
    MZdx                     v   U d Z ddlmZ ddlZddlmZmZ ddlmZ ddl	m
Z
mZmZmZ ddlmZmZmZ g d	Z ed
d      Zeed<    ede      Zeed<    edd      \  ZZ edd      \  ZZeef eedz  edz  z          eee      fgeefe ee      z  e ee      z  fgdZ edeeefe      Zeed<    edeeefe      Zeed<    ej:                         5   ej<                  d        ede      \  ZZZZej?                  eeeg eedz  edz  z          eee      gdd       ej?                  eeege ee      z  e ee      z  gdd       ddd       ejA                         x\  e_        e_        x\  e_        e_        \  e_        e_        ejA                         x\  e_        e_        x\  e_        e_        \  e_        e_        ejC                         x\  e_"        e_#        x\  e_"        e_#        \  e_"        e_#        ejC                         x\  e_$        e_%        x\  e_$        e_%        \  e_$        e_%        ejM                         x\  e_'        e_(        x\  e_'        e_(        \  e_'        e_(        ejM                         x\  e_)        e_*        x\  e_)        e_*        \  e_)        e_*         edd      Z+eed <    ede+      Z,eed!<    ed"d      \  ZZZ- ed#d      \  Z.Z/ZZZ0eee-f eedz  edz  z          eee      e-fge.e/e-fe. ee/      z  e. ee/      z  e-fgeee-f eedz  edz  z   e-dz  z          e
e- eedz  edz  z   e-dz  z         z         eee      fgeee0fe ee      z   ee0      z  e ee      z   ee0      z  e ee      z  fge.e/e-f ee.dz  e-dz  z          e
e- ee.dz  e-dz  z         z        e/fgeee0fe ee      z  e0e ee      z  fgd$Z1 ede,eee-fe1      Z2eed%<    ed&e,e.e/e-fe1      Z3eed'<    ed(e,eee0fe1      Z4eed)<    ej:                         5   ej<                  d        ed*e      \  ZZZ-Z.Z/ZZZ0e2j?                  e3eee-g eedz  edz  z          eee      e-gdd       e3j?                  e2e.e/e-ge. ee/      z  e. ee/      z  e-gdd       e2j?                  e4eee-g eedz  edz  z   e-dz  z          e
e- eedz  edz  z   e-dz  z         z         eee      gdd       e4j?                  e2eee0ge ee      z   ee0      z  e ee      z   ee0      z  e ee      z  gdd       e3j?                  e4e.e/e-g ee.dz  e-dz  z          e
e- ee.dz  e-dz  z         z        e/gdd       e4j?                  e3eee0ge ee      z  e0e ee      z  gdd       ddd       e2jA                         \  e2_        e2_        e2_-        e3jA                         \  e3_.        e3_/        e3_-        e4jA                         \  e4_        e4_        e4_0        e2jC                         \  e2_"        e2_#        e2_5        e3jC                         \  e3_6        e3_7        e3_5        e4jC                         \  e4_$        e4_%        e4_8        e2jM                         \  e2_'        e2_(        e2_9        e3jM                         \  e3_:        e3_;        e3_9        e4jM                         \  e4_)        e4_*        e4_<        y# 1 sw Y   xY w# 1 sw Y   SxY w)+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     3/usr/lib/python3/dist-packages/sympy/diffgeom/rn.py<module>rQ      sH     . 9 L L 2 2 5!
C x$	3 $u4 1;D15 !"1vQTAqD[(95A;'GH !5zAc%jL!CJ,+GH
 y1a&,Gc GQJEc E X 7H(#]6NAq!UOOD1a&adQTk*E!QK8!  7 	OOD1e*3u:qU|4!  77 :>9M9M9O O
bd O%Y[)+EIEYEYE[ [bh [-io0B
 FJEVEVEX X X-	0B$(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 X 7H(#'./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 $QTAqD[1a4%7 899 4:;@A;H!  7 	OOD1eS/3u:c#h.#!3# 1##&s81,-.s5z\;!  7
 	OOD3Q-c1fq!tm,d1T#q&1a4-5H3H.I3O!  7 	OOD1eS/3u:sAc%jL9!  7-76 --/ !113 $(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7 7z7 7s   A>\!F\.!\+.\8