
    \hr                     t   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 SK
Jr  S SKJr  S SKJr  S SKJrJr  S S	KJr  S S
KJr  \" S5      r\" S5      u  rrrrr\R=                  S\\R>                  5      r \ R=                  S\\ RB                  5      r"\"R=                  S\\"RF                  5      r$S r%S r&S r'g)    )Vector)
CoordSys3D)expressmatrix_to_vectororthogonalize)Rational)S)symbols)sqrt)cossin)ImmutableDenseMatrix)raisesNzq1 q2 q3 q4 q5ABCc                  N   [        [        R                  [        5      [        R                  :X  d   e[        [        R
                  [        5      [        R
                  L d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  :X  d   e[        [        R                  [        5      [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      * [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [         5      [         R                  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -
  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  :X  d   e[        [        R                  [        5      [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -   :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -
  :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [        [        5      -  [         R                  -  -
  [        [        5      [        [        5      -  [         R                  -  -   :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [        [        5      -  [         R                  -  -   [        [        5      [        [        5      -  [         R                  -  -
  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -
  [        R                  -  [        [        5      [        [        5      -  [        R                  -  -
  [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -   [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -   [        R                  -  [        [        5      [        [        5      -  [        R                  -  -   [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -
  [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      * [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [         5      [         R                  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -
  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  :X  d   e[        [        R                  [        5      [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -   :X  d   e[        [         R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [         R                  [        5      [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        [        5      -  [        R                  -  -   [        [        5      [        R                  -  -   :X  d   e[        [         R                  [        5      [        [        5      [        [        5      -  [        R                  -  [        [        5      [        [        5      -  [        R                  -  -
  [        [        5      [        R                  -  -   :X  d   e[        [         R                  [        5      [        R                  :X  d   e[        [         R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [         R                  [        5      [        [        5      * [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [         R                  [         5      [         R                  :X  d   e[        [         R                  [         5      [         R                  :X  d   e[        [         R                  [         5      [         R                  :X  d   e[        [         R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [         R                  [        5      [        R                  :X  d   e[        [         R                  [        5      [        [        5      * [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -
  [        R                  -  [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -   [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  :X  d   e[        [        R                  [        5      [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        [        5      -  [        R                  -  -   [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -   [        R                  -  [        [        5      [        [        5      -  [        [        5      [        [        5      -  [        [        5      -  -
  [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        [        5      -  [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        R                  -  -   :X  d   e[        [        R                  [        5      [        [        5      [        R                  -  [        [        5      [        [        5      -  [        R                  -  -
  [        [        5      [        [        5      -  [        R                  -  -   :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -
  :X  d   e[        [        R                  [         5      [         R                  :X  d   e[        [        R                  [         5      [        [        5      [         R                  -  [        [        5      [         R                  -  -   :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  :X  d   e[        [        R                  [        5      [        R                  s=:X  a  [        R                  :X  d   e   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -
  [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [        [        5      -  [         R                  -  -
  [        [        5      [        [        5      -  [         R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [        [        5      -  [         R                  -  -   [        [        5      [        [        5      -  [         R                  -  -
  [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [         R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      * [        R                  -  [        [        5      [        R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [         R                  -  -
  [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [         R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  [        5      R#                  5       :X  d   e[        R                  [        [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -   [        5      R#                  5       :X  d   e[         R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[         R                  [        [        [        5      * [        [        5      -  [        R                  -  [        [        5      [        [        5      -  [        R                  -  -   [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[         R                  [        [        [        5      [        [        5      -  [        R                  -  [        [        5      [        [        5      -  [        R                  -  -
  [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[         R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[         R                  [        [        [        5      * [        R                  -  [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[         R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[         R                  [        [        [        5      * [        R                  -  [        [        5      [        R                  -  -   [         5      R#                  5       :X  d   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        [        5      -  [        R                  -  -   [        [        5      [        [        5      -  [        R                  -  -
  [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [        R                  -  [        [        5      [        [        5      -  [        R                  -  -
  [        [        5      [        [        5      -  [        R                  -  -   [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [         R                  -  -
  [        5      R#                  5       :X  d   e[        R                  [        [        [        5      [         R                  -  [        [        5      [         R                  -  -   [        5      R#                  5       :X  d   eg N)r   r   zeror   r	   Zeror   ir   r   q3r   kjq2q1r   simplify     Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/vector/tests/test_functions.pytest_expressr"      s   6;;"fkk1111661'''133?c"gacckCGACCK7777133?c"gc"goacc1CGACCK?BB   133?s2whs2w.qss2SWQSS[@BB   133?c"gacckCGACCK7777133?s2whqsslSWQSS[8888133?acc!!!133?acc!!!133?acc!!!133?acc!!!133?acc!!!133?c"gacckCGACCK7777133?c"gacckCGACCK7777133?c"gacckCGACCK7777133?c"gc"goacc1CGACCK?BB   133?s2whs2w.qss2SWQSS[@BB    133?acc!!!133?acc!!!133?acc!!!133?s2wqss{SWQSS[8999133?s2wqss{SWQSS[8999133?acc!!!133?s2wqss{SWSW_QSS-@@GCGOACC   ! ! !133?s2wqss{SWSW_QSS-@@GCGOACC   ! ! !133?s2wqss{SWQSS[8999133?	RR3r73r7?3r72	2ACC7BB		RR3r73r7?3r72	2ACC7	89 9 9 133?	RR3r73r7?3r72	2ACC7BB		RR3r73r7?3r72	2ACC7	89 9 9 133?BxB/3c"gacckAGCGOACC   ! ! ! 133?s2wqss{SWQSS[8999133?Bx|c"gacck9:::133?acc!!!133?acc!!!133?acc!!!133?acc!!!133?acc!!!133?s2wqss{SWQSS[8999133?s2wqss{SWQSS[8999133?s2wqss{SWQSS[8999133?s2ws2wqss2SWQSS[@GCGOACC   ! ! !133?BxB/3c"gacckAGCGOACC   ! ! ! 133?s2wqss{SWQSS[8999133?BxB/3GCGOACC  "%b'!##+ . / / /133?s2ws2wqss2GCGOACC  "%b'!##+ . / / /133?acc!!!133?s2wqss{SWQSS[8999133?Bx|c"gacck9:::133?acc!!!133?acc!!!133?acc!!!133?s2wqss{SWQSS[8999133?acc!!!133?Bx|c"gacck9:::133?	RR3r73r7?3r72	2ACC7	RR3r73r7?3r72	2ACC7	8BB	   133?	RRs2ws2wqss22SWQSS[@B B B133?	RR3r73r7?3r72	2ACC7	RR3r73r7?3r72	2ACC7	8BB	   133?s2wqss{SWSW_QSS-@@GCGOACC   ! ! !133?s2wqss{SWQSS[8999133?s2wqss{SWSW_QSS-@@GCGOACC   ! ! !133?s2wqss{SWQSS[8999133?acc!!!133?s2wqss{SWQSS[8999133?acc!!!133?acc!!!133?acc*acc***** 33'3r7133;R4q9BBDDDD33'3r7133;R4q9BBDDDD33'3r7133;RR)<<GCGOACC "#%%-XZ0 0 033'3r7133;RR)<<BB!!), , ,33'3r7133;R4q9BBDDDD 33'3r7133;R4q9BBDDDD33'CG8ACC<#b'!##+5:CCEEEE33'3r7133;R4q9BBDDDD33'3r7133;R4q9BBDDDD33'3r7133;R4q9BBDDDD33'3r73r7?133.R<GCGOACC "#%%-XZ0 0 0 33'CG8CG+ACC/#b'!##+=GCGOACC "#%%-XZ0 0 033'3r7133;R4q9BBDDDD33'CG8CG+ACC/GCGOACC "%b'!##+.0133;8:> > > 33'3r73r7?133.GCGOACC "%b'!##+.0133;8:> > > 33'3r7133;R4q9BBDDDD33'CG8ACC<#b'!##+5:CCEEEE33'3r7133;R4q9BBDDDD33'CG8ACC<#b'!##+5:CCEEEE33'3r7133;RR)<<GCGOACC "#%%-XZ0 0 033'3r7133;R4q9BBDDDD33'3r7133;RR)<<GCGOACC "#%%-XZ0 0 033'3r7133;R4q9BBDDDD33'3r7133;R4q9BBDDDDr    c                  H   [        S/S/S//5      n [        U [        5      [        R                  S[        R                  -  -   S[        R
                  -  -   :X  d   e[        S/S/S//5      n [        U [        5      [        U [        5      s=:X  a  [        R                  :X  d   e   e[        [        /[        /[        //5      n [        U [        5      [        [        R                  -  [        [        R                  -  -   [        [        R
                  -  -   :X  d   eg )N         r   )Matrixr   r   r   r   r   r   r   r   r   r   r   )ms    r!   test_matrix_to_vectorr)      s    aS1#AAq!QSS1QSS5[1QSS5%8888aS1#AAq!%5a%; ;;    rdRD!"AAq!RVbf_r!##v%====r    c                     ^^	^
^^ [        S5      n [        SSS9u  pU R                  5       u  p4nUSU-  -   mSU-  SU-  -   m	SU-  SU-  -   m
SU-  U-   nSU-  SU-  -   nX-  X$-  -   mSU-  U-  SU-  U-  -   m[        TT	5      U R                  SU R
                  -  -   U R                  [        SS5      -  U R
                  * S-  -   /:X  d   e[        XgSS	9S[        S
5      -  U R                  -  S
-  [        S
5      U R
                  -  S
-  -   [        S
5      * U R                  -  S
-  S[        S
5      -  U R
                  -  S
-  -   /:X  d   e[        [        UU	U
4S j5        [        [        UU4S j5        g )Nr   za bT)integerr%   r&         )orthonormal
   c                     > [        T TT5      $ r   r   )v1v2v3s   r!   <lambda>$test_orthogonalize.<locals>.<lambda>   s    }RR8r    c                     > [        T T5      $ r   r1   )v6v7s   r!   r5   r6      s    }R4r    )
r   r
   base_vectorsr   r   r   r   r   r   
ValueError)r   abr   r   r   v4v5r2   r3   r4   r8   r9   s           @@@@@r!   test_orthogonalizer@      s}   3A5$'DAnnGA!	
QqSB	
1qsB	
1qsB	
1qB	
1qsB	
qsB	
1Q1QBR QSS1QSS5[!##hq!n2DtAv2M$NNNNT2
DH*acc	"	R!##~b0	0DH9acc/"2D$r(
TUTWTWGWXZGZ2Z[\ \ \
:89
:45r    N)(sympy.vector.vectorr   sympy.vector.coordsysrectr   sympy.vector.functionsr   r   r   sympy.core.numbersr   sympy.core.singletonr	   sympy.core.symbolr
   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   sympy.matrices.immutabler   r'   sympy.testing.pytestr   r   r   r   r   q4q5orient_new_axisr   r   r   r   r   r   r"   r)   r@   r   r    r!   <module>rN      s    & 0 K K ' " % 9 ? C 'sO-. BBc2qss#c2qss#c2qss#HEV>6r    