def _fc__unramfactor(self, content, det_4):
chi = kronecker_character(-det_4)
pfacs = prime_factors(det_4)
fd = fundamental_discriminant(-det_4)
l = [(p, valuation(content, p),
(valuation(det_4, p) - valuation(fd, p)) / 2) for p in pfacs]
return reduce(operator.mul,
[self._fc__unramfactor_at_p(p, ci, fi, chi)
for (p, ci, fi) in l])
def _fourier_coefficient_full_rank(self, mat):
'''
Assuming mat is a positive definite, half-integral matrix,
it returns the Fourier coefficient of self at the matrix.
We normalize the Siegel Eisenstein series so that the constant term is equal to 1.
cf. S. Takemori, Siegel Eisenstein series of degree n and Lambda-adic Eisenstein series.
'''
n = self.degree
k = self.weight
_mat_det = self._mat_det_full_rank(mat)
unramfac = reduce(operator.mul,
(siegel_series_polynomial(mat, p).subs(
{X: p ** (k - n - 1)})
for p in prime_factors(_mat_det)), ZZ(1))
return self._product_of_l_part(mat) * unramfac
def do_import(ll):
global count
print "Importing list of length %d" %(len(ll))
for F in ll:
count += 1
coeffs, T, D, r1, h, clgp, extras, reg, fu, nogrh, subs, reduc, zk = F
print "%d: %s"%(count, F)
#pol = coeff_to_poly(coeffs)
d = int(len(coeffs))-1
D = ZZ(D)
absD = abs(D)
s, dstr = make_disc_key(D)
# default for r1 is -1 if we should compute it
sig = [int(r1), int((d-r1)/2)]
data = {
'degree': d,
'disc_abs_key': dstr,
'disc_sign': s,
'coeffs': makels(coeffs),
'signature': makels(sig)
}
# Default is that polynomials are polredabs'ed
if reduc == 0:
data['reduced'] = 0
# See if we have it and build a label
index=1
is_new = True
for field in fields.find({'degree': d,
'signature': data['signature'],
'disc_abs_key': dstr}):
index +=1
if field['coeffs'] == data['coeffs']:
is_new = False
break
if is_new:
print "new field"
label = base_label(d,sig[0],absD,index)
data['label'] = label
data['ramps'] = [str(x) for x in prime_factors(D)]
subs = [[makels(z[0]), z[1]] for z in subs]
zk = [str(z) for z in zk]
zk = [z.replace('x','a') for z in zk]
data['zk'] = zk
data['subs'] = subs
dak = data['disc_abs_key']
if len(dak)<19:
dakhash=int(dak)
else:
dakhash = int(dak[0:19])
data['dischash'] = dakhash *data['disc_sign']
data['coeffhash'] = hashlib.md5(data['coeffs']).hexdigest()
############
if h>0:
data['class_number'] = h
data['class_group'] = makels(clgp)
if extras>0:
data['reg'] = reg
fu = [web_latex(PR(str(u))) for u in fu]
data['units'] = fu
if nogrh==0:
data['used_grh'] = True
#print "entering %s into database"%info
if saving:
data['galois'] = makeb(d, T)
fields.save(data)
else:
print "field already in database"
def do_import(ll):
global count
print "Importing list of length %d" % (len(ll))
for F in ll:
count += 1
coeffs, T, D, r1, h, clgp, extras, reg, fu, nogrh, subs, reduc, zk = F
print "%d: %s" % (count, F)
#pol = coeff_to_poly(coeffs)
d = int(len(coeffs)) - 1
D = ZZ(D)
absD = abs(D)
s, dstr = make_disc_key(D)
# default for r1 is -1 if we should compute it
sig = [int(r1), int((d - r1) / 2)]
data = {
'degree': d,
'disc_abs_key': dstr,
'disc_sign': s,
'coeffs': makels(coeffs),
'signature': makels(sig)
}
# Default is that polynomials are polredabs'ed
if reduc == 0:
data['reduced'] = 0
# See if we have it and build a label
index = 1
is_new = True
for field in fields.find({
'degree': d,
'signature': data['signature'],
'disc_abs_key': dstr
}):
index += 1
if field['coeffs'] == data['coeffs']:
is_new = False
break
if is_new:
print "new field"
label = base_label(d, sig[0], absD, index)
data['label'] = label
data['ramps'] = [str(x) for x in prime_factors(D)]
subs = [[makels(z[0]), z[1]] for z in subs]
zk = [str(z) for z in zk]
zk = [z.replace('x', 'a') for z in zk]
data['zk'] = zk
data['subs'] = subs
dak = data['disc_abs_key']
if len(dak) < 19:
dakhash = int(dak)
else:
dakhash = int(dak[0:19])
data['dischash'] = dakhash * data['disc_sign']
data['coeffhash'] = hashlib.md5(data['coeffs']).hexdigest()
############
if h > 0:
data['class_number'] = h
data['class_group'] = makels(clgp)
if extras > 0:
data['reg'] = reg
fu = [web_latex(PR(str(u))) for u in fu]
data['units'] = fu
if nogrh == 0:
data['used_grh'] = True
#print "entering %s into database"%info
if saving:
data['galois'] = makeb(d, T)
fields.save(data)
else:
print "field already in database"