Ë
    7^(h„  ã                   ó€   — d dl mZmZmZmZmZ d dlmZmZ d dl	m
Z
 d dlmZ d dlmZmZmZ d dlmZ d„ Zd„ Zd	„ Zd
„ Zy)é    )ÚmsigmaÚmgammaÚminkowski_tensorÚ
pat_matrixÚmdft)ÚIÚRational)ÚS)Úsqrt)ÚMatrixÚeyeÚzeros)Úwarns_deprecated_sympyc                  ó¤  — t        d«      } t        dddd«      | k(  sJ ‚t        dddd«      d| z  k(  sJ ‚t        d«      }t        dddd«      |k(  sJ ‚t        dddd«      d|z  k(  sJ ‚t        d«      }t        dddd«      |k(  sJ ‚t        dddd«      d|z  k(  sJ ‚t        d«      }t        dddd«      |k(  sJ ‚t        dddd«      d|z  k(  sJ ‚y )N))é   éÿÿÿÿr   )r   r   r   )r   r   r   é   r   )©r   r   r   ©r   r   r   ©r   r   r   r   )©r   r   r   r   r   )r   r   r   )r   r   )Úmat1Úmat2Úmat3Úmat4s       úg/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/physics/tests/test_physics_matrices.pyÚtest_parallel_axis_theoremr   	   s  € ô
 Ð9Ó:€DÜ�a˜˜A˜qÓ! TÒ)Ð)Ð)Ü�a˜˜A˜qÓ! Q t¡VÒ+Ð+Ð+ô Ð3Ó4€DÜ�a˜˜A˜qÓ! TÒ)Ð)Ð)Ü�a˜˜A˜qÓ! Q t¡VÒ+Ð+Ð+ô Ð3Ó4€DÜ�a˜˜A˜qÓ! TÒ)Ð)Ð)Ü�a˜˜A˜qÓ! Q t¡VÒ+Ð+Ð+ô Ð3Ó4€DÜ�a˜˜A˜qÓ! TÒ)Ð)Ð)Ü�a˜˜A˜qÓ! Q t¡VÒ+Ð+Ñ+ó    c                  óˆ  — t        d«      } t        d«      }t        d«      }| | k(  sJ ‚| |k7  sJ ‚| |z  |t        z  k(  sJ ‚|| z  |t        z  k(  sJ ‚||z  | t        z  k(  sJ ‚| | z  t        d«      k(  sJ ‚||z  t        d«      k(  sJ ‚||z  t        d«      k(  sJ ‚| dz  | z  dt        d«      z  k(  sJ ‚| |z  | z  | k(  sJ ‚y )Nr   r   é   )r   r   r   )Úsigma1Úsigma2Úsigma3s      r   Ú
test_Paulir$   "   sø   € ô �A‹Y€FÜ�A‹Y€FÜ�A‹Y€Fà�VÒÐÐØ�VÒÐÐð �&‰=˜F¤1™HÒ$Ð$Ð$Ø�&‰=˜F¤1™HÒ$Ð$Ð$Ø�&‰=˜F¤1™HÒ$Ð$Ð$à�&‰=œC ›FÒ"Ð"Ð"Ø�&‰=œC ›FÒ"Ð"Ð"Ø�&‰=œC ›FÒ"Ð"Ð"à�!‰8�F‰?˜a¤ A£™hÒ&Ð&Ð&Ø�&‰=˜Ñ F 7Ò*Ð*Ñ*r   c                  ó  — t        d«      } t        d«      }t        d«      }t        d«      }t        d«      }|| |z  |z  |z  t        z  k(  sJ ‚||z  ||z  z   t        d«      k(  sJ ‚| | z  t        d«      t        d   z  k(  sJ ‚||z  t        d«      t        d   z  k7  sJ ‚||z  t        d«      t        d   z  k(  sJ ‚t        dd	«      t        dd	«      t        dd	«      z  t        dd	«      z  t        dd	«      z  t        z  k(  sJ ‚y )
Nr   r   r   r    é   é   )r   r   )r   r   T)r   r   r   r   r   )Úgamma0Úgamma1Úgamma2Úgamma3Úgamma5s        r   Ú
test_Diracr-   :   s  € Ü�A‹Y€FÜ�A‹Y€FÜ�A‹Y€FÜ�A‹Y€FÜ�A‹Y€Fð �V˜f‘_ vÑ-°Ñ6¼Ñ:Ò:Ð:Ð:Ø�F‰?˜V f™_Ñ,´°a³Ò8Ð8Ð8Ø�F‰?œc !›fÔ'7¸Ñ'=Ñ=Ò=Ð=Ð=Ø�F‰?œc !›fÔ'7¸Ñ'=Ñ=Ò=Ð=Ð=Ø�F‰?œc !›fÔ'7¸Ñ'=Ñ=Ò=Ð=Ð=ä�!�T‹?Üˆq�$‹œ˜q $›Ñ'¬¨q°$«Ñ7¼¸qÀ$»ÑGÌÑIòJð Jñ Jr   c                  ó   — t        «       5  t        d«      t        dgg«      k(  sJ ‚	 d d d «       t        «       5  t        d«      dt        d«      z  t        ddgddgg«      z  k(  sJ ‚	 d d d «       t        «       5  t        d«      t        t        j
                  t        j
                  t        j
                  t        j
                  gt        j
                  t         dz  t        dd«      t        dz  gt        j
                  t        dd«      t        j
                  t        dd«      gt        j
                  t        dz  t        dd«      t         dz  gg«      k(  sJ ‚	 d d d «       y # 1 sw Y   �ŒDxY w# 1 sw Y   �ŒxY w# 1 sw Y   y xY w)Nr   r   r   r'   )r   r   r   r   r
   ÚHalfr   r	   © r   r   Ú	test_mdftr1   K   sJ  € Ü	Ó	!ñ (Ü�A‹wœ& 1 # ›-Ò'Ð'Ñ'÷(ä	Ó	!ñ ;Ü�A‹w˜!œD ›G™)¤F¨Q¨q¨E°1°R°&¨>Ó$:Ñ:Ò:Ð:Ñ:÷;ä	Ó	!ñ IÜ�A‹wœ&¤1§6¡6¬A¯F©F´Q·V±V¼Q¿V¹VÐ"DÜ#$§6¡6¬A¨2¨a©4´¸"¸Q³Ä!ÀAÁ#Ð"FÜ#$§6¡6¬8°B°q«>¼A¿F¹FÄHÈRÐPQÃNÐ"SÜ#$§6¡6¬A¨a©C´¸"¸Q³Ä!ÀÀAÁÐ"Fð"Hó Iò Ið 	Iñ I÷Ið I÷	(ñ (ú÷;ñ ;ú÷Ið Iús#   ‹E*º/E7Á<C$FÅ*E4Å7FÆFN)Úsympy.physics.matricesr   r   r   r   r   Úsympy.core.numbersr   r	   Úsympy.core.singletonr
   Ú(sympy.functions.elementary.miscellaneousr   Úsympy.matrices.denser   r   r   Úsympy.testing.pytestr   r   r$   r-   r1   r0   r   r   ú<module>r8      s3   ðß UÕ Uß ,Ý "Ý 9ß 5Ñ 5Ý 7ò,ò2+ò0Jó"	Ir   