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Python ComplexField.zeta方法代码示例

本文整理汇总了Python中sage.rings.all.ComplexField.zeta方法的典型用法代码示例。如果您正苦于以下问题:Python ComplexField.zeta方法的具体用法?Python ComplexField.zeta怎么用?Python ComplexField.zeta使用的例子?那么, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在sage.rings.all.ComplexField的用法示例。


在下文中一共展示了ComplexField.zeta方法的1个代码示例,这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞,您的评价将有助于系统推荐出更棒的Python代码示例。

示例1: zeta_symmetric

# 需要导入模块: from sage.rings.all import ComplexField [as 别名]
# 或者: from sage.rings.all.ComplexField import zeta [as 别名]
def zeta_symmetric(s):
    r"""
    Completed function `\xi(s)` that satisfies
    `\xi(s) = \xi(1-s)` and has zeros at the same points as the
    Riemann zeta function.

    INPUT:


    -  ``s`` - real or complex number


    If s is a real number the computation is done using the MPFR
    library. When the input is not real, the computation is done using
    the PARI C library.

    More precisely,

    .. math::

                xi(s) = \gamma(s/2 + 1) * (s-1) * \pi^{-s/2} * \zeta(s).



    EXAMPLES::

        sage: zeta_symmetric(0.7)
        0.497580414651127
        sage: zeta_symmetric(1-0.7)
        0.497580414651127
        sage: RR = RealField(200)
        sage: zeta_symmetric(RR(0.7))
        0.49758041465112690357779107525638385212657443284080589766062
        sage: C.<i> = ComplexField()
        sage: zeta_symmetric(0.5 + i*14.0)
        0.000201294444235258 + 1.49077798716757e-19*I
        sage: zeta_symmetric(0.5 + i*14.1)
        0.0000489893483255687 + 4.40457132572236e-20*I
        sage: zeta_symmetric(0.5 + i*14.2)
        -0.0000868931282620101 + 7.11507675693612e-20*I

    REFERENCE:

    - I copied the definition of xi from
      http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html
    """
    if not (is_ComplexNumber(s) or is_RealNumber(s)):
        s = ComplexField()(s)

    R = s.parent()
    if s == 1:  # deal with poles, hopefully
        return R(0.5)

    return (s / 2 + 1).gamma() * (s - 1) * (R.pi() ** (-s / 2)) * s.zeta()
开发者ID:rwst,项目名称:sage,代码行数:56,代码来源:transcendental.py


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