
    \h                         S SK JrJrJrJrJr  S SKJrJr  S SK	J
r
  S SKJr  S SKJrJrJr  S SKJr  S rS rS	 rS
 rg)    )msigmamgammaminkowski_tensor
pat_matrixmdft)IRational)S)sqrt)Matrixeyezeros)warns_deprecated_sympyc                     [        S5      n [        SSSS5      U :X  d   e[        SSSS5      SU -  :X  d   e[        S5      n[        SSSS5      U:X  d   e[        SSSS5      SU-  :X  d   e[        S5      n[        SSSS5      U:X  d   e[        SSSS5      SU-  :X  d   e[        S5      n[        SSSS5      U:X  d   e[        SSSS5      SU-  :X  d   eg )N))   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   )mat1mat2mat3mat4s       a/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/tests/test_physics_matrices.pytest_parallel_axis_theoremr   	   s   
 9:DaAq!T)))aAq!QtV+++ 34DaAq!T)))aAq!QtV+++ 34DaAq!T)))aAq!QtV+++ 34DaAq!T)))aAq!QtV+++    c                     [        S5      n [        S5      n[        S5      nX :X  d   eX:w  d   eX-  U[        -  :X  d   eX -  U[        -  :X  d   eX-  U [        -  :X  d   eX -  [        S5      :X  d   eX-  [        S5      :X  d   eX"-  [        S5      :X  d   eU S-  U -  S[        S5      -  :X  d   eX-  U -  U* :X  d   eg )Nr   r      )r   r   r   )sigma1sigma2sigma3s      r   
test_Paulir$   "   s     AYFAYFAYF =F1H$$$=F1H$$$=F1H$$$=CF"""=CF"""=CF"""!8F?aAh&&&=F7***r   c                     [        S5      n [        S5      n[        S5      n[        S5      n[        S5      nX@U-  U-  U-  [        -  :X  d   eX-  X!-  -   [        S5      :X  d   eX -  [        S5      [        S   -  :X  d   eX"-  [        S5      [        S   -  :w  d   eX"-  [        S5      [        S   -  :X  d   e[        SS	5      [        SS	5      [        SS	5      -  [        SS	5      -  [        SS	5      -  [        -  :X  d   eg )
Nr   r   r   r          )r   r   )r   r   T)r   r   r   r   r   )gamma0gamma1gamma2gamma3gamma5s        r   
test_Diracr-   :   s   AYFAYFAYFAYFAYF f_v-6::::?V_,a888?c!f'7'=====?c!f'7'=====?c!f'7'=====!T?q$q$'q$7q$GIJ J Jr   c                  D   [        5          [        S5      [        S//5      :X  d   e S S S 5        [        5          [        S5      S[        S5      -  [        SS/SS//5      -  :X  d   e S S S 5        [        5          [        S5      [        [        R
                  [        R
                  [        R
                  [        R
                  /[        R
                  [        * S-  [        SS5      [        S-  /[        R
                  [        SS5      [        R
                  [        SS5      /[        R
                  [        S-  [        SS5      [        * S-  //5      :X  d   e S S S 5        g ! , (       d  f       GNK= f! , (       d  f       GN= f! , (       d  f       g = f)Nr   r   r   r'   )r   r   r   r   r
   Halfr   r	    r   r   	test_mdftr1   K   s*   		!Aw&1#-''' 
"		!Aw!DG)FQqE1R&>$::::: 
"		!Aw&166AFFQVVQVV"D#$66A2a4"Q!A#"F#$668Bq>AFFHRPQN"S#$66AaC"Q!A"F"H I I 	I I 
"	!	 
"	!	!	!	!	!s#   E-0E?>C%F-
E<?
F
FN)sympy.physics.matricesr   r   r   r   r   sympy.core.numbersr   r	   sympy.core.singletonr
   (sympy.functions.elementary.miscellaneousr   sympy.matrices.denser   r   r   sympy.testing.pytestr   r   r$   r-   r1   r0   r   r   <module>r8      s3    U U , " 9 5 5 7,2+0J"	Ir   