o
    8Va@                     @   sp   d Z ddlmZmZmZmZ ddlmZ ddlm	Z	 dd Z
dd Zdd
dZedZe	dddddd ZdS )z!Known matrices related to physics    )MatrixIpisqrt)exp)
deprecatedc                 C   sR   | dkr
d}t|S | dkrdt  ft dff}t|S | dkr%d}t|S td)a  Returns a Pauli matrix `\sigma_i` with ``i=1,2,3``.

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Pauli_matrices

    Examples
    ========

    >>> from sympy.physics.matrices import msigma
    >>> msigma(1)
    Matrix([
    [0, 1],
    [1, 0]])
       ))r   r   r   r      r      )r	   )r   zInvalid Pauli index)r   
IndexErrorr   )imat r   8/usr/lib/python3/dist-packages/sympy/physics/matrices.pymsigma   s   r   c                 C   sj   | | }| | }| | }|d }|d }|d }	||	 ||f|||	 |f|||| ff}
| t |
 S )a  Returns the Parallel Axis Theorem matrix to translate the inertia
    matrix a distance of `(dx, dy, dz)` for a body of mass m.

    Examples
    ========

    To translate a body having a mass of 2 units a distance of 1 unit along
    the `x`-axis we get:

    >>> from sympy.physics.matrices import pat_matrix
    >>> pat_matrix(2, 1, 0, 0)
    Matrix([
    [0, 0, 0],
    [0, 2, 0],
    [0, 0, 2]])

    r
   )r   )mZdxZdyZdzZdxdyZdydzZdzdxZdxdxZdydyZdzdzr   r   r   r   
pat_matrix-   s   


r   Fc                 C   s   | dvrt d| dkrd}n1| dkrd}n*| dkr3dddt fddtdfdtddft dddff}n| dkr:d	}n| d
kr@d}t|}|rM| dv rM| }|S )a  Returns a Dirac gamma matrix `\gamma^\mu` in the standard
    (Dirac) representation.

    Explanation
    ===========

    If you want `\gamma_\mu`, use ``gamma(mu, True)``.

    We use a convention:

    `\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3`

    `\gamma_5 = i \cdot \gamma_0 \cdot \gamma_1 \cdot \gamma_2 \cdot \gamma_3 = - \gamma^5`

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Gamma_matrices

    Examples
    ========

    >>> from sympy.physics.matrices import mgamma
    >>> mgamma(1)
    Matrix([
    [ 0,  0, 0, 1],
    [ 0,  0, 1, 0],
    [ 0, -1, 0, 0],
    [-1,  0, 0, 0]])
    )r   r   r
   r      zInvalid Dirac indexr   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r
   r   )r   r   r   r   r   )r   r   r   r   )r   r
   r   r   )r   r   r   )Zmulowerr   r   r   r   r   mgammaK   s*   

r   )r   r   r   r   iO  z1DFT(n).as_mutable(), DFT(n), DFT(n).as_explicit()z1.9)ZissueZ
useinsteadZdeprecated_since_versionc                    s    fddt  D }tdt t   }dg  |d< t  D ]}d|| d< q t d D ]}t | D ]}|||   || |< || |< q5q.dt  t| S )z
    Deprecated. Use DFT from sympy.matrices.expressions.fourier instead.

    To get identical behavior to ``mdft(n)``, use ``DFT(n).as_mutable()``.
    c                    s   g | ]}d d t  D qS )c                 S   s   g | ]}d qS )Nr   ).0xr   r   r   
<listcomp>   s    z#mdft.<locals>.<listcomp>.<listcomp>)range)r    ynr   r   r"      s    zmdft.<locals>.<listcomp>r   r   )r#   r   r   r   r   r   )r&   r   baser   jr   r%   r   mdft   s   "r*   N)F)__doc__Zsympyr   r   r   r   Zsympy.functionsr   Zsympy.core.decoratorsr   r   r   r   Zminkowski_tensorr*   r   r   r   r   <module>   s    %
L