U
    9%e                     @   sd   d Z ddl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    )I)MutableDenseMatrix)
deprecatedc                 C   sH   | dkrd}n2| dkr*dt  ft dff}n| dkr8d}ntdt|S )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   
IndexErrorMatrix)imat r   U/var/www/html/Darija-Ai-API/env/lib/python3.8/site-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krt d| dkrd}nb| dkr,d}nT| dkrfdddt fddtdfdtddft dddff}n| dkrtd	}n| d
krd}t|}|r| dkr| }|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   )mulowerr   r   r   r   r   mgammaK   s*    

r   )r   r   r   r   zk
    The sympy.physics.matrices.mdft method is deprecated. Use
    sympy.DFT(n).as_explicit() instead.
    z1.9zdeprecated-physics-mdft)Zdeprecated_since_versionZactive_deprecations_targetc                 C   s   ddl m} ||  S )z
    .. deprecated:: 1.9

       Use DFT from sympy.matrices.expressions.fourier instead.

       To get identical behavior to ``mdft(n)``, use ``DFT(n).as_explicit()``.
    r   )DFT)Z"sympy.matrices.expressions.fourierr   Z
as_mutable)nr   r   r   r   mdft   s    r!   N)F)__doc__Zsympy.core.numbersr   Zsympy.matrices.denser   r   Zsympy.utilities.decoratorr   r   r   r   Zminkowski_tensorr!   r   r   r   r   <module>   s   %
L