
    \h                     R    S SK r S SKJr  S SKJr  S SKJr  S SKJrJ	r	  S r
S rS rg)	    N)symbols)exp)optimize)	SumApproxSeriesApproxc                  j    [        S5      n SU -   n[        U S0SS9n[        X/5      nUS-
  S:X  d   eg )Nx   )g#Bǻg#B;gؗҜ<boundsreltolr   )r   r   r   )r	   expr1
sum_approxapx1s       _/var/www/auris/envauris/lib/python3.13/site-packages/sympy/codegen/tests/test_approximations.pytest_SumApprox_trivialr      sA    AEE1o"6uEJE<(D!8q==    c                     [        S5      u  pn[        U5      U S-  US-  -   S-   -  nU SUS0n[        USS9n[        USS9n[        US	S9n[        X5/5      [        U5      -  US-  -
  R	                  5       S
:X  d   e[        X6/5      [        U5      -  US-  S-   -
  R	                  5       S
:X  d   e[        X7/5      [        U5      -  US-  S-   U S-  -   -
  R	                  5       S
:X  d   eg )Nzx y z   r
   )r   gMbP?)d   i  g{Gz?r   gh㈵>gdy=r   )r   r   r   r   simplify)r	   yzr   bnds1sum_approx_m2sum_approx_m5sum_approx_m11s           r   test_SumApprox_monotone_termsr      s   gGA!FAqD1a4K!O$E	1k*EU48MU48MeE:NUO,SV3q!t<FFHAMMMUO,SV3q!tax@JJLPQQQQU,-c!f41q1a4HRRTXYYYYr   c                     [        S5      u  pS[        U5      4 GH<  n[        S5      n [        U 5      U-  nU S0n[        USS9n[        USS9n[        USS9nX@   S   X@   S	   -   S
-  n[        R                  " U5      n	X-   U S
-  S
-  -   n
X-   U S
-  S
-  -   U S-  S-  -   nX-   U S
-  S
-  -   U S-  S-  -   U S-  S-  -   n[	        X5/5      n[	        X6/5      n[	        X7/5      nX-  U
-
  R                  5       S	:X  d   eX-  U-
  R                  5       S	:X  d   eX-  U-
  R                  5       S	:X  d   e[        USSS9n[	        UU/5      U:X  a  GM=   e   g )Nzx zr
   r	   )r
   g      ?r   g?g?r   r               )r   r   	max_order)r   r   r   mathr   r   )r	   r   factorr   r   series_approx_50series_approx_10series_approx_05cf0ref_50ref_10ref_05res_50res_10res_05max_ord3s                    r   test_SeriesApprox_trivialr4      s   5>DAc!f+CLAvG'uTB'uTB'uTBXa[58A;&)XXa[!Q$q&!Q$q&1a46)!Q$q&1a46)AqDG3%!34%!34%!34&002a777&002a777&002a777uTQGz*e333/ r   )r&   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   sympy.codegen.rewritingr   sympy.codegen.approximationsr   r   r   r   r4    r   r   <module>r:      s$     % 6 , @	Z4r   