
    \hx                     6   % S r SSKJr  SSKrSSKJrJr  SSKJr  SSK	J
r
JrJrJr  SSKJrJrJr  / S	Qr\" S
S5      r\\S'   \" S\5      r\\S'   \" SSS9u  rr\" SSS9u  rr\\4\" \S-  \S-  -   5      \" \\5      4/\\4\\" \5      -  \\" \5      -  4/S.r\" S\\\4\5      r\\S'   \" S\\\4\5      r\\S'   \R:                  " 5          \R<                  " S5        \" S\S9u  rrrr\R?                  \\\/\" \S-  \S-  -   5      \" \\5      /SSS9  \R?                  \\\/\\" \5      -  \\" \5      -  /SSS9  SSS5        \RA                  5       =u  \l        \l        =u  \l        \l        u  \l        \l        \RA                  5       =u  \l        \l        =u  \l        \l        u  \l        \l        \RC                  5       =u  \l"        \l#        =u  \l"        \l#        u  \l"        \l#        \RC                  5       =u  \l$        \l%        =u  \l$        \l%        u  \l$        \l%        \RM                  5       =u  \l'        \l(        =u  \l'        \l(        u  \l'        \l(        \RM                  5       =u  \l)        \l*        =u  \l)        \l*        u  \l)        \l*        \" SS5      r+\\S '   \" S\+5      r,\\S!'   \" S"SS9u  rrr-\" S#SS9u  r.r/rrr0\\\-4\" \S-  \S-  -   5      \" \\5      \-4/\.\/\-4\.\" \/5      -  \.\" \/5      -  \-4/\\\-4\" \S-  \S-  -   \-S-  -   5      \
" \-\" \S-  \S-  -   \-S-  -   5      -  5      \" \\5      4/\\\04\\" \5      -  \" \05      -  \\" \5      -  \" \05      -  \\" \5      -  4/\.\/\-4\" \.S-  \-S-  -   5      \
" \-\" \.S-  \-S-  -   5      -  5      \/4/\\\04\\" \5      -  \0\\" \5      -  4/S$.r1\" S\,\\\-4\15      r2\\S%'   \" S&\,\.\/\-4\15      r3\\S''   \" S(\,\\\04\15      r4\\S)'   \R:                  " 5          \R<                  " S5        \" S*\S9u  rrr-r.r/rrr0\2R?                  \3\\\-/\" \S-  \S-  -   5      \" \\5      \-/SSS9  \3R?                  \2\.\/\-/\.\" \/5      -  \.\" \/5      -  \-/SSS9  \2R?                  \4\\\-/\" \S-  \S-  -   \-S-  -   5      \
" \-\" \S-  \S-  -   \-S-  -   5      -  5      \" \\5      /SSS9  \4R?                  \2\\\0/\\" \5      -  \" \05      -  \\" \5      -  \" \05      -  \\" \5      -  /SSS9  \3R?                  \4\.\/\-/\" \.S-  \-S-  -   5      \
" \-\" \.S-  \-S-  -   5      -  5      \//SSS9  \4R?                  \3\\\0/\\" \5      -  \0\\" \5      -  /SSS9  SSS5        \2RA                  5       u  \2l        \2l        \2l-        \3RA                  5       u  \3l.        \3l/        \3l-        \4RA                  5       u  \4l        \4l        \4l0        \2RC                  5       u  \2l"        \2l#        \2l5        \3RC                  5       u  \3l6        \3l7        \3l5        \4RC                  5       u  \4l$        \4l%        \4l8        \2RM                  5       u  \2l'        \2l(        \2l9        \3RM                  5       u  \3l:        \3l;        \3l9        \4RM                  5       u  \4l)        \4l*        \4l<        g! , (       d  f       GN= f! , (       d  f       GN]= f)+at  Predefined R^n manifolds together with common coord. systems.

Coordinate systems are predefined as well as the transformation laws between
them.

Coordinate functions can be accessed as attributes of the manifold (eg `R2.x`),
as attributes of the coordinate systems (eg `R2_r.x` and `R2_p.theta`), or by
using the usual `coord_sys.coord_function(index, name)` interface.
    )AnyN)Dummysymbols)sqrt)acosatan2cossin   )ManifoldPatchCoordSystem)R2	R2_originrelations_2dR2_rR2_pR3	R3_originrelations_3dR3_rR3_cR3_szR^2   r   originr   zx yT)realz	rho theta)nonnegative))rectangularpolar)r   r   r   r   r   r   ignorezx y r theta)clsF)inversefill_in_gapszR^3   r   r   zx y zzrho psi r theta phi))r   cylindrical)r%   r   )r   	spherical)r&   r   )r%   r&   )r&   r%   r   r%   r   r&   r   zx y z rho psi r theta phi)=__doc__typingr   warningssympy.core.symbolr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r	   r
   diffgeomr   r   r   __all__r   __annotations__r   xyrthetar   r   r   catch_warningssimplefilter
connect_tocoord_functionsbase_vectorse_xe_ye_re_thetabase_oneformsdxdydrdthetar   r   zrhopsiphir   r   r   r   e_ze_rhoe_psie_phidzdrhodpsidphi     I/var/www/auris/envauris/lib/python3.13/site-packages/sympy/diffgeom/rn.py<module>rQ      s2     . 9 L L 2 2 5!
C x$	3 $u4 1;D15 !"1vQTAqD[(95A;'GH !5zAc%jL!CJ,+GH
 y1a&,Gc GQJEc E (#]6NAq!UOOD1a&adQTk*E!QK8!  7 	OOD1e*3u:qU|4!  7  :>9M9M9O O
bd O%Y[)+EIEYEYE[ [bh [-io0B
 FJEVEVEX X X-	0B$(QUQbQbQd d 
 d5Y]I$58N$, @D?Q?Q?S Sru S)y|Y\,<DGTWKOK]K]K_ _ ry _19<!14HDGT[
 5!
C x$	3 $
'
%1a!"7TJ S!UC '(AY&*1a4!Q$;&7q!a%H%J&)3]&)#c(lCCL!%D%F$%q!9$(A1q!t);$<$(41q!tad0B+C)C$D$)!QK$1#2 %&uc?$%c%jLS$9$%c%jLS$9$%c%jL$2#3 %(a=$(a!Q$$7$(4QA+>)>$?$'$)#* %&uc?$%c%jL#qU|#D#F#* y1a)\Jc Jy3Q-Nc NYE3Nc N (#'./JPU'V$Aq!S#q%OOD1a)adQTk*E!QK;!  7 	OOD3Q-SXs3s8|Q7!  7 	OOD1a)adQTkAqD014 $QTAqD[1a4%7 899 4:;@A;H!  7 	OOD1eS/3u:c#h.#!3# 1##&s81,-.s5z\;!  7
 	OOD3Q-c1fq!tm,d1T#q&1a4-5H3H.I3O!  7 	OOD1eS/3u:sAc%jL9!  7- 6 --/ !113 $(DF#335 
DH  $002 $(DH#'#4#4#6  
DJ%)%6%6%8 "$,
 !..0 $' $ 2 2 4 	49dg"&"4"4"6 diI z s   A5[72F\	7
\	
\