_url(ajax_more2, callback, *arg_list2, inline=True, text=text)
emf_logger.debug("arg_list1={0}".format(url1))
emf_logger.debug("arg_list2={0}".format(url2))
s0 = """<span id='%(nonce)s'>%(res)s """ % locals()
s1 = """[<a onclick="$('#%(nonce)s').load('%(url1)s', function() { MathJax.Hub.Queue(['Typeset',MathJax.Hub,'%(nonce)s']);}); return false;" href="#">%(text0)s</a>""" % locals()
t = """| <a onclick="$('#%(nonce)s').load('%(url2)s', function() { MathJax.Hub.Queue(['Typeset',MathJax.Hub,'%(nonce)s']);}); return false;" href="#">%(text1)s</a>]</span>""" % locals()
return (s0+s1+t)
else:
return res
def ajax_later(callback,*arglist,**kwds):
r"""
Try to make a function that gets called after displaying the page.
"""
text = kwds.get('text', 'more')
text = 'more'
emf_logger.debug("text={0}".format(text))
emf_logger.debug("arglist={0}".format(arglist))
emf_logger.debug("kwds={0}".format(kwds))
emf_logger.debug("callback={0}".format(callback))
#emf_logger.debug("req={0}".format(request.args
nonce = hex(random.randint(0, 1<<128))
# do not call the first time around
if kwds.has_key("do_now"):
if kwds['do_now']==1:
do_now=0
else:
do_now=1
else:
do_now=0
if not do_now:
url = ajax_url(ajax_later,callback,*arglist,inline=True,do_now=do_now,_ajax_sticky=True)
emf_logger.debug("ajax_url={0}".format(url))
s0 = """<span id='%(nonce)s'></span>""" % locals()
s1 = """<a class='later' href=# id='%(nonce)s' onclick='this_fun()'>%(text)s</a>""" % locals()
s2= """<script>
function this_fun(){
$.getJSON('%(url)s',{do_now:1},
function(data) {
$(\"span#%(nonce)s\").text(data.result);
});
return true;
};
</script>
""" % locals()
emf_logger.debug("s0+s1={0}".format(s2+s0))
return s2+s0+s1
else:
res = callback(do_now=do_now)
return jsonify(result=res)
