
    gx                        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                    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_$        e_%        e&                                x\  e_'        e_(        x\  e_'        e_(        \  e_'        e_(        e&                                x\  e_)        e_*        x\  e_)        e_*        \  e_)        e_*         edd          Z+eed <    ede+          Z,eed!<    ed"d          \  ZZZ- ed#d          \  Z.Z/ZZZ0eee-f eedz  edz  z              eee          e-fge.e/e-fe. ee/          z  e. ee/          z  e-fgeee-f eedz  edz  z   e-dz  z              e
e- eedz  edz  z   e-dz  z             z             eee          fgeee0fe ee          z   ee0          z  e ee          z   ee0          z  e ee          z  fge.e/e-f ee.dz  e-dz  z              e
e- ee.dz  e-dz  z             z            e/fgeee0fe ee          z  e0e ee          z  fgd$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Z0e2                    e3eee-g eedz  edz  z              eee          e-gdd           e3                    e2e.e/e-ge. ee/          z  e. ee/          z  e-gdd           e2                    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           e4                    e2eee0ge ee          z   ee0          z  e ee          z   ee0          z  e ee          z  gdd           e3                    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           e4                    e3eee0ge ee          z  e0e ee          z  gdd           ddd           n# 1 swxY w Y   e2                                 \  e2_        e2_        e2_-        e3                                 \  e3_.        e3_/        e3_-        e4                                 \  e4_        e4_        e4_0        e2!                                \  e2_"        e2_#        e2_5        e3!                                \  e3_6        e3_7        e3_5        e4!                                \  e4_$        e4_%        e4_8        e2&                                \  e2_'        e2_(        e2_9        e3&                                \  e3_:        e3_;        e3_9        e4&                                \  e4_)        e4_*        e4_<        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   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     M/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/diffgeom/rn.py<module>rQ      s8            . . . . . . . . 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   (5!

C   x$$	3 $ $ $wu4   17;D1115 !"1vQTAqD[(9(955A;;'GH !5zAcc%jjL!CCJJ,+GH 
 Ky1a&,GGc G G GKQJEEc E E E X 7 7H(###W]666NAq!UOOD1a&adQTk**EE!QKK8!  7 7 7 	OOD1e*33u::qU|4!  7 7 77 7 7 7 7 7 7 7 7 7 7 7 7 7 7 :>9M9M9O9O O
bd O%Y[)+EIEYEYE[E[ [bh [-io0B
 FJEVEVEXEX X X-	0B$(QUQbQbQdQd d 
 d5Y]I$58N$, @D?Q?Q?S?S Sru S)y|Y\,<DGTWKOK]K]K_K_ _ ry _19<!14HDGT[
 (5!

C   x$$	3 $ $ $
''
%
%
%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?$%cc%jjL#qU|#D#F# * Ky1a)\JJc J J JKy3Q-NNc N N NKYE3NNc N N N X 7 7H(###'.w/JPU'V'V'V$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&   6BFFF(G%[[ [