
    \h                     <   S SK Jr  S SKJr   " S S\5      r " S S\5      r " S S\5      r " S	 S
\5      r " S S\5      r " S S\5      r	 " S S\5      r
 " S S\5      r " S S\5      r " S S\5      r " S S\5      r " S S\5      rS rS rS rS rg)     )
MatrixExpr)Qc                   8    \ rS rSr\" S 5      r\" S 5      rSrg)Factorization   c                      U R                   S   $ )Nr   )argsselfs    a/var/www/auris/envauris/lib/python3.13/site-packages/sympy/matrices/expressions/factorizations.py<lambda>Factorization.<lambda>   s    		!    c                 .    U R                   R                  $ N)argshaper
   s    r   r   r      s    $((..r    N)__name__
__module____qualname____firstlineno__propertyr   r   __static_attributes__r   r   r   r   r      s    
,
-C01Er   r   c                   $    \ rS rSr\S 5       rSrg)LofLU   c                 $    [         R                  4$ r   )r   lower_triangularr
   s    r   
predicatesLofLU.predicates	       ""$$r   r   Nr   r   r   r   r   r    r   r   r   r   r   r          % %r   r   c                   $    \ rS rSr\S 5       rSrg)UofLU   c                 $    [         R                  4$ r   r   upper_triangularr
   s    r   r    UofLU.predicates   r"   r   r   Nr#   r   r   r   r&   r&      r$   r   r&   c                       \ rS rSrSrg)LofCholesky   r   Nr   r   r   r   r   r   r   r   r-   r-          $r   r-   c                       \ rS rSrSrg)UofCholesky   r   Nr/   r   r   r   r2   r2      r0   r   r2   c                   $    \ rS rSr\S 5       rSrg)QofQR   c                 $    [         R                  4$ r   r   
orthogonalr
   s    r   r    QofQR.predicates       r   r   Nr#   r   r   r   r5   r5           r   r5   c                   $    \ rS rSr\S 5       rSrg)RofQR   c                 $    [         R                  4$ r   r)   r
   s    r   r    RofQR.predicates   r"   r   r   Nr#   r   r   r   r>   r>      r$   r   r>   c                   $    \ rS rSr\S 5       rSrg)EigenVectors   c                 $    [         R                  4$ r   r8   r
   s    r   r    EigenVectors.predicates   r;   r   r   Nr#   r   r   r   rC   rC      r<   r   rC   c                   $    \ rS rSr\S 5       rSrg)EigenValues!   c                 $    [         R                  4$ r   r   diagonalr
   s    r   r    EigenValues.predicates"       

}r   r   Nr#   r   r   r   rH   rH   !        r   rH   c                   $    \ rS rSr\S 5       rSrg)UofSVD&   c                 $    [         R                  4$ r   r8   r
   s    r   r    UofSVD.predicates'   r;   r   r   Nr#   r   r   r   rQ   rQ   &   r<   r   rQ   c                   $    \ rS rSr\S 5       rSrg)SofSVD*   c                 $    [         R                  4$ r   rK   r
   s    r   r    SofSVD.predicates+   rN   r   r   Nr#   r   r   r   rV   rV   *   rO   r   rV   c                   $    \ rS rSr\S 5       rSrg)VofSVD.   c                 $    [         R                  4$ r   r8   r
   s    r   r    VofSVD.predicates/   r;   r   r   Nr#   r   r   r   r[   r[   .   r<   r   r[   c                 .    [        U 5      [        U 5      4$ r   )r   r&   exprs    r   lurb   4       ;d##r   c                 .    [        U 5      [        U 5      4$ r   )r5   r>   r`   s    r   qrre   7   rc   r   c                 .    [        U 5      [        U 5      4$ r   )rH   rC   r`   s    r   eigrg   :   s    tl4000r   c                 B    [        U 5      [        U 5      [        U 5      4$ r   )rQ   rV   r[   r`   s    r   svdri   =   s    $<vd|33r   N)sympy.matrices.expressionsr   sympy.assumptions.askr   r   r   r&   r-   r2   r5   r>   rC   rH   rQ   rV   r[   rb   re   rg   ri   r   r   r   <module>rl      s    1 #2J 2%M %%M %
 %  % M %M %
= - 
] ] ] $$14r   