B
    [              
   @   s  d Z ddlmZmZ ddlmZmZmZ ddlm	Z	m
Z
mZmZmZmZ eddZedeZed	ed
dgZededdgZdd dD \ZZZZejeeege	ed ed  e
eegddd ejeeegeee eee gddd [[[[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_"eddZ#ede#Z$ed	e$d
ddgZ%ede$dddgZ&ede$dddgZ'dd dD \ZZZ(Z)Z*ZZZ+e%je&eee(ge	ed ed  e
eee(gddd e&je%e)e*e(ge)ee* e)ee* e(gddd e%je'eee(ge	ed ed  e(d  ee(e	ed ed  e(d   e
eegddd e'je%eee+geee ee+ eee ee+ eee gddd e&je'e)e*e(ge	e)d e(d  ee(e	e)d e(d   e*gddd e'je&eee+geee e+eee gddd [[[([)[*[[[+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%_0e& \e&_1e&_2e&_0e' \e'_!e'_"e'_3d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.
    )print_functiondivision   )ManifoldPatchCoordSystem)sqrtatan2acossincosDummyzR^2   originZrectangularxyZpolarrthetac             C   s   g | ]}t |qS  )r   ).0sr   r   0lib/python3.7/site-packages/sympy/diffgeom/rn.py
<listcomp>   s    r   )r   r   r   r   F)ZinverseZfill_in_gapszR^3   zZcylindricalrhopsiZ	sphericalphic             C   s   g | ]}t |qS r   )r   )r   r   r   r   r   r   =   s    )r   r   r   r   r   r   r   r   N)4__doc__Z
__future__r   r   Zdiffgeomr   r   r   Zsympyr   r	   r
   r   r   r   ZR2Z	R2_originZR2_rZR2_pr   r   r   r   Z
connect_toZcoord_functionsZbase_vectorsZe_xZe_yZe_rZe_thetaZbase_oneformsZdxZdyZdrZdthetaZR3Z	R3_originZR3_rZR3_cZR3_sr   r   r   r   Ze_zZe_rhoZe_psiZe_phiZdzZdrhoZdpsiZdphir   r   r   r   <module>	   sr    
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