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=========
Constants
=========

.. currentmodule:: numpy

NumPy includes several constants:

%(constant_list)s
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    ``pi = 3.1415926535897932384626433...``

    References
    ----------
    https://en.wikipedia.org/wiki/Pi

    �eaE
    Euler's constant, base of natural logarithms, Napier's constant.

    ``e = 2.71828182845904523536028747135266249775724709369995...``

    See Also
    --------
    exp : Exponential function
    log : Natural logarithm

    References
    ----------
    https://en.wikipedia.org/wiki/E_%28mathematical_constant%29

    �euler_gammau�
    ``γ = 0.5772156649015328606065120900824024310421...``

    References
    ----------
    https://en.wikipedia.org/wiki/Euler-Mascheroni_constant

    �infa�
    IEEE 754 floating point representation of (positive) infinity.

    Returns
    -------
    y : float
        A floating point representation of positive infinity.

    See Also
    --------
    isinf : Shows which elements are positive or negative infinity

    isposinf : Shows which elements are positive infinity

    isneginf : Shows which elements are negative infinity

    isnan : Shows which elements are Not a Number

    isfinite : Shows which elements are finite (not one of Not a Number,
    positive infinity and negative infinity)

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Also that positive infinity is not equivalent to negative infinity. But
    infinity is equivalent to positive infinity.

    `Inf`, `Infinity`, `PINF` and `infty` are aliases for `inf`.

    Examples
    --------
    >>> np.inf
    inf
    >>> np.array([1]) / 0.
    array([ Inf])

    �nana�
    IEEE 754 floating point representation of Not a Number (NaN).

    Returns
    -------
    y : A floating point representation of Not a Number.

    See Also
    --------
    isnan : Shows which elements are Not a Number.

    isfinite : Shows which elements are finite (not one of
    Not a Number, positive infinity and negative infinity)

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.

    `NaN` and `NAN` are aliases of `nan`.

    Examples
    --------
    >>> np.nan
    nan
    >>> np.log(-1)
    nan
    >>> np.log([-1, 1, 2])
    array([        NaN,  0.        ,  0.69314718])

    �newaxisa
    A convenient alias for None, useful for indexing arrays.

    Examples
    --------
    >>> newaxis is None
    True
    >>> x = np.arange(3)
    >>> x
    array([0, 1, 2])
    >>> x[:, newaxis]
    array([[0],
    [1],
    [2]])
    >>> x[:, newaxis, newaxis]
    array([[[0]],
    [[1]],
    [[2]]])
    >>> x[:, newaxis] * x
    array([[0, 0, 0],
    [0, 1, 2],
    [0, 2, 4]])

    Outer product, same as ``outer(x, y)``:

    >>> y = np.arange(3, 6)
    >>> x[:, newaxis] * y
    array([[ 0,  0,  0],
    [ 3,  4,  5],
    [ 6,  8, 10]])

    ``x[newaxis, :]`` is equivalent to ``x[newaxis]`` and ``x[None]``:

    >>> x[newaxis, :].shape
    (1, 3)
    >>> x[newaxis].shape
    (1, 3)
    >>> x[None].shape
    (1, 3)
    >>> x[:, newaxis].shape
    (3, 1)

    �NZEROa�
    IEEE 754 floating point representation of negative zero.

    Returns
    -------
    y : float
        A floating point representation of negative zero.

    See Also
    --------
    PZERO : Defines positive zero.

    isinf : Shows which elements are positive or negative infinity.

    isposinf : Shows which elements are positive infinity.

    isneginf : Shows which elements are negative infinity.

    isnan : Shows which elements are Not a Number.

    isfinite : Shows which elements are finite - not one of
               Not a Number, positive infinity and negative infinity.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). Negative zero is considered to be a finite number.

    Examples
    --------
    >>> np.NZERO
    -0.0
    >>> np.PZERO
    0.0

    >>> np.isfinite([np.NZERO])
    array([ True])
    >>> np.isnan([np.NZERO])
    array([False])
    >>> np.isinf([np.NZERO])
    array([False])

    �PZEROa�
    IEEE 754 floating point representation of positive zero.

    Returns
    -------
    y : float
        A floating point representation of positive zero.

    See Also
    --------
    NZERO : Defines negative zero.

    isinf : Shows which elements are positive or negative infinity.

    isposinf : Shows which elements are positive infinity.

    isneginf : Shows which elements are negative infinity.

    isnan : Shows which elements are Not a Number.

    isfinite : Shows which elements are finite - not one of
               Not a Number, positive infinity and negative infinity.

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). Positive zero is considered to be a finite number.

    Examples
    --------
    >>> np.PZERO
    0.0
    >>> np.NZERO
    -0.0

    >>> np.isfinite([np.PZERO])
    array([ True])
    >>> np.isnan([np.PZERO])
    array([False])
    >>> np.isinf([np.PZERO])
    array([False])

    �NANz�
    IEEE 754 floating point representation of Not a Number (NaN).

    `NaN` and `NAN` are equivalent definitions of `nan`. Please use
    `nan` instead of `NAN`.

    See Also
    --------
    nan

    �NaNz�
    IEEE 754 floating point representation of Not a Number (NaN).

    `NaN` and `NAN` are equivalent definitions of `nan`. Please use
    `nan` instead of `NaN`.

    See Also
    --------
    nan

    �NINFa�
    IEEE 754 floating point representation of negative infinity.

    Returns
    -------
    y : float
        A floating point representation of negative infinity.

    See Also
    --------
    isinf : Shows which elements are positive or negative infinity

    isposinf : Shows which elements are positive infinity

    isneginf : Shows which elements are negative infinity

    isnan : Shows which elements are Not a Number

    isfinite : Shows which elements are finite (not one of Not a Number,
    positive infinity and negative infinity)

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Also that positive infinity is not equivalent to negative infinity. But
    infinity is equivalent to positive infinity.

    Examples
    --------
    >>> np.NINF
    -inf
    >>> np.log(0)
    -inf

    �PINFz�
    IEEE 754 floating point representation of (positive) infinity.

    Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for
    `inf`. For more details, see `inf`.

    See Also
    --------
    inf

    �infty�Inf�Infinity�
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