def elliptic_curves(v, B=100, filename=None):
from hmf import HilbertModularForms
F = open(filename,'a') if filename else None
for N in ideals_of_norm(v):
H = HilbertModularForms(N)
for i, E in enumerate(H.elliptic_curve_factors()):
v = E.aplist(B)
s = '%s\t%s\t%s\t%s'%(N.norm(), no_space(canonical_gen(N)), i, ' '.join([no_space(x) for x in v]))
print s
if F:
F.write(s+'\n')
F.flush()
def elliptic_curves(v, B=100, filename=None):
from hmf import HilbertModularForms
F = open(filename, 'a') if filename else None
for N in ideals_of_norm(v):
H = HilbertModularForms(N)
for i, E in enumerate(H.elliptic_curve_factors()):
v = E.aplist(B)
s = '%s\t%s\t%s\t%s' % (N.norm(), no_space(
canonical_gen(N)), i, ' '.join([no_space(x) for x in v]))
print s
if F:
F.write(s + '\n')
F.flush()
def test_hecke_invariance_of_new_subspace(Bmin=2, Bmax=300):
from tables import ideals_of_bounded_norm
from hmf import HilbertModularForms, next_prime_of_characteristic_coprime_to
for N in ideals_of_bounded_norm(Bmax):
if N.norm() < Bmin: continue
print N.norm()
H = HilbertModularForms(N)
NS = H.new_subspace()
p = next_prime_of_characteristic_coprime_to(F.ideal(1), N)
q = next_prime_of_characteristic_coprime_to(p, N)
print p, q
T_p = NS.T(p)
T_q = NS.T(q)
assert T_p*T_q == T_q*T_p, "Hecke operators T_{%s} and T_{%s} at level %s (of norm %s) don't commute"%(p, q, N, N.norm())
def test_hecke_commutes(Bmin=2, Bmax=50):
from tables import ideals_of_bounded_norm
from hmf import HilbertModularForms, next_prime_of_characteristic_coprime_to
for N in ideals_of_bounded_norm(Bmax):
if N.norm() < Bmin: continue
print N.norm()
H = HilbertModularForms(N)
p = next_prime_of_characteristic_coprime_to(F.ideal(1), N)
q = next_prime_of_characteristic_coprime_to(p, N)
print p, q
T_p = H.T(p)
T_q = H.T(q)
assert T_p * T_q == T_q * T_p, "Hecke operators T_{%s} and T_{%s} at level %s (of norm %s) don't commute" % (
p, q, N, N.norm())
def f(N):
set_random_seed(0) # to replicate any linear algebra issues?
level = no_space(canonical_gen(N)).replace('*','').replace('-','_')
F = open(os.path.join(dir,'%s.txt'%level),'w')
H = HilbertModularForms(N)
level = no_space(canonical_gen(N))
try:
D = H.elliptic_curve_factors()
F.write('count %s %s %s\n'%(N.norm(), level, len(D)))
F.flush()
for i, E in enumerate(D):
v = E.aplist(B)
s = '%s\t%s\t%s\t%s'%(N.norm(), level, i, ' '.join([no_space(x) for x in v]))
print s
F.write(s+'\n')
F.flush()
except Exception, msg:
F.write('exception %s %s "%s"\n'%(N.norm(), level, msg))
def f(N):
set_random_seed(0) # to replicate any linear algebra issues?
level = no_space(canonical_gen(N)).replace('*', '').replace('-', '_')
F = open(os.path.join(dir, '%s.txt' % level), 'w')
H = HilbertModularForms(N)
level = no_space(canonical_gen(N))
try:
D = H.elliptic_curve_factors()
F.write('count %s %s %s\n' % (N.norm(), level, len(D)))
F.flush()
for i, E in enumerate(D):
v = E.aplist(B)
s = '%s\t%s\t%s\t%s' % (N.norm(), level, i, ' '.join(
[no_space(x) for x in v]))
print s
F.write(s + '\n')
F.flush()
except Exception, msg:
F.write('exception %s %s "%s"\n' % (N.norm(), level, msg))