Ë
    7^(hü  ã                   ór   — d Z ddlmZ ddlmZ ddlmZ d„ Zd„ Z	dd„Z
 ed«      Z ed	d
d¬«      d„ «       Zy)z!Known matrices related to physicsé    )ÚI)ÚMutableDenseMatrix)Ú
deprecatedc                 ó¢   — | 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]])
    é   ))r   r   ©r   r   é   r   é   )r   )r   éÿÿÿÿzInvalid Pauli index)r   Ú
IndexErrorÚMatrix)ÚiÚmats     úT/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/physics/matrices.pyÚmsigmar      st   € ð" 	ˆA‚vð
ˆô  �#‹;Ðð 
ˆaŠà”�ˆGÜ�ˆFð
ˆô �#‹;Ðð 
ˆaŠð
ˆô �#‹;Ðô Ð.Ó/Ð/ó    c                 óŽ   — | |z  }| |z  }| |z  }|dz  }|dz  }|dz  }	||	z   ||f|||	z   |f||||z   ff}
| t        |
«      z  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   )ÚmÚdxÚdyÚdzÚdxdyÚdydzÚdzdxÚdxdxÚdydyÚdzdzr   s              r   Ú
pat_matrixr   -   s�   € ð$ ˆ3ˆr‰6€DØˆ3ˆr‰6€DØˆ3ˆr‰6€DØˆq‰5€DØˆq‰5€DØˆq‰5€DØ�4‰K˜˜tÐ$Ø�$˜‘+˜tÐ$Ø�$˜˜t™Ð$ð&€Cð ŒV�C‹[‰=Ðr   c                 óæ   — | dvrt        d«      ‚| dk(  rd}nE| dk(  rd}n=| dk(  r)d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        «      }|r| dv 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
   é   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$   r(   r"   r    )r&   r%   r!   r"   )r   r	   r
   r    )r   r   r   )ÚmuÚlowerr   r   s       r   Úmgammar+   K   s¸   € ð> 
�Ñ ÜÐ.Ó/Ð/Ø	ˆQ‚wð
‰ð 
ˆqŠð
‰ð 
ˆqŠà��1”q�bˆMØ�”1�aˆLØ”�1�aˆLÜˆR��A�qˆMð	
‰ð 
ˆqŠð
‰ð 
ˆqŠð
ˆô 	ˆs‹€AÙØ�ÑØ�ˆAØ€Hr   )r!   r'   r#   r$   zk
    The sympy.physics.matrices.mdft method is deprecated. Use
    sympy.DFT(n).as_explicit() instead.
    z1.9zdeprecated-physics-mdft)Údeprecated_since_versionÚactive_deprecations_targetc                 ó:   — ddl m}  || «      j                  «       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   )ÚDFT)Ú"sympy.matrices.expressions.fourierr/   Ú
as_mutable)Únr/   s     r   Úmdftr3   Ÿ   s   € õ  7Ùˆq‹6×ÑÓÐr   N)F)Ú__doc__Úsympy.core.numbersr   Úsympy.matrices.denser   r   Úsympy.utilities.decoratorr   r   r   r+   Úminkowski_tensorr3   © r   r   ú<module>r:      s[   ðÙ 'å  Ý =Ý 0ò"òJó<HñX ð ó Ð ñ ðð #Ø8ôñ	óñ	r   