
    gJ@                     
   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 ZZd9S ):    )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                                        t          d          } t          t          t                    t          d          }| |k    sJ d S Nr   )r   r   r   e1e2s     Z/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_series.pytest_sinr*      C    	Qq!		B	A1		B888888    c                      t          t                                        t          d          } t          t          t                    t          d          }| |k    sJ d S r%   )r   r   r   r&   s     r)   test_cosr.      r+   r,   c                      t          t                                        t          d          } t          t          t                    t          d          }| |k    sJ d S r%   )r   r   r   r&   s     r)   test_expr0      r+   r,   c                      t          t          t                                                  t          d          } t          t          t          t                              t          d          }| |k    sJ d S r%   )r   r   r   r   r&   s     r)   	test_exp2r2   $   sQ    	SVV		Aq	!	!B	CFFQ	"	"B888888r,   c            	         t          dt                    dk    sJ t          t          j                            t                              dk    sJ t          t                                                     t          t                                         t                    k    sJ t          t          d            t          t          d            t          t                                         t          d          t          t          dz                                  t                    	                    t          t          dz
            z
  
                                dk    sJ t          t                                         t          dd           fdt          d          D             t          d          t          dz
  t          d          z   gk    sJ t          t                                         t          dd d	          fd
t          d          D             t          d          dt          z
  t          d          z  gk    sJ t          t                                         t          dd          t          k    sJ t          t                                         t          ddd          
                                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                               t                                                    dt          z  t"          z  k    sJ t           | t          t                    t                                                               | dt                    k    sJ  | t          t                    t                                         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                               t                    ddt          z  z   k    sJ dt          z   t'          t          dz            z                                   dk    sJ dt          z                                   J t          t,          d            t/          d          }t          t                    t"          z                      t          d|          t          t"          |z            t'          t          t          t"          |z            z  t                    z   k    sJ t          dt          z                                 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                                         t          t2          dd	          t          k    sJ t          t                                         t          t2           dd	          t           k    sJ t          t                                          t          t2          dd	          t          k    sJ t          t                                          t          t2           dd	          t           k    sJ t          t          t5          t                    z                                 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                                 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                                 d          dt          t5          t                    z  z   t'          t          dz  t5          t                    dz  z            z   k    sJ d S )N   r   c                  ^    t          t          t          z                                             S N)r   r   r   r    r,   r)   <lambda>z!test_issue_5223.<locals>.<lambda>.   s    s1q5zz0022 r,   c                  ,    t          j        d          S )N dir)r   r   r7   r,   r)   r8   z!test_issue_5223.<locals>.<lambda>/   s    qxB/// r,   r    c                 .    g | ]}t                    S r7   next.0ies     r)   
<listcomp>z#test_issue_5223.<locals>.<listcomp>4       &&&DGG&&&r,      -)r    r<   c                 .    g | ]}t                    S r7   r?   rA   s     r)   rE   z#test_issue_5223.<locals>.<listcomp>6   rF   r,   r;      )r<   r             c                  d    dt          t                    z  t          z                                  S Nr4   )r   r   r   r   r7   r,   r)   r8   z!test_issue_5223.<locals>.<lambda>G   s     #a&&2~5577 r,   logx)r    rQ      +pTpositivez3/2)r   r   r@   r   Zerolseriesr   r"   
ValueErrorsubsremoveOranger   absr   r   r   r   doitr   r   getnr   r   nseriesr   r   r   )DrQ   rU   rD   s      @r)   test_issue_5223rc   *   s>   !Q<<1q!!""a''''q66==??c!ffmmA......
:22333
://000FFMM!QAJJa  %%aQ//018a@ @ @ @Aad##A&&&&U1XX&&&3q66a!eSVV^3D*EEEEEAad,,A&&&&U1XX&&&3q66AE3q66>*BBBBBq66==A3=''1,,,,q66==A3!=,,4466	ArAvJQBFQ;q() ) ) ) 	A1QTAqDAIq!Q**11!4499;;r!tAvEEEE#a&&!$$&&''11Q7722221A 6A6;;!!Aq''AAaGG"3aa1Qll"BQQq!tAvq\\"QTUVWYZVZT[T["[\ \ \ \ A1ay1a),,33A66"qs(BBBBEAadGGO!!##q((((E<<>>!!!
977888&>>DVVaK  ad 33AdFa#af++q)))* * * * qs88??1bA?&&!A#1QT6
*:Qq2wB=P=P*PPPPPq66==B!=--2222q66==RC1#=..1"4444r77>>!R1#>..!3333r77>>!bSA3>//A25555qQx==!$$	Ac!ffHq!tCFFAI~a''!AqDQN*;*;;< < < < 	sT"""AtAwwz#a&& !!((1(--	AqxxKA1a4A	>!2!223 3 3 3 s1vvc!ff}$$q$))Q3q66\Aad3q6619n<M<M-MMMMMMMr,   c                     t          t          t          t          dz  dt          z  z
  z            t          dt          fd          } |                     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 d S )NrJ   r   none)condsrG   r4   rL   rR   rN         )r   r   r!   r   r   r   r   r   r   r   r   exprs    r)   test_issue_6350rl   \   s   SAqD1Q3J((1a*FCCCD;;q!QR1Q446N?477#:51a==!;K#KERSTURVRVWXRXMM#Y[\]_[_`adefgdhdhijdj`k[k#lQ	%1a.. !uQw/26$7	qttAvtAwwq1Q446{*5!A$$q>>9%!Q--GaPQddSTfUWXY[W[\$] 
qttAvtAwwq1Q446{*51a==!+;;E!A$$q&MMI1R4P$Q 
qttAvtAwwq1Q446{*5!A$$q>>9%!Q--GaPQddSTfUWXY[W[\	$] `aabdeae_f_f	$g g g g g g gr,   c                     t          t          t                    t                                        t                    t	          t                                        t                    k    sJ t          t	          t                    t                                        t          d                                          t          t                                        t          d          k    sJ t          t          dz  t                                        t                    dt          dz  z  k    sJ t          t          dz  t                                        t                    dk    sJ t          t	          t                    t                                        t                    dk    sJ t          t          t                    t                                        t                    t           k    sJ t          dt                                        t                    t          dt                    k    sJ t          t          t                    t                                        t                                                    t          t                                        t                    k    sJ dt          t          t                    t                                        t                    z   t          t                                        t                    k    sJ t          t          t                    t                                        t                                                    dt          z                      t                    k    sJ t          t          t                    t                                        t                    t          t          t                    t                                                                        t                                                    k    sJ d S )NrJ   r=   rG   r   r4   )r   r   r   r   r   r   r_   as_leading_termr   r   r   r\   r7   r,   r)   test_issue_11313ro   e   s   CFFA%%a((CFFMM!,<,<<<<<c!ffa  ''Q'//4466#a&&--Q-:O:OOOOOadA..q11Qq!tV;;;;adA..q11Q6666c!ffa  0033q8888c!ffa  0033r9999 a++A..*Q2B2BBBBBc!ffa  ''**//11SVV]]15E5EEEEExA""))!,,,Aa0@0@@@@@c!ffa  ''**//11ac\\!__DDDDCFFA%%a((HSVVQ,?,?,D,D,F,F,M,Ma,P,P,X,X,Z,ZZZ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          }|                     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   }|                                 |k    sJ |                     t
                    |k    sJ |                               | k    s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 |                    t                    	                                |	                                                    t                    k    sJ |                              	                                t          t          t
          z            k    sJ t          t          fd
           t          t          t
          z   t
                                        t                    	                                t          z   k    sJ d S )Nr   zrJ   rL   rR   x   rN      rG   c                  t    t          t          dt          z  z   t                                                     S )NrG   )r   r   r   r   rq   s   r)   r8   z%test_series_of_Subs.<locals>.<lambda>   s'    tA!GQ2299;; r,   )	sympy.abcrr   r   r   r   r   r   r   r   r_   r"   rZ   )subs1subs2subs3subs1_seriesrr   s       @r)   test_series_of_Subsr{   y   s   QAEQ#a&&!Q''EQUaVaV,,E<<??e####AqMMD!Q$q!Q$7$77QT#Xq! Aww'L<<>>\))))<<??l****<<??e####<<??tAqDQKNAq99adU3q66\!^Q"" #%)#a&&!Q%7%7 8:;AqD'' B C C C C<<??!!UZZ\\%8%8%;%;;;;;<<??!!S1XX----
:;;;;<<<Aq!##A&&++--Q666666r,   c            
         t          d          }  | t                                        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                                        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                                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                                 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                                        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 d S )
Nfr   rJ   rH   r;   rG   r4   c                       e Zd ZdS )test_issue_3978.<locals>.TestFN)__name__
__module____qualname__r7   r,   r)   TestFr      s        r,   r   )r   r   r   r   r   r   )r}   r   s     r)   test_issue_3978r      s\   A1Q44;;q!QC;((AaDD1T*QQqTT1--q!4444qDj1q!,,a333A5689!Q$@@ @ @ @ 1Q44;;q!QAaDD1T*QQqTT1--q!4444qDj1q!,,a333A5689!Q$@@ @ @ @ 1QT77>>!Q""AaDD1a4Z!a00!Q7777!AqD''AB B B B1QT!V99Aq!$$AaDD1a4Z!a00!Q7777!AqD''AB B B B        588??1a##ad:eeAhh**Aq111)2qDjq1a00!Q7779):<=adGG)D D D D D D Dr,   )
richardsonshanks)Sum)Integerc                     ddt           z  z   t           z  } t          t          | t           dd                                          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                                          d          t          t          d                                          d          k    sJ t          t          |t           dd                                          d          t          t          d                                          d          k    sJ d S )	Nr4   
      rg      rN   rG   rR   )
r    roundr   evalfr   r   r   r!   r   r   )rD   As     r)   test_accelerationr      s   	
QqS1AAq"b))//11266%		2:N:NNNNNGBKK!a% 1$q!Qi00A1b!!''))1--s1vv||~~q1I1IIIII1b!$$**,,b11U3q66<<>>25N5NNNNNNNr,   c            	      `   t          dt          t          t          t                    z            z  t          d          dt          dz  dt          t                    dz  z  z  z   dt          dz  z  dt          t                    dz  z  z  z   t	          t          dz            z   k    sJ d S )Nr4   r   rG   rR   rN   rt   rL   )r   r   r   r   r   r7   r,   r)   test_issue_5852r      s    !C#a&&MM/1a((A1aA	k0B,B	!Q$3q6619- !!Q$-( ( ( ( ( ( (r,   c                  (   t          dt          z   t          dz  z                                 t          dd          t          d          t          t          d          z  z
  t          dz  t          d           t          d          dz  z
  z  z   t          dz  t          d           t          d          dz  z   z  z   t          dz  dt          d          z  d	z  t          d          dz  z   z  z   t	          t          dz            z   k    sJ d S )
Nr4   rG   r   rR   rJ   rL   rN   irt   )r   r   r   r   r   r7   r,   r)   test_issue_4583r      s    q1uq!t|##Aq!,,A3q660A	1s1vvgAq !1"$%qD3q66'CFF1H*<$=1>	1c#a&&jmc!ffQh&'1(*+AqD''12 2 2 2 2 2 2r,   c                      dt           z  t          dd          z  } | dz                       t                     | k    sJ d S )Nr4   rG   rJ   )r   r
   rn   eqs    r)   test_issue_6318r      sA    
A#A	BF##A&&",,,,,,r,   c                      t           dz  t          dd          z  } |                                 t           t          dd          z  k    sJ d S )NrG   rJ   rN   )r   r
   r   r   s    r)   test_x_is_base_detectionr      sD    
Q$!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 d S )NrJ   rg   rG   )r   r   r   r   r   r7   r,   r)   test_issue_7203r      sf    #a&&!R##
a"fq[]QB{QG4445 5 5 5 5 5r,   c                  x   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 d S )Nza, bTrV   ri   r=   r4   rG   rJ   rL   rN   rt   rR   rs     rh     )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	$&1a419a++&, , , , , , ,r,   c                  4    t          dd          dk    sJ d S )Nr4   ri   r=   r   r7   r,   r)   test_issue_8805r      s#    !q>>>Qr,   c                  @   t           dz  t           z   dz   t           dz  t           dz  z   z  } t          | t           t                    t           dz  dt           dz  z  z
  t           dz  z   dt           z  z   t          t           dz  t           t          f          z   k    sJ d S )NrG   r4   rJ   rS   rN   )r   r   r   r   r   s    r)   test_issue_9549r      s    	
AA!Q$A+&A!Qq2w1a4/!b'9AaC?!AGaQSWBUBUUUU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 d S )	Nr4   r   r   rJ   rN   rR   rL   )r   r   r   r7   r,   r)   test_issue_10761r      sZ    !QUQU]#Q**adQTkAqD.@1QT77.JJJJJJJr,   c                     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 d S )Nr4   rG   rN   ri   r      r=   rL   "      r   i  rK   i     iC     )r   r   r   r   r   s    r)   test_issue_12578r      s    	
Q!a1g!!	!QqTT!V,A18AqB1qAv:!Q$#6AqD#@3q"u9#LsSTVXSXy#XQU
$1b5[$!#$QU88$, , , , , , ,r,   c                     t          dd          } t          dd          \  }}| dz   |z  t          |          z  | dz  t          |          z  z   | |z  t          |          z  z   | t          |          z  z
  | z
  dz   | t          |          z  dz
  dz  z  }ddt          |          z  d	z
  dz  z  d
t          |          z  dt          |          z  d	z
  dz  z  z
  | dz
  d|z  t          d|z            z  dt          |          z  z
  d
t          d|z            z  z   dz   z  dt          |          z  d	z
  dz  dt          |          z  d	z
  z  z  z   d
|z  t          |          z  dt          |          z  d	z
  dz  z  z   t          | t          j        z
  dz  | t          j        f          z   }|                    | dd                                          |k    sJ d S )NbetaTrV   ztheta varphirealrG   r4         ?      ?g      ?g      пg      ?g      ?)r   r   r   r   r   Halfr   trigsimp)r   thetavarphirk   sols        r)   test_issue_12791r      s   6D)))DN666ME61WHVOCJJ&qU);;VCJJ!%c%jj1378:;<>B3u::oPQ>QTU=UVD CJJ$q((4E

?CE

NS<PST;T+TT#:fS5\\1CE

NB
s1U7||
"# $&)#e**ns&:Q%>CJJQT@T%UWW v+c%jj
 #c%jj.3"6!:
:; TAF]Qqv
/
/	0C ;;tS!$$--//3666666r,   c                     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           d S )Nzx ar   c                  4    t           t          z             S r6   r   r   r   s   r)   r8   z"test_issue_14384.<locals>.<lambda>   s    fQT1oo r,   c                  :    t           t          dz   z             S rP   r   r   s   r)   r8   z"test_issue_14384.<locals>.<lambda>   s    fQQZ33 r,   c                  h    t          t          t          t                     z                       S r6   )r   r   r   r   r   s   r)   r8   z"test_issue_14384.<locals>.<lambda>   s!    fS3q66]]A66 r,   )r   r   r   r   r"   r   )r   r   s    @r)   test_issue_14384r      s    5>>DAq!Q$??ad""""!bd)Q1r!t9,,,,#aAh--##s1SVV8}}4444
9----...
93333444
9666677777r,   c                  h   t          t          t          dd          z  t          t                    z  t          d          t          t          dd          z  dt	          t                    z  z   t	          t                    dz  z   t          t          dd          z  dz  z   t          t          dd          z  dz  z   t          t          d	d          z  d
z  z   t          t          dd          z  dz  z   t          t          dd          z  dz  z   t          t          dz            z   k    sJ d S )Nr   rG   r   r4   rJ   rL   rR   rt   rh   rs   	   r      r   )r   r   r
   r   r   r   r7   r,   r)   test_issue_14885r      s   !Xb!__$SVV+Q22q(2q//7IAdSTggI7UQ	8x1~~%a'8(*+Xa^^*;B*>8?ABHQPQNNARSVAV8W	8Aq>>#8 !8B?? 24 788:;AqD''8B C C C 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 d S )Nrg   rR   r4   rJ   rG   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 d S )
NrG   rJ   ri   rN   }   rR   rt   rL   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[T[%[[[[[(1a4..!q)))QTAqD[1QT6!8-Ca1gg-MMMMM(3q66""A+++q1a4x!AqD&(/BQq!tWW/LLLLLLLr,   c                      t          t                                        t          dd          t          d          t          t          dz
  t          df          z   k    sJ d S )Nr4   r=   )r   r   r   r   r7   r,   r)   test_issue_11884r     sN    q66==A=##s1vv!a%!Q0@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 d S )Nr4   rN   r=   i    rJ   r   rG   ri   rM   )r   r   r   r   r   r   s    r)   test_issue_18008r     s    	1q!a%y=A1q5	Ma!ea!e_<=A18ArQ2r!Q$w<!R1W+#=1Q3#G!A$$q&#PSTUVSV#V	!b'Ar7$      r,   c                      t          t          dt          z
  z            } |                     t          dd                                                                          t          d           dz  k    sJ d S )Nr4   gCl?r=   l   I l     o )r   r   r   r\   	nsimplifyr   )r}   s    r)   test_issue_18842r     st    Aq1uIA88Au8""**,,668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          |                    | 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 d S )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   ri   z0.00092592592592592596126289F   )	precisionrh   z0.0027777777777777783174695rL   z0.016666666666666656027029rR   z0.083333333333333300951828rN   z0.33333333333333337034077rJ   z1.0rG   )r   r   r   r   r	   )r   rk   s     r)   test_issue_19534r   "  sI   	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
 d2hhrk!"#
 &)) *
 +... 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88B;+<'=
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!"$eBhB&=b&H3&NO(P"2%(&(+(, -'- 0Fb/H	'I LO	'O P	(P #2%
(& ),
(, 
--( 0ER/G)H( KN)N O( PR)R#%RJ UWWYTYK%ZJ ]^K%^DN T[[Q""B''2bAAAABEI1R@@@2q5HI0B???"a%GH 0B???"a%GH /2>>>QF	G
 ER(((2q501 ER(((2-. ER((()	
 	
 	
 	
 	
 	
r,   c                  r   t          d          \  } }}}t          t          | |z   ||z  z             |dd          t          | |z             t          |          z   k    sJ t          t          | |z   |z   ||z  z             |dd          t          | |z   |z             t          |          z   k    sJ d S )Nza b c xr   r4   )r   r   r   r   )r   r   cr   s       r)   test_issue_11407r   W  s    ##JAq!Q$q1uqs{##Q1--a!eqtt1CCCCC$q1uqy1Q3''Aq11T!a%!)__qtt5KKKKKKKr,   c                      t          t          dz            t          dz  z                      t          d          dt          z  t          dt                    z   k    sJ d S )N2   3   r   r=   r4   )r   r   r   r   r7   r,   r)   test_issue_14037r   ]  sO    2JJq"u$$Q!$,,!a1gg======r,   c                      t          t                    t          z                      t          d           fdt          d          D             } | dt          z  dt          dz  gk    sJ d S )Nr=   c                 .    g | ]}t                    S r7   r?   )rB   rC   rk   s     r)   rE   z$test_issue_20551.<locals>.<listcomp>c  s    ,,,Qd4jj,,,r,   rJ   r4   rG   )r   r   r   r]   )termsrk   s    @r)   test_issue_20551r   a  si    FF1HQ$''D,,,,%((,,,EQqS!QqSM!!!!!!r,   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  }|                    t          d                                          |t          dz  z  |t          z  z   |z   t	          t          dz            z   k    sJ d S )Nzp_0 p_1 p_2 p_3 b_0 b_1 b_2r4   rG   rJ   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(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IIIIr,   c                  l   dt          d          z   dz  } ddt          z
  t          dz  z
  z                      t          d| z  d                                          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 d S )
Nr4   rR   rG   i4ih  i  i  r   r   )r   r   r   factorr   )fis    r)   test_issue_21245r   o  s   
d1gg+qBq1uq!t|$$Q"a007799	d1gg	Q	&T!WWQ	6
QAQK 1$q!Qa[/&:
;
;
<?@477{
qay.1	?$q''!)ma/?1	22 2 2 2 2 2r,   c                     t          dt          z  t          t                     z             t          dt          z            z
  } |                     t          t                    ddt          dz  z  z  ddt          dz  z  z  z
  dz   t          t          dz  t          t          f          z   t          t                     z  k    sJ d S )Nr4   rt   rN   rG   r   )r   r   r   r   r   r   rj   s    r)   test_issue_21938r   w  s    qsS!WW}AaC(D;;q"!R1W+1QT6
":Q">1r7QPRGATAT"TVY[\Z\V]V]!]]]]]]]r,   c                      dt          dt          dz  z
            z  } |                     t          d          }|j        rt	          |j                  dk    sJ d S )Nr4   rG   r   rh   )r   r   r   is_Addlenargs)rk   results     r)   test_issue_23432r  |  sU    T!ad(^^D[[C  F=2S--222222r,   c                  |    t          t          dt          dz  z
            t          d          } | j        dk    sJ d S )Nr4   rG   g?T)r   r   r   r   )ress    r)   test_issue_23727r    s:    
a!Q$hC
(
(C:r,   c                  8   t          t           t          z  dt          z  dz   z                                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                      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                      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                      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                      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                      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 d S )NrG   r4   r   rJ   rg      rK   )
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<3ORSTUWXTXRYRY3YYYYY2qs1uuQqSzz)11!Q::b1jSTUVSVWYSYFYCZ>Z	1z1}nQBE",q|A~b/@@A?BDEadGG?L L L L L qSQBrE1Q3q5M"**1a33s2q57QrT#a&&[;P7Q7Q
RU3r1uQw2c!ff,---!Bs2q57QrT#a&&[;P7Q7Q0QRUVWRXRX0XX
Y8Z\]^_ab^b\c\c8d d d d d1"R%1Q- ((Aq11S!Bs1vv5F5F1RPQRUWXVXY[V[\_`a\b\bVbRcRcIcdghidjdjIj5jmnoprsosmtmt5ttttt !B$!A,''1a00C"SVV4D4Dqs2vaxPSTUVXTXY\]^Y_Y_T_P`P`G`adefagagGg4gjklmoplpjqjq4qqqqqqSAbD!A#a%L!))!Q22c!B$s1Q3xx-6H6H1Q3r6RS8TWXYZ\X\]`abcdad]e]eXeTfTfKfgjklmnkngogoKo6orstuwxtxryry6yyyy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   rv   r   r   r    r!   sympy.testing.pytestr"   
sympy.corer#   r*   r.   r0   r2   rc   rl   ro   r{   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 G G G G G G G G > > > > > > > > > > > > > > > > " " " " " " / / / / / / / / G G G G G G G G G G 9 9 9 9 9 9 E E E E E E E E E E 9 9 9 9 9 9 9 9 9 9 9 9 9 9             & & & & & &                         ' ' ' ' ' ' ! ! ! ! ! !        /N /N /Ndg g g[ [ [(7 7 7,D D D( 9 8 8 8 8 8 8 8 ) ) ) ) ) ) & & & & & &O O O( ( (
2 2 2- - -
, , ,
5 5 5
, , ,  V V V
K K K, , ,7 7 7 8 8 8C C C  M M M
A A A  - - -2
 2
 2
jL L L> > >" " "J J J2 2 2^ ^ ^
3 3 3  
z z z z zr,   