ó
    Š*£hü  ã                   ón   • S r SSKJr  SSKJr  SSKJr  S rS r	SS jr
\" S5      r\" S	S
SS9S 5       rg)z!Known matrices related to physicsé    )ÚI)ÚMutableDenseMatrix)Ú
deprecatedc                 ó‚   • U S:X  a  SnO,U S:X  a  S[         * 4[         S44nOU S:X  a  SnO[        S5      e[        U5      $ )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]])
é   ))r   r   ©r   r   é   r   é   )r   )r   éÿÿÿÿzInvalid Pauli index)r   Ú
IndexErrorÚMatrix)ÚiÚmats     ÚS/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/physics/matrices.pyÚmsigmar      sZ   € ð" 	ˆAƒvð
‰ð 
ˆa‹à”�ˆGÜ�ˆFð
‰ð 
ˆa‹ð
‰ô
 Ð.Ó/Ð/Ü�#‹;Ðó    c                 ó„   • U* U-  nU* U-  nU* U-  nUS-  nUS-  nUS-  n	X‰-   XF4XGU	-   U4XeX‡-   44n
U [        U
5      -  $ )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	   )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$ð&€Cð ŒV�C‹[‰=Ðr   c                 ó  • U S;  a  [        S5      eU S:X  a  SnOIU S:X  a  SnO@U S:X  a)  SSS[        * 4SS[        S4S[        SS4[        * SSS44nOU S:X  a  S	nOU S
:X  a  Sn[        W5      nU(       a	  U S;   a  U* nU$ )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$   r(   r"   r    )r&   r%   r!   r"   )r   r	   r
   r    )r   r   r   )ÚmuÚlowerr   r   s       r   Úmgammar+   K   s¸   € ð> 
�Ó ÜÐ.Ó/Ð/Ø	ˆQƒwð
‰ð 
ˆq‹ð
‰ð 
ˆq‹à��1”q�bˆMØ�”1�aˆLØ”�1�aˆLÜˆR��A�qˆMð	
‰ð 
ˆq‹ð
‰ð 
ˆq‹ð
ˆô 	ˆs‹€AÞØ�ÓØ�ˆAØ€Hr   )r!   r'   r#   r$   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:   • SSK Jn  U" U 5      R                  5       $ )zž
.. 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ô<HñX ð ó Ð ñ ðð #Ø8ññ	óñ	r   