§
    OŠtjü  ã                   ó†   — 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dS )z!Known matrices related to physicsé    )ÚI)ÚMutableDenseMatrix)Ú
deprecatedc                 ó–   — | dk    rd}n2| dk    rdt            ft           dff}n| dk    rd}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]])
    é   ))r   r   ©r   r   é   r   é   )r   )r   éÿÿÿÿzInvalid Pauli index)r   Ú
IndexErrorÚMatrix)ÚiÚmats     úT/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/physics/matrices.pyÚmsigmar      sk   € ð" 	ˆA‚v€vð
ˆˆð 
ˆaŠˆà•�ˆGÝ�ˆFð
ˆˆð 
ˆaŠˆð
ˆˆõ
 Ð.Ñ/Ô/Ð/Ý�#‰;Œ;Ðó    c                 ó–   — | |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   -   sƒ   € 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 �V�C‰[Œ[‰=Ðr   Fc                 ó  — | dvrt          d¦  «        ‚| dk    rd}nM| dk    rd}nD| 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$   r(   r"   r    )r&   r%   r!   r"   )r   r	   r
   r    )r   r   r   )ÚmuÚlowerr   r   s       r   Úmgammar+   K   sÚ   € ð> 
�Ð Ð ÝÐ.Ñ/Ô/Ð/Ø	ˆQ‚w€wð
ˆˆð 
ˆqŠˆð
ˆˆð 
ˆqŠˆà��1•q�bˆMØ�•1�aˆLØ•�1�aˆLÝˆR��A�qˆMð	
ˆˆð 
ˆqŠˆð
ˆˆð 
ˆqŠˆð
ˆõ 	ˆs‰Œ€AØð Ø�ÐÐØ�ˆAØ€Hr   )r!   r'   r#   r$   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                 óH   — 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   )ÚDFT)Ú"sympy.matrices.expressions.fourierr/   Ú
as_mutable)Únr/   s     r   Úmdftr3   Ÿ   s0   € ð  7Ð6Ð6Ð6Ð6Ð6Øˆ3ˆq‰6Œ6×ÒÑÔ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:      sØ   ðØ 'Ð 'à  Ð  Ð  Ð  Ð  Ð  Ø =Ð =Ð =Ð =Ð =Ð =Ø 0Ð 0Ð 0Ð 0Ð 0Ð 0ð"ð "ð "ðJð ð ð<Hð Hð Hð HðX �6ð ñ ô Ð ð €ðð #Ø8ðñ ô ð	ð 	ñô ð	ð 	ð 	r   