def get_twodim_cocycle(self,sign = 1,use_magma = True,bound = 5, hecke_data = None, return_all = False, outfile = None):
F = self.group().base_ring()
if F == QQ:
F = NumberField(PolynomialRing(QQ,'x').gen(),names='r')
component_list = []
good_components = []
if F.signature()[1] == 0 or (F.signature() == (0,1) and 'G' not in self.group()._grouptype):
Tinf = self.hecke_matrix(oo).transpose()
K = (Tinf-sign).kernel().change_ring(QQ)
if K.dimension() >= 2:
component_list.append((K, [(oo,Tinf)]))
fwrite('Too charpoly = %s'%Tinf.charpoly().factor(),outfile)
else:
K = Matrix(QQ,self.dimension(),self.dimension(),0).kernel()
if K.dimension() >= 2:
component_list.append((K, []))
disc = self.S_arithgroup().Gpn._O_discriminant
discnorm = disc.norm()
try:
N = ZZ(discnorm.gen())
except AttributeError:
N = ZZ(discnorm)
if F == QQ:
x = QQ['x'].gen()
F = NumberField(x,names='a')
q = ZZ(1)
g0 = None
num_hecke_operators = 0
if hecke_data is not None:
qq = F.ideal(hecke_data[0])
pol = hecke_data[1]
Aq = self.hecke_matrix(qq.gens_reduced()[0], use_magma = use_magma).transpose().change_ring(QQ)
fwrite('ell = (%s,%s), T_ell charpoly = %s'%(qq.norm(), qq.gens_reduced()[0], Aq.charpoly().factor()),outfile)
U0 = component_list[0][0].intersection(pol.subs(Aq).left_kernel())
if U0.dimension() != 2:
raise ValueError('Hecke data does not suffice to cut out space')
good_component = (U0.denominator() * U0,component_list[0][1] + [(qq.gens_reduced()[0],Aq)])
row0 = good_component[0].matrix().rows()[0]
col0 = [QQ(o) for o in row0.list()]
clcm = lcm([o.denominator() for o in col0])
col0 = [ZZ(clcm * o ) for o in col0]
# phi1 = sum([a * phi for a,phi in zip(col0,self.gens())],self(0))
# phi2 = self.apply_hecke_operator(phi1,qq.gens_reduced()[0], use_magma = use_magma)
# return [phi1, phi2], [(ell, o.restrict(good_component[0])) for ell, o in good_component[1]]
flist = []
for row0 in good_component[0].matrix().rows():
col0 = [QQ(o) for o in row0.list()]
clcm = lcm([o.denominator() for o in col0])
col0 = [ZZ(clcm * o ) for o in col0]
flist.append(sum([a * phi for a,phi in zip(col0,self.gens())],self(0)))
return flist,[(ell, o.restrict(good_component[0])) for ell, o in good_component[1]]
while len(component_list) > 0 and num_hecke_operators < bound:
verbose('num_hecke_ops = %s'%num_hecke_operators)
verbose('len(components_list) = %s'%len(component_list))
q = q.next_prime()
verbose('q = %s'%q)
fact = F.ideal(q).factor()
dfact = F.ideal(disc.gens_reduced()[0]).factor()
for qq,e in fact:
verbose('Trying qq = %s'%qq)
if qq in [o for o,_ in dfact]:
verbose('Skipping because qq divides D...')
continue
if ZZ(qq.norm()).is_prime() and not qq.divides(F.ideal(disc.gens_reduced()[0])):
try:
Aq = self.hecke_matrix(qq.gens_reduced()[0],g0 = g0,use_magma = use_magma).transpose().change_ring(QQ)
except (RuntimeError,TypeError) as e:
verbose('Skipping qq (=%s) because Hecke matrix could not be computed...'%qq.gens_reduced()[0])
continue
except KeyboardInterrupt:
verbose('Skipping qq (=%s) by user request...'%qq.gens_reduced()[0])
num_hecke_operators += 1
sleep(1)
continue
verbose('Computed hecke matrix at qq = %s'%qq)
fwrite('ell = (%s,%s), T_ell charpoly = %s'%(qq.norm(), qq.gens_reduced()[0], Aq.charpoly().factor()),outfile)
old_component_list = component_list
component_list = []
num_hecke_operators += 1
for U,hecke_data in old_component_list:
V = Aq.decomposition_of_subspace(U)
for U0,is_irred in V:
if U0.dimension() == 1:
continue
if U0.dimension() == 2 and is_irred:
good_components.append((U0.denominator() * U0,hecke_data+[(qq.gens_reduced()[0],Aq)]))
else: # U0.dimension() > 2 or not is_irred
component_list.append((U0.denominator() * U0,hecke_data + [(qq.gens_reduced()[0],Aq)]))
if len(good_components) > 0 and not return_all:
flist = []
for row0 in good_components[0][0].matrix().rows():
col0 = [QQ(o) for o in row0.list()]
clcm = lcm([o.denominator() for o in col0])
col0 = [ZZ(clcm * o ) for o in col0]
flist.append(sum([a * phi for a,phi in zip(col0,self.gens())],self(0)))
return flist,[(ell, o.restrict(good_components[0][0])) for ell, o in good_components[0][1]]
if len(component_list) == 0 or num_hecke_operators >= bound:
break
if len(good_components) == 0:
if not return_all:
raise ValueError('Group does not seem to be attached to an abelian surface')
else:
return []
if return_all:
ans = []
for K,hecke_data in good_components:
flist = []
for row0 in K.matrix().rows():
col0 = [QQ(o) for o in row0.list()]
clcm = lcm([o.denominator() for o in col0])
col0 = [ZZ(clcm * o ) for o in col0]
flist.append(sum([a * phi for a,phi in zip(col0,self.gens())],self(0)))
ans.append((flist,[(ell, o.restrict(K)) for ell, o in hecke_data]))
return ans
else:
flist = []
for row0 in good_components[0][0].matrix().rows():
col0 = [QQ(o) for o in row0.list()]
clcm = lcm([o.denominator() for o in col0])
col0 = [ZZ(clcm * o ) for o in col0]
flist.append(sum([a * phi for a,phi in zip(col0,self.gens())],self(0)))
return flist,[(ell, o.restrict(good_components[0][0])) for ell, o in good_components[0][1]]
