def get_cocycle_from_elliptic_curve(self,E,sign = 1,use_magma = True):
if sign == 0:
return self.get_cocycle_from_elliptic_curve(E,1,use_magma) + self.get_cocycle_from_elliptic_curve(E,-1,use_magma)
if not sign in [1, -1]:
raise NotImplementedError
F = self.group().base_ring()
if F.signature()[1] == 0 or (F.signature() == (0,1) and 'G' not in self.group()._grouptype):
K = (self.hecke_matrix(oo).transpose()-sign).kernel().change_ring(QQ)
else:
K = Matrix(QQ,self.dimension(),self.dimension(),0).kernel()
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')
E = E.change_ring(F)
def getap(q):
if F == QQ:
return E.ap(q)
else:
Q = F.ideal(q).factor()[0][0]
return ZZ(Q.norm() + 1 - E.reduction(Q).count_points())
q = ZZ(1)
g0 = None
while K.dimension() > 1:
q = q.next_prime()
for qq,e in F.ideal(q).factor():
if ZZ(qq.norm()).is_prime() and not qq.divides(F.ideal(disc.gens_reduced()[0])):
try:
ap = getap(qq)
except (ValueError,ArithmeticError):
continue
try:
K1 = (self.hecke_matrix(qq.gens_reduced()[0],g0 = g0,use_magma = use_magma).transpose()-ap).kernel()
except RuntimeError:
continue
K = K.intersection(K1)
if K.dimension() != 1:
raise ValueError,'Did not obtain a one-dimensional space corresponding to E'
col = [ZZ(o) for o in (K.denominator()*K.matrix()).list()]
return sum([a * self.gen(i) for i,a in enumerate(col) if a != 0],self(0))
def get_rational_cocycle_from_ap(self,getap,sign = 1,use_magma = True):
F = self.group().base_ring()
if F.signature()[1] == 0 or (F.signature() == (0,1) and 'G' not in self.group()._grouptype):
K = (self.hecke_matrix(oo).transpose()-sign).kernel().change_ring(QQ)
else:
K = Matrix(QQ,self.dimension(),self.dimension(),0).kernel()
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
while K.dimension() > 1:
q = q.next_prime()
for qq,e in F.ideal(q).factor():
if ZZ(qq.norm()).is_prime() and not qq.divides(F.ideal(disc.gens_reduced()[0])):
try:
ap = getap(qq)
except (ValueError,ArithmeticError):
continue
try:
K1 = (self.hecke_matrix(qq.gens_reduced()[0],g0 = g0,use_magma = use_magma).transpose()-ap).kernel()
except RuntimeError:
continue
K = K.intersection(K1)
if K.dimension() != 1:
raise ValueError,'Group does not have the required system of eigenvalues'
col = [ZZ(o) for o in (K.denominator()*K.matrix()).list()]
return sum([ a * self.gen(i) for i,a in enumerate(col) if a != 0], self(0))
