+
    ‹°³jü  ã                   óv   € R t ^ RIHt ^ RIHt ^ RIHt R tR t	RR lt
]! R4      t]! RRR	R
7      R 4       tR# )z!Known matrices related to physics)ÚI)ÚMutableDenseMatrix)Ú
deprecatedc                óˆ   € V ^8X  d   RpM.V ^8X  d   ^ \         ) 3\         ^ 33pMV ^8X  d   RpM\        R4      h\        V4      # )zèReturns 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]])
zInvalid Pauli index))é    é   ©r   r   )r   )r   éÿÿÿÿ)r   Ú
IndexErrorÚMatrix)ÚiÚmats   & ÚW/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/physics/matrices.pyÚmsigmar      sZ   € ð" 	ˆA„vð
‰ð 
ˆaŒà”�ˆGÜ�ˆFð
‰ð 
ˆaŒð
‰ô
 Ð.Ó/Ð/Ü�#‹;Ðó    c                óÔ   € V) V,          pV) V,          pV) V,          pV^,          pV^,          pV^,          p	W‰,           WF3WGV	,           V3WeW‡,           33p
V \        V
4      ,          # )ag  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   )ÚmÚdxÚdyÚdzÚdxdyÚdydzÚdzdxÚdxdxÚdydyÚdzdzr   s   &&&&       r   Ú
pat_matrixr   -   sw   € ð$ ˆ3ˆr�6€DØˆ3ˆr�6€DØˆ3ˆr�6€DØˆq�5€DØˆq�5€DØˆq�5€DØ�K˜Ð$Ø˜•+˜tÐ$Ø˜�Ð$ð&€Cð ŒV�C‹[�=Ðr   c                ó  € V R9  d   \        R4      hV ^ 8X  d   RpMMV ^8X  d   RpMCV ^8X  d*   ^ ^ ^ \        ) 3^ ^ \        ^ 3^ \        ^ ^ 3\        ) ^ ^ ^ 33pMV ^8X  d   RpM	V ^8X  d   Rp\        X4      pV'       d   V R9   d   V) pV# )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]])
zInvalid Dirac index)r   r   é   é   é   )©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> 
�Ô ÜÐ.Ó/Ð/Ø	ˆQ„wð
‰ð 
ˆqŒð
‰ð 
ˆqŒà��1”q�bˆMØ�”1�aˆLØ”�1�aˆLÜˆR��A�qˆMð	
‰ð 
ˆqŒð
‰ð 
ˆqŒð
ˆô 	ˆs‹€AßØ�ÔØ�ˆAØ€Hr   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:   € ^ RI Hp V! V 4      P                  4       # )zž
.. deprecated:: 1.9

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

   To get identical behavior to ``mdft(n)``, use ``DFT(n).as_explicit()``.
)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)r!   r'   r#   r$   )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ô<HñX ð ó Ð ñ ðð #Ø8ôñ	óò	r   