+
    ‹°³jx  ã                   óè  a € R t=0 t R t^ RIHt ^ RIt^ RIHtHt ^ RIH	t	 ^ RI
HtHtHtHt ^RIHtHtHt . ROt]! R^4      t] ^ k ]! R]4      t] ^k ]! R	R
R7      w  tt]! RR
R7      w  ttR]]3]	! ]^,          ]^,          ,           4      ]! ]]4      3.R]]3]]! ]4      ,          ]]! ]4      ,          3./t]! R]]]3]4      t] ^k ]! R]]]3]4      t] ^k ]P:                  ! 4       ;_uu_ 4        ]P<                  ! R4       ]! R]R7      w  tttt]P?                  ]]].]	! ]^,          ]^,          ,           4      ]! ]]4      .RRR7       ]P?                  ]]].]]! ]4      ,          ]]! ]4      ,          .RRR7       RRR4       ]PA                  4       ;w  ]n        ]n        ;w  ]n        ]n        w  ]n        ]n        ]PA                  4       ;w  ]n        ]n        ;w  ]n        ]n        w  ]n        ]n        ]PC                  4       ;w  ]n"        ]n#        ;w  ]n"        ]n#        w  ]n"        ]n#        ]PC                  4       ;w  ]n$        ]n%        ;w  ]n$        ]n%        w  ]n$        ]n%        ]PM                  4       ;w  ]n'        ]n(        ;w  ]n'        ]n(        w  ]n'        ]n(        ]PM                  4       ;w  ]n)        ]n*        ;w  ]n)        ]n*        w  ]n)        ]n*        ]! R^4      t+] ^k ]! R]+4      t,] ^k ]! RR
R7      w  ttt-]! RR
R7      w  t.t/ttt0R]]]-3]	! ]^,          ]^,          ,           4      ]! ]]4      ]-3.R ].]/]-3].]! ]/4      ,          ].]! ]/4      ,          ]-3.R!]]]-3]	! ]^,          ]^,          ,           ]-^,          ,           4      ]! ]-]	! ]^,          ]^,          ,           ]-^,          ,           4      ,          4      ]! ]]4      3.R"]]]03]]! ]4      ,          ]! ]04      ,          ]]! ]4      ,          ]! ]04      ,          ]]! ]4      ,          3.R#].]/]-3]	! ].^,          ]-^,          ,           4      ]! ]-]	! ].^,          ]-^,          ,           4      ,          4      ]/3.R$]]]03]]! ]4      ,          ]0]]! ]4      ,          3./t1]! R],]]]-3]14      t2] ^k ]! R],].]/]-3]14      t3] ^k ]! R],]]]03]14      t4] ^k ]P:                  ! 4       ;_uu_ 4        ]P<                  ! R4       ]! R]R7      w  ttt-t.t/ttt0]2P?                  ]3]]]-.]	! ]^,          ]^,          ,           4      ]! ]]4      ]-.RRR7       ]3P?                  ]2].]/]-.].]! ]/4      ,          ].]! ]/4      ,          ]-.RRR7       ]2P?                  ]4]]]-.]	! ]^,          ]^,          ,           ]-^,          ,           4      ]! ]-]	! ]^,          ]^,          ,           ]-^,          ,           4      ,          4      ]! ]]4      .RRR7       ]4P?                  ]2]]]0.]]! ]4      ,          ]! ]04      ,          ]]! ]4      ,          ]! ]04      ,          ]]! ]4      ,          .RRR7       ]3P?                  ]4].]/]-.]	! ].^,          ]-^,          ,           4      ]! ]-]	! ].^,          ]-^,          ,           4      ,          4      ]/.RRR7       ]4P?                  ]3]]]0.]]! ]4      ,          ]0]]! ]4      ,          .RRR7       RRR4       ]2PA                  4       w  ]2n        ]2n        ]2n-        ]3PA                  4       w  ]3n.        ]3n/        ]3n-        ]4PA                  4       w  ]4n        ]4n        ]4n0        ]2PC                  4       w  ]2n"        ]2n#        ]2n5        ]3PC                  4       w  ]3n6        ]3n7        ]3n5        ]4PC                  4       w  ]4n$        ]4n%        ]4n8        ]2PM                  4       w  ]2n'        ]2n(        ]2n9        ]3PM                  4       w  ]3n:        ]3n;        ]3n9        ]4PM                  4       w  ]4n)        ]4n*        ]4n<        R#   + '       g   i     ELË; i  + '       g   i     ELb; i)%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.
)ÚAnyN)ÚDummyÚsymbols)Úsqrt)ÚacosÚatan2ÚcosÚsin)ÚManifoldÚPatchÚCoordSystemzR^2Úoriginzx yT)Úrealz	rho theta)ÚnonnegativeÚrectangularÚpolarÚignorezx y r theta)ÚclsF)ÚinverseÚfill_in_gapszR^3zx y zzrho psi r theta phiÚcylindricalÚ	sphericalzx y z rho psi r theta phic                ó€  € V ^8„  d   Qh/ ^ \         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R&   ^\         9   d
   \        ;R	&   # )
é   ÚR2Ú	R2_originÚR2_rÚR2_pÚR3Ú	R3_originÚR3_rÚR3_cÚR3_s)Ú__conditional_annotations__r   )Úformats   "ÚR/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/diffgeom/rn.pyÚ__annotate__r&      sÁ   € ÷ ñ ÷4 Ò „CÑ ñ5÷8 %Ò $Œ3Ñ $ñ9÷L HÒ G„cÑ GñM÷N FÒ E„cÑ EñO÷L Ò „CÑ ñM÷P %Ò $Œ3Ñ $ñQ÷D KÒ J„cÑ JñE÷F OÒ N„cÑ NñG÷H OÒ N„cÑ NòIó    )r   r   Úrelations_2dr   r   r   r   Úrelations_3dr    r!   r"   )r   r   )r   r   )r   r   )r   r   )r   r   )r   r   )r   r   )r   r   )>r#   Ú__doc__Útypingr   ÚwarningsÚsympy.core.symbolr   r   Ú(sympy.functions.elementary.miscellaneousr   Ú(sympy.functions.elementary.trigonometricr   r   r   r	   Údiffgeomr
   r   r   Ú__all__r   r   ÚxÚyÚrÚthetar(   r   r   Úcatch_warningsÚsimplefilterÚ
connect_toÚcoord_functionsÚbase_vectorsÚe_xÚe_yÚe_rÚe_thetaÚbase_oneformsÚdxÚdyÚdrÚdthetar   r   ÚzÚrhoÚpsiÚphir)   r    r!   r"   Úe_zÚe_rhoÚe_psiÚe_phiÚdzÚdrhoÚdpsiÚdphir&   )r#   s   @r%   Ú<module>rP      s=  øðöõ Û ç .Ý 9ß LÓ Lß 2Ñ 2ò€ñ �5˜!Ó
€Ó á�x Ó$€	Ó $áˆu˜4Ô �€€1Ù�;¨DÔ1�€€5ð   1˜v©¨Q°­T°A°qµD­[Ó(9¹5ÀÀA»;Ð'GÐHØ  5˜z¨A©c°%«j­L¸!¹CÀ»J½,Ð+GÐHð€ñ
 ˜ y°1°a°&¸,ÓG€Ó GÙ˜ ¨Q°¨J¸ÓE€Ó Eð ×Ò×ÕØ×Ò˜(Ô#Ù˜]°Ô6�N€A€qˆ!ˆUØ‡O�O�D˜1˜a˜&Ù˜a �d Q¨¥T�kÓ*©E°!°Q«KÐ8Ø!°ð ô 7ð 	‡O�O�D˜1˜e˜*Ø™3˜u›:� q©¨U«¥|Ð4Ø!°ð ô 7÷ ð :>×9MÑ9MÓ9OÐ O�
€„€b„dÐ OÑ%ˆYŒ[˜)œ+©¨¬°´ØEI×EYÑEYÓE[Ð [�€„€b„hÐ [Ñ-�”˜iœoÑ0B°´¸¼
ð FJ×EVÑEVÓEXÐ X�€„ˆŒÐ XÑ-�” 	¤Ñ0B°´¸$¼(ØQU×QbÑQbÓQdÐ dÑ €„ˆŒ
Ð dÑ5�Y”] IÔ$5Ñ8N¸¼À$Ä,ð @D×?QÑ?QÓ?SÐ S�€„€r„uÐ SÑ)ˆyŒ|˜Yœ\Ñ,<¨D¬G°T´WØKO×K]ÑK]ÓK_Ð _Ñ €„€r„yÐ _Ñ1�9”< Ô!1Ñ4H°D´G¸T¼[ñ
 �5˜!Ó
€Ó á�x Ó$€	Ó $á
�' Ô
%�€€1€aÙ!Ð"7ÀTÔJÑ €€Sˆ!ˆU�Cð # a¨¨A YÙ&*¨1¨a­4°!°Qµ$­;Ó&7¹¸qÀ!»ÀaÐ%Hð%Jà" c¨3° ]Ø&)©#¨c«(¥l°C¹¸C»µLÀ!Ð%Dð%Fà  A q¨! 9Ù$(¨¨A­°°1µ­°q¸!µtÕ);Ó$<Ù$(¨©4°°1µ°q¸!µtµ¸aÀ½dÕ0BÓ+CÕ)CÓ$DÙ$)¨!¨Q£Kð$1ð#2ð ! A u¨c ?Ø$%¡c¨%£j¥L±°S³Õ$9Ø$%¡c¨%£j¥L±°S³Õ$9Ø$%¡c¨%£j¥Lð$2ð#3ð ! C¨¨a =Ù$(¨¨a­°!°Qµ$­Ó$7Ù$(¨©4°°Qµ¸¸A½µÓ+>Õ)>Ó$?Ø$'ð$)ð#*ð ! A u¨c ?Ø$%¡c¨%£j¥L°#°q¹¸U»µ|Ð#Dð#Fð#€ñ* ˜ y°1°a¸°)¸\ÓJ€Ó JÙ˜ y°3¸¸Q°-ÀÓN€Ó NÙ˜ Y°°E¸3°ÀÓN€Ó Nð ×Ò×ÕØ×Ò˜(Ô#Ù'.Ð/JÐPUÔ'VÑ$€A€qˆ!ˆS�#�q˜% Ø‡O�O�D˜1˜a ˜)Ù˜a �d Q¨¥T�kÓ*©E°!°Q«K¸Ð;Ø!°ð ô 7ð 	‡O�O�D˜3  Q˜-Ø™S ›X� s©3¨s«8¥|°QÐ7Ø!°ð ô 7ð 	‡O�O�D˜1˜a ˜)Ù˜a �d Q¨¥T�k¨A¨q­DÕ0Ó1±4¸Ù $ Q¨¥T¨A¨q­D¥[°1°aµ4Õ%7Ó 8õ99ó 4:Ù;@ÀÀA»;ðHà!°ð ô 7ð 	‡O�O�D˜1˜e S˜/Ø™3˜u›:�¡c¨#£hÕ.°±#Ø!ó3#õ 1#Ù#& s£8õ1,Ø-.©s°5«z­\ð;à!°ð ô 7ð
 	‡O�O�D˜3  Q˜-Ù˜c 1�f q¨!¥t�mÓ,©d°1±T¸#¸q½&À1ÀaÅ4½-Ó5HÕ3HÓ.IÈ3ÐOØ!°ð ô 7ð 	‡O�O�D˜1˜e S˜/Ø™3˜u›:� s¨A©c°%«j­LÐ9Ø!°ð ô 7÷- ð6 ×-Ñ-Ó/Ñ €„ˆŒ�”Ø!×1Ñ1Ó3Ñ €„ˆ$Œ(�D”FØ#×3Ñ3Ó5Ñ €„ˆŒ
�D”Hð  $×0Ñ0Ó2Ñ €„ˆ$Œ(�D”HØ#'×#4Ñ#4Ó#6Ñ  €„
ˆDŒJ˜œØ%)×%6Ñ%6Ó%8Ñ "€„ˆ$Œ,˜œ
ð !×.Ñ.Ó0Ñ €„ˆŒ�$”'Ø $× 2Ñ 2Ó 4Ñ €„	ˆ4Œ9�d”gØ"&×"4Ñ"4Ó"6Ñ €„ˆŒ�d–i÷I ×Ðú÷z ×Ðús   Ã8BaÓ9Ha áa	á a1	