OtjxUdZddlmZddlZddlmZmZddlmZddl m Z m Z m Z m Z ddlmZmZmZgd Zed d Zeed <ed eZeed<edd\ZZedd\ZZeefeed zed zze eefgeefee ezee ezfgdZedeeefeZeed<edeeefeZeed<ej5ejdede\ZZZZeeeegeed zed zze eegddeeeegee ezee ezgdddddn #1swxYwYe 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_$e_%e&x\e_'e_(x\e_'e_(\e_'e_(e&x\e_)e_*x\e_)e_*\e_)e_*eddZ+eed <ed e+Z,eed!<ed"d\ZZZ-ed#d\Z.Z/ZZZ0eee-feed zed zze eee-fge.e/e-fe.e e/ze.e e/ze-fgeee-feed zed zze-d zze e-eed zed zze-d zzz e eefgeee0fee eze e0zee eze e0zee ezfge.e/e-fee.d ze-d zze e-ee.d ze-d zzz e/fgeee0fee eze0ee ezfgd$Z1ede,eee-fe1Z2eed%<ed&e,e.e/e-fe1Z3eed'<ed(e,eee0fe1Z4eed)<ej5ejded*e\ZZZ-Z.Z/ZZZ0e2e3eee-geed zed zze eee-gdde3e2e.e/e-ge.e e/ze.e e/ze-gdde2e4eee-geed zed zze-d zze e-eed zed zze-d zzz e eegdde4e2eee0gee eze e0zee eze e0zee ezgdde3e4e.e/e-gee.d ze-d zze e-ee.d ze-d zzz e/gdde4e3eee0gee eze0ee ezgdddddn #1swxYwYe2 \e2_e2_e2_-e3 \e3_.e3_/e3_-e4 \e4_e4_e4_0e2!\e2_"e2_#e2_5e3!\e3_6e3_7e3_5e4!\e4_$e4_%e4_8e2&\e2_'e2_(e2_9e3&\e3_:e3_;e3_9e4&\e4_)e4_*e4_<dS)+atPredefined 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)Dummysymbols)sqrt)acosatan2cossin)ManifoldPatch CoordSystem) R2 R2_origin relations_2dR2_rR2_pR3 R3_origin relations_3dR3_rR3_cR3_szR^2roriginrzx yT)realz rho theta) nonnegative)) rectangularpolar)rrrrrrignorez x y r theta)clsF)inverse fill_in_gapszR^3rrzx y zzrho psi r theta phi))r cylindrical)r%r)r spherical)r&r)r%r&)r&r%rr%rr&rzx y z rho psi r theta phi)=__doc__typingrwarningssympy.core.symbolrr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrrr r diffgeomr r r__all__r__annotations__rxyrthetarrrcatch_warnings simplefilter connect_tocoord_functions base_vectorse_xe_ye_re_theta base_oneformsdxdydrdthetarrzrhopsiphirrrre_ze_rhoe_psie_phidzdrhodpsidphiO/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/diffgeom/rn.pyrQs8 ........999999LLLLLLLLLLLL2222222222    (5!  Cx$$ 3$$$wu4   1 7;D 1 1 15!"1vQTAqD[(9(955A;;'GH !5zAcc%jjL!CCJJ,+GH K y1a&, G GcGGG KQJ E EcEEEX77H(###W]666NAq!UOOD1a&adQTk**EE!QKK8!777 OOD1e*33u::qU|4!777 777777777777777:>9M9M9O9OO bdO %Y[)+EIEYEYE[E[[bh[-io0B FJEVEVEXEXXX- 0B$(QUQbQbQdQdd d5Y]I$58N$,@D?Q?Q?S?SS ruS)y|Y\,+>)>$?$?$'$)#*%&uc?$%cc%jjL#qU|#D#F# * K y1a)\ J JcJJJ K y3Q- N NcNNN K YE3 N NcNNNX77H(###'.w/JPU'V'V'V$Aq!S#q%OOD1a)adQTk**EE!QKK;!777 OOD3Q-SSXXs33s88|Q7!777 OOD1a)adQTkAqD01144 $QTAqD[1a4%7 8 8994:4:;@5A;;H!777 OOD1eS/33u::cc#hh.##!3#3#1##&3s881,-.ss5zz\;!777  OOD3Q-c1fq!tm,,dd1TT#q&1a4-5H5H3H.I.I3O!777 OOD1eS/33u::sAcc%jjL9!777-7777777777777776--//!1133$(DF#3355 DH $0022$(DH#'#4#4#6#6  DJ%)%6%6%8%8"$, !..00$' $ 2 2 4 4 49dg"&"4"4"6"6diiis&6BFFF(G%[[ [