def Optimize_Representation(rep):
K = magma.BaseRing(rep[1])
F = magma.BaseRing(K)
if (not magma.IsQQ(F)) or (magma.Degree(K) == 1):
return rep
R = magma.PolynomialRing(magma.Rationals())
g = magma.DefiningPolynomial(K)
g = R(str(gp.polredabs(R(magma.Eltseq(g)))))
L = magma.NumberField(g)
return magma.TransferMatrices(rep, K, L)
def __init__(self, X, periods=""):
self.X = X
self.g = magma.Genus(self.X)
self.F = magma.BaseRing(self.X)
if periods:
self._P_ = periods
else:
self._P_ = magma.PeriodMatrix(self.X)
def __init__(self, X, prec, bound=0, molin_neurohr=False, periods=""):
self.X = X
self.g = magma.Genus(self.X)
self.F = magma.BaseRing(self.X)
self.prec = magma(prec)
self.bound = magma(bound)
self.molin_neurohr = magma(molin_neurohr)
self._eqsCC_ = magma.EmbedCurveEquations(self.X, self.prec)
self._eqsF_ = magma.DefiningEquations(self.X)
if periods:
self._P_ = periods
else:
self._P_ = self.period_matrix()
self._calculate_geometric_representation_()
def Relative_Splitting_Field_Extra(fs, bound=0):
bound_set = (bound != 0)
F = magma.BaseRing(fs[1])
overQQ = (magma.Degree(F) == 1)
if overQQ:
R = PolynomialRing(QQ, 'x')
fs = sorted(fs, key=lambda f: -magma.Degree(f))
K = F
for f in fs:
if not magma.HasRoot(f, K):
for tup in magma.Factorization(f, K):
K = magma.ExtendRelativeSplittingField(K, F, tup[1])
if overQQ:
g = magma.DefiningPolynomial(K)
g = R(str(gp.polredabs(R(magma.Eltseq(g)))))
K = magma.NumberField(g)
else:
K = magma.ClearFieldDenominator(K)
if bound_set and magma.Degree(K) >= bound:
K = magma.DefineOrExtendInfinitePlaceFunction(K)
return K
K = magma.DefineOrExtendInfinitePlaceFunction(K)
return K