
    \hnB                        S SK Jr  S SKJrJrJrJr  S SKJrJ	r	J
r
JrJrJr  S SKJr  S SKJrJr  S SKJrJrJr  S SKJr  S SKJrJrJr  S S	KJr  S S
KJ r J!r!  S SK"J#r#  S SK$J%r%  S SK&J'r'J(r(J)r)J*r*  S SK+J,r,  S SK-J.r.  S r/S r0S r1S r2S r3S r4S r5S r6S r7S SK8J9r9J:r:  S SK;J<r<  S SKJ=r=  S r>S r?S r@S rAS  rBS! rCS" rDS# rES$ rFS% rGS& rHS' rIS( rJS) rKS* rLS+ rMS, rNS- rOS. rPS/ rQS0 rRS1 rSS2 rTS3 rUS4 rVS5 rWS6 rXS7 rYS8 rZS9 r[S: r\g;)<    )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                      [        [        5      R                  [        S5      n [        [        [        5      [        S5      nX:X  d   eg Nr   )r   r   r   e1e2s     V/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_series.pytest_sinr*      1    	Qq!	B	A1	B8O8    c                      [        [        5      R                  [        S5      n [        [        [        5      [        S5      nX:X  d   eg r%   )r   r   r   r&   s     r)   test_cosr.      r+   r,   c                      [        [        5      R                  [        S5      n [        [        [        5      [        S5      nX:X  d   eg r%   )r   r   r   r&   s     r)   test_expr0      r+   r,   c                      [        [        [        5      5      R                  [        S5      n [        [        [        [        5      5      [        S5      nX:X  d   eg r%   )r   r   r   r   r&   s     r)   	test_exp2r2   $   s;    	SV		Aq	!B	CFQ	"B8O8r,   c            	      (   [        S[        5      S:X  d   e[        [        R                  R                  [        5      5      S:X  d   e[        [        5      R                  5       [        [        5      R                  [        5      :X  d   e[        [        S 5        [        [        S 5        [        [        5      R                  [        S5      [        [        S-   5      R                  [        5      R                  [        [        S-
  5      -
  R                  5       S:X  d   e[        [        5      R                  [        SS S9n [        S5       Vs/ s H  n[        U 5      PM     sn[        S5      [        S-
  [        S5      -  * /:X  d   e[        [        5      R                  [        SS SS9n [        S5       Vs/ s H  n[        U 5      PM     sn[        S5      S[        -
  [        S5      -  /:X  d   e[        [        5      R                  [        SSS	9[        :X  d   e[        [        5      R                  [        SSS
S9R                  5       [        [        [        * S-   -  -
  [        [        * S-   S-  -  S-  -   :X  d   e[         nU" [        S-  [        S
-  ["        S-  -  -   [        S["        S5      R                  [        5      R%                  5       S[        -  ["        -  :X  d   e[        U" [        [        5      [        5      R                  5       5      U" S[        5      :X  d   eU" [        [        5      [        5      R                  S
S9U" S[        5      U" [        [        5      -   U" [        S-  S-  [        5      -   U" [        S
-  S-  [        5      -   ['        [        S
-  5      -   :X  d   e[)        [        [        SS
4["        S[        45      R                  [        5      SS[        -  -   :X  d   eS[        -   ['        [        S-  5      -   R+                  5       S:X  d   eS[        -   R+                  5       b   e[        [,        S 5        [/        S5      n[        [        5      ["        -  R1                  [        SUS9[        ["        U-  5      ['        [        [        ["        U-  5      -  [        5      -   :X  d   e[        S[        -  5      R                  [        [2        SS9S[        -  SS[        S
-  -  -  -
  ['        [        S-  [        [2        45      -   :X  d   e[        [        5      R                  [        [2        SSS9[        :X  d   e[        [        5      R                  [        [2        * SSS9[        * :X  d   e[        [        * 5      R                  [        [2        SSS9[        :X  d   e[        [        * 5      R                  [        [2        * SSS9[        * :X  d   e[        [        [5        [        5      -  5      R                  S
S9S[        [5        [        5      -  -   [        S-  [5        [        5      S-  -  S-  -   ['        [        S
-  [5        [        5      S
-  -  5      -   :X  d   e[/        SSS9n[        [7        U5      S
-  [5        U5      -  5      R                  S
S9SU[        S5      -  [5        U5      -  -   ['        US
-  [5        U5      S
-  -  5      -   :X  d   e[        [        [        5      [5        [        5      -  5      R                  SS9S[        [5        [        5      -  -   ['        [        S-  [5        [        5      S-  -  5      -   :X  d   eg s  snf s  snf )N   r   c                  J    [        [        [        -   5      R                  5       $ N)r   r   r   r    r,   r)   <lambda>!test_issue_5223.<locals>.<lambda>.   s    s1q5z002r,   c                  *    [         R                  " SS9$ )N dir)r   r   r7   r,   r)   r8   r9   /   s    qxxB/r,   r       -)r    r=   r<      )r=   r             c                  P    S[        [        5      -  [        -  R                  5       $ Nr4   )r   r   r   r   r7   r,   r)   r8   r9   G   s    #a&2~557r,   logx)r    rH      +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DrH   rL   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&XDGX&3q6a!eSV^3D*EEEEAad,A"1X&XDGX&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                  L   [        [        [        [        S-  S[        -  -
  -  5      [        S[        4SS9n U R                  [        SS5      S[        S5      S-  -  * [        S5      -  [        [        S5      S-  5      S-  -  [        [        S5      S-  5      -  S[        -  [        [        S5      S-  -  -  -  [        S5      [        -  [        [        S5      * S-  5      -  [        [        S5      * S-  5      -  S[        -  -  -
  S[        S5      S-  -  [        S5      -  [        [        S5      S-  -  -  [        [        S5      * S-  5      -  [        [        S5      S-  5      -  [        [        S5      S-  5      -  S[        -  -  -
  S[        S5      S-  -  [        S5      -  [        [        S	5      S-  -  -  [        [        S5      S-  5      S-  -  [        [        S5      S-  5      -  S
[        -  -  -
  S[        S5      S-  -  [        S5      -  [        [        S5      S-  -  -  [        [        S5      * S-  5      -  [        [        S5      S-  5      -  [        [        S5      S-  5      -  S[        -  -  -
  [        [        S-  5      -   :X  d   eg )NrA   r   none)condsr?   r4   rC   rI   rE         )r   r   r!   r   r   r   r   r   r   r   r   exprs    r)   test_issue_6350rf   \   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                     [        [        [        5      [        5      R                  [        5      [	        [        5      R                  [        5      :X  d   e[        [	        [        5      [        5      R                  [        SS9R                  5       [        [        5      R                  [        SS9:X  d   e[        [        S-  [        5      R                  [        5      S[        S-  -  :X  d   e[        [        S-  [        5      R                  [        5      S:X  d   e[        [	        [        5      [        5      R                  [        5      S:X  d   e[        [        [        5      [        5      R                  [        5      [        * :X  d   e[        S[        5      R                  [        5      [        S[        5      :X  d   e[        [        [        5      [        5      R                  [        5      R                  5       [        [        5      R                  [        5      :X  d   eS[        [        [        5      [        5      R                  [        5      -   [        [        5      R                  [        5      :X  d   e[        [        [        5      [        5      R                  [        5      R                  5       S[        -  R                  [        5      :X  d   e[        [        [        5      [        5      R                  [        5      [        [        [        5      [        5      R                  5       R                  [        5      R                  5       :X  d   eg )NrA   r>   r?   r   r4   )r   r   r   r   r   r   rW   as_leading_termr   r   r   rT   r7   r,   r)   test_issue_11313ri   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                    ^ SSK Jm  [        [        [        5      [        [
        5      n [        [        [        5      [        T5      -  [        [
        5      n[        [        [        T-  5      [        T4[
        [        45      nU R                  [        5      U :X  d   e[        [        [        [
        5      [        [        S-  * S-  [        [
        5      -   [        [        S-  S-  [        [
        5      -   [        [
        S-  5      -   nU R                  5       U:X  d   eU R                  [
        5      U:X  d   eU R                  T5      U :X  d   eUR                  T5      [        TS-  [        [        5      -  S-  [        [
        5      [        TS	-  * [        [        5      -  S	-  [        [
        5      -   [        [        [        5      [        [
        5      -   [        TS-  5      -   :X  d   eUR                  [        5      R                  5       UR                  5       R                  [        5      :X  d   eUR                  T5      R                  5       [        [        [
        -  5      :X  d   e[        [        U4S
 j5        [        [        [
        -   [
        T5      R                  [        5      R                  5       [        T-   :X  d   eg )Nr   zrA   rC   rI   x   rE      r?   c                  ^   > [        [        S[        -  -   [        T 5      R                  5       $ )Nr?   )r   r   r   r   rk   s   r)   r8   %test_series_of_Subs.<locals>.<lambda>   s    tA!GQ299;r,   )	sympy.abcrl   r   r   r   r   r   r   r   rW   r"   rR   )subs1subs2subs3subs1_seriesrl   s       @r)   test_series_of_Subsrv   y   s
   QAEQ#a&!Q'EQUaVaV,E<<?e###AqMD!Q$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            
      &   [        S5      n U " [        5      R                  [        SSSS9U " S5      [        [        [	        U " [        5      [        5      [        S5      -  -   [        S-  [        [	        U " [        5      [        [        5      [        S5      -  S-  -   [        [        S-  5      -   :X  d   eU " [        5      R                  [        SS5      U " S5      [        [        [	        U " [        5      [        5      [        S5      -  -   [        S-  [        [	        U " [        5      [        [        5      [        S5      -  S-  -   [        [        S-  5      -   :X  d   eU " [        S-  5      R                  [        SS5      U " S5      [        S-  [        [	        U " [        5      [        5      [        S5      -  -   [        [        S-  5      -   :X  d   eU " [        S-  S-   5      R                  [        SS5      U " S5      [        S-  [        [	        U " [        5      [        5      [        S5      -  -   [        [        S-  5      -   :X  d   e " S S	[         5      nU" [        5      R                  [        SS5      U" S5      [        [        [	        U" [        5      [        5      [        S5      -  -   [        S-  [        [	        U" [        5      [        [        5      [        S5      -  S-  -   [        [        S-  5      -   :X  d   eg )
Nfr   rA   r@   r<   r?   r4   c                       \ rS rSrSrg)test_issue_3978.<locals>.TestF   r7   N)__name__
__module____qualname____firstlineno____static_attributes__r7   r,   r)   TestFrz      s    r,   r   )r   r   r   r   r   r   )rx   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                  h   SS[         -  -   [         -  n [        [        U [         SS5      R                  5       S5      [        [        R                  " 5       S5      :X  d   e[        [        S5      [        S-   -  [        -  [        S[         45      n[        [        U[         S5      R                  5       S5      [        [        S5      R                  5       S5      :X  d   e[        [        U[         SS5      R                  5       S5      [        [        S5      R                  5       S5      :X  d   eg )	Nr4   
      ra      rE   r?   rI   )
r    roundr   evalfr   r   r   r!   r   r   )rZ   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            	         [        S[        [        [        [        5      -  5      -  [        S5      S[        S-  S[        [        5      S-  -  -  -   S[        S-  -  S[        [        5      S-  -  -  -   [	        [        S-  5      -   :X  d   eg )Nr4   r   r?   rI   rE   rn   rC   )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                     [        S[        -   [        S-  -   5      R                  [        SS5      [        S5      [        [        S5      -  -
  [        S-  [        S5      * [        S5      S-  -
  -  -   [        S-  [        S5      * [        S5      S-  -   -  -   [        S-  S[        S5      -  S	-  [        S5      S-  -   -  -   [	        [        S-  5      -   :X  d   eg )
Nr4   r?   r   rI   rA   rC   rE   irn   )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                  l    S[         -  [        SS5      -  n U S-   R                  [         5      U :X  d   eg )Nr4   r?   rA   )r   r
   rh   eqs    r)   test_issue_6318r      s3    
A#A	BF##A&",,,r,   c                  ~    [         S-  [        SS5      -  n U R                  5       [         [        SS5      -  :X  d   eg )Nr?   rA   rE   )r   r
   r   r   s    r)   test_x_is_base_detectionr      s5    
Q$!Q	B99;!Xa^++++r,   c                      [        [        [        5      [        [        S5      S[        [        -
  S-  S-  -   [	        [        [        -
  S-  [        [        45      -   :X  d   eg )NrA   ra   r?   )r   r   r   r   r   r7   r,   r)   test_issue_7203r      sO    #a&!R#
a"fq[]QB{QG445 5 5r,   c                  B   [        SSS9u  pX-  n[        [        U5      USS9SX-  -   U S-  US-  -  S-  -   U S-  US-  -  S	-  -   U S
-  US
-  -  S-  -   U S-  US-  -  S-  -   U S	-  US	-  -  S-  -   U S-  US-  -  S-  -   [        U S-  US-  -  X5      -   :X  d   eg )Nza, bTrM   rc   r>   r4   r?   rA   rC   rE   rn   rI   rm     rb     )r   r   r   r   )abr   s      r)   !test_exp_product_positive_factorsr      s    6D)DA	A#a&!q!QWq!tAqDy{%:	1QT	!&d1a4il&#%&T!Q$Ys]&356T!Q$Ys]&C	1QT	$&1a419a+&, , , ,r,   c                  $    [        SSS9S:X  d   eg )Nr4   rc   r>   r   r7   r,   r)   test_issue_8805r      s    !q>Qr,   c            	         [        S5      u  pp#pEnXX#[        -  -   [        -  -   [        -  -   SX4[        -  -  XB-  XS-  -
  US-  -  -   [        -  US-  U-  XE-  U-  -
  X4U-  US-  -
  -  -
  US-  -  -   [        -  -   -  nUR                  [        SS9nU[        XB-  U-  XB* U-  XT-  -   -  -   -  [        S-  XA-  U-  XB-  U* U-  XT-  -   -  U-  -   XA* U-  X#-  XT-  -
  S-  -   XR-  XC-  -  -   Xd-  -   US-  US-  -  -
  -  -   -  -   U-   [        [        S-  5      -   :X  d   eUR                  " 5       U[        S-  -  U[        -  -   U-   [        [        S-  5      -   :X  d   eg )Nzp0 p1 p2 p3 b0 b1 b2r4   r?   rA   r>   )r   r   r   r   simplify)	p0p1p2p3b0b1b2Qr   s	            r)   test_issue_9173r      s    !78B"b	rQ$wk>1
q2!t9beBEk2q5-@#@!"C
Abr"eBEk**BE1#234"5  5 6A XXa!X_FQbSVBE\!223AqD"%(25SVBE\DD ; #b&"%+)9"9"%-"GE#a%A+# ; 5    "##$QT7+ + + + ??1a4"Q$ 3a1g ====r,   c                     [         S-  [         -   S-   [         S-  [         S-  -   -  n [        U [         [        5      [         S-  S[         S-  -  -
  [         S-  -   S[         -  -   [        [         S-  [         [        45      -   :X  d   eg )Nr?   r4   rA   rJ   rE   )r   r   r   r   r   s    r)   test_issue_9549r      ss    	
AA!Q$A+&A!Qq2w1a4/!b'9AaC?!AGaQSWBUUUUUr,   c                      [        S[        S-  [        S-  -   -  [        S5      [        S-  [        S-  -
  [        S-  -   [        [        S-  5      -   :X  d   eg )	Nr4   r   r   rA   rE   rI   rC   )r   r   r   r7   r,   r)   test_issue_10761r      sL    !QUQU]#Q*adQTkAqD.@1QT7.JJJJr,   c                  t   SS[         S-  SS[         -  -  -
  S-  -  -
  [        S5      S-  -  n U R                  " [         SSS9SS[         S-  -  -
  S[         S-  -  -
  S	[         S-  -  -
  S
[         S-  -  -
  S[         S-  -  -
  S[         S-  -  -
  S[         S-  -  -
  [        [         S-  5      -   :X  d   eg )Nr4   r?   rE   rc   r      r>   rC   "      r   i  rB   i     iC     )r   r   r   r   r   s    r)   test_issue_12578r      s    	
Q!a1g!!	!QqT!V,A88AqB1qAv:!Q$#6AqD#@3q"u9#LsSTVXSXy#XQU
$1b5[$!#$QU8$, , , ,r,   c                  4   [        SSS9n [        SSS9u  pU S-  * U-  [        U5      -  U S-  [        U5      -  -   X-  [        U5      -  -   U [        U5      -  -
  U -
  S-   U [        U5      -  S-
  S-  -  nSS[        U5      -  S	-
  S-  -  S
[        U5      -  S[        U5      -  S	-
  S-  -  -
  U S-
  SU-  [        SU-  5      -  S[        U5      -  -
  S
[        SU-  5      -  -   S-   -  S[        U5      -  S	-
  S-  S[        U5      -  S	-
  -  -  -   S
U-  [        U5      -  S[        U5      -  S	-
  S-  -  -   [        U [        R
                  -
  S-  U [        R
                  45      -   nUR                  U SS5      R                  5       U:X  d   eg )NbetaTrM   ztheta varphirealr?   r4         ?      ?g      ?g      пg      ?g      ?)r   r   r   r   r   Halfr   trigsimp)r   thetavarphire   sols        r)   test_issue_12791r      s   6D)DN6ME1WHVOCJ&qU);;CJ!%c%j1378:;<>B3u:oPQ>QTU=UVD CJ$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                  ~  ^ [        S5      u  mn [        TU -  T5      TU -  :X  d   e[        TSU -  -  T5      TSU -  -  :X  d   e[        [        U [        T5      -  5      T5      [        U [        T5      -  5      :X  d   e[	        [
        U4S j5        [	        [
        U4S j5        [	        [
        U4S j5        g )Nzx ar   c                  *   > [        T [        -  T 5      $ r6   r   r   r   s   r)   r8   "test_issue_14384.<locals>.<lambda>  s    fQT1or,   c                  0   > [        T [        S-   -  T 5      $ rG   r   r   s   r)   r8   r   	  s    fQQZ3r,   c                  N   > [        [        [        [        T 5      -  5      T 5      $ r6   )r   r   r   r   r   s   r)   r8   r   
  s    fS3q6]A6r,   )r   r   r   r   r"   r   )r   r   s    @r)   test_issue_14384r     s    5>DAq!Q$?ad"""!bd)Q1r!t9,,,#aAh-#s1SV8}444
9-.
934
967r,   c                     [        [        [        SS5      -  [        [        5      -  [        S5      [        [        SS5      -  S[	        [        5      -  -   [	        [        5      S-  -   [        [        SS5      -  S-  -   [        [        SS5      -  S-  -   [        [        S	S5      -  S
-  -   [        [        SS5      -  S-  -   [        [        SS5      -  S-  -   [        [        S-  5      -   :X  d   eg )Nr   r?   r   r4   rA   rC   rI   rn   rb   rm   	   r      r   )r   r   r
   r   r   r   r7   r,   r)   test_issue_14885r     s    !Xb!_$SV+Q2q(2q/7IAdSTgI7UQ	8x1~%a'8(*+Xa^*;B*>8?ABHQPQNARSVAV8W	8Aq>#8 !8B? 24 788:;AqD'8B C C Cr,   c                     [        [        [        5      [        [        * 5      SS[        S-  -  -  SS[        S-  -  -  -   S[        -  -
  [        S-  -
  [        [        S-  [        [        * 45      -   :X  d   e[        [        [        5      [        [        5      SS[        S-  -  -  SS[        S-  -  -  -   S[        -  -
  [        S-  -   [        [        S-  [        [        45      -   :X  d   eg )Nra   rI   r4   rA   r?   r   )r   r   r   r   r   r   r7   r,   r)   test_issue_15539r     s    $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                  V   [        [        [        5      [        5      [        [        S-  -
  S[        S-  -  S-  -   S[        S-  -  S-  -
  S[        S-  -  S-  -   [        [        S-  5      -   :X  d   e[        [        [        S-  5      [        SS	9[        S-  [        S-  -
  S[        S-  -  S-  -   [        [        S-  5      -   :X  d   e[        [        [	        [        5      5      [        SS	9[        [        S-  -
  S[        S-  -  S-  -   [        [        S-  5      -   :X  d   eg )
Nr?   rA   rc   rE   }   rI   rn   rC   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                      [        [        5      R                  [        SSS9[        S5      [        [        S-
  [        S45      -   :X  d   eg )Nr4   r>   )r   r   r   r   r7   r,   r)   test_issue_11884r     s;    q6==A=#s1v!a%!Q0@'@@@@r,   c                     [         S[         S[         -
  -  -   -  S[         S[         -
  -  -   S[         -
  S[         -
  -  -
  -  n U R                  " [         [        SS9SS[         S-  -  -  SS[         S-  -  -  -
  SS	[         -  -  -
  [        S5      S-  -   [         S-  -   [	        [         S
-  [         [        45      -   :X  d   eg )Nr4   rE   r>   i    rA   r   r?   rc   rD   )r   r   r   r   r   r   s    r)   test_issue_18008r   #  s    	1q!a%y=A1q5	Ma!ea!e_<=A88ArQ2r!Q$w<!R1W+#=1Q3#G!A$q&#PSTUVSV#V	!b'Ar7$   r,   c                      [        [        S[        -
  -  5      n U R                  [        SSS9R                  5       R	                  5       [        S5      * S-  :X  d   eg )Nr4   gCl?r>   l   I l     o )r   r   r   rT   	nsimplifyr   )rx   s    r)   test_issue_18842r   )  sW    Aq1uIA88Au8"**,668	
?	,,- - -r,   c                     [        SSS9n SU -  SU -  SU -  S-   -  SU -  -   S-   -  S	-  S
U -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -
  SU -  -   U S[        S5      S-  -
  -  -   S-   -  S-  -   S
U -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -
  SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -
  SU -  -   S-   -  -   SU -  -
  U [        S5      S-  S-   -  -   S-   -  S-  -   U SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -
  SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -
  SU -  -   S-   -  -
  S U -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -
  SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  SU -  SU -  S-   -  SU -  SU -  SU -  S-   -  SU -  -   S-   -  -   SU -  -   S-   -  -
  SU -  -   S-   -  -   S!U -  -
  S-   -  -   S"U -  -   S-   -  S#-  -   U S#-  -   S$-   n[        UR                  U S%S&5      S#5      [	        S'S(S)9* U S*-  -  [	        S+S(S)9U S,-  -  -   [	        S-S(S)9U S.-  -  -   [	        S/S(S)9U S0-  -  -   [	        S1S(S)9U S2-  -  -   [	        S3S(S)9U S4-  -  -   [	        S3S(S)9U -  -   [	        S3S(S)9-   :X  d   eg )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   rc   z0.00092592592592592596126289F   )	precisionrb   z0.0027777777777777783174695rC   z0.016666666666666656027029rI   z0.083333333333333300951828rE   z0.33333333333333337034077rA   z1.0r?   )r   r   r   r   r	   )r   re   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!"$eBhB&=b&H3&NO(P"2%(&(+(, -'- 0Fb/H	'I LO	'O P	(P #2%
(& ),
(, 
--( 0ER/G)H( KN)N O( PR)R#%RJ UWWYTYK%ZJ ]^K%^DN T[[Q"B'2bAABEI1R@2q5HI0B?"a%GH 0B?"a%GH /2>QF	G
 ER(2q501 ER(2-. ER()	
 	
 	
r,   c                     [        S5      u  pp#[        [        X-   X#-  -   5      USS5      [        X-   5      [        U5      -   :X  d   e[        [        X-   U-   X#-  -   5      USS5      [        X-   U-   5      [        U5      -   :X  d   eg )Nza b c xr   r4   )r   r   r   r   )r   r   cr   s       r)   test_issue_11407r   d  s    #JA!$quqs{#Q1-aeqt1CCCC$quqy13'Aq1T!%!)_qt5KKKKr,   c                      [        [        S-  5      [        S-  -  R                  [        SS9S[        -  [        S[        5      -   :X  d   eg )N2   3   r   r>   r4   )r   r   r   r   r7   r,   r)   test_issue_14037r   j  s?    2Jq"u$$Q!$,!a1g===r,   c                      [        [        5      [        -  R                  [        S S9n [        S5       Vs/ s H  n[	        U 5      PM     nnUS[        -  S[        S-  /:X  d   eg s  snf )Nr>   rA   r4   r?   )r   r   r   rU   rO   )re   r[   termss      r)   test_issue_20551r   n  s\    F1HQ$'D"'(,(Qd4j(E,QqS!QqSM!!! -s   A'c                     [        S5      u  pp#pEnXX#[        -  -   [        -  -   [        -  -   SX4[        -  -  XB-  XS-  -
  US-  -  -   [        -  US-  U-  XE-  U-  -
  X4U-  US-  -
  -  -
  US-  -  -   [        -  -   -  nUR                  [        SS9R                  5       U[        S-  -  U[        -  -   U-   [	        [        S-  5      -   :X  d   eg )Nzp_0 p_1 p_2 p_3 b_0 b_1 b_2r4   r?   rA   r>   )r   r   r   ratsimpr   )p_0p_1p_2p_3b_0b_1b_2r   s           r)   test_issue_20697r   t  s   (/0M(N%Cc#	sU{Ao%q(	(1!e
'A6@ 21 #Qs
SWS[ 83C
q&A < !6 10 , 	A 88A8##%QTCE)9C)?!AqD')IIIIr,   c                     S[        S5      -   S-  n SS[        -
  [        S-  -
  -  R                  [        SU -  S5      R                  5       S[        S5      -  S-
  S[        S5      -  [        -  -   S[        -  -   [	        [        SS[        S5      -   -  -
  S-  [        SS[        S5      -   -  45      -   S[        S5      -  S-   S-  [        [        S5      [        -  -   S-
  -  -  :X  d   eg )Nr4   rI   r?   iS         )r   r   r   factorr   )fis    r)   test_issue_21245r  |  s    
d1g+qBq1uq!t|$$Q"a0779	T!Wr	BtAwJqL	(2a4	/!QAQK5H14LqT!WoO 3  
 #$T!W9q=1"4a$q'!)ma6G"H	JJ J Jr,   c                  N   [        S[        -  [        [        * 5      -   5      [        S[        -  5      -
  n U R                  [        [        5      SS[        S-  -  -  SS[        S-  -  -  -
  S-   [        [        S-  [        [        45      -   [        [        * 5      -  :X  d   eg )Nr4   rn   rE   r?   r   )r   r   r   r   r   r   rd   s    r)   test_issue_21938r    s    qsS!W}AaC(D;;q"!R1W+1QT6
":Q">1r7QPRGAT"TVY[\Z\V]!]]]]r,   c                      S[        S[        S-  -
  5      -  n U R                  [        S5      nUR                  (       a  [	        UR
                  5      S:X  d   eg )Nr4   r?   r   rb   )r   r   r   is_Addlenargs)re   results     r)   test_issue_23432r    sH    T!ad(^D[[C F==S-2222r,   c                  p    [        [        S[        S-  -
  5      [        S5      n U R                  S:X  d   eg )Nr4   r?   g?T)r   r   r   r	  )ress    r)   test_issue_23727r    s.    
a!Q$hC
(C::r,   c                  T	   [        [        * [        -  S[        -  S-   -  5      R	                  [        SS5      SS[        -  [        -  [        -  -   S[        S-  -  [        S-  -  -   [        [        S-  5      -   :X  d   e[        [        * [        -  S[        -  S-   -  5      [        S[        -   5      -  R	                  [        SS5      S[        [        S[        -  [        -  -   -  -   [        S-  [        S-  * S-  S[        S-  -  S-  -   S[        -  [        -  [        -  -
  -  -   [        [        S-  5      -   :X  d   eS[        -  [        * [        -  S[        -  S-   -  -  R	                  [        SS5      [        [        S-  S-  [        [        -  [        S5      -  -
  5      [        [        S-  [        [        S-  S-  [        [        -  [        S5      -  -
  5      -  S[        -  [        -  [        [        S-  S-  [        [        -  [        S5      -  -
  5      -  [        S5      -  -
  -  -   [        [        S-  5      -   :X  d   eS[        * [        -  S[        -  S-   -  -  R	                  [        SS5      [        [        * [        -  [        S5      -  5      S[        -  [        -  [        -  [        [        * [        -  [        S5      -  5      -  [        S5      -  -
  [        [        S-  5      -   :X  d   e[        [        [        -  S[        -  S-   -  -  R	                  [        SS5      [        [        [        -  [        [        5      -  5      S[        -  [        -  [        -  [        [        [        -  [        [        5      -  5      -  [        [        5      -  -   [        [        S-  5      -   :X  d   e[        [        -  [        [        -  S[        -  S-   -  -  R	                  [        SS5      [        [        [        -  [        [        [        -  5      -  5      S[        -  [        -  [        -  [        [        [        -  [        [        [        -  5      -  5      -  [        [        [        -  5      -  -   [        [        S-  5      -   :X  d   eg )Nr?   r4   r   rA   ra      rB   )
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,   c                  &    [        [        S 5        g )Nc                  F    S[         -  R                  [         [        S5      $ )Nr?   ra   )r   r   r   r7   r,   r)   r8   "test_issue_26856.<locals>.<lambda>  s    1}}QB7r,   )r"   rR   r7   r,   r)   test_issue_26856r    s    
:78r,   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   rq   r   r   r    r!   sympy.testing.pytestr"   
sympy.corer#   r*   r.   r0   r2   r]   rf   ri   rv   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  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J^
3
z 9r,   