o *ήc @sdZddlmZddlZddlmZmZddlmZddl m Z m Z m Z m Z ddlmZmZmZgd Zed d Zed eZed dd\ZZeddd\ZZeefeed ed e eefgeefee eee efgdZedeeefeZedeeefeZeFededed\ZZZZejeeegeed ed e eegdddejeeegee eee egdddWdn1swYe\e_e_\e_e_\e_e_e\e_e_\e_e_\e_e_e \e_!e_"\e_!e_"\e_!e_"e \e_#e_$\e_#e_$\e_#e_$e%\e_&e_'\e_&e_'\e_&e_'e%\e_(e_)\e_(e_)\e_(e_)eddZ*ed e*Z+eddd\ZZZ,eddd\Z-Z.ZZZ/eee,feed ed e eee,fge-e.e,fe-e e.e-e e.e,fgeee,feed ed e,d e e,eed ed e,d e eefgeee/fee ee e/ee ee e/ee efge-e.e,fee-d e,d e e,ee-d e,d e.fgeee/fee ee/ee efgdZ0ede+eee,fe0Z1ede+e-e.e,fe0Z2ed e+eee/fe0Z3eeded!ed\ZZZ,Z-Z.ZZZ/e1je2eee,geed ed e eee,gddde2je1e-e.e,ge-e e.e-e e.e,gddde1je3eee,geed ed e,d e e,eed ed e,d e eegddde3je1eee/gee ee e/ee ee e/ee egddde2je3e-e.e,gee-d e,d e e,ee-d e,d e.gddde3je2eee/gee ee/ee egdddWdn 1s wYe1\e1_e1_e1_,e2\e2_-e2_.e2_,e3\e3_e3_e3_/e1 \e1_!e1_"e1_4e2 \e2_5e2_6e2_4e3 \e3_#e3_$e3_7e1%\e1_&e1_'e1_8e2%\e2_9e2_:e2_8e3%\e3_(e3_)e3_;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^2originzx yT)realz rho theta) nonnegative)) rectangularpolar)rrrrignorez x y r theta)clsF)inverse fill_in_gapszR^3zx y zzrho psi r theta phi))r cylindrical)r$r)r spherical)r%r)r$r%)r%r$r$r%zx y z rho psi r theta phi)<__doc__typingrwarningssympy.core.symbolrr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrrrr diffgeomr r r __all__rrxyrthetarrrcatch_warnings simplefilter connect_tocoord_functions base_vectorse_xe_ye_re_theta base_oneformsdxdydrdthetarrzrhopsiphirrrre_ze_rhoe_psie_phidzdrhodpsidphirLrL8/tmp/pip-target-vg8gfxp4/lib/python/sympy/diffgeom/rn.pys    $    ( (((((  "    0