
    \h              	       h   S SK Js  Jr  S SKrS SKrS SKr	\R                  " S5      u  rr\R                  " SS5      u  rr\R                  " \5      \R                   " \5      -   \R"                  " \5      -   \R$                  " \5      -   \R&                  " \5      -   \R(                  " \5      -   \R*                  " \5      -   \R,                  " \5      -   \R.                  " \5      -   \R0                  " \5      -   \R2                  " \5      -   \R4                  " \5      -   \R6                  " \5      -   \R8                  " \5      -   \R:                  " \5      -   \R<                  " \5      -   r\S-  \R0                  " \S5      -   r\R@                  " S5      \!" S5      -   \"" S	5      -   r#S\-  S
\-  -   r$\\-   r%\RL                  " \$RO                  5       RQ                  \5      \$RO                  5       RQ                  \5      \%RO                  5       RQ                  \5      \%RO                  5       RQ                  \5      /5      RS                  SS5      r*\$RO                  5       RQ                  \5      r+\%RO                  5       RQ                  \5      r,\$R[                  \5      RQ                  \S 5      r.\$R[                  \5      RQ                  \S5      r/\RL                  " \RL                  " \$\%/5      RS                  SS5       V s/ s H  o R[                  \5      PM     sn 5      RS                  \RL                  " \$\%/5      RS                  SS5      R`                  S    \RL                  " \$\%/5      RS                  SS5      R`                  S   5      r1\$R[                  \5      r2\$Rg                  \S\-  05      r4\RL                  " \RL                  " \$\%/5      RS                  SS5       V s/ s H  o Rg                  \S
05      PM     sn 5      RS                  \RL                  " \$\%/5      RS                  SS5      R`                  S    \RL                  " \$\%/5      RS                  SS5      R`                  S   5      r5\Rl                  " S5      r7\Rl                  " S5      r8\R                  " S5      r9\8Ru                  \7S\9\7Rv                  /5        S\7R                  -  S
\7R                  -  -
  \7Rv                  -   r<\8R                  \8R                  -   \8Rv                  -   r=\R|                  " \<\=5      r#\RL                  " \R|                  " \<\=5      \R|                  " \<S\=-  5      /5      RS                  SS5      r?\R                  " \<\=5      r,S\<R                  5       -  S
\<R                  5       -  -   rB\R                  " S
\7R                  -  \7R                  5      \R                  " \7R                  \7R                  5      -   \R                  " S\7Rv                  -  \7Rv                  5      -   rD\DR                  \85      r*\RL                  " / SQ5      RS                  S
S5      r\S    \7R                  -  \S   \7R                  -  -   \S   \7Rv                  -  -   rFgs  sn f s  sn f )    Nzx yzx_ y_      
   g      ?gffffff?   abthetaAxis)r   r   r   )Gsympy.physics.mechanicsphysics	mechanics_mesympy_smmathmnumpy_npdynamicsymbolsxyx_dy_dcossintancoshsinhtanhacosasinatanlogexpsqrt	factorialceilingfloorsigneAbsintroundr   e1e2Matrixexpandcoeffreshapeamr	   ccollectd1d2shapefmfsubsggmReferenceFrameframe_aframe_br
   orientzv1v2dotbmcross	magnitudedouterdyadic	to_matrixv)is   0e/var/www/auris/envauris/lib/python3.13/site-packages/sympy/parsing/autolev/test-examples/ruletest7.py<module>rR      s   % %   
% 1gq)SGGAJswwqz#''!*$SXXa[0!<SXXa[HRSTUXU]U]^_U``adaiaijkallmpmtmtuvmwwx{xx  AB  yC  C  DG  DL  DL  MN  DO  O  PS  P]  P]  ^_  P`  `  ad  al  al  mn  ao  o  ps  py  py  z{  p|  |  }@  }E  }E  FG  }H  HF3771b>GGDM#c(5:%qS1WqSZZ""1%ryy{'8'8';RYY[=N=Nq=QSUS\S\S^SdSdefSghiqqrsuvwKKMKKM\\!_1Q\\!_1QZZcjj"R&9&A&A!Q&GH&G1&GHIQQSVS]S]_abd^eSfSnSnoprsStR{R{|}R~  BE  BL  BL  NP  QS  MT  BU  B]  B]  ^_  ab  Bc  Aj  Aj  kl  Am  nLLOIIq1gZZ

Br7(;(C(CAq(IJ(I11(IJKSSUXU_U_acdf`gUhUpUpqrtuUvT}T}~  UA  DG  DN  DN  PR  SU  OV  DW  D_  D_  `a  cd  De  Cl  Cl  mn  Co  p


S
!


S
!7# w		 2 3wyy[799WYY&YYwyy"GGBOZZRQrT!234<<QBIIb"bllnQr||~%%	1WYY;			*399WYY		+J	J399UVW^W`W`U`bibkbkKl	l JJw1%aDNAaDN"AaDN2# I Ks   	Z*1Z/