+
    iA
                     D    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)sympify)DMFsubs)mpc           
        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!  qP                  V	P                  4       4      NK#  	  p
p	\        V4       Uu. uF  qV,          ) W,          ,          NK  	  ppV P                  p\        V4      V8  d   \        R4      hV P                  pV! WV^ ,          W4      .p\        VR,          4       F,  w  rVP!                  V! WV,          WR,          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.
EulerzNot Enough Initial Conditions   NN)annihilatororderparentbase	get_field_euler_rk4
listofpolynewto_listrangey0len	TypeErrorx0	enumerateappendr   )funcpointsderivativesmethodannaRKmethjdmfiredr   r   sols   &&&&            y/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/holonomic/numerical.py_evalfr*   	   s6    

C		A

A	A'*~~
6~!55~C
6%*1X
.XF7SVXC
.	B
2w{788	BB*
+C&*%

4AYr7A67 & '*+s!!s++s| 7
. ,s   !'E4E9E>c           
        \        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,          WV,          ,          ,           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mpmr   
_to_mpmathr   precr   r   r   )r'   r   x1r   r    ABr&   y_0hf_0f_0_ns   &&&&&       r)   r   r   +   s     	rww'Arww'A35
62a71:  )2C
6	A
b'CE1X56AA"''JSVSS JJu).q2AFQQZ22 7 3s   1E%Ec           
        \        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,          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,          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,          WV,          ^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   f_1_nf_2_nf_3_nr6   f_1f_2f_3s   &&&&&             r)   r   r   ?   s   
 	rww'Arww'A35
62a71:  )2C
6	AEEEE
b'C1X56AA"''JSVSS JJu(-a
41q6CF1HQJC
41XqSd;<GGPTWTZ]`]cde]efg]gTghh JJu(-a
41q6CF1HQJC
41XqSd;<GGPTWTZ]`]cde]efg]gTghh JJu&+Aqk
2kq6CF1HkC
21XD9:EEbggNRURX[^_`[abc[cRcdd JJuDI!HMHqFQAqx#a&0Q78:::HMM9 7 5
 5
 3
 Ns   1O1 ,O65,O;
&P A#PN)FRK4)
__doc__sympy.core.sympifyr   sympy.holonomic.holonomicr   mpmathr   r*   r   r        r)   <module>rF      s"    / & - D3(#NrE   