Ë
    7^(h&
  ã                   óJ   — d Z ddlmZ ddlmZmZmZmZmZ ddl	Z
ddlmZ d„ Zy)aL  
unit test describing the hyperbolic half-plane with the Poincare metric. This
is a basic model of hyperbolic geometry on the (positive) half-space

{(x,y) \in R^2 | y > 0}

with the Riemannian metric

ds^2 = (dx^2 + dy^2)/y^2

It has constant negative scalar curvature = -2

https://en.wikipedia.org/wiki/Poincare_half-plane_model
é    )Údiag)Útwoform_to_matrixÚmetric_to_Christoffel_1stÚmetric_to_Christoffel_2ndÚmetric_to_Riemann_componentsÚmetric_to_Ricci_componentsN)ÚImmutableDenseNDimArrayc                  óP  — t         j                  j                  } t         j                  j                  j                  }|j
                  }|j                  }|j                  } | ||«       | ||«      z   |dz  z  }t        |«      }t        |dz  |dz  «      }||k(  sJ ‚t        |«      }|d   dk(  sJ ‚|d   |dz   k(  sJ ‚|d   |dz   k(  sJ ‚|d   dk(  sJ ‚|d   |dz   k(  sJ ‚|d	   dk(  sJ ‚|d
   dk(  sJ ‚|d   |dz  k(  sJ ‚t        |«      }	|	d   dk(  sJ ‚|	d   |dz   k(  sJ ‚|	d   |dz   k(  sJ ‚|	d   dk(  sJ ‚|	d   |dz   k(  sJ ‚|	d	   dk(  sJ ‚|	d
   dk(  sJ ‚|	d   |dz  k(  sJ ‚t        |«      }
|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   |dz   k(  sJ ‚|
d   |dz  k(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   |dz  k(  sJ ‚|
d   |dz   k(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚|
d   dk(  sJ ‚t        |«      }|d   |dz   k(  sJ ‚|d   dk(  sJ ‚|d   dk(  sJ ‚|d   |dz   k(  sJ ‚|t        |dz   dd|dz   gd «      k(  sJ ‚|d   |d!   z   |d"z  z  }|dk(  sJ ‚|d"z  dk(  sJ ‚y )#Néþÿÿÿ)r   r   r   r   )r   r   é   éýÿÿÿ)r   r   r   )r   r   r   )r   r   r   )r   r   r   )r   r   r   )r   r   r   éÿÿÿÿ)r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   )r   r   )r   r   )é   r   )r   r   r   )ÚsympyÚdiffgeomÚTensorProductÚrnÚR2ÚyÚdyÚdxr   r   r   r   r   r   r	   )ÚTPr   r   r   r   ÚgÚautomatÚmatÚgamma1Úgamma2ÚRmÚRicÚRs                úh/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.pyÚtest_H2r"      sç  € Ü	�‰×	%Ñ	%€BÜ	�‰×	Ñ	×	Ñ	€BØ
�‰€AØ	�‰€BØ	�‰€BÙ	ˆB�‹‘b˜˜R“jÑ	  ! b¡'Ñ)€AÜ Ó"€GÜ
ˆq�2‰w˜˜B™Ó
 €CØ�'Š>Ðˆ>ä& qÓ)€FØ�'‰?˜aÒÐÐØ�'‰?˜q 2™w˜hÒ&Ð&Ð&Ø�'‰?˜q 2™w˜hÒ&Ð&Ð&Ø�'‰?˜aÒÐÐà�'‰?˜q 2™w˜hÒ&Ð&Ð&Ø�'‰?˜aÒÐÐØ�'‰?˜aÒÐÐØ�'‰?˜a "™gÒ%Ð%Ð%ä& qÓ)€FØ�'‰?˜aÒÐÐØ�'‰?˜q 2™w˜hÒ&Ð&Ð&Ø�'‰?˜q 2™w˜hÒ&Ð&Ð&Ø�'‰?˜aÒÐÐà�'‰?˜q 2™w˜hÒ&Ð&Ð&Ø�'‰?˜aÒÐÐØ�'‰?˜aÒÐÐØ�'‰?˜a "™gÒ%Ð%Ð%ä	% aÓ	(€BØˆj‰>˜QÒÐÐØˆj‰>˜QÒÐÐØˆj‰>˜QÒÐÐØˆj‰>˜QÒÐÐàˆj‰>˜QÒÐÐØˆj‰>˜a "™g˜XÒ%Ð%Ð%Øˆj‰>˜Q ™WÒ$Ð$Ð$Øˆj‰>˜QÒÐÐàˆj‰>˜QÒÐÐØˆj‰>˜Q ™WÒ$Ð$Ð$Øˆj‰>˜a "™g˜XÒ%Ð%Ð%Øˆj‰>˜QÒÐÐàˆj‰>˜QÒÐÐØˆj‰>˜QÒÐÐØˆj‰>˜QÒÐÐØˆj‰>˜QÒÐÐä
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'€CØˆt‰9˜˜R™˜Ò Ð Ð Øˆt‰9˜Š>Ðˆ>Øˆt‰9˜Š>Ðˆ>Øˆt‰9˜˜R™˜Ò Ð Ð àÔ)¨A°©G¨8°Q¸¸AÀ¹G¸8Ð*DÀfÓMÒMÐMÐMð 
ˆT‰�S˜‘YÑ	  1¡Ñ$€AØ�Š7€Nˆ7ð ˆQ‰3�"Š9Ð‰9ó    )Ú__doc__Úsympy.matrices.denser   Úsympy.diffgeomr   r   r   r   r   Úsympy.diffgeom.rnr   Úsympy.tensor.arrayr	   r"   © r#   r!   ú<module>r*      s)   ðñõ &÷Võ Vó Ý 6óDr#   