o 8VaH @sdZddlmZddlZddlmZmZmZmZm Z m Z m Z ddl m Z mZmZgdZe dd Zed eZe d d d \ZZe dd d\ZZeefeed ed eeefgeefee eeeefgdZedeeefeZedeeefeZeFede de d\ZZZZejeeegeed ed eeegdddejeeegee eeeegdddWdn1swYe\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_$e_%e#\e_&e_'\e_&e_'\e_&e_'e ddZ(ed e(Z)e dd d \ZZZ*e dd d\Z+Z,ZZZ-eee*feed ed eeee*fge+e,e*fe+e e,e+ee,e*fgeee*feed ed e*d ee*eed ed e*d eeefgeee-feeee e-eeeee-ee efge+e,e*fee+d e*d ee*ee+d e*d e,fgeee-feeee-ee efgdZ.ede)eee*fe.Z/ede)e+e,e*fe.Z0ede)eee-fe.Z1eede de d\ZZZ*Z+Z,ZZZ-e/je0eee*geed ed eeee*gddde0je/e+e,e*ge+e e,e+ee,e*gddde/je1eee*geed ed e*d ee*eed ed e*d eeegddde1je/eee-geeee e-eeeee-ee egddde0je1e+e,e*gee+d e*d ee*ee+d e*d e,gddde1je0eee-geeee-ee egdddWdn 1swYe/\e/_e/_e/_*e0\e0_+e0_,e0_*e1\e1_e1_e1_-e/\e/_e/_ e/_2e0\e0_3e0_4e0_2e1\e1_!e1_"e1_5e/#\e/_$e/_%e/_6e0#\e0_7e0_8e0_6e1#\e1_&e1_'e1_9dS) 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)sqrtatan2acossincossymbolsDummy)ManifoldPatch CoordSystem) R2 R2_origin relations_2dR2_rR2_pR3 R3_origin relations_3dR3_rR3_cR3_szR^2originzx yT)realz rho theta)Z nonnegative)) rectangularpolar)rrrrignorez x y r theta)clsF)ZinverseZ 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__typingrwarningsZsympyrrrrrrr Zdiffgeomr r r __all__rrxyrZthetarrrcatch_warnings simplefilterZ connect_toZcoord_functionsZ base_vectorsZe_xZe_yZe_rZe_thetaZ base_oneformsZdxZdyZdrZdthetarrzZrhoZpsiZphirrrrZe_zZe_rhoZe_psiZe_phiZdzZdrhoZdpsiZdphir-r-3/usr/lib/python3/dist-packages/sympy/diffgeom/rn.pys $  $    ( (((((  "    0