本文整理匯總了Python中sage.rings.all.ComplexField.pi方法的典型用法代碼示例。如果您正苦於以下問題：Python ComplexField.pi方法的具體用法？Python ComplexField.pi怎麽用？Python ComplexField.pi使用的例子？那麽, 這裏精選的方法代碼示例或許可以為您提供幫助。您也可以進一步了解該方法所在類sage.rings.all.ComplexField的用法示例。
在下文中一共展示了ComplexField.pi方法的1個代碼示例，這些例子默認根據受歡迎程度排序。您可以為喜歡或者感覺有用的代碼點讚，您的評價將有助於係統推薦出更棒的Python代碼示例。
示例1: map_to_complex_numbers
# 需要導入模塊: from sage.rings.all import ComplexField [as 別名]
# 或者: from sage.rings.all.ComplexField import pi [as 別名]
def map_to_complex_numbers(self, z, prec=None):
"""
Evaluate ``self`` at a point `z \in X_0(N)` where `z` is given by
a representative in the upper half plane, returning a point in
the complex numbers.
All computations are done with ``prec`` bits
of precision. If ``prec`` is not given, use the precision of `z`.
Use self(z) to compute the image of z on the Weierstrass equation
of the curve.
EXAMPLES::
sage: E = EllipticCurve('37a'); phi = E.modular_parametrization()
sage: tau = (sqrt(7)*I - 17)/74
sage: z = phi.map_to_complex_numbers(tau); z
0.929592715285395 - 1.22569469099340*I
sage: E.elliptic_exponential(z)
(...e-16 - ...e-16*I : ...e-16 + ...e-16*I : 1.00000000000000)
sage: phi(tau)
(...e-16 - ...e-16*I : ...e-16 + ...e-16*I : 1.00000000000000)
"""
if prec is None:
try:
prec = z.parent().prec()
except AttributeError:
prec = 53
CC = ComplexField(prec)
if z in QQ:
raise NotImplementedError
z = CC(z)
if z.imag() <= 0:
raise ValueError("Point must be in the upper half plane")
# TODO: for very small imaginary part, maybe try to transform under
# \Gamma_0(N) to a better representative?
q = (2 * CC.gen() * CC.pi() * z).exp()
# nterms'th term is less than 2**-(prec+10) (c.f. eclib code)
nterms = (-(prec + 10) / q.abs().log2()).ceil()
# Use Horner's rule to sum the integral of the form
enumerated_an = list(enumerate(self._E.anlist(nterms)))[1:]
lattice_point = 0
for n, an in reversed(enumerated_an):
lattice_point += an / n
lattice_point *= q
return lattice_point