+
    ‹°³j&
  ã                   óL   € R t ^ RIHt ^ RIHtHtHtHtHt ^ RI	t
^ RIHt R tR# )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
)Údiag)Útwoform_to_matrixÚmetric_to_Christoffel_1stÚmetric_to_Christoffel_2ndÚmetric_to_Riemann_componentsÚmetric_to_Ricci_componentsN)ÚImmutableDenseNDimArrayc                  óä  € \         P                  P                  p \         P                  P                  P                  pVP
                  pVP                  pVP                  pV ! WD4      V ! W34      ,           VR,          ,          p\        V4      p\        VR,          VR,          4      pWv8X  g   Q h\        V4      pVR,          ^ 8X  g   Q hVR,          VR,          ) 8X  g   Q hVR,          VR,          ) 8X  g   Q hVR,          ^ 8X  g   Q hVR,          VR,          ) 8X  g   Q hVR	,          ^ 8X  g   Q hVR
,          ^ 8X  g   Q hVR,          VR,          8X  g   Q h\        V4      p	V	R,          ^ 8X  g   Q hV	R,          VR,          ) 8X  g   Q hV	R,          VR,          ) 8X  g   Q hV	R,          ^ 8X  g   Q hV	R,          VR,          ) 8X  g   Q hV	R	,          ^ 8X  g   Q hV	R
,          ^ 8X  g   Q hV	R,          VR,          8X  g   Q h\        V4      p
V
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          VR,          ) 8X  g   Q hV
R,          VR,          8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          VR,          8X  g   Q hV
R,          VR,          ) 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q hV
R,          ^ 8X  g   Q h\        V4      pVR,          VR,          ) 8X  g   Q hVR,          ^ 8X  g   Q hVR,          ^ 8X  g   Q hVR,          VR,          ) 8X  g   Q hV\        VR,          ) ^ ^ VR,          ) .R 4      8X  g   Q hVR,          VR!,          ,           V^,          ,          pVR8X  g   Q hV^,          R8X  g   Q hR# )"é   Néþÿÿÿ)é    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   )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                Úk/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/diffgeom/tests/test_hyperbolic_space.pyÚtest_H2r"      sá  € Ü	�‰×	%Ñ	%€BÜ	�‰×	Ñ	×	Ñ	€BØ
�‰€AØ	�‰€BØ	�‰€BÙ	ˆB‹‘b˜“jÕ	  ! b¥'Õ)€AÜ Ó"€GÜ
ˆq�2�w˜˜B�Ó
 €CØŒ>Ðˆ>ä& qÓ)€FØ�'�?˜aÔÐÐØ�'�?˜q 2�w˜hÔ&Ð&Ð&Ø�'�?˜q 2�w˜hÔ&Ð&Ð&Ø�'�?˜aÔÐÐà�'�?˜q 2�w˜hÔ&Ð&Ð&Ø�'�?˜aÔÐÐØ�'�?˜aÔÐÐØ�'�?˜a "�gÔ%Ð%Ð%ä& qÓ)€FØ�'�?˜aÔÐÐØ�'�?˜q 2�w˜hÔ&Ð&Ð&Ø�'�?˜q 2�w˜hÔ&Ð&Ð&Ø�'�?˜aÔÐÐà�'�?˜q 2�w˜hÔ&Ð&Ð&Ø�'�?˜aÔÐÐØ�'�?˜aÔÐÐØ�'�?˜a "�gÔ%Ð%Ð%ä	% aÓ	(€BØˆj�>˜QÔÐÐØˆj�>˜QÔÐÐØˆj�>˜QÔÐÐØˆj�>˜QÔÐÐàˆj�>˜QÔÐÐØˆj�>˜a "�g˜XÔ%Ð%Ð%Øˆj�>˜Q �WÔ$Ð$Ð$Øˆj�>˜QÔÐÐàˆj�>˜QÔÐÐØˆj�>˜Q �WÔ$Ð$Ð$Øˆj�>˜a "�g˜XÔ%Ð%Ð%Øˆj�>˜QÔÐÐàˆj�>˜QÔÐÐØˆj�>˜QÔÐÐØˆj�>˜QÔÐÐØˆj�>˜QÔÐÐä
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'€CØˆt�9˜˜R�˜Ô Ð Ð Øˆt�9˜Œ>Ðˆ>Øˆt�9˜Œ>Ðˆ>Øˆt�9˜˜R�˜Ô Ð Ð àÔ)¨A°­G¨8°Q¸¸AÀ½G¸8Ð*DÀfÓMÔMÐMÐMð 
ˆT��S˜•YÕ	  1¥Õ$€AØ�Œ7€Nˆ7ð ˆQ�3�"Œ9ÐŠ9ó    )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 6ôDr#   