
    \h                     n    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 physics    )I)MutableDenseMatrix)
deprecatedc                     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      $ )zReturns 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mats     N/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/matrices.pymsigmar      sZ    " 	Av
 
aGF
 
a

 .//#;    c                     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   )mdxdydzdxdydydzdzdxdxdxdydydzdzr   s              r   
pat_matrixr   -   sw    $ 3r6D3r6D3r6Dq5Dq5Dq5DK$+t$$&C VC[=r   c                    U S;  a  [        S5      eU S:X  a  SnOIU S:X  a  SnO@U S:X  a)  SSS[        * 4SS[        S4S[        SS4[        * SSS44nOU S:X  a  S	nOU S
:X  a  Sn[        W5      nU(       a	  U S;   a  U* nU$ )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
      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$   r(   r"   r    )r&   r%   r!   r"   )r   r	   r
   r    )r   r   r   )mulowerr   r   s       r   mgammar+   K   s    > 
 .//	Qw
 
q
 
q1qbM1aL1aLRAqM	
 
q
 
q
 	sAAHr   )r!   r'   r#   r$   zk
    The sympy.physics.matrices.mdft method is deprecated. Use
    sympy.DFT(n).as_explicit() instead.
    z1.9zdeprecated-physics-mdft)deprecated_since_versionactive_deprecations_targetc                 :    SSK Jn  U" U 5      R                  5       $ )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)"sympy.matrices.expressions.fourierr/   
as_mutable)nr/   s     r   mdftr3      s      7q6r   N)F)__doc__sympy.core.numbersr   sympy.matrices.denser   r   sympy.utilities.decoratorr   r   r   r+   minkowski_tensorr3    r   r   <module>r:      s[    '   = 0"J<HX      #8		r   