
    sgJ@                        d dl mZ d dlmZmZmZmZ d dlmZm	Z	m
Z
mZmZmZ d dlmZ d dlmZmZ d dlmZmZmZ d dlmZ d dlmZmZmZ d d	lmZ d d
lm Z m!Z! d dl"m#Z# d dl$m%Z% d dl&m'Z'm(Z(m)Z)m*Z* d dl+m,Z, d dl-m.Z. d Z/d Z0d Z1d Z2d Z3d Z4d Z5d Z6d Z7d dl8m9Z9m:Z: d dl;m<Z< d dlm=Z= d Z>d Z?d Z@d ZAd  ZBd! ZCd" ZDd# ZEd$ ZFd% ZGd& ZHd' ZId( ZJd) ZKd* ZLd+ ZMd, ZNd- ZOd. ZPd/ ZQd0 ZRd1 ZSd2 ZTd3 ZUd4 ZVd5 ZWd6 ZXd7 ZYd8 ZZy9):    )N)
DerivativeFunction	PoleErrorSubs)EFloatRationaloopiI)S)Symbolsymbols)LambertWexplog)sqrt)atancossin)gamma)Integral	integrate)Oseries)xynk)raises)
EulerGammac                      t        t              j                  t        d      } t        t        t              t        d      }| |k(  sJ y Nr   )r   r   r   e1e2s     Q/var/www/html/venv/lib/python3.12/site-packages/sympy/series/tests/test_series.pytest_sinr*      3    	Qq!	B	A1	B8O8    c                      t        t              j                  t        d      } t        t        t              t        d      }| |k(  sJ y r%   )r   r   r   r&   s     r)   test_cosr.      r+   r,   c                      t        t              j                  t        d      } t        t        t              t        d      }| |k(  sJ y r%   )r   r   r   r&   s     r)   test_expr0      r+   r,   c                      t        t        t                    j                  t        d      } t        t        t        t                    t        d      }| |k(  sJ y r%   )r   r   r   r   r&   s     r)   	test_exp2r2   $   s=    	SV		Aq	!B	CFQ	"B8O8r,   c            	      H   t        dt              dk(  sJ t        t        j                  j                  t                    dk(  sJ t        t              j                         t        t              j                  t              k(  sJ t        t        d        t        t        d        t        t              j                  t        d      t        t        dz         j                  t              j                  t        t        dz
        z
  j                         dk(  sJ t        t              j                  t        dd       } t        d      D cg c]  }t        |        c}t        d      t        dz
  t        d      z   gk(  sJ t        t              j                  t        dd d      } t        d      D cg c]  }t        |        c}t        d      dt        z
  t        d      z  gk(  sJ t        t              j                  t        dd	      t        k(  sJ t        t              j                  t        ddd
      j                         t        t        t         dz   z  z
  t        t         dz   dz  z  dz  z   k(  sJ t         } |t        dz  t        d
z  t"        dz  z  z   t        dt"        d      j                  t              j%                         dt        z  t"        z  k(  sJ t         |t        t              t              j                                |dt              k(  sJ  |t        t              t              j                  d
       |dt               |t        t              z    |t        dz  dz  t              z    |t        d
z  dz  t              z   t'        t        d
z        z   k(  sJ t)        t        t        dd
ft"        dt        f      j                  t              ddt        z  z   k(  sJ dt        z   t'        t        dz        z   j+                         dk(  sJ dt        z   j+                         J t        t,        d        t/        d      }t        t              t"        z  j1                  t        d|      t        t"        |z        t'        t        t        t"        |z        z  t              z   k(  sJ t        dt        z        j                  t        t2        d      dt        z  ddt        d
z  z  z  z
  t'        t        dz  t        t2        f      z   k(  sJ t        t              j                  t        t2        dd      t        k(  sJ t        t              j                  t        t2         dd      t         k(  sJ t        t               j                  t        t2        dd      t        k(  sJ t        t               j                  t        t2         dd      t         k(  sJ t        t        t5        t              z        j                  d
      dt        t5        t              z  z   t        dz  t5        t              dz  z  dz  z   t'        t        d
z  t5        t              d
z  z        z   k(  sJ t/        dd      }t        t7        |      d
z  t5        |      z        j                  d
      d|t        d      z  t5        |      z  z   t'        |d
z  t5        |      d
z  z        z   k(  sJ t        t        t              t5        t              z        j                  d      dt        t5        t              z  z   t'        t        dz  t5        t              dz  z        z   k(  sJ y c c}w c c}w )N   r   c                  J    t        t        t        z         j                         S N)r   r   r   r    r,   r)   <lambda>z!test_issue_5223.<locals>.<lambda>.   s    s1q5z002 r,   c                  .    t        j                  d      S )N dir)r   r   r7   r,   r)   r8   z!test_issue_5223.<locals>.<lambda>/   s    qxxB/ r,   r       -)r    r<   r;      )r<   r             c                  P    dt        t              z  t        z  j                         S Nr4   )r   r   r   r   r7   r,   r)   r8   z!test_issue_5223.<locals>.<lambda>G   s    #a&2~557 r,   logx)r    rG      +pTpositivez3/2)r   r   nextr   Zerolseriesr   r"   
ValueErrorsubsremoveOranger   absr   r   r   r   doitr   r   getnr   r   nseriesr   r   r   )eiDrG   rK   s        r)   test_issue_5223r\   *   s   !Q<1q!"a'''q6==?c!fmmA....
:23
:/0FMM!QAJa %%aQ/018a@ @ @Aad#A"1X&DG&3q6a!eSV^3D*EEEEAad,A"1X&DG&3q6AE3q6>*BBBBq6==A3='1,,,q6==A3!=,446	ArAvJQBFQ;q() ) ) 	AQTAqDAIq!Q*11!499;r!tAvEEE#a&!$$&'1Q7222A6A6;!Aq'AaG"3a1Ql"BQq!tAvq\"QTUVWYZVZT["[\ \ \ A1ay1a),33A6"qs(BBBEAadGO!!#q(((E<<>!!!
978&>DVaK  ad 3AdFa#af+q))* * * qs8??1bA?&!A#1QT6
*:Qq2wB=P*PPPPq6==B!=-222q6==RC1#=.1"444r7>>!R1#>.!333r7>>!bSA3>/A2555qQx=!$	Ac!fHq!tCFAI~a''!AqDQN*;;< < < 	sT"AtAwz#a& !((1(-	AqxKA1a4A	>!223 3 3 s1vc!f}$$q$)Q3q6\Aad3q619n<M-MMMMK '&s   ^ ^c                  P   t        t        t        t        dz  dt        z  z
  z        t        dt        fd      } | j                  t        dd      dt        d      dz  z   t        d      z  t        t        d      dz        dz  z  t        t        d      dz        z  dt        z  t        t        d      dz  z  z  z  t        d      t        z  t        t        d       dz        z  t        t        d       dz        z  dt        z  z  z
  dt        d      dz  z  t        d      z  t        t        d      dz  z  z  t        t        d       dz        z  t        t        d      dz        z  t        t        d      dz        z  dt        z  z  z
  dt        d      dz  z  t        d      z  t        t        d	      dz  z  z  t        t        d      dz        dz  z  t        t        d      dz        z  d
t        z  z  z
  dt        d      dz  z  t        d      z  t        t        d      dz  z  z  t        t        d       dz        z  t        t        d      dz        z  t        t        d      dz        z  dt        z  z  z
  t        t        dz        z   k(  sJ y )Nr@   r   none)condsr>   r4   rB   rH   rD         )r   r   r!   r   r   r   r   r   r   r   r   exprs    r)   test_issue_6350re   \   sU   SAqD1Q3J(1a*FCD;;q!QR1Q46N?47#:51a=!;K#KERSTURVWXRXM#Y[\]_[_`adefgdhijdj`k[k#lQ	%1a. !uQw/26$7	qtAvtAwq1Q46{*5!A$q>9%!Q-GaPQdSTfUWXY[W[\$] 
qtAvtAwq1Q46{*51a=!+;;E!A$q&MI1R4P$Q 
qtAvtAwq1Q46{*5!A$q>9%!Q-GaPQdSTfUWXY[W[\	$] `aabdeae_f	$g g g gr,   c                     t        t        t              t              j                  t              t	        t              j                  t              k(  sJ t        t	        t              t              j                  t        d      j                         t        t              j                  t        d      k(  sJ t        t        dz  t              j                  t              dt        dz  z  k(  sJ t        t        dz  t              j                  t              dk(  sJ t        t	        t              t              j                  t              dk(  sJ t        t        t              t              j                  t              t         k(  sJ t        dt              j                  t              t        dt              k(  sJ t        t        t              t              j                  t              j                         t        t              j                  t              k(  sJ dt        t        t              t              j                  t              z   t        t              j                  t              k(  sJ t        t        t              t              j                  t              j                         dt        z  j                  t              k(  sJ t        t        t              t              j                  t              t        t        t              t              j                         j                  t              j                         k(  sJ y )Nr@   r=   r>   r   r4   )r   r   r   r   r   r   rV   as_leading_termr   r   r   rS   r7   r,   r)   test_issue_11313rh   e   s.   CFA%%a(CFMM!,<<<<c!fa ''Q'/446#a&--Q-:OOOOadA..q1Qq!tV;;;adA..q1Q666c!fa 003q888c!fa 003r999 a++A.*Q2BBBBc!fa ''*//1SV]]15EEEExA"))!,,Aa0@@@@c!fa ''*//1ac\\!_DDDCFA%%a(HSVQ,?,D,D,F,M,Ma,P,X,X,ZZZZr,   c                     ddl m t        t        t              t        t
              } t        t        t              t              z  t        t
              }t        t        t        z        t        ft
        t        f      }| j                  t              | k(  sJ t        t        t        t
              t        t        dz   dz  t        t
              z   t        t        dz  dz  t        t
              z   t        t
        dz        z   }| j                         |k(  sJ | j                  t
              |k(  sJ | j                        | k(  sJ |j                        t        dz  t        t              z  dz  t        t
              t        d	z   t        t              z  d	z  t        t
              z   t        t        t              t        t
              z   t        dz        z   k(  sJ |j                  t              j                         |j                         j                  t              k(  sJ |j                        j                         t        t        t
        z        k(  sJ t        t        fd
       t        t        t
        z   t
              j                  t              j                         t        z   k(  sJ y )Nr   zr@   rB   rH   x   rD      r>   c                  ^    t        t        dt        z  z   t               j                         S )Nr>   )r   r   r   r   rj   s   r)   r8   z%test_series_of_Subs.<locals>.<lambda>   s!    tA!GQ299; r,   )	sympy.abcrk   r   r   r   r   r   r   r   rV   r"   rQ   )subs1subs2subs3subs1_seriesrk   s       @r)   test_series_of_Subsrt   y   s
   QAEQ#a&!Q'EQUaVaV,E<<?e###AqMD!Q$q!Q$77QT#Xq! Aw'L<<>\)))<<?l***<<?e###<<?tAqDQKNAq9adU3q6\!^Q" #%)#a&!Q%7 8:;AqD' B C C C<<?!UZZ\%8%8%;;;;<<?!S1X---
:;<Aq!##A&++-Q666r,   c            
      "   t        d      }  | t              j                  t        ddd       | d      t        t        t	         | t              t              t        d      z  z   t        dz  t        t	         | t              t        t              t        d      z  dz  z   t        t        dz        z   k(  sJ  | t              j                  t        dd       | d      t        t        t	         | t              t              t        d      z  z   t        dz  t        t	         | t              t        t              t        d      z  dz  z   t        t        dz        z   k(  sJ  | t        dz        j                  t        dd       | d      t        dz  t        t	         | t              t              t        d      z  z   t        t        dz        z   k(  sJ  | t        dz  dz         j                  t        dd       | d      t        dz  t        t	         | t              t              t        d      z  z   t        t        dz        z   k(  sJ  G d d	t               } |t              j                  t        dd       |d      t        t        t	         |t              t              t        d      z  z   t        dz  t        t	         |t              t        t              t        d      z  dz  z   t        t        dz        z   k(  sJ y )
Nfr   r@   r?   r;   r>   r4   c                       e Zd Zy)test_issue_3978.<locals>.TestFN)__name__
__module____qualname__r7   r,   r)   TestFrx      s    r,   r|   )r   r   r   r   r   r   )rv   r|   s     r)   test_issue_3978r}      s   AQ4;;q!QC;(aD1T*QqT1-q!444qDj1q!,a33A5689!Q$@@ @ @ Q4;;q!QaD1T*QqT1-q!444qDj1q!,a33A5689!Q$@@ @ @ QT7>>!Q"aD1a4Z!a0!Q777!AqD'AB B BQT!V9Aq!$aD1a4Z!a0!Q777!AqD'AB B B  8??1a#ad:eAh*Aq11)2qDjq1a0!Q779):<=adG)D D D Dr,   )
richardsonshanks)Sum)Integerc                  `   ddt         z  z   t         z  } t        t        | t         dd      j                         d      t        t	        j                         d      k(  sJ t        t        d      t        dz   z  t        z  t        dt         f      }t        t        |t         d      j                         d      t        t        d      j                         d      k(  sJ t        t        |t         dd      j                         d      t        t        d      j                         d      k(  sJ y )	Nr4   
      r`      rD   r>   rH   )
r    roundr~   evalfr   r   r   r!   r   r   )rY   As     r)   test_accelerationr      s    	
QqS1AAq"b)//126%	2:NNNNGBK!a% 1$q!Qi0A1b!'')1-s1v||~q1IIII1b!$**,b1U3q6<<>25NNNNr,   c            	         t        dt        t        t        t              z        z  t        d      dt        dz  dt        t              dz  z  z  z   dt        dz  z  dt        t              dz  z  z  z   t	        t        dz        z   k(  sJ y )Nr4   r   r>   rH   rD   rm   rB   )r   r   r   r   r   r7   r,   r)   test_issue_5852r      sz    !C#a&M/1a(A1aA	k0B,B	!Q$3q619- !!Q$-( ( ( (r,   c                     t        dt        z   t        dz  z         j                  t        dd      t        d      t        t        d      z  z
  t        dz  t        d       t        d      dz  z
  z  z   t        dz  t        d       t        d      dz  z   z  z   t        dz  dt        d      z  d	z  t        d      dz  z   z  z   t	        t        dz        z   k(  sJ y )
Nr4   r>   r   rH   r@   rB   rD   irm   )r   r   r   r   r   r7   r,   r)   test_issue_4583r      s    q1uq!t|##Aq!,A3q60A	1s1vgAq !1"$%qD3q6'CF1H*<$=1>	1c#a&jmc!fQh&'1(*+AqD'12 2 2 2r,   c                  j    dt         z  t        dd      z  } | dz   j                  t               | k(  sJ y )Nr4   r>   r@   )r   r
   rg   eqs    r)   test_issue_6318r      s3    
A#A	BF##A&",,,r,   c                  |    t         dz  t        dd      z  } | j                         t         t        dd      z  k(  sJ y )Nr>   r@   rD   )r   r
   r   r   s    r)   test_x_is_base_detectionr      s5    
Q$!Q	B99;!Xa^++++r,   c                      t        t        t              t        t        d      dt        t        z
  dz  dz  z   t	        t        t        z
  dz  t        t        f      z   k(  sJ y )Nr@   r`   r>   )r   r   r   r   r   r7   r,   r)   test_issue_7203r      sO    #a&!R#
a"fq[]QB{QG445 5 5r,   c                  T   t        dd      \  } }| |z  }t        t        |      |d      d| |z  z   | dz  |dz  z  dz  z   | dz  |dz  z  d	z  z   | d
z  |d
z  z  dz  z   | dz  |dz  z  dz  z   | d	z  |d	z  z  dz  z   | dz  |dz  z  dz  z   t        | dz  |dz  z  | |      z   k(  sJ y )Nza, bTrL   rb   r=   r4   r>   r@   rB   rD   rm   rH   rl     ra     )r   r   r   r   )abr   s      r)   !test_exp_product_positive_factorsr      s    6D)DAq	AA#a&!q!Q1Wq!tAqDy{%:	1QT	!&d1a4il&#%&T!Q$Ys]&356T!Q$Ys]&C	1QT	$&1a419a+&, , , ,r,   c                  (    t        dd      dk(  sJ y )Nr4   rb   r=   r   r7   r,   r)   test_issue_8805r      s    !q>Qr,   c                     t         dz  t         z   dz   t         dz  t         dz  z   z  } t        | t         t              t         dz  dt         dz  z  z
  t         dz  z   dt         z  z   t        t         dz  t         t        f      z   k(  sJ y )Nr>   r4   r@   rI   rD   )r   r   r   r   r   s    r)   test_issue_9549r      ss    	
AA!Q$A+&A!Qq2w1a4/!b'9AaC?!AGaQSWBUUUUUr,   c                      t        dt        dz  t        dz  z   z  t        d      t        dz  t        dz  z
  t        dz  z   t        t        dz        z   k(  sJ y )	Nr4   r   r   r@   rD   rH   rB   )r   r   r   r7   r,   r)   test_issue_10761r      sL    !QUQU]#Q*adQTkAqD.@1QT7.JJJJr,   c                  x   ddt         dz  ddt         z  z  z
  dz  z  z
  t        d      dz  z  }  | j                  t         dd      ddt         dz  z  z
  dt         dz  z  z
  d	t         dz  z  z
  d
t         dz  z  z
  dt         dz  z  z
  dt         dz  z  z
  dt         dz  z  z
  t        t         dz        z   k(  sJ y )Nr4   r>   rD   rb   r      r=   rB   "      r   i  rA   i     iC     )r   r   r   r   r   s    r)   test_issue_12578r      s    	
Q!a1g!!	!QqT!V,A188AqB1qAv:!Q$#6AqD#@3q"u9#LsSTVXSXy#XQU
$1b5[$!#$QU8$, , , ,r,   c                  B   t        dd      } t        dd      \  }}| dz   |z  t        |      z  | dz  t        |      z  z   | |z  t        |      z  z   | t        |      z  z
  | z
  dz   | t        |      z  dz
  dz  z  }ddt        |      z  d	z
  dz  z  d
t        |      z  dt        |      z  d	z
  dz  z  z
  | dz
  d|z  t        d|z        z  dt        |      z  z
  d
t        d|z        z  z   dz   z  dt        |      z  d	z
  dz  dt        |      z  d	z
  z  z  z   d
|z  t        |      z  dt        |      z  d	z
  dz  z  z   t        | t        j
                  z
  dz  | t        j
                  f      z   }|j                  | dd      j                         |k(  sJ y )NbetaTrL   ztheta varphirealr>   r4         ?      ?g      ?g      пg      ?g      ?)r   r   r   r   r   Halfr   trigsimp)r   thetavarphird   sols        r)   test_issue_12791r      s   6D)DN6ME61WHVOCJ&qU);;VCJ!%c%j1378:;<>B3u:oPQ>QTU=UVD CJ$q((4E
?CE
NS<PST;T+TT#:fS5\1CE
NB
s1U7|
"# $&)#e*ns&:Q%>CJQT@T%UWW v+c%j
 #c%j.3"6!:
:; TAFF]Qqvv
/	0C ;;tS!$--/3666r,   c                  r   t        d      \  } t        | z        | z  k(  sJ t        d| z  z        d| z  z  k(  sJ t        t        | t              z              t        | t              z        k(  sJ t	        t
        fd       t	        t
        fd       t	        t
        fd       y )Nzx ar   c                  *    t         t        z         S r6   r   r   r   s   r)   r8   z"test_issue_14384.<locals>.<lambda>   s    fQT1o r,   c                  0    t         t        dz   z         S rF   r   r   s   r)   r8   z"test_issue_14384.<locals>.<lambda>   s    fQQZ3 r,   c                  N    t        t        t        t               z               S r6   )r   r   r   r   r   s   r)   r8   z"test_issue_14384.<locals>.<lambda>   s    fS3q6]A6 r,   )r   r   r   r   r"   r   )r   r   s    @r)   test_issue_14384r      s    5>DAq!Q$?ad"""!bd)Q1r!t9,,,#aAh-#s1SV8}444
9-.
934
967r,   c                     t        t        t        dd      z  t        t              z  t        d      t        t        dd      z  dt	        t              z  z   t	        t              dz  z   t        t        dd      z  dz  z   t        t        dd      z  dz  z   t        t        d	d      z  d
z  z   t        t        dd      z  dz  z   t        t        dd      z  dz  z   t        t        dz        z   k(  sJ y )Nr   r>   r   r4   r@   rB   rH   rm   ra   rl   	   r      r   )r   r   r
   r   r   r   r7   r,   r)   test_issue_14885r      s    !Xb!_$SV+Q2q(2q/7IAdSTgI7UQ	8x1~%a'8(*+Xa^*;B*>8?ABHQPQNARSVAV8W	8Aq>#8 !8B? 24 788:;AqD'8B C C Cr,   c                     t        t        t              t        t               ddt        dz  z  z  ddt        dz  z  z  z   dt        z  z
  t        dz  z
  t        t        dz  t        t         f      z   k(  sJ t        t        t              t        t              ddt        dz  z  z  ddt        dz  z  z  z   dt        z  z
  t        dz  z   t        t        dz  t        t        f      z   k(  sJ y )Nr`   rH   r4   r@   r>   r   )r   r   r   r   r   r   r7   r,   r)   test_issue_15539r     s    $q'1rc"r1QT6{Q!Q$Z'?!A#'E1'L
AGa"X
(      $q'1b!b!AqD&kAqAvJ&>1&Dr!t&K
AGaW
'   r,   c                  \   t        t        t              t              t        t        dz  z
  dt        dz  z  dz  z   dt        dz  z  dz  z
  dt        dz  z  dz  z   t        t        dz        z   k(  sJ t        t        t        dz        t        d	      t        dz  t        dz  z
  dt        dz  z  dz  z   t        t        dz        z   k(  sJ t        t        t	        t                    t        d	      t        t        dz  z
  dt        dz  z  dz  z   t        t        dz        z   k(  sJ y )
Nr>   r@   rb   rD   }   rH   rm   rB   r=   )r   r   r   r   r   r7   r,   r)   test_issue_7259r     s    (1+q!QAX!Q$q%81QT6!8%Cc!Q$hrk%QTUVWYZVZT[%[[[[(1a4.!q)QTAqD[1QT6!8-Ca1g-MMMM(3q6"A+q1a4x!AqD&(/BQq!tW/LLLLr,   c                      t        t              j                  t        dd      t        d      t        t        dz
  t        df      z   k(  sJ y )Nr4   r=   )r   r   r   r   r7   r,   r)   test_issue_11884r     s;    q6==A=#s1v!a%!Q0@'@@@@r,   c                     t         dt         dt         z
  z  z   z  dt         dt         z
  z  z   dt         z
  dt         z
  z  z
  z  }  | j                  t         t        d      ddt         dz  z  z  ddt         dz  z  z  z
  dd	t         z  z  z
  t        d      dz  z   t         dz  z   t	        t         d
z  t         t        f      z   k(  sJ y )Nr4   rD   r=   i    r@   r   r>   rb   rC   )r   r   r   r   r   r   s    r)   test_issue_18008r     s    	1q!a%y=A1q5	Ma!ea!e_<=A188ArQ2r!Q$w<!R1W+#=1Q3#G!A$q&#PSTUVSV#V	!b'Ar7$   r,   c                      t        t        dt        z
  z        } | j                  t        dd      j                         j	                         t        d       dz  k(  sJ y )Nr4   gCl?r=   l   I l     o )r   r   r   rS   	nsimplifyr   )rv   s    r)   test_issue_18842r     sW    Aq1uIA88Au8"**,668	
?	,,- - -r,   c                     t        dd      } d| z  d| z  d| z  dz   z  d| z  z   dz   z  d	z  d
| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z
  d| z  z   | dt        d      dz  z
  z  z   dz   z  dz  z   d
| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z
  d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z
  d| z  z   dz   z  z   d| z  z
  | t        d      dz  dz   z  z   dz   z  dz  z   | d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z
  d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z
  d| z  z   dz   z  z
  d | z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z
  d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  d| z  d| z  dz   z  d| z  d| z  d| z  dz   z  d| z  z   dz   z  z   d| z  z   dz   z  z
  d| z  z   dz   z  z   d!| z  z
  dz   z  z   d"| z  z   dz   z  d#z  z   | d#z  z   d$z   }t        |j                  | d%d&      d#      t	        d'd()       | d*z  z  t	        d+d()      | d,z  z  z   t	        d-d()      | d.z  z  z   t	        d/d()      | d0z  z  z   t	        d1d()      | d2z  z  z   t	        d3d()      | d4z  z  z   t	        d3d()      | z  z   t	        d3d()      z   k(  sJ y )5NdtTr   r   g      ?g       @r   g      ?-   1   gPFvBgI?gwkN?gh/?gh/?g	%?gIp?r      r      gaAοgi?gi/?gϥ;} @gvQ?go?gUUUUUU?g@g?br@gF)7^@g~j`?g~?g#@r   r4   r   rb   z0.00092592592592592596126289F   )	precisionra   z0.0027777777777777783174695rB   z0.016666666666666656027029rH   z0.083333333333333300951828rD   z0.33333333333333337034077r@   z1.0r>   )r   r   r   r   r	   )r   rd   s     r)   test_issue_19534r   "  s   	D	!Bb5%(CFSL)E"H4s:;B>rE+B.B="2%uRxR#'>r'IC'OPQ"2%'>r'A3r6C<'P!"$eBhB&=b&H3&NO(P"2%(&(+(, -- 0Gr/I	J
 d2hrk!"#
 &)) *
 +... 1327Nr7QSVWYSY\_S_7`"2%uRxR#'>r'IC'OP8Q"2%'>r'A3r6C<'P!"$eBhB&=b&H3&NO(P"2%(&(+(, -8-
 ""$&>r&A3r6C<&P"2%uRxR#'>r'IC'OP'Q"2%'>r'A3r6C<'P!"$eBhB&=b&H3&NO(P"2%(&(+(, -'- 0Fb/H	'I LO	'O P	8P ""$
8% (*48B;+<'=
8> AD
8D 
1E FI
1II" &r)3r6C<8!"$eBhB&=b&H3&NOP!"$&=b&@#b&3,&O!"$eBhB&=b&H3&NO'P"2%'&(+', --
 ""$&>r&A3r6C<&P"2%uRxR#'>r'IC'OP'Q"2%'>r'A3r6C<'P!"$eBhB&=b&H3&NO(P"2%(&(+(, -'- 0Fb/H	'I LO	'O P	P #2%'>r'A3r6C<'P"2%uRxR#'>r'IC'OP(Q"2%'>r'A3r6C<'P!"$eBhB&=b&H3&NO(P"2%(&(+(, -(-
 ""$&>r&A3r6C<&P"2%uRxR#'>r'IC'OP'Q"2%'>r'A3r6C<'P!"$eBhB&=b&H3&NO(P"2%(&(+(, -'- 0Fb/H	'I LO	'O P	(P #2%
(& ),
(, 
--( 0ER/G)H( KN)N O( PR)R#%RJ UWWYTYK%ZJ ]^K%^DN T[[Q"B'2bAABEI1R@2q5HI0B?"a%GH 0B?"a%GH /2>QF	G
 ER(2q501 ER(2-. ER()	
 	
 	
r,   c                  $   t        d      \  } }}}t        t        | |z   ||z  z         |dd      t        | |z         t        |      z   k(  sJ t        t        | |z   |z   ||z  z         |dd      t        | |z   |z         t        |      z   k(  sJ y )Nza b c xr   r4   )r   r   r   r   )r   r   cr   s       r)   test_issue_11407r   W  s    #JAq!Q$q1uqs{#Q1-a!eqt1CCCC$q1uqy1Q3'Aq1T!a%!)_qt5KKKKr,   c                      t        t        dz        t        dz  z  j                  t        d      dt        z  t        dt              z   k(  sJ y )N2   3   r   r=   r4   )r   r   r   r   r7   r,   r)   test_issue_14037r   ]  s?    2Jq"u$$Q!$,!a1g===r,   c                      t        t              t        z  j                  t        d       } t        d      D cg c]  }t	        |        }}|dt        z  dt        dz  gk(  sJ y c c}w )Nr=   r@   r4   r>   )r   r   r   rT   rN   )rd   rZ   termss      r)   test_issue_20551r   a  s[    F1HQ$'D"'(,Qd4j,E,QqS!QqSM!!! -s   A&c                     t        d      \  } }}}}}}| |||t        z  z   t        z  z   t        z  z   d||t        z  z  ||z  ||z  z
  |dz  z  z   t        z  |dz  |z  ||z  |z  z
  |||z  |dz  z
  z  z
  |dz  z  z   t        z  z   z  }|j                  t        d      j                         |t        dz  z  |t        z  z   |z   t	        t        dz        z   k(  sJ y )Nzp_0 p_1 p_2 p_3 b_0 b_1 b_2r4   r>   r@   r=   )r   r   r   ratsimpr   )p_0p_1p_2p_3b_0b_1b_2Qs           r)   test_issue_20697r   g  s   (/0M(N%Cc3S#	sSU{Ao%q(	(1c!eC
c'A6@ 21 #Qs
SWS[ 83C
q&A < !6 10 , 	A 88A8##%QTCE)9C)?!AqD')IIIIr,   c                     dt        d      z   dz  } ddt        z
  t        dz  z
  z  j                  t        d| z  d      j                         ddt        d      z  z
  dt        z  z   dt        d      z  t        z  z   t	        t        ddt        d      z   z  z
  dz  t        ddt        d      z   z  f      z   dt        d      z   dd	t        d      z  z   dz  z  t        t        d      t        z  z   dz
  z  z  k(  sJ y )
Nr4   rH   r>   i4ih  i  i  r   r   )r   r   r   factorr   )fis    r)   test_issue_21245r   o  s    
d1g+qBq1uq!t|$$Q"a0779	d1g	Q	&T!WQ	6
QAQK 1$q!Qa[/&:
;
<?@47{
qay.1	?$q'!)ma/?1	22 2 2r,   c                  L   t        dt        z  t        t               z         t        dt        z        z
  } | j                  t        t              ddt        dz  z  z  ddt        dz  z  z  z
  dz   t        t        dz  t        t        f      z   t        t               z  k(  sJ y )Nr4   rm   rD   r>   r   )r   r   r   r   r   r   rc   s    r)   test_issue_21938r   w  s    qsS!W}AaC(D;;q"!R1W+1QT6
":Q">1r7QPRGAT"TVY[\Z\V]!]]]]r,   c                      dt        dt        dz  z
        z  } | j                  t        d      }|j                  rt	        |j
                        dk(  sJ y )Nr4   r>   r   ra   )r   r   r   is_Addlenargs)rd   results     r)   test_issue_23432r   |  sH    T!ad(^D[[C F==S-2222r,   c                  n    t        t        dt        dz  z
        t        d      } | j                  dk(  sJ y )Nr4   r>   g?T)r   r   r   r   )ress    r)   test_issue_23727r     s.    
a!Q$hC
(C::r,   c                  H	   t        t         t        z  dt        z  dz   z        j	                  t        dd      ddt        z  t        z  t        z  z   dt        dz  z  t        dz  z  z   t        t        dz        z   k(  sJ t        t         t        z  dt        z  dz   z        t        dt        z         z  j	                  t        dd      dt        t        dt        z  t        z  z   z  z   t        dz  t        dz   dz  dt        dz  z  dz  z   dt        z  t        z  t        z  z
  z  z   t        t        dz        z   k(  sJ dt        z  t         t        z  dt        z  dz   z  z  j	                  t        dd      t        t        dz  dz  t        t        z  t        d      z  z
        t        t        dz  t        t        dz  dz  t        t        z  t        d      z  z
        z  dt        z  t        z  t        t        dz  dz  t        t        z  t        d      z  z
        z  t        d      z  z
  z  z   t        t        dz        z   k(  sJ dt         t        z  dt        z  dz   z  z  j	                  t        dd      t        t         t        z  t        d      z        dt        z  t        z  t        z  t        t         t        z  t        d      z        z  t        d      z  z
  t        t        dz        z   k(  sJ t        t        t        z  dt        z  dz   z  z  j	                  t        dd      t        t        t        z  t        t              z        dt        z  t        z  t        z  t        t        t        z  t        t              z        z  t        t              z  z   t        t        dz        z   k(  sJ t        t        z  t        t        z  dt        z  dz   z  z  j	                  t        dd      t        t        t        z  t        t        t        z        z        dt        z  t        z  t        z  t        t        t        z  t        t        t        z        z        z  t        t        t        z        z  z   t        t        dz        z   k(  sJ y )Nr>   r4   r   r@   r`      rA   )
r   r   r   r   r   r   r   r#   r   r   r7   r,   r)   test_issue_24266r     s   2qs1u&&q!Q/2!Bq=1RU71a4<3ORSTUWXTXRY3YYYY2qs1uuQqSz)11!Q:b1jSTUVSVWYSYFYCZ>Z	1z1}nQBE",q|A~b/@@A?BDEadG?L L L L qSQBrE1Q3q5M"**1a3s2q57QrT#a&[;P7Q
RU3r1uQw2c!f,--!Bs2q57QrT#a&[;P7Q0QRUVWRX0XX
Y8Z\]^_ab^b\c8d d d d1"R%1Q- ((Aq1S!Bs1v5F1RPQRUWXVXY[V[\_`a\bVbRcIcdghidjIj5jmnoprsosmt5tttt !B$!A,''1a0C"SV4Dqs2vaxPSTUVXTXY\]^Y_T_P`G`adefagGg4gjklmoplpjq4qqqqqSAbD!A#a%L!))!Q2c!B$s1Q3x-6H1Q3r6RS8TWXYZ\X\]`abcdad]eXeTfKfgjklmnkngoKo6orstuwxtxry6yyyyr,   N)[sympy.core.evalfr   sympy.core.functionr   r   r   r   sympy.core.numbersr   r	   r
   r   r   r   sympy.core.singletonr   sympy.core.symbolr   r   &sympy.functions.elementary.exponentialr   r   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   r   sympy.series.orderr   sympy.series.seriesr   ro   r   r   r    r!   sympy.testing.pytestr"   
sympy.corer#   r*   r.   r0   r2   r\   re   rh   rt   r}   sympy.series.accelerationr~   r   sympy.concrete.summationsr   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   r7   r,   r)   <module>r     s    G G > > " / G G 9 E E 9 9   &     ' !/Ndg[(7,D( 9 ) &O(
2-
,
5
,V
K,7 8CM
A-2
jL>"J2^
3
zr,   