
    Ed                     .   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de          Z 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deeefe          Z ej                    5   ej        d            ede          \  ZZZZe                    eeeg eedz  edz  z              eee          gdd           e                    eeege ee          z  e ee          z  gdd           ddd           n# 1 swxY w Y   e                                x\  e_        e_        x\  e_        e_        \  e_        e_        e                                x\  e_        e_        x\  e_        e_        \  e_        e_        e                                 x\  e_!        e_"        x\  e_!        e_"        \  e_!        e_"        e                                 x\  e_#        e_$        x\  e_#        e_$        \  e_#        e_$        e%                                x\  e_&        e_'        x\  e_&        e_'        \  e_&        e_'        e%                                x\  e_(        e_)        x\  e_(        e_)        \  e_(        e_)         edd          Z* ede*          Z+ edd          \  ZZZ, edd          \  Z-Z.ZZZ/e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e/fe ee          z   ee/          z  e ee          z   ee/          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e/fe ee          z  e/e ee          z  fgdZ0 ede+eee,fe0          Z1 ede+e-e.e,fe0          Z2 ed e+eee/fe0          Z3 ej                    5   ej        d            ed!e          \  ZZZ,Z-Z.ZZZ/e1                    e2eee,g eedz  edz  z              eee          e,gdd           e2                    e1e-e.e,ge- ee.          z  e- ee.          z  e,gdd           e1                    e3e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           e3                    e1eee/ge ee          z   ee/          z  e ee          z   ee/          z  e ee          z  gdd           e2                    e3e-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           e3                    e2eee/ge ee          z  e/e ee          z  gdd           ddd           n# 1 swxY w Y   e1                                \  e1_        e1_        e1_,        e2                                \  e2_-        e2_.        e2_,        e3                                \  e3_        e3_        e3_/        e1                                 \  e1_!        e1_"        e1_4        e2                                 \  e2_5        e2_6        e2_4        e3                                 \  e3_#        e3_$        e3_7        e1%                                \  e1_&        e1_'        e1_8        e2%                                \  e2_9        e2_:        e2_8        e3%                                \  e3_(        e3_)        e3_;        dS )"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   originzx yT)realz	rho theta)nonnegative))rectangularpolar)r   r   r   r   ignorezx y r theta)clsF)inversefill_in_gapszR^3   zx y zzrho psi r theta phi))r   cylindrical)r%   r   )r   	spherical)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   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     1lib/python3.11/site-packages/sympy/diffgeom/rn.py<module>rP      s
           . . . . . . . . 9 9 9 9 9 9 L L L L L L L L L L L L 2 2 2 2 2 2 2 2 2 2   XeQE(B	wu4   17;D1115 !"1vQTAqD[(9(955A;;'GH !5zAcc%jjL!CCJJ,+GH 
 {=)aV\BB{7I5z<@@ X 7 7H(###W]666NAq!UOOD1a&adQTk**EE!QKK8!  7 7 7 	OOD1e*33u::qU|4!  7 7 77 7 7 7 7 7 7 7 7 7 7 7 7 7 7 :>9M9M9O9O O
bd O%Y[)+EIEYEYE[E[ [bh [-io0B
 FJEVEVEXEX X X-	0B$(QUQbQbQdQd d 
 d5Y]I$58N$, @D?Q?Q?S?S Sru S)y|Y\,<DGTWKOK]K]K_K_ _ ry _19<!14HDGT[
 XeQE(B	
''
%
%
%1a!'"7TJJJ S!UC '(AY&*d1a4!Q$;&7&7q!a%H%J&)3]&)##c((lCCL!%D%F$%q!9$(DA1q!t);$<$<$(D441q!tad0B+C+C)C$D$D$)E!QKK$1#2 %&uc?$%cc%jjLS$9$%cc%jjLS$9$%cc%jjL$2#3 %(a=$(Da!Q$$7$7$(D44QA+>+>)>$?$?$'$)#* %&uc?$%cc%jjL#qU|#D#F# * {=)aAYEE{=)c3]LII{;	Auc?LII X 7 7H(###'.w/JPU'V'V'V$Aq!S#q%OOD1a)adQTk**EE!QKK;!  7 7 7 	OOD3Q-SSXXs33s88|Q7!  7 7 7 	OOD1a)adQTkAqD01144 $QTAqD[1a4%7 8 899 4: 4:;@5A;;H!  7 7 7 	OOD1eS/33u::cc#hh.##!3# 3# 1##&3s881,-.ss5zz\;!  7 7 7
 	OOD3Q-c1fq!tm,,dd1TT#q&1a4-5H5H3H.I.I3O!  7 7 7 	OOD1eS/33u::sAcc%jjL9!  7 7 7-7 7 7 7 7 7 7 7 7 7 7 7 7 7 76 --// !1133 $(DF#3355 
DH  $0022 $(DH#'#4#4#6#6  
DJ%)%6%6%8%8 "$,
 !..00 $' $ 2 2 4 4 	49dg"&"4"4"6"6 diiis&   !BF  FF:G%Z++Z/2Z/