
    g_                        d dl mZ d dlmZ d dlmZmZ d dlmZm	Z	 d dl
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 d d
lmZmZmZ d dlmZm Z m!Z! d dl"m#Z#m$Z$m%Z% d dl&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z. d dl/m0Z0m1Z1m2Z2 d dl3m4Z4m5Z5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZE d dlFmGZGmHZHmIZImJZJ d dlKmLZLmMZMmNZNmOZOmPZPmQZQ d dlRmSZSmTZTmUZU d dlVmWZW d dlXmYZYmZZZ d dl[m\Z\m]Z] d dl^m_Z_m`Z` d dlambZb d dlcmdZd d dlemfZf d dl[mgZg d dlhmiZi d dljmkZkmlZl d dlmmnZnmoZo d d lpmqZqmrZrmsZsmtZt  ed!d"d"#          Zud$ Zvd% Zwd& Zxd' Zyd( Zzd) Z{d* Z|d+ Z}d, Z~d- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zd8 Zd9 Zd: Zd; Zd< Zekd=             Zd> Zd? Zd@ ZdA ZdB ZdC ZdD ZdE ZdF ZdG ZdH ZdI ZdJ ZdK ZdL ZdM ZekdN             ZdO ZdP ZdQ ZdR ZdS ZdT ZdU ZdV ZekdW             ZdX ZdY ZdZ Zd[ Zd\ Zd] Zd^ Zd_ Zd` Zda Zdb Zdc Zdd Zde Zdf Zdg Zdh Zdi Zdj Zdk Zdl Zdm Zdn Zdo Zdp Zdq Zdr Zds Zdt Zdu Zdv Zdw Zdx Zdy Zdz Zd{ Zd| Zd} Zd~ Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zekd             Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z d Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdÄ ZdĄ Zdń ZdƄ ZdǄ ZdȄ ZdɄ Zdʄ Zd˄ Zd̄ Zd̈́ ZdS )    )product)Sum)Functiondiff)
EulerGammaGoldenRatio)Mod)EIRationaloopizoo)S)Symbolsymbols)	fibonacci)binomial	factorialsubfactorial)Absresign)LambertWexplog)atanhasinhacoshacothacschasechtanhsinh)ceilingfloorfrac)cbrt	real_rootsqrt)	Piecewise)acosacotacscasecasinatancoscotcscsecsintan)besselibesselybesseljbesselk)Eierferfcerfifresnelcfresnels)digammagamma
uppergamma)meijerg)Integral	integrate)Limitlimit)
logcombinesimplify)hyperexpand)AccumBounds)Mul)
heuristics)Order)XFAILraises)
elliptic_e
elliptic_k)xyzknTintegerpositivec            	      ,   t          t          t          t                    t          u sJ t          t          t          t                     t           u sJ t          t           t          t                    t           u sJ t          t          dz  t          t                     t          u sJ t          t          dz   t          t                    t           u sJ t          t          t          t                    z  t          dd          dk    sJ t          dt          z  t          t                    dk    sJ t          t	          t                    t          t                    t          u sJ t          t	          t                     t          t                    t           u sJ t          t	          t                    t          z  t          t                    t          u sJ t          dt          z  t	          t                     z
  t          t                    dk    sJ t          t          dt          z  z   t          t                    t          u sJ t          t          t          dz  z
  t          t                    t           u sJ t          dt          z   dt          d          z   z  t          d          dk    sJ t          dt          z   t          z  t          d          t          t          dz   t          z  t          d          k    sJ t          dt          z   t          z  t          dd          t          t          dz   t          z  t          dd          k    sJ t          dt          z   t          z   t          z  t          dd          t          dt          z   t          z   t          z  t          dd          k    sJ t          t          t          z  t          t                    z  t          d          t           t          t                    z  k    sJ t          t          t          t          z             t          z  t          d          t          t          t                              t          z  k    sJ t          t          dt          z  dz             t          t                    dk    sJ t          t          j        t          t                     t          j        u sJ t          t          d          t          z  t          t          j                  t          j        u sJ t          dt          dz
  z  t          dd          t          u sJ t          dt          dz
  z  t          dd          t           u sJ t          ddt          z
  dz  z  t          dd          t           u sJ t          ddt          z
  dz  z  t          dd          t          u sJ t          dt          t                    z  t          t          d          t           u sJ t          dt          t                    z  t          t          d          t          u sJ t          dt          t                    z  t          t          dz  d          t           u sJ t          dt          t                    z  t          t          dz  d          t          u sJ t          dt!          t          dz            z  t          dt          z  t#          dd          z  d          t          u sJ t          dt!          t          dz            z  t          dt          z  t#          dd          z  d          t           u sJ t          dt%          t                    dz  z  t          t          t#          dd          z  d          t           u sJ t          dt%          t                    dz  z  t          t          t#          dd          z  d          t          u sJ t          t!          t                    t          t                    t'          t          j        t          j                  k    sJ t          t%          t                    t          t                    t'          t          j        t          j                  k    sJ t          t-          t                    t          t                    t'          t          j        t          j                  k    sJ t          t/          t                    t          t                    t'          t          j        t          j                  k    sJ t          t          t                    t          z  t          dd	          dk    sJ t          t          dz  t          dd	          dk    sJ t          dt          dz  z  t          dd	          t          u sJ t          dt          z  t          dd	          t0          u sJ t          ddt          z  z   t          d          t          u sJ t          ddt          z  z   t          dd          t           u sJ t          t          d
z  t          dd          t          u sJ t          t          dz  t          dd          t           u sJ t          dt          t                    z  t          dd          t           t2          z  k    sJ t          t          dz  t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t           z  t          dd          t           ddt          z
  z  z  k    sJ t          dt          t                    z   t          z  t          d          t          t          t                    dz   t          z  t          d          k    sJ t          dt5          t                    z  t          dd          t          k    sJ t          dt5          t                    z  t          dd          t           k    sJ t          dt7          t                    z  t          dd          t          k    sJ t          dt7          t                    z  t          dd          t           k    sJ t          t          dt          z            dt          t                    z  z   t          dd          t          k    sJ t          t          dt          z            dt          z  z   t          dd          t          k    sJ d S )N   r   +dir   -      +-)rI   rU   r   r   r   r*   rH   rV   r   r2   rC   r   NaNrP   r6   r   r7   r   r3   rM   NegativeInfinityInfinityr5   r4   r   r   r0   r$        Z/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_limits.pytest_basic1rp   )   sk
   Ar??b    Ass""""!Qs""""Aq2#"$$$$!Q$22#%%%%3q661aS)))Q....1a!!!!QB2%%%%#a&&!R  RC''''Q1b!!R''''1sA2ww2&&!++++QqS!R  B&&&&QT1b!!bS((((!a%1tAww;'A..!3333!a%"a##ua!eb[!Q'?'?????!a%"a,,,q1urk1aS0Q0Q0QQQQQ!a%!)b!QC000E1q519r/1aUX4Y4Y4YYYYY1SVVQ""rc$q''k1111QUAq!$$SVVR7777qsQwB''1,,,,B315((((q!Q&&!%////AEAqc***b0000AEAqc***rc1111AEA:q!---"4444AEA:q!---33333q661bc***rc11113q661bc***b00003q661bd,,,33333q661bd,,,22223q!t99a!B$!Q!7SAAARGGGG3q!t99a!B$!Q!7SAAAbSHHHH3q6619a"Xa^^"3#>>>2#EEEE3q6619a"Xa^^"3#>>>"DDDDQB;q/A1:#N#NNNNNQB;q/A1:#N#NNNNNQB;q/A1:#N#NNNNNQB;q/A1:#N#NNNNN Q1aT***a////Aq!&&&!++++1a4A4(((B.... 1a%%%,,,, QqS!Q2%%%% QqS!QC(((RC////R!QC(((B....R!QC(((RC////477Aqc***sAg5555Aq!%%%****a!QC(((A----RCA3'''B3a"f~+=====!c!ff*r!1a((E3q66A:2BAq,I,IIIII 477Aq,,,2222477Aq,,,3333477Aq,,,2222477Aq,,,3333QqSAc!ffH$a#666"<<<<QqSAaCAS111R777777rn   c                     t          t          t          z  t          dd          dk    sJ t          t          t                    dz
  t          z  t          d          dk    sJ t          ddt          z  z   t          t                    dk    sJ t          t          dt          z             t          t                    dk    sJ t          t          t          t                     z   t          t                    t          u sJ t          t          t          t          dz             z   t          t                    t          u sJ t          t          t          t          t                               z   t          t                    t          u sJ t          ddt          z  z   t          t                     z
  t          t                    dk    sJ d S )Nr   r_   r`   rb   ri   r^      rI   rU   r   r   rm   rn   ro   test_basic2rt   p   s_   Aq!%%%****#a&&1*aA&&!++++QqS!R  A%%%%#ac((Ar""b((((S!WWa$$****S!Q$ZZB''2----S#a&&\\!1b))R////acCGG#Q++r111111rn   c                      t          dt          z  t          dd          t          u sJ t          dt          z  t          dd          t           u sJ d S )Nrb   r   r_   r`   rc   rI   rU   r   rm   rn   ro   test_basic3rw   {   sV    1a$$$****1a$$$++++++rn   c                     t          dt          z  t          t          z  z   t          d          dk    sJ t          dt          z  t          t          z  z   t          d          dt          z   k    sJ t          dt          dz  z  t          t          dz  z  z   t          d          dt          dz  z
  k    sJ t          t          t          dz             t          t                    z
  t          t                    dk    sJ t          dt          dz  dz   z  t          dt          f          dt          z  t          d          z  d	z  k    sJ d S )
Nr^   r   rb      rh   rg   i   rd   	   )rI   rU   rV   r*   r   rG   r   rm   rn   ro   test_basic4r{      s	   1qsAq!!Q&&&&1qsAq!!QU****1a4!AG)#Q++sQqSy8888a!etAww&2..!3333Q1q\Aq":..!B$tAww,q.@@@@@@rn   c            	         t          dd          \  } }}t          | |z            t          |           t          |          z
  z
  }|                    | t                    dk    sJ ||z                      | t                    dk    sJ t          dd          \  }}|dz  |dz
  |dz   z  t          |dz             z  |dz  dz   dz  z  d|dz  dz   |dz   z  z  z   d|z  t	          ||z            z  |dz  dz  d	z
  t          |dz  |dz  z             z  z   |dz  dz   dz  z  z
  z  }t          ||t                    t
          |d
z  z  |dz  dz   dz  z  k    sJ d S )Nza b cTr\   r   ztau xr^   rb   rg         ?rd   )r   r   rI   r   r1   r   )abcAtaurU   exprs          ro   test_logr      s   g---GAq!AaCCFFSVVO$A771b>>QE==B1$$$$Wt,,,FC6C!GcAg&s1q5zz136A:/AAQIa%H E VD3KK/36!8c>3sAvdH D D 3 1fqj1_%% &D q"CFCFQJ?!:::::::rn   c                      t          t          t          dz
  d          dz   t          dz   z  t          dd          t          dd          k    sJ d S )N   rd   r^   rg   r_   rb      )rI   r)   rU   r   rm   rn   ro   test_piecewiser      sK    )AE1%%)AE2Ar3??8Ar??RRRRRRrn   c                  <   dt          t                    z  t          dt          z  dz
  t          t          dddt          z  dz
  dz  z  z
                      z  dt          z  dz
  dk    fddt          z  z
  t          t          dddt          z  dz
  dz  z  z
                      z  df          z  } t          t          dz  dz  t          dk    ft          dz  dz
  df          }t          t          dz
  d	z  t          d
k     ft          dz
  d	z  t          dk    ft          t          t          dz
                      df          }t	          | t          d          dk    sJ t	          |t          d          dk    sJ t	          |t          d
          dk    sJ d S )Nr^      rb   r   Tr~   g      ?rz   re   ri   rd   )r*   rU   r+   r   rI   )func1func2func3s      ro   test_piecewise2r      s   d1ggIi!A#'3tA1Q37Q,4F/G/G+H+H!H!A#PQ'K !1Wc$q1acAg\>'9":":;;;TBD D DEq!tAvqCx(1Q3;*=>>EA{AF+q1uk1q5-ADQQRUDTDTVZC[\\E1""""1""""2!######rn   c                       G d dt                     } t           | t                    t          t                    t	           | t                    t          t                    k    sJ d S )Nc                   $    e Zd Zed             ZdS )test_basic5.<locals>.myc                 :    |t           j        u rt           j        S d S N)r   rl   rj   )clsargs     ro   evalztest_basic5.<locals>.my.eval   s    aj  u ! rn   N)__name__
__module____qualname__classmethodr   rm   rn   ro   myr      s-        		 	 
	 	 	rn   r   )r   rI   rU   r   rH   )r   s    ro   test_basic5r      sm        X   
 A2%1q""5"5555555rn   c                      t          t          t          z  t          t          z  z   t          d          t          t          z  dt          z  z   k    sJ d S Nr^   )rI   rU   rV   rW   rm   rn   ro   test_issue_3885r      s=    1qsAq!!QqS1Q3Y......rn   c                     t          t          t                    t          z  t          d          dk    sJ t          t          t                    t          z  t          d                                          dk    sJ t          t          t          dd          j        t          t          dt          d          fk    sJ d S )Nr   rb   rf   r`   )rH   r6   rU   doitargsr   rm   rn   ro   
test_Limitr      s    Q1a  A%%%%Q1a  %%''1,,,,Aqd###(Q1fTll,CCCCCCCrn   c                     t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          d	d          d	k    sJ t          t          t                    t          d	d          d
k    sJ t          t          t          dt          z            z  dz  t          dd          t          dd          k    sJ t          t          t          dz             t          t                    z
  t          t                    t          t          j         t          d          dz            k    sJ t          t          t          t                              t          t                    dk    sJ t          t          t          t                              t          t                     dk    sJ t          t          t          t                              t          t                    dk    sJ t          t          t          t                              t          t                     dk    sJ d S )Nrg   r_   rc   rh   ri   r   rb   r^         rd   r~   )
rI   r&   rU   r   r   rM   r   Halfr1   r%   rm   rn   ro   
test_floorr      s   q1b#&&",,,,q1b#&&",,,,q1b#&&",,,,q1b#&&",,,,q1a%%****q1a%%++++q1a%%****q1a%%****q1a%%****q1a%%****q1c3''3....q1c3''3.... 51::aAs++x1~~====q3w%((*Ar22k16'1Q44PQ66R6RRRRR tAwwB''1,,,,tAwwRC((B....a!!1b))Q....a!!1rc**b000000rn   c                     t          t          t          t                              t          dd          dk    sJ t          t          t          t                              t          dd          dk    sJ t          t          t	          t                              t          dd          dk    sJ t          t          t	          t                              t          dd          dk    sJ t          t          dt          t                    z             t          dd          dk    sJ t          t          dt          t                    z             t          dd          dk    sJ t          t          dt	          t                    z             t          dd          dk    sJ t          t          dt	          t                    z             t          dd          dk    sJ d S )Nr   r_   rc   ri   re   r   )rI   r&   r6   rU   r2   rm   rn   ro   &test_floor_requires_robust_assumptionsr      sx   s1vv1c**a////s1vv1c**b0000s1vv1c**a////s1vv1c**a////q3q66z""Aq#..!3333q3q66z""Aq#..!3333q3q66z""Aq#..!3333q3q66z""Aq#..!333333rn   c                     t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          dd          dk    sJ t          t          t                    t          d	d          d
k    sJ t          t          t                    t          d	d          d	k    sJ t          t          t          dt          z            z  dz  t          dd          t          dd          k    sJ t          t          t          dz             t          t                    z
  t          t                    t          t          j         t          d          dz            k    sJ d S )Nrg   r_   ri   rc   r   rb   r^   rd   r      r~   )rI   r%   rU   r   r   rM   r   r   rm   rn   ro   test_ceilingr      sN   QC((B....QC((B....QC((A----QC((B....Q3''1,,,,Q3''1,,,,Q3''1,,,,Q3''1,,,,Q3''1,,,,Q3''1,,,,QS))S0000QS))S0000 71Q3<<!1a--!Q????S!!GAJJ.266+qvgqQRttTUv:V:VVVVVVVrn   c                     t          t          t          t                              t          dd          dk    sJ t          t          t          t                              t          dd          dk    sJ t          t          t	          t                              t          dd          dk    sJ t          t          t	          t                              t          dd          dk    sJ t          t          dt          t                    z             t          dd          dk    sJ t          t          dt          t                    z             t          dd          dk    sJ t          t          dt	          t                    z             t          dd          dk    sJ t          t          dt	          t                    z             t          dd          dk    sJ d S )Nr   r_   rb   rc   re   r   )rI   r%   r6   rU   r2   rm   rn   ro   (test_ceiling_requires_robust_assumptionsr      sx   Q!Q,,1111Q!Q,,1111Q!Q,,1111Q!Q,,1111SVV$$aC00A5555SVV$$aC00A5555SVV$$aC00A5555SVV$$aC00A555555rn   c                  B   t          t          t                    t          t                    t	          dd          k    sJ t          t          t                    dt          z  z  t          t                    t	          dd          k    sJ t          t          t                    dt          z  z  t          t                     t	          dt                    k    sJ t          t          t                    t          z  t          t                    t	          dt                    k    sJ t          t          t          t                              t          dd          dk    sJ t          t          t          t                              t          dd          dk    sJ t          t          t          t                              t          dd          dk    sJ t          t          t          dz            t          dd          dk    sJ t          t          d            t          t          dt          z  dz             t          dd          dk    sJ t          t          dt          z  dz             t          dd          dk    sJ t          t          t          t          j
        z             t          dd          t          d          dz  k    sJ t          t          dt          z            t          d          t	          dd          k    sJ d S )	Nr   rb   r_   rc   rf   r^   c                  T    t          t          t                    t          dd          S Nr   rf   )rI   r'   rU   rm   rn   ro   <lambda>ztest_frac.<locals>.<lambda>  s    uT!WWaD99 rn   rg   )rI   r'   rU   r   rM   r6   r2   rR   
ValueErrorr   r   rm   rn   ro   	test_fracr      sR   a!R  K1$5$55555a1Q3B'';q!+<+<<<<<a1Q3RC((K2,>,>>>>>a!Q##{1b'9'99999c!ffq!S))Q....c!ffq!S))Q....c!ffq!T**a////adQ4((A----
:99:::bdQhAs++q0000bdQhAs++q0000a!&j!!1a..!A$$q&8888acAq!![A%6%6666666rn   c                  *   t          t          t          t                    t          z            t          dd          dk    sJ t          t          t          t                    t          z            t          dd          dk    sJ t          t          t	          t                     t          z            t          dd          dk    sJ t          t          t	          t                     t          z            t          dd          dk    sJ d S )Nr   r_   rc   rg   )rI   r&   r6   rU   r7   rm   rn   ro   test_issue_14355r     s    s1vvax!Q,,1111s1vvax!Q,,1111Awqy!!1a--3333Awqy!!1a--333333rn   c                  >   t          dd          } t          t          |           t          d| z            z  | d          dk    sJ t          t          |           t	          | dz             z   t	          |           z
  | t
                    t          dz  k    sJ d S )NrU   Trealrb   r   r^   )r   rI   r1   r6   r*   r   r   rU   s    ro   	test_atanr     s    sAaQqS!1a((A----a4A;;&a0!R88BqD@@@@@@rn   c            
         t          t          t                    t          d          dk    sJ t          t          t          t                              t          d          dk    sJ t          t          t	          t                              t          d          dk    sJ t          t          t          t          dz                       t          d          t          d          k    sJ t          t          t          t          z             t          t          t          z
            z
  dt          z  z  t          d          t          t                    k    sJ t          t          t          t                    t          dz  z            t          t                    dk    sJ t          t          t          t          t                    t          dz  z            t          t          t          dz             t          dz   dz  z            z  dz
  z  t          t                    dk    sJ t          t          t          t          dz
            dz  dz
            t          dd          t          k    sJ t          t          t          t                              t          d          t          k    sJ t          t          t          t          t                                        t          d          t          k    sJ t          dd          } t          t          t          |           dz             t          |           z  | t                    dk    sJ t          | t          d| z  t          z             t          t          d| z  z
            z
  z  dz  | d          dk    sJ t          t	          |           t          |           z  | t          d	          d
k    sJ d S )Nr   rb   r^   rd   r_   rW   Tr}   rc   ri   )rI   absrU   r6   r2   r   rV   r   r   r   r   r   rW   s    ro   test_set_signsr     s   QA!####SVVa##q((((SVVa##q((((SQZZ!Q''3q661111 #a!e**s1q5zz)AaC0!Q77477BBBB SVVAqD[!!1b))Q....CAq!t$$SQUQUQJ)>%?%??!CDaLLPQQQQQ SQZZ]Q&''As33r9999 SVVa##r))))SQ[[!!1a((B.... 	sT"""ASVVaZQ'B//14444 C!aLL3q1Q3w<</02Aq99Q>>>> QQB,,222222rn   c                     t          dd          } t          t          d| z            t          |           z   | dd          t	          dd          k    sJ t          t          dt          t          |                     t          t          d| z                      z  z             | d          t          d          k    sJ d S )	NrU   Tr   rb   r   r_   ri   r^   )r   rO   r6   r1   rM   rI   r   r*   r   s    ro   test_heuristicr   8  s    sAc!A#hha(!Q44B8J8JJJJJQd1ggtC!HH~~55661==QGGGGGGrn   c                      t          dd          } d| z  t          |  t          z            z  }t          |t          t                    dk    sJ |                    t          t                    dk    sJ d S )NrW   Tr}   ri   r   )r   r   rU   rI   r   )rW   fs     ro   test_issue_3871r   >  sk    sT"""A
1S!AYYAAr??a771b>>Qrn   c                     t          d          } t          dd          }t          d|| z  z   | z  | t                    t          |          k    sJ t          d|d| z  z  z   | z  | t                    t          |dz            k    sJ t          d|d| z  dz   z  z   | z  | t                    t          |dz            k    sJ t          |dz
  |dz   z  |z  |t                    t          d          k    sJ t          ddd|z  z   |z  z   |t                    dt          j        z   k    sJ t          dd|z  z   |z  d|z  |z  z  |t                    t          t	          d	                    k    sJ d S )
NrY   rU   Tr   rb   r^   rg   r   z1/3)r   rI   r   r   r   Exp1rY   rU   s     ro   test_exponentialr   E  sr   sAsA!ac'Aq"%%Q////!a1g+!1b))S1XX5555!a1qk/A%q"--QqS99991q51q5/A%q"--R8888a!A#g\!1b))QZ7777!ac'AqsQh&2..#ahh--??????rn   c                      t          d          } t          dt          | t          |           z   z  z   | z  | t                    t          t                    k    sJ d S )NrY   rb   )r   rI   rU   r6   r   r   )rY   s    ro   test_exponential2r   P  sN    sA!aSVVn$q(!R00CFF::::::rn   c                      t          dt          z  t                    } t          | t          t                    }|                                t          u sJ d S r   rF   rU   rH   r   r   r   ls     ro   	test_doitr   U  s=    QAaBA6688r>>>>>>rn   c            
         t          t          t                    t          t          dz             z
  t          t                    t	          dd          k    sJ t          t          t                    t          t          dz             z
  dz   t          t                    t	          dd          k    sJ t          t          t                    t          t                    t          t                    z  z
  t          t                    t	          dd          k    sJ dt          d          z   dz  } dt          d          z   dz  }t          t	          | |          ddt          d          z   z  d          }t          t          t          t          t                    
                    t                    t          d	t          f                                          
                    t                              t          t                    |k    sJ t          t	          dt          d          dz  z   t          d          dz  dz             ddt          d          z
  z            }t          t          t          t          t                    
                    t                    t          d	t          f                                          
                    t                              t          t                    |k    sJ t          t          t                    dz   dz  t          z  t          t                    t	          d	t                    k    sJ dt           z  t          t                    dz   t          z  z  }t          |t          t                    t	          d	t                    k    sJ d S )
Nrb   rg   r^   ri   rd   rh   F)evaluater   )rI   r6   rX   r   rM   r2   rN   rK   r   rY   rewriter   r   rU   )lohit1t2es        ro   test_series_AccumBoundsr   [  s   Q#a!e**$a,,B0B0BBBBBQ#a!e**$q(!R00KA4F4FFFFF Q#a&&Q-'B//;r13E3EEEEE s1vv+qB
c!ff*aB	[R  !R#a&&[/E	B	B	BB#c!ffnnS11Aq!9==BBDDLLSQQRRTUWYZZ^`````	[c!ffQhAq155q!c!ff*~	F	FB#c!ffnnS11Aq!9==BBDDLLSQQRRTUWYZZ^`````3q66A:q.1$a,,Ar0B0BBBBB 	
QBQ!aAAr??k!R00000000rn   c                     t          t          dt                    t          t                    dk    sJ t          t          dt                    t          t                     dk    sJ t          t          dt                    t          t          t          z            t          t          z  k    sJ t          t          dt                    t          t           t          z            t           t          z  k    sJ t          t          dt                    t          t                    dk    sJ t          t          dt                    t          t                     dk    sJ t          t          dt                    t          t          t          z            t           k    sJ t          t          dt                    t          t           t          z            t           k    sJ t          t          dt                    t          t                    t          k    sJ t          t          dt                    t          t                     t           k    sJ t          t          dt                    t          t          t          z            dk    sJ t          t          dt                    t          t           t          z            dk    sJ t          t          dt                    t          t                    dk    sJ t          t          dt                    t          t                     t           t          z  k    sJ t          t          dt                    t          t          t          z            dk    sJ t          t          dt                    t          t           t          z            dk    sJ t          t          dt                    t          t                    dk    sJ d S Nrb   r   )rI   r:   rU   r   r   r9   r8   r;   rm   rn   ro   !test_bessel_functions_at_infinityr   r  s    A2&&!++++AB3''1,,,,A1R4((BqD0000AA2b5))bSU2222A2&&!++++AB3''1,,,,A1R4((RC////AA2b5))bS0000A2&&",,,,AB3''B3....A1R4((A----AA2b5))Q....A2&&!++++AB3''B3q50000A1R4((A----AA2b5))Q.... A2&&!++++++rn   c                      t          dt          z  t                    } t          | t          t                    }|                    d          |k    sJ d S )Nr^   Fdeepr   r   s     ro   
test_doit2r     sI    QAaBA66u6""""""rn   c                      t          t          t          t                    z  t          t                    dz
  z  t          t                     dk    sJ d S r   rs   rm   rn   ro   test_issue_2929r     s@    !c!ff*s1vvz*As33q888888rn   c                  *   t          dt          t                    z
  t          dz  z  t          t          j                  ddt          t          j                  z  z
  k    sJ t          t          t          t          dz             dz             t          d          t          dt          d          z             k    sJ t          t          t          t          dz             dz             t          d          dt          d          z   k    sJ d S )Nrb   r^   r   r   )rI   r2   rU   r   r   r6   r   rm   rn   ro   test_issue_3792r     s    !c!ff*ad"Aqv..!aAFm2CCCCCSQZZ!^$$a++s1s1vv:>>>>SQZZ!^$$a++q3q66z999999rn   c                  <   t          dt          dz   z  t          d          t          dd          k    sJ t          dt          t          z   z  t          d          t          j        dt          z   z  k    sJ t          t          t                    t          dz  dz   z  t          d          t          d          dz  k    sJ t          t          t                    t          dz  t          z   z  t          d          t          d          dt          z   z  k    sJ d S )Nrb   rd   r^   re      r   )rI   rU   r   r   r   Oner   rm   rn   ro   test_issue_4090r     s    AEAq!!Xa^^3333AFQ""aeQVn4444QA"Aq))SVVAX5555QA#Q**c!ffa"fo======rn   c                      t          t          t                    t          dd          t          u sJ t          t          t                    t          t          dz  d          dk    sJ d S )Nr   r_   r`   r^   )rI   r3   rU   r   r   rm   rn   ro   test_issue_4547r     s\    QA3'''2----QBqDc***a//////rn   c                     t          t          dz  t          t                    t          dz  cxk    r	t          u sn J t          t          dz  t          d          dk    sJ t          t          dz  t          d          dk    sJ t          t          dz  t          t                    dk    sJ t          t          dz  t          d          t          j        k    sJ d S )Nr~      r   r   g      )rI   rU   r   r   r   rm   rn   ro   test_issue_5164r     s    CB2s70000b000000CB1$$$$CA!####TAr""a''''TAq!!QV++++++rn   c                  x    ddt           z  z   dt           z  z  } t          | t           d          t          k    sJ d S )N      ?r   )rU   rI   r
   )funcs    ro   test_issue_5383r     s<    cAg1-Dq!!!!!!!rn   c                     t           t          d          dz  z   t          t                     z  t           z
  t          dt          z            dz  z   t          t	          t                               z
  t          d          dt           z  z  z   t           dz  z  } t          | t           t                    t          d          dz  k    sJ d S )Nrb   r^   r   rd   ih  )rU   r   r   r   r   rI   r   r   s    ro   test_issue_14793r     s    1aZ3q66!A%AbD		!3IaLLaDD"Q$K()*A.Dq"1c))))))rn   c                  N   t          t          t          t           gddgddt          j        t          dd          gddg                    } g t          t          t           t          t           t          z  t          t           dt          dd          z  z  t          ddddddddt          t          t          t           t          t           t          z  t          t           dt          dd          z  z  ddddddddR }t          |           t          |          k    sJ t          t          | |                    D ]G\  }\  }}|\  }}}}|||z  z  }		 t          |	t          d|          |k    sJ 7# t          $ r 	 J w xY wd S )	Nri   rb   r^   rd   rc   r_   r   r`   )listr   rU   r   r   r   r   r   len	enumerateziprI   AssertionErrorprint)
testsresultsir   resrV   sr   deqs
             ro   test_issue_5183r    sR   !aRaQA7s% % & &E'r '2 's 'B 'A 'r 'B3Xa^^/C+C 'R '''''''!"'$%''''3' "'%'CE'+-'02sB!Q3G/G' ' ' ' ' '  ' "#' %&' 'G u::W%%%%#Cw$7$788 
 
;D#
1a1X	Qq)))S00000 	 	 	 	
 
s   5FF"c                     t          t          t                    t          z  t          t                    dk    sJ t          t	          t                    t          t                    t
          dz  k    sJ t          t          t                    t          t                    t          u sJ t          t          t                    t          z  t          t                    dk    sJ t          t          t                    t          t          j	                  t          t
                    k    sJ t          dd          } t          | t          d| z            z  | d          dk    sJ d S )Nr   r^   rTr   rb   )rI   r6   rU   r   r1   r   rC   r2   r   r   r*   r   r  s    ro   test_issue_5184r    s   Q1b!!Q&&&&a!R  BqD((((q1b!!R''''Q1b!!Q&&&&q1af%%b1111sA3qs88Q""a''''''rn   c                  ~    t          dt          z   dt          z  z  t          j        z
  t          d          dk    sJ d S r   )rI   rV   r   r   rm   rn   ro   test_issue_5229r
    s8    !a%1Q3!&(!Q//1444444rn   c                  v   t          t          t          t          gt           dz  dt          dz  t          t          t          dd          z  gddg                    } ddt           t          ddt           t          ddt          t           ddt          t           ddt          t           f}t          |           t          |          k    sJ t          t          | |                    D ]N\  }\  }}|\  }}} |t                    }	 t          |t          ||          |k    sJ ># t          $ r 	 J w xY wd S )Nr^   r   rd   rc   r_   r`   )r   r   r3   r7   r   r   r   r   r   r   rU   rI   r   r   )	r   r   r   r   r   r   r   r  r  s	            ro   test_issue_4546r    sE   #s#a%BqD"b!Q.?@s% % & &E !bS"aRCQB31b2#q!R"6Gu::W%%%%#Cw$7$788 
 
;D#1aQqTT	Qq)))S00000 	 	 	 	
 
s   	D((D6c                      t          dt          t          d          z  z   dt          z  z  t          d          dk    sJ t          ddt          z  z  ddt          z  z  z   t          z  t          d          dk    sJ d S )Nrb   rd   r   re   )rI   rU   r   rm   rn   ro   test_issue_3934r    ss    !aQi-1Q3'A..!3333!ac(Q1X%)1a00A555555rn   c            	         t          t          t          dd          z  dt          t          dd          z  z   z  t          t                    dk    sJ t          t          dz  dt          dz  z   z  t          t                    dk    sJ d S )NM   rd   rb   gfffffFY@)rI   rU   r   r   rm   rn   ro   test_calculate_seriesr    sy     HROO#QHROO);%;<aDDIIIIE1q%x<(!R00A555555rn   c                     t          t          dz  dt          dz  z   z  t          t                    dk    sJ t          t          dz  dt          dz  z   z  t          t                    dk    sJ t          t          dz  dt          dz  z   z  t          t                    dk    sJ t          t          dz  t          dz   dz  t          t                     z   z  t          t                    dk    sJ d S )Nr   rb   d   i]    rI   rU   r   r   rm   rn   ro   test_issue_5955r  	  s    !R%!ae)$a,,1111!S&1q#v:&2..!3333!T'A4K(!R00A5555!T'AED=3r7723a<<AAAAAArn   c                      t          t          dt          t                    z            t          t	          t                              z  t          d          dk    sJ d S r   )rI   r   r6   rU   r3   rm   rn   ro   test_newissuer    sF    Qs1vvXs3q66{{*Aq11Q666666rn   c                     t          t          t          z
  t          t                    t          t          t          z
  t          t                    k    sJ t          dt          t	          t                    z   z  t          z
  t          d          t          dt          t	          t                    z   z  t          z
  t          d          k    sJ t          t          t          z  t          t                    t          t          t          z  t          t                    k    sJ t          t          t          z
  dt          z  z   t          t                    t          t          t          z
  dt          z  z   t          t                    k    sJ d S r   )rI   rU   r   rH   r6   rm   rn   ro   test_extended_real_liner    s    RB5RB#7#77777AAJ"$a++uQCFF
^b5H!Q/O/OOOOOAq"r!tQ!3!33333R!A#q"%%q2v!|Q)C)CCCCCCCrn   c                      t          dd          } t          |           t          z  t          d|           k    sJ t          t          | dz  dz
  z  | t                    t          u sJ d S )NrU   Tr}   rb   r^   r   )r   rP   r   rI   r   s    ro   test_order_oor    sf    sT"""A88B;%1++%%%%QTAX2&&",,,,,,rn   c                  ^    t          t          d            t          t          d            d S )Nc                  l    t          t          t          t          z            t          t                    S r   rI   r   rU   rV   r   rm   rn   ro   r   z!test_issue_5436.<locals>.<lambda>#  s    c!A#hh2(>(> rn   c                  n    t          t          t           t          z            t          t                    S r   r  rm   rn   ro   r   z!test_issue_5436.<locals>.<lambda>$  s    c1"Q$iiB(?(? rn   rR   NotImplementedErrorrm   rn   ro   test_issue_5436r#  "  s2    
 > >???
 ? ?@@@@@rn   c                  ^    t          t          d            t          t          d            d S )Nc                  <    t          t          t          dd          S )Nr   r`   rH   rU   rm   rn   ro   r   z test_Limit_dir.<locals>.<lambda>(  s    eAq!333 rn   c                  <    t          t          t          dd          S )Nr   0r`   r&  rm   rn   ro   r   z test_Limit_dir.<locals>.<lambda>)  s    uQ1#666 rn   )rR   	TypeErrorr   rm   rn   ro   test_Limit_dirr*  '  s0    
933444
:6677777rn   c                      t          t          dz   dz  t          dz   dz  dz   z  t          t                    dk    sJ t          t          dz   dz  t          dz   dz  dz   z  t          t                     dk    sJ d S )Nrb   r  rv   rm   rn   ro   test_polynomialr,  ,  sx    !a%$Q 12Ar::a????!a%$Q 12As;;q@@@@@@rn   c                     t          dt          z  dt          t          z   z  t          t          t          z   z  t          z  z   t          z  z
  t          t                    t          dz
  t          t          z  z  k    sJ t          dt          z  dt          t          z   z  t          t          t          z   z  t          z  z   t          z  z
  t          t                     t          dz
  t          t          z  z  k    sJ d S Nrb   )rI   rV   rU   rW   r   rm   rn   ro   test_rationalr/  1  s    11q5	Aq1uIaK/22Ar::q1uqsmKKKK11q5	Aq1uIaK/22As;;A!}LLLLLLrn   c                      t          t          t                    t          z  t          dt          z            t          z  z
  t          d          t
          t          t          t          z
            z  k    sJ d S Nr^   r   )rI   r   rU   rW   rV   r   r   rm   rn   ro   test_issue_5740r2  6  sP    QC!HHQJ&1--DQKK??????rn   c                      t          ddd          } | dz   t          | dz   z  z  t          | dz   z  dz
  z  t          t          dz
  z  z
  }t          |t          d                                          | dz  k    sJ d S )NrY   TrZ   rb   r^   )r   rU   rI   cancel)rY   r  s     ro   test_issue_6366r5  :  s{    sD4000A	
QAE
AAJN+aQi7AAq>>  ""ac))))))rn   c                     t          t                    } t          | t          t                    t          u sJ t          t          | z  t          t                    dk    sJ t          | t	          dt
          z  t          z            t          t          z  t          z  z  z  t          t                    dk    sJ t          | t          t                     t          t                     k    sJ d S )Nr   r^   rb   )r   rU   rI   r   r*   r   r
   rC   r   s    ro   test_factorialr8  @  s    !AAr??b    1a!!!! D2aLL!A#)*Ar22a7777AsubSzz))))))rn   c                     dt           dz  z  dz  t           t          dd          z  z
  t          dt           dz  z  dz  t          j        z
  z  dt           dz  z  dz  z   dt           dz  z  dz  z
  t          dd          z   dt          dz   z  z  z   } t          | t          t                    dt           dz  z  dz  dt           dz  z  dz  z   dt           z  dz  z
  t          dd          z
  k    sJ d S )	Nre   rd   r   r^   #   ry      rb   )rU   r   rV   r   r   rI   r   r   s    ro   test_issue_6560r=  J  s    	
1a4Ahq!nn$	$1QT6!8af+<(=1WQY)')+AqD)35=a^^)DFGQi(Q 
QAAr??a1fQh1a41AaCE9HQNNJJJJJJJrn   c                     t          d          t          dd          } t          d          }t          dd          }t          dd          }d	z  | z
  d
z   z  | | z
  d
z   z  z   z  |z  | d
z
  | z
  d	z   z  | | z
  d
z   z  z   z  |z  z  z   z
  |z  z
  z                      ||d
z             t          t          fd           t	                              ||          t
                    d
k    sJ t	                              ||          t
                                                    d	|d
z   z  | z   d
z
  | d
z   |d
z   z  z  k    sJ d S )NrY   r  Tr}   r   pmnegativer^   rb   c                  0    t           t                    S r   )rI   r   )r   rY   s   ro   r   z!test_issue_5172.<locals>.<lambda>Y  s    dAr(:(: rn   )r   subsrR   r"  rI   r   rK   )r  r   r?  r@  r   rY   s       @@ro   test_issue_5172rE  O  s   sAsT"""AsAsT"""AsT"""AqS!a%!)_a!QUQY-/014UQA	]A1q519$56::;=>?ABAKD99QAD
 : : : : :;;;1a!R((A----1a!R((1133	
QUa!	a!eq1u--. . . . . .rn   c                      t          d          } t          t          t          t          | z   z            t          t                    dk    sJ d S )Nr   rb   )r   rI   r*   rU   r   r   s    ro   test_issue_7088rH  _  s>    sAaQi!R((A------rn   c                     t          t          t          t          z  dz             t          d          t          t          d          z
  k    sJ t          t          t          t          z  dz             t          dd          t          d          k    sJ t          t          t          t          z  dz
            t          d          t          d           k    sJ t          t          t          t          z  dz
            t          dd          t           t          d          z   k    sJ t          t          t          t          z  dz             t          d          t          d           k    sJ t          t          t          t          z  dz             t          dd          t          d          k    sJ t          t          t          t          z  dz
            t          d          t          d          k    sJ t          t          t          t          z  dz
            t          dd          dt          z  t          d          z
  k    sJ t          t          t          dt          z  z             t          d          t          t          d          z  k    sJ t          t          t          dt          z  z             t          dd          t           t          t          d          z  z   k    sJ t          t          t          dt          z  z
            t          d          t          t          t          d          z  z
  k    sJ t          t          t          dt          z  z
            t          dd          t           t          d          z  k    sJ t          t          dt          z            t          d          t          dz  k    sJ t          t          dt          z            t          dd          t           dz  k    sJ t          t          t                    t          t                    t          dz  k    sJ t          t          t                    t          t                     t           dz  k    sJ t          t          t          t          d          dz  t          z  z             t          d          t          t          t          t          d          dz            z  z
  k    sJ t          t          t          t          d          dz  t          z  z             t          dd          t           t          t          d          dz            z  k    sJ t          t          t          t          d          dz  t          z  z
            t          d          t          t          t          d          dz            z  k    sJ t          t          t          t          d          dz  t          z  z
            t          dd          t           t          t          t          d          dz            z  z   k    sJ t          t          t                    t          d          t          dz  k    sJ t          t          t                    t          dd          t           dz  k    sJ t          t          t          t          z  t          d          dz  z             t          d          t          t          d          dz            k    sJ t          t          t          t          z  t          d          dz  z             t          dd          t          t          d          dz             k    sJ t          t          t          t          z  t          d          dz  z
            t          d          dt          z  t          t          d           dz            z
  k    sJ t          t          t          t          z  t          d          dz  z
            t          dd          t          t          d           dz            k    sJ t          t          t          t          z  t          d          dz  z             t          d          t          t          d          dz            k    sJ t          t          t          t          z  t          d          dz  z             t          dd          t          t          t          d          dz            z
  k    sJ t          t          t          t          z  t          d          dz  z
            t          d          t           t          t          d          dz            z   k    sJ t          t          t          t          z  t          d          dz  z
            t          dd          t          t          d          dz             k    sJ t          t          t          t          z  dz
            t          d          t          t          z  k    sJ t          t          t          t          z  dz
            t          dd          t           t          z  k    sJ t          t          t           t          z  dz
            t          d          t           t          z  k    sJ t          t          t           t          z  dz
            t          dd          t          t          z  k    sJ t          t          t          t          z  dz
            t          d          t          k    sJ t          t          t          t          z  dz
            t          dd          t           k    sJ t          t          t           t          z  dz
            t          d          t           k    sJ t          t          t           t          z  dz
            t          dd          t          k    sJ t          t!          t          t          z  dz
            t          d          dt          d          dz  z  k    sJ t          t!          t          t          z  dz
            t          dd          dt          d          dz  z   k    sJ t          t!          t           t          z  dz
            t          d          dt          d          dz  z   k    sJ t          t!          t           t          z  dz
            t          dd          dt          d          dz  z  k    sJ d S )Nr^   r   rc   rg   rb   ri   rd   )rI   r0   r   rU   r   r,   r1   r   r   r-   r   r    r/   r.   r   r*   r(   rm   rn   ro   test_branch_cutsrJ  d  s	   acAg1%%d1gg5555acAg1c**d1gg5555acAg1%%$q''1111acAg1c**rcDGGm;;;;acAg1%%$q''1111acAg1c**d1gg5555acAg1%%b1111acAg1c**adT"XXo====a!A#g1%%5883333a!A#g1c**rcAeAhhJ.>>>>>a!A#g1%%aaj8888a!A#g1c**qbqk9999acAq!!RT))))acAq#&&2#a%////a!R  BqD((((a!bS!!bSU****a!A$$q&(l##Q**b1U1Q446]]?.BBBBBa!A$$q&(l##Q3//A2eAaDDFmm3CCCCCa!A$$q&(l##Q**aadd1fo====a!A$$q&(l##Q3//B351a==3HHHHHa!Q2a4''''a!Q$$A----acAaDDFl##Q**d1Q446ll::::acAaDDFl##Q3//D1aLL=@@@@acAaDDFl##Q**adT1Q44%']].BBBBBacAaDDFl##Q3//41a==@@@@acAaDDFl##Q**d1Q446ll::::acAaDDFl##Q3//2QqTT!V3DDDDDacAaDDFl##Q**rcD1aLL.@@@@@acAaDDFl##Q3//D1aLL=@@@@QqS1Wq!$$",,,,QqS1Wq!S))aRU2222aRTAX1%%!B....aRTAX1c**ad2222acAg1%%****acAg1c**qb0000qbdQhA&&1",,,,qbdQhAs++q0000acAg1%%"!Q7777acAg1c**add1f~o====qbdQhA&&B!A$$q&>/9999qbdQhAs++add1f~======rn   c                  \   t          d          } t          dt          dt          z             t          |           dz  z  z
  t          dt          z
            t	          |           dz  z  z
  z  }t          |t          d          dt	          |           dz  t          j        z
  z  k    sJ d S )Nr   rb   r^   r   )r   rW   r*   r6   r2   rI   r   r   )r   r   s     ro   test_issue_6364rL    s    sA	1tAE{{3q6619$$tAE{{3q6619'<<=AAq>>QA	AF 23333333rn   c                      t          t          dt          t                     z            t          dz  z  t          d          t          dt          z            k    sJ d S r1  )rI   r   r<   rU   r   rm   rn   ro   test_issue_6682rN    sL    Qr1"vvXq!t#Q**c!J,.?.???????rn   c                     t          d          } t          | t          z  t          d          t          t	          |           z  k    sJ t          |  t          z  t          d          t           t	          |           z  k    sJ t          |  t          z  t          t                    t           t	          |           z  k    sJ t          | t          z  t          t                    t          t	          |           z  k    sJ d S )Nr   r   )r   rI   rU   r   r   rG  s    ro   test_issue_4099rP    s    sA1ar$q''z))))!Aq!DGG++++!Aq""T!WW,,,,1a477
******rn   c            	      `   t          d          } t          t          dt          t          | z             z             t          dt          t                    z             z
  | z  | d          t          t                    dt          t          t                    dz             z  z  k    sJ d S )Ndxrb   r   r^   )r   rI   r*   r   rU   )rR  s    ro   test_issue_4503rS    s    	B$q3q2v;;''$q3q66z*:*::B>AFFA$s1vvz"""#$ $ $ $ $ $rn   c                      t          ddddt                     } t          |           }t          |t          dd          dk    sJ t          |t          t                    t           k    sJ d S )Nrm   )rb   )r   r   rf   )rE   rU   rL   rI   r   )Ggs     ro   test_issue_6052rW    sf    BdQB''AAAAq$1$$$$Ar??rc!!!!!!rn   c                     t          t                    t          dt          dt          z                      z  } t          t          t	          | t          t                    z  | z  t          d          dk    sJ t          t          t	          | t          t                    z  | z  t          d                                          dk    sJ d S )Nrb   ry   r   r^   g       @)r*   rU   r8   rI   r   evalfr   s    ro   test_issue_7224rZ    s    7771T!A#YY'''D4a###D(!Q//144444a###D(!Q//55773>>>>>>rn   c                  z    t          t          t          dd          dz
  z  t          t                    dk    sJ d S )Nrb   g    eAr   )rI   rY   r   r   rm   rn   ro   test_issue_8208r\    s9    Xa%%)*Ar22a777777rn   c                      t          t          t          dd          z  dz
  t          t                    dz
  t          dd          z  z  t          d          dk    sJ d S )Nrb   r   r^   rd   r   r   )rI   rU   r   r*   rm   rn   ro   test_issue_8229r^    sT    !Xa^^#a'$q''A+A)FF2NNRSSSSSSSrn   c                      t          dd          \  } }t          t          d|| z  z
            |t                    dk    sJ d S )Nzd tTr}   rb   ri   )r   rI   r=   r   )r  ts     ro   test_issue_8433ra    sI    54(((DAqQ1Wq"%%++++++rn   c                      t          ddd          } t          dd          }t          || z  t          |           z  t          |           z  | t                    dk    sJ d S )NrX   T)r[   nonnegativelamdar}   r   )r   rI   r   r   r   )rX   rd  s     ro   test_issue_8481re    sg    sDd333A7T***ECKK')A,,62>>!CCCCCCrn   c                     t          t          t          t          dz            t          t                    t          k    sJ t          t          t          t          dz            dt           z  z  t          t                    dk    sJ d S )Nr^   rd   r   )rI   r   rY   r   rm   rn   ro   test_issue_8462rg    si    !QqS!!1b))R////!QqS!!A1"I-q"55::::::rn   c                      t          ddd          } t          d          }t          || z  |t                     t          t          d| z            z  k    sJ d S )NrY   TrZ   rU   ri   )r   rI   r   r   r   s     ro   test_issue_8634ri    sY    sD4000AsAAq2#"T2']]"2222222rn   c                     t          dd          } t          dd          }t          | t          z  | t          dz
  z  z
  | t                    dk    sJ t          | t          z  | t          dz
  z  z
  | t                    t          k    sJ t          | t          z  | t          dz
  z  z
  | t                    t          k    sJ t          | t          z  | t          |z
  d	z
  z  z
  | t                    t          k    sJ t          dd          } t          | t          z  | t          d	z
  z  z
  | t                    t          k    sJ t          | t          z  | t          d
z   z  z
  | t                    t           k    sJ d S )NrU   Tr   rX   r}   r   re   g      @rb   r^   )r   rI   rY   r   )rU   rX   s     ro   test_issue_8635_18176rk    sX   sAsT"""AAAE
"Ar**a////AAE
"Ar**b0000AAG$a,,2222AAEAI&2.."4444sT"""AAAE
"Ar**b0000AAE
"Ar**rc111111rn   c                  r    t          t          t                    t          t                    t          u sJ d S r   )rI   r   rU   r   rm   rn   ro   test_issue_8730rm    s+    a!R((B......rn   c                  
    t          dd          t          dd           t          t                    t                    z  z  d z   z  z  t                    dk    sJ t	          t
           fd           d S )	NrY   Tr[   r   r}   rb   r   c                  |    t          t                    t                    z  z   z  z  t                    S r   )rI   r   r   r   rY   s   ro   r   z!test_issue_9252.<locals>.<lambda>  s1    s1vv3q66.BQT.I1b(Q(Q rn   )r   rI   r   r   rR   r"  rq  s   @@ro   test_issue_9252rr    s    sD!!!AsT"""A#a&&Ac!ffH%Q
2Ar::a????
 Q Q Q Q QRRRRRrn   c                  j    t          t          t                    dz  t          dd          dk    sJ d S )Nr;  r   rc   )rI   r6   rU   rm   rn   ro   test_issue_9558rt    s1    QQ3''1,,,,,,rn   c                      t          dt          z  t          t          dt          z  t                    dz  z  z  t          t                    t          k    sJ d S )Nr   r^   )rI   rX   r   r   r   rm   rn   ro   test_issue_10801rv    sF    Q!hqsA..112Ar::b@@@@@@rn   c                      t          dd          \  } }t          t          | |z            t          |           z  | d          |k    sJ d S )Nzs xTr   r   )r   rI   r=   )r  rU   s     ro   test_issue_10976rx    sO    5t$$$DAqQqS#a&&!Q''1,,,,,,rn   c                      t          t          t                    t          t          d          z  t          z  t	          dt
          z  t          z            z  z  t          t                    dk    sJ d S Nrb   r^   )rI   r   rY   r   r*   r   r   rm   rn   ro   test_issue_9041r{    sQ    1!CFF(Qad1f!=>2FF!KKKKKKrn   c                  8   t          d          \  } }}t          | | |          j        |hk    sJ t          | | |d          j        |hk    sJ t          | |z   | |z   |          j        |hk    sJ t          | dz   |z   | dz  |          j        ||hk    sJ d S )Nzx, y, arc   r^   )r   rH   free_symbols)rU   rV   r   s      ro   test_issue_9205r~    s    i  GAq!Aq>>&1#----Aq#+s2222QAq!!.1#5555!Q$AqD!$$1aV;;;;;;rn   c                     t          dt          t          d          z  t          dz  z  t          t                    dk    sJ t          dt          t          d          dz   z  t          dz  z  t          t                    dk    sJ d S )N   rd   rb   )rI   r   rY   r   rm   rn   ro   test_issue_9471r  	  sq    2Aa>1a4'2..!33332Aa
#QT)1R00B666666rn   c                      t          t          t          dz             t          t                    z  t          t                    t          k    sJ d S r.  )rI   r   rY   r   r   rm   rn   ro   test_issue_10382r    s<    1q5!!)A,,.266+EEEEEErn   c                      t          t          t          dt          z                      t          t                    dk    sJ d S rz  )rI   r>   r   rU   r   rm   rn   ro   test_issue_11496r    s5    c!A#hhB''1,,,,,,rn   c                      t          t          t          t          z   t          z  t          t          z  z
  t          z  t          d                    t          t          t          dz
  z  z  k    sJ d S Nr   rb   )rK   rI   rU   rV   rY   rm   rn   ro   test_issue_11879r    sN    EAaC!8AqD=!+Q2233qQqSzAAAAAArn   c                      t          d          } t          d| z  | t                    dk    sJ t          dd| z  z  | t                    t          dd          k    sJ d S )NrX   r   rb   g333333?rd   
   )r   rI   r   r   )rX   s    ro   test_limit_with_Floatr    sa    A1b!!Q&&&&S!VQ##x2666666rn   c                      t          dt          z  dt           dz
  z  z  t          dz   dz  z  t          dz  z  t          t                    t          dd          k    sJ d S Nrd   rb   r^   )rI   rU   r   r   rm   rn   ro   test_issue_10610r     sV    Aa1"q&k!1q51*,QT11b99Xa^^KKKKKKrn   c                  2   t          t          t                    t          t                    z   t          dd          t          d          k    sJ t          t          t                    t          t                    z   t          dd          t          d          dt          z  t
          z  z   k    sJ t          t          d            t          t          t                    t          t                    z   t          t                    t          k    sJ t          t          t                    t          t                    z   t          dd          t          d          k    sJ t          t          t                    t          t                    z   t          dd          t           k    sJ t          t          d            t          t          t                    t          t                    z   t          t                    t          k    sJ d S )Nr   r_   r^   rc   c                  ~    t          t          t                    t          t                    z   t          dd          S r   )rI   r   rU   r"   rm   rn   ro   r   z"test_issue_10868.<locals>.<lambda>'  %    uSVVeAhh%61dCC rn   c                  ~    t          t          t                    t          t                    z   t          dd          S r   )rI   r   rU   r!   rm   rn   ro   r   z"test_issue_10868.<locals>.<lambda>+  r  rn   )
rI   r   rU   r"   r   r   rR   r   r   r!   rm   rn   ro   test_issue_10868r  $  sl   Q%(("Aq#..#a&&8888Q%(("Aq#..#a&&1Q3r6/AAAA
:CCDDDQ%(("Ar**b0000Q%(("Aq#..#a&&8888Q%(("Aq#..2#5555
:CCDDDQ%(("Ar**b000000rn   c                      t          t          t          t                    z   t          z  t          t                    dk    sJ d S r.  )rI   rY   r2   r   rm   rn   ro   test_issue_6599r  /  s3    !c!ff*aB''1,,,,,,rn   c                  j   t          dt          z  dt          dz  z  z   t          dz  t          t                    z   z  t          t                     dk    sJ t          dt          z  dt          dz  z  z   t          dz  t          t                    z   z  t          t                    t          u sJ d S )Nrd   r^   r  rs   rm   rn   ro   test_issue_12555r  3  s    !Q$ArE/aec!ffn5q2#>>!CCCC!Q$ArE/aec!ffn5q"==CCCCCCrn   c                  J   t          dd          \  } }}t          ddd          \  }}}}}}}	||z  ||z  z  | z  |z  t          |dz  |d|z  z  z  |dz  z  |dz
  z  |d|z  z  |dz  z  |dz  z  |dz
  z  z   |d|z  z  |d|z  z  z  |dz  z  |dz
  z  |dz  d|z  z
  dz   z  z   d|d|z  z  z  ||dz   z  z  |z  | z  |z  |dz  d|z  z
  dz   z  z
  d||dz   z  z  |d|z  z  z  |z  | z  |z  |dz  d|z  z
  dz   z  z   d||dz   z  z  ||dz   z  z  |dz  z  |dz
  z  z
  |dz
  |dz  d|z  z
  dz   z  z            z
  || z  |z
  | z
  dz   z  }
|
                    ||                              d          t	          |
||                              d          k    sJ d S )	Nzr z xTr   za b s0 K F0 s T)r\   r   r^   rb   r   )r   r*   rD  factorrI   )r  rW   rU   r   r   s0KF0r  Tfxs              ro   test_issue_12769r  8  sY   gD)))GAq!#$54PPPAq"aQ
a%1*Q,r/D"a%AaC.A"5q1u"=
QqS	!Q$q!tQU##$&(1Q3iAaC&8Q&>A&F1qQRs
UV&W#X	"qs)AAJq "2%q!taczQ7#8 	
"q1u+a!A#hq "2%q!taczA~6#7 	
"q1u+a!a%j A%q1u-	#. 23QA!a0H	"J K K K NOqSTUXXY\\]M]	
_B 771b>>  d ++uRB/?/?/F/FD/F/Q/QQQQQQQrn   c                  j   t          t          d          ddt          z  dz
  z  z  dt          z  t          z  z  dt          z  dz   dt          z  dt          j        z  z   z  z  dt          z  dz   dt          z  dt          j        z  z
  z  z  t          t
                    t          d	d
          k    sJ d S )N   re   rb   i@  r^   r   i   $   )rI   r*   rU   r   r   r   r   rm   rn   ro   test_issue_13332r  D  s    b!bdQh-'q14acAg1qx5PP1qBqD1QV8O,-./5 58@R8H8HI I I I I Irn   c                     t          t          dz  t          t          t                    z  z   t          t                    z   t          t                     t          u sJ t          t          dz  t          t          t                    z  z   t          t                    z   t          t                    t          u sJ t          t          t          t                    z   dz                                  t          t                    t          u sJ t          t          t          t                    z   dz                                  t          t                    t          u sJ t          t          t          t                    z   dz                                  t          t                     t          u sJ t          t          t          t                    z   dz                                  t          t                     t          u sJ d S r   )rI   rU   r6   r2   r   expandrm   rn   ro   test_issue_12564r  I  s^   A#a&&3q66)1rc22b8888A#a&&3q66)1b11R77771s1vv:/))++Q33r99991s1vv:/))++Q33r99991s1vv:/))++Q44::::1s1vv:/))++Q44::::::rn   c                  ^    t          t          d            t          t          d            d S )Nc                      t          t          t                    t          t                                                    S r   )rH   r   rU   r   r   rm   rn   ro   r   z"test_issue_14456.<locals>.<lambda>S  s$    c!ffa(=(=(B(B(D(D rn   c                      t          t          dz  t          dz   z  t          t                                                    S )Nr^   rb   )rH   rU   r   r   rm   rn   ro   r   z"test_issue_14456.<locals>.<lambda>T  s*    adAaCj!S(A(A(F(F(H(H rn   r!  rm   rn   ro   test_issue_14456r  R  s2    
 D DEEE
 H HIIIIIrn   c                      t          dt          dt          z  t          z  t          dz  z
            z  t          dt          z  dt          z  dz
  z            t           u sJ d S )Nrd   r      r^   )rI   r5   r   rU   r   rm   rn   ro   test_issue_14411r  W  sU    3qtAv!|$$$a2r"uqy)9::rcAAAAAArn   c                      t          t          t          dz   dz  dz   t          dz  dz   z  dz
  z  t          t                    dk    sJ d S rz  rv   rm   rn   ro   test_issue_13382r  [  sH    a!eaZ!^adQh/!34a<<AAAAAArn   c            	          t          t          dt          t          t          dz             z   dz   t          t          t                    z   z  z   z  t          t                    dk    sJ d S )Nri   rb   rI   rU   r   r   rm   rn   ro   test_issue_13403r  _  sQ    B!c!a%jj.1,q3q66z::;QCCqHHHHHHrn   c                  8   t          t          dz   t          t                    dz  z  t          dz
  t          dz   dz  z  t          t          dz             dz  z  z   t          dz  t          t                    dz  z  z  t          t                    dk    sJ d S r  r  rm   rn   ro   test_issue_13416r  c  s~    1a4%A	/QUQUQJ$6s1q5zz1}$DDq!tCPQFFTUI~VXY[]^^bcccccccrn   c                  D   t          t          dz  dt          z  dddt          z  z  z
  t          z   dz   z  t          z
  t          dz   dz  t          dz  z   t          z  z
  z  t          t                    t          dz  dz  t          dz  dz  z
  t          dz  z   k    sJ d S )Nr^   rb   r   rd   r  ry   r   )rI   rY   rU   r   rm   rn   ro   test_issue_13462r  g  s    Aqsa!QqS'kA--12Q61a4%'AaC-9JJKQPRSSWXZ[W[\^W^abdeaefgagWgjklnjnWnnnnnnnrn   c                      t          d          } t          t          | t          z
            t          t                    dk    sJ t          t          t          t                    t          z
            t          t                    dk    sJ d S )Nr   ri   )r   rI   r=   rU   r   r*   rG  s    ro   test_issue_13750r  k  si    sAQUQ##r))))T!WWq[!!1b))R//////rn   c                     t          t          t          t                    t	          t                    z  t          t
                    t                    sJ t          t          t          t                    t          t                    z  t          t
                    t                    sJ t          t          t          t	          t          t                                        t          t
                    t                    sJ t          ddt          dz  t          t                    z   z  z   t          dz  t          z   z  t          t
                    t          k    sJ d S rz  )	
isinstancerI   r6   rU   r   r   rH   r2   r
   rm   rn   ro   test_issue_14276r  q  s    eCFFCFFNAr22E:::::eCFFCFFNAr22E:::::eCCFF,,a44e<<<<<!aAA''1a4!84a<<AAAAAArn   c                      t          dt          t                    t          t                    z  z  dt          z  z  t          t                    dk    sJ d S r.  )rI   r   rU   r   rm   rn   ro   test_issue_14514r  x  sC    !SVVSVV^$!,a44999999rn   c                     t          t          t                    dz  t          t                    z
  t	          t                    t          t                    z  z   t          t                    t          t          j	        t          j
                  k    sJ t          t          t                    dz  t          t                    z
  t          t                    t          t                    z  z   t          t                    t          t          j	        t          j
                  k    sJ t          t          t                    t	          t                    dz  z
  t          t                    t          t          j	        t          j
                  k    sJ t          t          t                    t	          t                    dz  z
  t          t                    t          t          j	        t          j                  k    sJ t          t          t                    t	          t                    dz  z
  t          t                    t          t          j	        t          j                  k    sJ t          t          t                    dz  t	          t                    dz  z
  t          t                    t          t          j	        t          j                  k    sJ t          t	          t                    dz  t          t                    dz  z   t          t                    z
  t          t                    t          t          j         t          j
                  k    sJ d S r   )rI   r6   rU   r2   r7   r4   r   rM   r   rk   rl   r3   r   rm   rn   ro   test_issues_14525r  |  s   QSVV#c!ffSVVm3Q;;{1K]_`_i?j?jjjjjQSVV#c!ffSVVm3Q;;{1K]_`_i?j?jjjjjQ#a&&!)#Q++{1;Mqz/Z/ZZZZZQ#a&&!)#Q++{1;Mqu/U/UUUUUQ#a&&!)#Q++{1;Mqu/U/UUUUUQSVVQY&2..+a>PRSRW2X2XXXXXQSVVQY&Q/B77;vqz;Z;ZZZZZZZrn   c                      t          t          t                    t          t          t          dz  z
            z  t          dz   z  t          t                    dk    sJ d S )Nr^   rb   r   )rI   r*   rU   r2   r   rm   rn   ro   test_issue_14574r    sG    aQAX&!a%0!R88A======rn   c                     t          t          t                    t          t                    t          j        k    sJ t          dt          t                    z   t          t                    dt          j        z   k    sJ t          dt          t                    z  t          t                    t          dd          k    sJ t          t          t                    t          t                    t          j        k    sJ t          t          t                    t          t                     t          dd          k    sJ t          dt          t                    z  t          t                     dk    sJ d S )Nrd   re   r^   ri   r   rg   )rI   rA   rU   r   r   r   r   r@   rm   rn   ro   test_issue_10102r    s   !a$$....Xa[[!R((AJ66668A;;2&&(1a..8888!a$$....!a"%%"a88888A;;B3''2------rn   c                  2    t          t          d            d S )Nc                      t          t          t          t          z            t	          t
          t          z            z  t          t                    S r   )rI   r   r   rU   r6   r   r   rm   rn   ro   r   z"test_issue_14377.<locals>.<lambda>  s+    c!A#hhs2a4yy.@!R(H(H rn   r!  rm   rn   ro   test_issue_14377r    s    
 H HIIIIIrn   c                     t           dz  dt           dz  z  dt           dz  dz
  z  t           dz  z  t          t           dz  dz             z  z
  dt           dz  dz
  z  t           dz  z  t          t           dz  t           z   dz             z  z   t           z   dz   z  } t          | t           t                    t	          d          dz  k    sJ d S )Nr^   rg   rd   rb   )rU   rB   rI   r   r   r<  s    ro   test_issue_15146r    s    	
1AqD1adQh<!Q$.A1B1BBB	1a4!8q!tgadQhl3334678:;< 	=AAr??add1f$$$$$$rn   c                  0   dt           z  ddt            z  ddt           z  z  t           z   dz   z  z   z  t           dz   z  t           dz   z  } t          | t           t                    t          d          k    sJ t	          t           d          dz  dt           z  t          t                     z  z   dt           z  z   t          t           dz             dt          t                     z  z   dt           z  z   z  } t          | t           t                    dk    sJ d S )Nr^   rg   rb   r   r  re   rd   )rU   rI   r   r   r   r   r<  s    ro   test_issue_15202r    s    	
Aq1r7Bq!tGaK!O,,	-q1u	5Q?AAr??c!ff$$$$	QA1Yq\\)	)AqD	0Yq1u5E5E)TU,,5VY[]^Y^5^_AAr??b      rn   c                      t          t          dz  t          dz   dz  z
  t          dz  z  t          t                    dk    sJ d S )Ni  rb   i  i0rv   rm   rn   ro   test_issue_15282r    s?    !T'QUTM)QW4a<<EEEEEErn   c                      t          t           t          t          t                    dz             z   t          z  t          t          d          dk    sJ d S )Nrb   rc   r`   r   )rI   rU   r   r   r   rm   rn   ro   test_issue_15984r    sF    1"s3q66A:&)1bc:::a??????rn   c                      t          t          t          d          t          t                    z  t          t                    dk    sJ d S r.  )rI   rD   rU   rC   r   rm   rn   ro   test_issue_13571r    s:    Aq!!E!HH,a44999999rn   c                      t          t          t          t                              t          d          t          t          t          j                            k    sJ d S r.  )rI   r,   r?   rU   r   r   rm   rn   ro   test_issue_13575r    sA    d1gg1%%d15kk):):::::::rn   c                     t          t          t                    t          z  t          dd                                          dk    sJ t          t          dz  t          dd                                          dk    sJ t          dt          dz  z  t          dd                                          t          u sJ t          dt          z  t          dd                                          t
          u sJ d S )Nr   rf   r`   rb   r^   )rH   r6   rU   r   r   r   rm   rn   ro   test_issue_17325r    s    Q1aT***//11Q6666Aq!&&&++--22221a4A4(((--//255551a%%%**,,333333rn   c                  l    t          t                                        t          d          dk    sJ d S )Nr   )r   rU   rI   rm   rn   ro   test_issue_10978r    s/    A;;Q""a''''''rn   c                  x    t          t          t          dz            t          t                    t          u sJ d S r   )rI   r&   rY   r   rm   rn   ro   test_issue_14313_commentr    s/    qsQ##r))))))rn   c                      ddt           z  z
  t           z                      t                     } t          | t           dd          dk    sJ d S )Nrb   r_   r`   )rU   r   rI   )r  s    ro   test_issue_15323r    sI    
ac'AAAAqc"""a''''''rn   c                      t          t          t          t                                t          t                    z  t          d          dk    sJ d S r.  )rI   r   r   rU   rm   rn   ro   test_issue_12571r    sC    (CFF7###CFF*Aq11Q666666rn   c                      t          t          dz  t          dz   t          z  t          z  z  t          dz   t          dz   z  t          dz   z  z  t          t                    t          d          k    sJ d S r  r  rm   rn   ro   test_issue_14590r    s[    !Q$Q	A~%QQQ(?@!RHHCPQFFRRRRRRrn   c                      t          d          \  } }t          t          |z  t          |z  z
  t          | z  t          | z  z
  z  t          t                    |t          |  |z   z  z  | z  k    sJ d S )Na b)r   rI   rU   rV   r   r   s     ro   test_issue_14393r    sc    5>>DAq!Q$A+1q!t,a33qaR!V}QFFFFFFrn   c                      t          t          t          dz             dt          dz   z  z  t          t                    dt          z  z  z
  t          t                    t	          d          k    sJ d S )Nrb   ri   )rI   r   rY   r   r   rm   rn   ro   test_issue_14556r    s\    1q5!!Aq1uI.1!1DDaLLPSTVPWPWWWWWWWrn   c                      t          dt          d          dz  t          dz   z  z   dt          z  z  dt          d          dz  t          dz
  z  z  z  t          t                    t          k    sJ d S )Nrb   r^   rd   r   rI   r   rU   r   rm   rn   ro   test_issue_14811r    se    11a1q5)*ad3a1Q446QU:K6LMqRTUUY[[[[[[[rn   c                  |    t          t          t                    t          d          t          d          k    sJ d S )Ni ʚ;)rI   r   rU   rm   rn   ro   test_issue_16222r    s1    QJ''3z??::::::rn   c                      t          t          t          dz   z  t          dz   t          z  z   t          t          dz   z  z  t          z  t          t                    t          t          d                    k    sJ d S r.  r  rm   rn   ro   test_issue_16714r    sY    1q1u:Q
*a!a%j81<aDDCPQFFSSSSSSrn   c                     t          dd          } t          t          t          | z   t                    t          |  z  z  t          t                    dt          | dz             z  k    sJ t          ddd          } t          t          t          | z   t                    t          |  z  z  t          t                    dt          | dz             z  k    sJ d S )NrW   Tr}   rb   )r\   r[   )r   rI   r   rY   r   rC   r   s    ro   test_issue_16722r    s    d###A!a%##ArE)1b11QuQU||^CCCCdD111A!a%##ArE)1b11QuQU||^CCCCCCrn   c                     t          t          dz   dz   t          dz   dz   t          t          dz             z  z  t          dz   z  t          t                    z  t          dz   z  t          t                    dk    sJ t          t          dz   dz  t          t                    z  t          dz   t          dz   z  t          t          dz             z  z  t          t                    dk    sJ t          t          dz   t          t                    z  t          t          t          dz             z  z  t          t                    dk    sJ d S )Nrb   r^   r   rd   )rI   rY   r   r   rm   rn   ro   test_issue_17431r    s!   1q5A+AEQ;)AE2B2B"BCa%$Q<<(+,q5234b: :=>? ? ? ?!a%!IaLL(1q51q5/)AE:J:J*JKb    !a%9Q<<'1yQ/?/?+?@!RHHAMMMMMMrn   c                      t          t          t          t                               t          t          t                              t          z  z
  t          d          t          k    sJ d S r.  )rI   r<   r   rU   r   rm   rn   ro   test_issue_17671r    sH    SVVGs3q66{{1},a33zAAAAAArn   c                      t          dd          \  } }}}t          | dz   |z  t          | dz   dz  |dz  z  ||z  z   |z             z
  |t                    | d| z  dz   z  k    sJ d S )Nza b c xTr}   rb   r^   )r   rI   r*   r   )r   r   r   rU   s       ro   test_issue_17751r    s    T222JAq!Q!a%T1q51*QT/AaC"7!";<<<aDDAaCRSGTTTTTTrn   c                     t          t          t                    t          t                    z  t	          d          t          z  t          z  z  t          t
                    t          d          t          t                    z  k    sJ d S rz  )rI   r   rY   r*   r   r   r   rm   rn   ro   test_issue_17792r    sZ    1d1gg%s1vvax!m3Q;;tAwwtBxx?OOOOOOOrn   c                      t          t          t          t                              t          dd          dk    sJ t          t          t          t                              t          dd          dk    sJ d S )Nr   rc   ri   r_   rb   )rI   r   r6   rU   rm   rn   ro   test_issue_18118r    s^    c!ffq!S))R////c!ffq!S))Q......rn   c                      t          t          t          t                              t          t          t                              z  t          dd          dk    sJ d S )Nr   r_   rb   )rI   r6   r*   rU   rm   rn   ro   test_issue_18306r    sD    T!WWd3q66ll*Aq#66!;;;;;;rn   c                      t          t          t          dt          z            t          z             t          t          t                    t          dz  z             z  t          t                    dk    sJ d S )Nrd   r  )rI   r   r   rU   r   rm   rn   ro   test_issue_18378r    sV    S1XX\""3s1vv3#7#77B??1DDDDDDrn   c                      t          dt          d          dz  t          z  z
  dt          z  z  t          t                    t          u sJ t          t           t          z  t          t                    t          u sJ d S )Nrb   r^   rd   )rI   r   rU   r   r   rm   rn   ro   test_issue_18399r    sc    !add1fQh,!A#&2..#55551"q!R  C''''''rn   c                  *   t          t          t                    dt          t                    z  z  t          t
          d          t          t          t                    dt          t                    z  z  t          t
          d          k    sJ d S )Nr^   rc   r`   )rI   r7   rU   r*   r   r   rH   rm   rn   ro   test_issue_18442r    sl    Q!d2hh-(!RS999U3q66APTUWPXPXMCZ\]_agj=k=k=kkkkkkkrn   c                     t          t          t          t                              t          z  t          d          dk    sJ t          t          t          t                              t          z  t          dd          dk    sJ d S )Nr   rb   rc   )rI   r   r   rU   rm   rn   ro   test_issue_18452r    sd    SVVaA&&!++++SVVaAs++q000000rn   c                     t          t          t                    dt          z  z  t          t                    t	          t          t                    dt          z  z  t          t          d          k    sJ t          t          t                    dt          z  z  t          t                    t	          t          t                    dt          z  z  t          t          d          k    sJ t          t          t                    dt          z  z  t          t                    t	          t          t                    dt          z  z  t          t          d          k    sJ t          t          t                    dz   dt          z  z  t          t                    dk    sJ t          t          t                    dz   dt          z  z  t          t                    dk    sJ t          t          t                    dz
  dt          z  z  t          t                    t	          t          t                    dz
  dt          z  z  t          t          d          k    sJ t          t          t                    dz   dt          z  z  t          t                    t          dd          k    sJ t          t          t                    dz  dt          z  z  t          t                    t          dt                    k    sJ t          t          t                    dz  dt          z  z  t          t                    t          dd          k    sJ t          t          t                    dz   dt          z  z  t          t                     t          dt                    k    sJ t          t          t                    dz  dt          z  z  t          t                     t          dt                    k    sJ t          t          t                    dz  dt          z  z  t          t                     t          dt                    k    sJ d S )Nrb   rc   r`   r^   r  r   )rI   r6   rU   r   rH   r2   r7   rM   rm   rn   ro   test_issue_18473r    s   Q!A#2&&%A1q"#*N*N*NNNNNQ!A#2&&%A1q"#*N*N*NNNNNQ!A#2&&%A1q"#*N*N*NNNNN#a&&1*!$a,,1111#a&&2+1%q"--2222#a&&1*!$a,,s1vvzQqS6I1bVY0Z0Z0ZZZZZ#a&&1*!$a,,Aq0A0AAAAA#a&&!)qs#a,,Ar0B0BBBBB#a&&!)qs#Q++{1a/@/@@@@@#a&&1*!$a"--Q1C1CCCCC#a&&!)qs#Q,,Ar0B0BBBBB#a&&!)qs#a"--Q1C1CCCCCCCrn   c                      t          dt          dt          z            z  t          dt          z            dz   z  dt          z  z  t          t                    t          d          k    sJ d S Nr^   rd   rb   )rI   r   rU   r   rm   rn   ro   test_issue_18482r  .  sU    !C!HH*c!A#hhl+qs3Q;;s1vvEEEEEErn   c            	      P   t          t          t                    t          dt	          t                    z
            z  t          d          t          d          k    sJ t          t          t                    t          dt	          t                    z
            z  t          dd          t          d          k    sJ t          t          t                    t          dt	          t                    z
            z  t          dd          t          d           k    sJ d S )Nrb   r   r^   r_   r`   rc   )rI   r6   rU   r*   r2   rm   rn   ro   test_issue_18508r
  2  s    QQs1vvX&1--a8888QQs1vvX&1#666$q''AAAAQQs1vvX&1#666477(BBBBBBrn   c                  2    t          t          d            d S )Nc                  r    t          t          dt          z
  t          z            t          t                    S r   )rI   r   rY   rU   r   rm   rn   ro   r   z"test_issue_18521.<locals>.<lambda>9  s"    c1q5A+.>.>2(F(F rn   r!  rm   rn   ro   test_issue_18521r  8  s    
 F FGGGGGrn   c                  &   t          dd          \  } }t          t          |           | |          t          |          k    sJ t          t          t          |                     | |          t          t          |                    k    sJ d S )Nr  Tr}   )r   rI   r   r   r  s     ro   test_issue_18969r  <  s    54(((DAq!a##x{{2222Xa[[!!1a((C,<,<<<<<<<rn   c                      t          t          t          t                    dt          z  z  z  t          t                    t	          d          k    sJ d S r.  )rI   rY   r   r   r   rm   rn   ro   test_issue_18992r  B  s?    IaLL1Q3'(!R00CFF::::::rn   c                      t          d          } t          t          |           t          | dz
            t          | dz             z  z  | d          dk    sJ d S )NrU   rb   r^   r   ri   )r   rI   rC   r   s    ro   test_issue_19067r  F  sT    sAq5Q<<a!e45q!<<BBBBBBrn   c                      t          t          dt          z  dt           z  z  z  t          t                    dk    sJ d S r  rv   rm   rn   ro   test_issue_19586r  K  s8    QT!qb'\"Ar**a//////rn   c                  z    t          d          } t          dd          }t          | |z   | d          dk    sJ d S )NrY   r?  T)zeror   )r   rI   )rY   r?  s     ro   test_issue_13715r  O  sF    sAsAQ1""""""rn   c            
         t          t          dz  t           dz
  t          dt          z            z  t          dz   t          dt          dz   z            z  z   z  t           dz   z  t          t                    dk    sJ d S r  )rI   rY   r6   r   rm   rn   ro   test_issue_15055r  U  sl    AQAaC(AE3q!a%y>>+AABQBFKQPRSSWXXXXXXXrn   c            
         t          dd          \  } }t          d          \  }}}t          ||z  |z  t          |           t          d|z  |z  |z  | |dz  z  z             z  z
  | |z  z   ||z  z  |d          |||z  z   |z  k    sJ d S )Nzm viTr}   zB ti drg   r^   r   )r   rI   r*   )r@  viBtir  s        ro   test_issue_16708r  Y  s    FT***EArx  HAr1!B$r'DGGDAaQQwY)>$?$???!B$F2NPQSTUUZ[^`ac^cZcegYgggggggrn   c                     t          t          ddt          z            t          t          dt                    dz  z  z  t          t                    dt	          d          z  t
          z  dz  k    sJ t          t          ddt          z            t          t          dt                    dz  z  z  t          t                     dt	          d          z  t
          z  dz  k    sJ d S )Nrb   rd   r^   rg   )rI   r8   rU   r   r*   r   rm   rn   ro   test_issue_19154r!  _  s    AqD!!1gammQ&6#67R@@Ad1ggIbLQRNRRRRAqD!!1gammQ&6#67bSAARQZPR]ST_TTTTTTrn   c                     t          dd          } t          dd          }t          dd          }t          dd          }t          dd          }t          d          }d	|d
z  z  | z  |z  |d|z  | z  |z  z  z  }|d
z  |d
z  z  }||| z  |z  z  dz
  }| d|z  |z  z  |d
|z  |d
z  z  z  z
  |||| z  |z  z  dz   z  d
|z  |d	z  z  z  z
  |d|z  | z  |z  z  |z  z   }	t          t          |	          |            }
t	          |
d|z  |z  z
  | t
                    dk    sJ t	           |
j                    d|z  |z  z
  | t
                    dk    sJ d S )NbetaTr}   hr@  omegarV  rb   rd   r^   r~   r   r   )r   r   r   r   rI   r   rK   )r#  r$  r@  wrV  r   qr?  r  Zr
   s              ro   test_issue_19453r)  d  s   &4(((DsT"""AsT"""Aw&&&AsT"""AAA	!Q$tAa#a%*Q,''A	1QT	A	AdF1HA	
AaCE
Q!AqD\!Aq1T6!8}q'8$91Q3q!t8$DD#a%*Q,!	"A	c!ffd		ASU1WdB''1,,,,Aa'r22a777777rn   c                  z    t          t          d           dz  t          z  t          t                    dk    sJ d S )Nrb   r   r   r  rm   rn   ro   test_issue_19739r+  w  s5    1Q44%'Aq"%%******rn   c                      t          dt           z  t          dt          dz   z  dz             z  t          t                    dk    sJ d S )Nr^   r   rb   )rI   rU   r*   r   rm   rn   ro   test_issue_19766r-  {  sD    aRa!a%j1n---q"55::::::rn   c                  D   t          d          } t          t          | t          z            t          z  t          t                    t          t          | t          z            t          z  t          t          d          k    sJ t          dd          } t          t          | t          z            t          z  t          t                    t          t          | t          z            t          z  t          t          d          k    sJ t          dd          } t          t          | t          z            t          t                    t          dd          k    sJ t          t          | t          z            t          z  t          t                    d	k    sJ d S )
Nr@  rc   r`   Tr   )nonzerori   rb   r   )r   rI   r2   rU   r   rH   rM   )r@  s    ro   test_issue_19770r0    s'   sAQqS!Q##uS1XXaZBC'H'H'HHHHHsAQqS!Q##uS1XXaZBC'H'H'HHHHHsD!!!AQqS1b!![Q%7%77777QqS!Q##q((((((rn   c            	         t          t          t                    t          t          t                              z  t          t          dz            t          t          t                    t          t          t                              z  t          t          dz  d          k    sJ t          t          t                    t          t          t                              z  t          t          dz  d          t          t          t                    t          t          t                              z  t          t          dz  d          k    sJ t          t          t                    t          t          t                              z  t          t          dz  d          t          t          t                    t          t          t                              z  t          t          dz  d          k    sJ t          t          t          t                              t          t          dz            t          dd          k    sJ t           dt          t                     z  z  t          t           t                    k    sJ t          dt          t                    z  z  t          t           t                    k    sJ t          dt          t                     z  z  t          t           t                    k    sJ t           dt          t                    z  z  t          t           t                    k    sJ d S )Nr^   r_   r`   rc   rf   ri   rb   )rI   r7   rU   r6   r   rH   rM   r   rm   rn   ro   test_issue_7535r2    s7   QCFF#Q1--s1vvc#a&&kk7I1bQRdX[1\1\1\\\\\QCFF#Q1#666%As3q66{{@RTUWYZ[W[ad:e:e:eeeeeQCFF#Q1$7775QCPQFFASUVXZ[\X\bf;g;g;gggggSVVQr!t$$B(:(:::::3#rc((
{B3333333qRy>["b111111qbSz?k2#r2222223#b''	?k2#r22222222rn   c                      t          t          dz   dt          z  z  t          z
  t          z  t          d          t           dz  k    sJ d S )Nrb   r   r^   )rI   rU   r
   rm   rn   ro   test_issue_20365r4    sA    1q5AaC.1$a'A..1"Q$666666rn   c                      t          dt          z   dt          z  z  ddt          z  z   ddt          z  z  z  z
  t          t                    z  t          d          t          dz  k    sJ d S )Nrb   r^   r   )rI   rU   r0   r
   rm   rn   ro   test_issue_21031r6    sZ    1q5AaC.A!Gq!A#w#77a@!QGG1Q3NNNNNNrn   c                      t          t          t          t          z            dt          z  dz
  z  t          d          t          dz  k    sJ d S )Nrd   r   r   )rI   r6   r   rU   rm   rn   ro   test_issue_21038r8    s@    RTAaC"H%q!,,1444444rn   c                     t          t                    t          dt          z            z  } t          | t          dd          dk    sJ t          | t          dd          dk    sJ t          | t          dd          dk    sJ d S )Nrb   r   r_   rc   rf   )r   rU   r6   rI   r   s    ro   test_issue_20578r:    s    q66C!HHDa#!####a#!####a$1$$$$$$rn   c                  D   t          t                    } |                     t          t                    t          k    sJ |                     t          t                     t           k    sJ t          t          t                               } |                     t          t                    t          t                     k    sJ |                     t          t                     t          t                    k    sJ t          t          t                              } |                     t          t                    t          t                    k    sJ |                     t          t                     t          t                     k    sJ |                     t          t                    t          t                    k    sJ t          t          t          dt          z                                } |                     t          t                    t          t          t                               k    sJ |                     t          t                     t          t          t                              k    sJ |                     t          t                    t          t          t                               k    sJ |                     t          t                     t          t          t                              k    sJ d S )N)logxrb   )r   rU   nseriesrV   r7  s    ro   test_issue_21227r>    s!   AA99QQ91$$$$99QaR9  QB&&&&SVVGA99QQ93r77****99QaR9  CFF****CFFA99QQ93q66))))99QaR9  CGG++++99QQ93q66))))CAaCMMA99QQ93sA2ww<<////99QaR9  CAKK////99QQ93sA2ww<<////99QaR9  CAKK//////rn   c                      t           dz
  t          dt           dz
  z            z  }  | j        t           d          dk    sJ  | j                                        t           d          dk    sJ d S r   )rU   r2   rI   r  )r   s    ro   test_issue_21415r@    sj    Q3AqsG
C39Qq>>Q3:<<a""a''''''rn   c                      t          t          t          dz             t          t                    z  t          t                    t          k    sJ d S r.  )rI   r$   rY   r   r
   rm   rn   ro   test_issue_21530rB    s:    a!eT!WW$a,,111111rn   c                      t          d          dz
  dz  } t          t          | z
  t          dz  t          z   dz
  z  t          |           t          d          dz  k    sJ d S )Nre   rb   r^   )r*   rI   rU   r  s    ro   test_issue_21550rD    sW    	a1aA!a%!Q$(Q,'A..$q''!);;;;;;rn   c                      t          t          t          dz   z  t          t                    dz   z  dz   t          z  t          d          } | t          d          dz  dt          d          z  z   k    sJ d S )Nrb      l   qjl   S[	)rI   rU   r   r   )outs    ro   test_issue_21661rH    sh    
QUs1vvz*Q.!3Q
;
;C!M""2%SWW(<<<<<<<<rn   c                      t          t          t          t                    t          t          z  z                      t          d          t          d          t          d          dz  k    sJ d S )Nr   r   rb   i 	 )rI   r:   rW   rU   rD  r   rm   rn   ro   test_issue_21701rJ    sP    '!Q--1$**1a00!Q771Q44;FFFFFFrn   c                      t          dd          } t          dt          dt          | z
  dz  z   z  z  t                    } |j        t          t
                    t          j        k    sJ d S )Nr   Tr   rb   r^   )r   rG   r   rU   rI   r   r   r   )r   r   s     ro   test_issue_21721rL    s^    sA!Ra!eaZ()1--A171b>>QV######rn   c                  T   dt          dt          z  t          z  t          z            z
  dt          dt          z  t          z  t          z  dz            z
  z  } |                     t          d          dk    sJ t          |                               t          d          dk    sJ d S )Nrb   rg   re   r   )r   r   r   rW   rI   r   )terms    ro   test_issue_21756rO    s    BqDGAISAb1%5%5!56D::aq    d88>>!Q1$$$$$$rn   c                      t          d          } t          | dz   t          dz  z   dt          dz  z
  z                                | dd          t          k    sJ d S )Nr   r^   rb   rc   )r   r*   rU   rI   r   rG  s    ro   test_issue_21785rQ    sY    sA!Q$AAqD)**00As;;q@@@@@@rn   c                  p    t          dt          z  dt           z  z  t          t                    dk    sJ d S )Nri   r^   r   rv   rm   rn   ro   test_issue_22181rS    s4    "q1r7"Ar**a//////rn   c            	      \   t          d          t          t          d          t          t          dz            z  dz            z  dz  } t          d          t          z  t          t          d          t          t          dz            z  dt          d          z  t          z  dz  z
             t          t          d          t          t          dz            z  dt          d          z  t          z  dz  z             
 z   z  dz  }t          | t          t                     t          d           t          z  dz  k    sJ t          |t          t                     t          d           t          z  dz  k    sJ t          | t          t           d          t          d          t          z  dz  k    sJ t          |t          t           d          dk    sJ t          t          t          z
            t          t           t          z
            z
  }t          |d	
          }t          |t          t                    t          |t          t                    cxk    rt          t          z  k    sn J t          t          t          dz            t          z
             t          t          t          dz            t          z             z   x}}t          |t          t          d          dt          z  t          z  k    sJ t          |t          t          d          dk    sJ d S )Nr  r^   r   r;  re   <   rc   r   T)forcer_   )
r*   r1   r7   rU   r   r   rI   r   rJ   r   )e1e2r   expr2s       ro   test_issue_22220rZ    s   	b$tBxxAaC(*++	+B	.B	b!c$q''#ac((*QtBxxZ\!^;<<<$q''#ac((*QtBxxZ\!^;<<<= 
>>@
AB Qb	"R////Qb	"R////QS!!T"XXb[^3333QS!!Q&&&& q1u::QBF#Dt4(((Eq"ua!4!4<<<<"<<<<<< AaC1%%%s3qs88a<'8'889D4q"c""ac"f,,,,q"c""a''''''rn   c                     t          dd          \  } }t          |dz   | z  |dz   | dz   z  || dz   z  z
  z  |t                    d| dz   z  k    sJ t          |dz   | z  |dz   | dz   z  || dz   z  z
                                  z  |t                    d| dz   z  k    sJ t          |dz   | z  ||| z   |dz   | z  z   z  |dz   | z  z   z  |t                    d| dz   z  k    sJ d S )Nzk, nTr}   rb   )r   rI   r   r  )rX   rY   s     ro   test_issue_22334r\    s   FT***DAq!A#AaC1Q3<1!*45q"==AEJJJJ!A#AaC1Q3<1!*4<<>>>2FF!QQRU)SSSS!A#1q!teq1uqj01QUQJ>?BGG1aRSe9TTTTTTrn   c                      t          t          ddt          z  z             t          t                    z  t          t                    t          d          k    sJ d S rz  )rI   r   rU   r*   r   rm   rn   ro   test_sympyissue_22986r^    sD    q1Q3wQ'B//477::::::rn   c                      dt           z  dt            z  z
  dt           z  dt            z  z   z  } t          | t           t                     dk    sJ d S )Nr^   ri   )rU   rI   r   r7  s    ro   test_issue_23231r`    sM    	
AQB!Q$aR.)AAsr!!!!!!rn   c                      t          dt          z   t          dz  z  t          dt          z            z  t          dt          f          t          k    sJ d S )Nrb   r^   ri   r   )rG   rU   r   r   rm   rn   ro   test_issue_23596rb    sD    q1uadlC1II-1bz::b@@@@@@rn   c                  X   t          t           t          dz  z  t          z   dz
            } t          t           t          dz  z  t          t          z  z   dz
            }t          | t          dd          t          d           t          z  k    sJ t          | t          dd          t          d           t          z  k    sJ t          |t          dd          t          d          t          z  k    sJ t          |t          dd          t          d           t          z  k    sJ d S )Nr^   rd   r   r_   rc   )r*   r   rU   rI   )expr1rY  s     ro   test_issue_23752re    s    !AqD1q!!E!AqD1Q3"##E1c""tAwwhqj00001c""tAwwhqj00001c""d1ggai////1c""tAwwhqj000000rn   c                     t          t          t          dz  t          t                    z                                          t                    } |                     t          t                    dk    sJ |                                                     t          t                    dk    sJ | 	                    t                                        t          t                    dk    sJ | 	                    t                                                                        t          t                    dk    sJ d S r   )r   r7   r   r#   rU   r   rI   r   rK   r   r6   )r  s    ro   test_issue_24276rg  "  s    	SAd1gg			$	$Q	'	'B88Ar??a;;==q"%%****::c??  B''1,,,,::c??##%%++Ar22a777777rn   c                  X   t          dd          t          dd          } t          dd          }t          dd	          }t          t          fd
           t          t	          t
          |           t
          || z  d          dk    sJ t          t	          t
          |           t
          || z  d          | k    sJ t          t	          t
          |          t
          ||z  d          |k    sJ t          t	          t
          |          t
          ||z  d          dk    sJ d S )Nr   Tr   r   r}   r   rA  rY   ro  c                  V    t          t          t                     t                     S r   )rI   r	   rU   rG  s   ro   r   z"test_issue_25230.<locals>.<lambda>.  s    c!QiiA(>(> rn   r_   r   rc   )r   rR   r"  rI   r	   rU   )r   r   rY   r   s      @ro   test_issue_25230rj  )  s   s4   Ast$$$Ast$$$Asd###A
 > > > >???QAqsC((A----QAqsC((A----QAqsC((A----QAqsC((A------rn   c                  h   t          t          t          t                              t          t          d          t           t
          z  k    sJ t          t          t          t                              t          t          d          t          t
          z  k    sJ t          t          t          t                              t          t          d          t          dz  k    sJ t          t          t          t                              t          t          d          dk    sJ t          t          t          t                              t          t          d          t          dz  k    sJ t          t          t          t                              t          t          d          dk    sJ d S )Nrc   r^   r   )rI   r0   r   rU   r   r   r,   r1   r   r-   r/   r.   rm   rn   ro   test_issue_25582rl  5  s   c!ffq"c**rc!e3333c!ffq"c**bd2222c!ffq"c**bd2222c!ffq"c**a////c!ffq"c**bd2222c!ffq"c**a//////rn   c                  V   t          t          t          t                    t          z            t          dd          t          dz  k    sJ t          t          t          dt          z                      t          dd          t          dz  k    sJ t          t          t          dt          z                      t          dd          dk    sJ t          t          t          t                    t          z            t          dd          t          dz  k    sJ t          t          t          dt          z                      t          dd          t           t          z  k    sJ t          t          t          dt          z                      t          dd          dk    sJ t          t          t          t                    t          z            t          dd          dk    sJ t          t          t          dt          z                      t          dd          t          t          z  k    sJ t          t          t          dt          z                      t          dd          t          dz  k    sJ t          t          t          t                    t          z            t          dd          t          dz  k    sJ t          t          t          dt          z                      t          dd          dk    sJ t          t          t          dt          z                      t          dd          t          dz  k    sJ t          t          t          t                    t          z            t          dd          dk    sJ t          t          t          dt          z                      t          dd          t          dz  k    sJ t          t          t          dt          z                      t          dd          t          t          z  k    sJ t          t          t          t                    t          z            t          dd          t          dz  k    sJ t          t          t          dt          z                      t          dd          dk    sJ t          t          t          dt          z                      t          dd          t           t          z  k    sJ t          t          t          t                    t          z            t          dd          t          k    sJ t          t          t          dt          z                      t          dd          t           t          z  dz  k    sJ t          t          t          dt          z                      t          dd          dk    sJ t          t          t          t                    t          z            t          dd          t          dt!          d          z             k    sJ t          t          t          dt          z                      t          dd          t          k    sJ t          t          t          dt          z                      t          dd          dk    sJ t          t#          t          t                    t          z            t          dd          dk    sJ t          t#          t          dt          z                      t          dd          t          k    sJ t          t#          t          dt          z                      t          dd          t          t          z  dz  k    sJ t          t%          t          t                    t          z            t          dd          t          k    sJ t          t%          t          dt          z                      t          dd          dk    sJ t          t%          t          dt          z                      t          dd          t           t          z  dz  k    sJ t          t'          t          t                    t          z            t          dd          dk    sJ t          t'          t          dt          z                      t          dd          t          t          z  dz  k    sJ t          t'          t          dt          z                      t          dd          t          k    sJ t          t)          t          t                    t          z            t          dd          t          dt!          d          z             k    sJ t          t)          t          dt          z                      t          dd          dk    sJ t          t)          t          dt          z                      t          dd          t          k    sJ d S )Nr   rf   r   rb   r_   r^   rc   )rI   r1   r6   rU   r   r   r0   r   r   r,   r-   r/   r.   r   r   r   r*   r   r    r"   r!   rm   rn   ro   test_issue_25847rn  ?  s6   c!ffQhAt,,14444c!A#hhAs++r!t3333c!A#hhAs++q0000 c!ffQhAt,,14444c!A#hhAs++s1u4444c!A#hhAs++q0000 c!ffQhAt,,1111c!A#hhAs++r!t3333c!A#hhAs++r!t3333 c!ffQhAt,,14444c!A#hhAs++q0000c!A#hhAs++r!t3333 c!ffQhAt,,1111c!A#hhAs++r!t3333c!A#hhAs++r!t3333 c!ffQhAt,,14444c!A#hhAs++q0000c!A#hhAs++s1u4444 s1vvax!Q--3333s1Q3xx!Q,,2a7777s1Q3xx!Q,,1111 s1vvax!Q--Qa[1A1AAAAAs1Q3xx!Q,,2222s1Q3xx!Q,,1111 s1vvax!Q--2222s1Q3xx!Q,,2222s1Q3xx!Q,,"Q6666 s1vvax!Q--3333s1Q3xx!Q,,1111s1Q3xx!Q,,2a7777 s1vvax!Q--2222s1Q3xx!Q,,"Q6666s1Q3xx!Q,,2222 s1vvax!Q--Qa[1A1AAAAAs1Q3xx!Q,,1111s1Q3xx!Q,,222222rn   c                      t          t          dt          dz             t          dt                    z  t          t                    t          j        k    sJ d S r  )rI   r8   rU   r   r   r   rm   rn   ro   test_issue_26040rp  }  sB    AE""71a==0!R88AFBBBBBBrn   c                  \   t          dt          z  t          dz  dt          z  z   dz   z            } t          dt          z  t          dz  dt          z  z   dz   z            }ddt          dz  z  z
  | dz  z  dz  t          dz  dt          z  z
  dz   | z  |z  dz  z
  }t          dz  t          dz  dt          dz  z  z
  t          dz  z
  dt          dz  z  z   t          dz  z
  dt          dz  z  z
  t          dz  z   z  }t	          ||z  t          d	          t          d           dz  k    sJ d S )
Nr   r^   rb   rd   ry   r   r   re   r   )rS   rU   rT   r   rI   r   )r   rX   rW  rX  s       ro   test_issue_26250rr    s   1Q31qs
Q'((A1Q31qs
Q'((AQq!tV8QT/!
q!tAaCxz1nQ.q0
0B	Q1qAv1$qAv-14qAv=1D	EBB1!A$$q((((((rn   N(   	itertoolsr   sympy.concrete.summationsr   sympy.core.functionr   r   
sympy.corer   r   sympy.core.modr	   sympy.core.numbersr
   r   r   r   r   r   sympy.core.singletonr   sympy.core.symbolr   r   %sympy.functions.combinatorial.numbersr   (sympy.functions.combinatorial.factorialsr   r   r   $sympy.functions.elementary.complexesr   r   r   &sympy.functions.elementary.exponentialr   r   r   %sympy.functions.elementary.hyperbolicr   r   r   r    r!   r"   r#   r$   #sympy.functions.elementary.integersr%   r&   r'   (sympy.functions.elementary.miscellaneousr(   r)   r*   $sympy.functions.elementary.piecewiser+   (sympy.functions.elementary.trigonometricr,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   sympy.functions.special.besselr8   r9   r:   r;   'sympy.functions.special.error_functionsr<   r=   r>   r?   r@   rA   'sympy.functions.special.gamma_functionsrB   rC   rD   sympy.functions.special.hyperrE   sympy.integrals.integralsrF   rG   sympy.series.limitsrH   rI   sympy.simplify.simplifyrJ   rK   sympy.simplify.hyperexpandrL   !sympy.calculus.accumulationboundsrM   sympy.core.mulrN   rO   sympy.series.orderrP   sympy.testing.pytestrQ   rR   sympyrS   rT   	sympy.abcrU   rV   rW   rX   rY   rp   rt   rw   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  r
  r  r  r  r  r  r  r  r#  r*  r,  r/  r2  r5  r8  r=  rE  rH  rJ  rL  rN  rP  rS  rW  rZ  r\  r^  ra  re  rg  ri  rk  rm  rr  rt  rv  rx  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  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  r  r  r!  r)  r+  r-  r0  r2  r4  r6  r8  r:  r>  r@  rB  rD  rH  rJ  rL  rO  rQ  rS  rZ  r\  r^  r`  rb  re  rg  rj  rl  rn  rp  rr  rm   rn   ro   <module>r     s         ) ) ) ) ) ) 0 0 0 0 0 0 0 0 . . . . . . . .       < < < < < < < < < < < < < < < < " " " " " " / / / / / / / / ; ; ; ; ; ; X X X X X X X X X X @ @ @ @ @ @ @ @ @ @ G G G G G G G G G G h h h h h h h h h h h h h h h h h h h h F F F F F F F F F F L L L L L L L L L L : : : : : :Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z O O O O O O O O O O O O ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] P P P P P P P P P P 1 1 1 1 1 1 ; ; ; ; ; ; ; ; . . . . . . . . : : : : : : : : 2 2 2 2 2 2 9 9 9 9 9 9       * * * * * * $ $ $ $ $ $ . . . . . . . . ( ( ( ( ( ( ( (                        
F3t,,,D8 D8 D8N2 2 2, , ,
A A A; ; ;S S S
$ $ $6 6 6/ / /D D D1 1 124 4 4W W W&6 6 67 7 7 4 4 4A A A3 3 3>H H H  @ @ @; ; ;
  1 1 1., , ,2 # # #9 9 9: : :> > >0 0 0
, , ," " "
* * *  0( ( (5 5 5  *6 6 6
	6 	6 	6B B B7 7 7D D D - - -A A A
8 8 8
A A A
M M M
@ @ @* * ** * *K K K
 . . .. . .
-> -> ->`4 4 4@ @ @+ + +$ $ $" " "? ? ?8 8 8T T T, , ,
D D D; ; ;
3 3 3	2 	2 	2/ / /S S S- - -A A A
- - -
L L L< < <7 7 7
F F F- - -B B B7 7 7L L L1 1 1- - -D D D
	R 	R 	RI I I
; ; ;J J J
B B BB B BI I Id d do o o0 0 0B B B: : :[ [ [> > >. . .J J J% % %! ! !F F F@ @ @: : :; ; ;4 4 4( ( (* * * ( ( (
7 7 7S S SG G G
X X X\ \ \; ; ;T T TD D DN N NB B BU U U
P P P/ / /
< < <E E E( ( (
l l l1 1 1
D D D F F FC C CH H H= = =; ; ;C C C
0 0 0# # #Y Y Yh h hU U U
8 8 8&+ + +; ; ;	) 	) 	)3 3 37 7 7O O O5 5 5% % %0 0 02( ( (2 2 2< < <
= = =
G G G$ $ $% % %A A A
0 0 0( ( (,U U U; ; ;" " "
A A A1 1 18 8 8	. 	. 	.0 0 0;3 ;3 ;3|C C C) ) ) ) )rn   