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  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
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mZmZmZ ddlmZmZmZ d	d
dddddddddgZeddƒZeed	< edeƒZeed
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e-eed ed  e-d  ƒ ƒeeeƒfgeee0feeeƒ ee0ƒ eeeƒ ee0ƒ eeeƒ fge.e/e-fee.d e-d  ƒe
e-ee.d e-d  ƒ ƒe/fgeee0feeeƒ e0eeeƒ fgd(œZ1ede,eee-fe1ƒZ2eed< ed)e,e.e/e-fe1ƒZ3eed< ed*e,eee0fe1ƒZ4eed< e ¡ ° e d¡ ed+ed!\ZZZ-Z.Z/ZZZ0e2je3eee-geed ed  ƒeeeƒe-gd"d"d# e3je2e.e/e-ge.ee/ƒ e.ee/ƒ e-gd"d"d# e2je4eee-geed ed  e-d  ƒe
e-eed ed  e-d  ƒ ƒeeeƒgd"d"d# e4je2eee0geeeƒ ee0ƒ eeeƒ ee0ƒ eeeƒ gd"d"d# e3je4e.e/e-gee.d e-d  ƒe
e-ee.d e-d  ƒ ƒe/gd"d"d# e4je3eee0geeeƒ e0eeeƒ gd"d"d# W 5 Q R X e2  ¡ \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_<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.
é    )ÚAnyN)ÚDummyÚsymbols)Úsqrt)ÚacosÚatan2ÚcosÚsiné   )ÚManifoldÚPatchÚCoordSystemÚR2Ú	R2_originÚrelations_2dÚR2_rÚR2_pÚR3Ú	R3_originÚrelations_3dÚR3_rÚR3_cÚR3_szR^2é   Úoriginzx yT)Úrealz	rho theta)Znonnegative))ÚrectangularÚpolar)r   r   r   r   Úignorezx y r theta)ÚclsF)ZinverseZfill_in_gapszR^3é   zx y zzrho psi r theta phi))r   Úcylindrical)r!   r   )r   Ú	spherical)r"   r   )r!   r"   )r"   r!   r!   r"   zx y z rho psi r theta phi)=Ú__doc__Útypingr   ÚwarningsZsympy.core.symbolr   r   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   r   r	   Zdiffgeomr   r   r   Ú__all__r   Ú__annotations__r   ÚxÚyÚrÚthetar   r   r   Úcatch_warningsÚsimplefilterZ
connect_toZcoord_functionsZbase_vectorsZe_xZe_yZe_rZe_thetaZbase_oneformsZdxZdyZdrZdthetar   r   ÚzÚrhoÚpsiÚphir   r   r   r   Ze_zZe_rhoZe_psiZe_phiZdzZdrhoZdpsiZdphi© r2   r2   úP/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/diffgeom/rn.pyÚ<module>   s
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