
    \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\\-   S-  \\-
  S-  -   r\\-
  S-  r\S-  \S-  -   S\-  \-  -   r\R$                  " \\/5      R'                  SS5      r\R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5      r\\R$                  " \\/5      R'                  SS5      -   r\R$                  " \ V s/ s H  o R/                  5       PM     sn 5      R'                  \R0                  S    \R0                  S   5      r\R$                  " \R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5       V s/ s H  o R/                  5       PM     sn 5      R'                  \R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5      R0                  S    \R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5      R0                  S   5      r\R$                  " \\R$                  " \\/5      R'                  SS5      -    V s/ s H  o R/                  5       PM     sn 5      R'                  \\R$                  " \\/5      R'                  SS5      -   R0                  S    \\R$                  " \\/5      R'                  SS5      -   R0                  S   5      r\R/                  5       r\R/                  5       r\R<                  " \\5      r\R$                  " \ V s/ s H  n \R=                  U \5      PM     sn 5      R'                  \R0                  S    \R0                  S   5      r \R$                  " \\R$                  " \\/5      R'                  SS5      -    V s/ s H  n \R=                  U \5      PM     sn 5      R'                  \\R$                  " \\/5      R'                  SS5      -   R0                  S    \\R$                  " \\/5      R'                  SS5      -   R0                  S   5      r\RC                  \5      r\RC                  \5      r"\R$                  " \ V s/ s H  o RC                  \5      PM     sn 5      R'                  \R0                  S    \R0                  S   5      r\R$                  " \\R$                  " \\/5      R'                  SS5      -    V s/ s H  o RC                  \5      PM     sn 5      R'                  \\R$                  " \\/5      R'                  SS5      -   R0                  S    \\R$                  " \\/5      R'                  SS5      -   R0                  S   5      r#\RH                  " S5      r%\RH                  " S5      r&\&RO                  \%S	\R$                  " / S
Q5      R'                  SS5      5        \\%R                  -  \\%R                  -  -   \\-  \%RP                  -  -   r)\)RC                  \\&5      r*\R$                  " \ V s/ s H"  o RC                  \RW                  S5      5      PM$     sn 5      R'                  \R0                  S    \R0                  S   5      r,\R$                  " \R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5       V s/ s H"  o RC                  \RW                  S5      5      PM$     sn 5      R'                  \R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5      R0                  S    \R$                  " \\-   S-  \\-
  S-  /5      R'                  SS5      R0                  S   5      r-\)R]                  \&5      r/gs  sn f s  sn f s  sn f s  sn f s  sn f s  sn f s  sn f s  sn f s  sn f )    Nzx yzx_ y_         abDCM)	r   r   r   r   r   r   r   r   r   t)0sympy.physics.mechanicsphysics	mechanics_mesympy_smmathmnumpy_npdynamicsymbolsxyx_dy_de1e2e3Matrixreshapem1m2m3expandshapeamcmemfgfactorr   bmdiffr   dmReferenceFrameframe_aframe_borientzv1eSymbolfmgmdth)is   0e/var/www/auris/envauris/lib/python3.13/site-packages/sympy/parsing/autolev/test-examples/ruletest5.py<module>r:      s	   % %   
% 1gq)ScAXqsQhcAXT!Q$Yqs1u_ZZB  A&ZZ!A#1Q3(#$,,Q2

Aa5!!!Q''ZZR(RR()112**Q-"AOZZSZZ!A#1Q3(0C%D%L%LQPQ%RS%R%RST\\^a^h^hklmnknqrjrtuvwtwz{s{i|^}  _F  _F  GH  JK  _L  ^S  ^S  TU  ^V  Y\  Yc  Yc  fg  hi  fi  lm  em  op  qr  or  uv  nv  dw  Yx  Y@  Y@  AB  DE  YF  XM  XM  NO  XP  QZZR

Aa5(9(A(A!Q(G%GH%G%GHIQQSUVYV`V`bcdeafVgVoVopqstVuSuR|R|}~R  CE  FI  FP  FP  RS  TU  QV  FW  F_  F_  `a  cd  Fe  Ce  Bl  Bl  mn  Bo  pKKMKKMJJQZZ2.2aAq!2./77

1zzRS}UZZ2cjj!A.?.G.G1.M+MN+MaAq!+MNOWWY[\_\f\fhijkgl\m\u\uvwyz\{Y{  YC  YC  DE  YF  IK  LO  LV  LV  XY  Z[  W\  L]  Le  Le  fg  ij  Lk  Ik  Hr  Hr  st  Hu  vIIaLIIaLZZB'BqB'(00"A

1NZZBszz1Q%'8'@'@A'F$FG$Fq$FGHPPRTUXU_U_abcd`eUfUnUnoprsUtRtQ{Q{|}Q~  BD  EH  EO  EO  QR  ST  PU  EV  E^  E^  _`  bc  Ed  Bd  Ak  Ak  lm  An  o


S
!


S
! wszz*=>FFq!L Mwyy[799QqS]*IIaZZ"5"Q

3("56>>zz!}rjjYZm\ZZ#**qsQh!ax=P2Q2Y2YZ[]^2_`2_Q

3(2_`aiiknkukuxyz{x{~w  BC  DE  BE  HI  AI  wJ  lK  lS  lS  TU  WX  lY  k`  k`  ab  kc  fi  fp  fp  st  uv  sv  yz  rz  |}  ~  |  BC  {C  qD  fE  fM  fM  NO  QR  fS  eZ  eZ  [\  e]  ^GGG' )SH /N (G 6`s6   9^ ^%^*3^/5^4>^9>^> )_)_