+
    ‹°³jA
  ã                   óD   € R t ^ RIHt ^ RIHt ^ RIHt RR ltR tR t	R# )	z)Numerical Methods for Holonomic Functions)Úsympify)ÚDMFsubs)Úmpc           
     ó  € V P                   pVP                  pVP                  P                  pVP	                  4       pVR8X  d   \
        pM\        pVP                   U	u. uF!  q—P                  V	P                  4       4      NK#  	  p
p	\        V4       Uu. uF  qºV,          ) W¥,          ,          NK  	  ppV P                  p\        V4      V8  d   \        R4      hV P                  pV! WÎV^ ,          WÕ4      .p\        VR,          4       F,  w  r¹VP!                  V! WÁV,          WŸR,          V4      4       K.  	  V'       g#   V Uu. uF  p\#        V^ ,          4      NK  	  up# \#        V4      # u up	i u upi u upi )z_
Numerical methods for numerical integration along a given set of
points in the complex plane.
ÚEulerzNot Enough Initial Conditionsºé   NNéÿÿÿÿ)ÚannihilatorÚorderÚparentÚbaseÚ	get_fieldÚ_eulerÚ_rk4Ú
listofpolyÚnewÚto_listÚrangeÚy0ÚlenÚ	TypeErrorÚx0Ú	enumerateÚappendr   )ÚfuncÚpointsÚderivativesÚmethodÚannÚaÚRÚKÚmethÚjÚdmfÚiÚredr   r   Úsols   &&&&            ÚZ/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/holonomic/numerical.pyÚ_evalfr*   	   s6  € ð ×
Ñ
€CØ�	‰	€AØ�
‰
�‰€AØ	�‰‹€Aà�ÔÜ‰äˆà'*§~¢~Ó
6¡~ !�5‰5�—‘“Ö¡~€CÐ
6Ü%*¨1¤XÓ
.¡X ��Fˆ7�S•V×Ð¡X€CÐ
.à	�‰€BÜ
ˆ2ƒw�„{ÜÐ7Ó8Ð8Ø	�‰€BÙ�˜ � BÓ*Ð
+€Cä˜& �*Ö%‰ˆØ�
‰
‘4˜ A�Y¨¨r­7°AÓ6Ö7ñ &÷ Ù'*Ó+¡s !”˜˜!�–¡sÑ+Ð+ä�s‹|Ðùò 7ùÚ
.ùò ,s   Á!'E4ÂE9ÅE>c           
     ó–  € \        V4      P                  \        P                  4      p\        V4      P                  \        P                  4      pV Uu. uF+  p\        V4      P                  \        P                  4      NK-  	  ppWe,
          p	VR,          p
^ p\	        V4       FQ  pV\        \        W,          VRR7      4      P                  \        P                  4      W‡,          ,          ,          pKS  	  V
P                  V4       \	        V4       Uu. uF  qxV,          WšV,          ,          ,           NK!  	  up# u upi u upi )zg
Euler's method for numerical integration.
From x0 to x1 with initial values given at x0 as vector y0.
r   T©Úmpm©r   Ú
_to_mpmathr   Úprecr   r   r   )r'   r   Úx1r   r    ÚAÚBr&   Úy_0ÚhÚf_0Úf_0_ns   &&&&&       r)   r   r   +   sí   € ô 	�‹×ÑœrŸw™wÓ'€AÜ�‹×ÑœrŸw™wÓ'€AÙ35Ó
6±2¨aŒ7�1‹:× Ñ ¤§¡Ö)±2€CÐ
6Ø	�€AØ
ˆb�'€CØ€Eä�1ŽXˆØ”œ ¥¨°Ô5Ó6×AÑAÄ"Ç'Á'ÓJÈSÍVÕSÕSŠñ à‡J�JˆuÔä).¨q¬Ó2© A��F�Q˜Q�•Z×Ð©Ñ2Ð2ùò 7ùò 3s   Á1EÄ%Ec           
     ó  € \        V4      P                  \        P                  4      p\        V4      P                  \        P                  4      pV Uu. uF+  p\        V4      P                  \        P                  4      NK-  	  ppWe,
          p	^ p
^ p^ p^ pVR,          p\	        V4       FQ  pV
\        \        W,          VRR7      4      P                  \        P                  4      W‡,          ,          ,          p
KS  	  VP                  V
4       \	        ^V4       Uu. uF&  qxV,          Wç,          V	,          ^,          ,           NK(  	  pp\	        V4       Fy  pV\        \        W,          WY^,          ,           RR7      4      P                  \        P                  4      W‡,          Wç,          V	,          ^,          ,           ,          ,          pK{  	  VP                  V4       \	        ^V4       Uu. uF&  qxV,          W÷,          V	,          ^,          ,           NK(  	  pp\	        V4       Fy  pV\        \        W,          WY^,          ,           RR7      4      P                  \        P                  4      W‡,          W÷,          V	,          ^,          ,           ,          ,          pK{  	  VP                  V4       \	        ^V4       Uu. uF   qxV,          VV,          V	,          ,           NK"  	  pp\	        V4       Fl  pV\        \        W,          WY,           RR7      4      P                  \        P                  4      W‡,          VV,          V	,          ,           ,          ,          pKn  	  VP                  V4       \	        V4       Uu. uF]  qxV,          WžV,          ^W÷,          ,          ,           ^VV,          ,          ,           VV,          ,           ,          ^,          ,           NK_  	  up# u upi u upi u upi u upi u upi )z)
Runge-Kutta 4th order numerical method.
r   Tr,   r.   )r'   r   r1   r   r    r2   r3   r&   r4   r5   r7   Úf_1_nÚf_2_nÚf_3_nr6   Úf_1Úf_2Úf_3s   &&&&&             r)   r   r   ?   sè  € ô
 	�‹×ÑœrŸw™wÓ'€AÜ�‹×ÑœrŸw™wÓ'€AÙ35Ó
6±2¨aŒ7�1‹:× Ñ ¤§¡Ö)±2€CÐ
6Ø	�€Aà€EØ€EØ€EØ€Eà
ˆb�'€CÜ�1ŽXˆØ”œ ¥¨°Ô5Ó6×AÑAÄ"Ç'Á'ÓJÈSÍVÕSÕSŠñ à‡J�JˆuÔä(-¨a°¬Ó
4© 1ˆq�6�C•F˜1•H˜Q•J×Ð©€CÐ
4Ü�1ŽXˆØ”œ ¥¨¨q­S­°dÔ;Ó<×GÑGÌÏÉÓPÐTWÕTZÐ]`Õ]cÐdeÕ]eÐfgÕ]gÕTgÕhÕhŠñ à‡J�JˆuÔä(-¨a°¬Ó
4© 1ˆq�6�C•F˜1•H˜Q•J×Ð©€CÐ
4Ü�1ŽXˆØ”œ ¥¨¨q­S­°dÔ;Ó<×GÑGÌÏÉÓPÐTWÕTZÐ]`Õ]cÐdeÕ]eÐfgÕ]gÕTgÕhÕhŠñ à‡J�JˆuÔä&+¨A¨q¤kÓ
2¡k ˆq�6�C˜•F˜1•H×Ð¡k€CÐ
2Ü�1ŽXˆØ”œ ¥¨­°DÔ9Ó:×EÑEÄbÇgÁgÓNÐRUÕRXÐ[^Ð_`Õ[aÐbcÕ[cÕRcÕdÕdŠñ à‡J�JˆuÔäDIÈ!ÄHÓMÁH¸q��F�Q˜A�˜q ¥�x�¨¨#¨a­&­Õ0°°QµÕ7Õ8¸Õ:×:Ð:ÁHÑMÐMùò9 7ùò 5ùò
 5ùò
 3ùò
 Ns   Á1O1Ä ,O6Ç5,O;Ë
&P ÎA#PN)FÚRK4)
Ú__doc__Úsympy.core.sympifyr   Úsympy.holonomic.holonomicr   Úmpmathr   r*   r   r   © ó    r)   Ú<module>rF      s"   ðÙ /å &Ý -å ôòD3ô(#NrE   