
    \h                        S SK Jr  S SKJr  S SKJrJr  S SKJrJ	r	  S SK
Jr  S SKJrJrJrJrJrJr  S SKJr  S SKJrJr  S S	KJr  S S
KJrJrJr  S SKJrJ r J!r!  S SK"J#r#J$r$J%r%  S SK&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.  S SK/J0r0J1r1J2r2  S SK3J4r4J5r5J6r6  S SK7J8r8  S SK9J:r:J;r;J<r<J=r=J>r>J?r?J@r@JArAJBrBJCrCJDrDJErE  S SKFJGrGJHrHJIrIJJrJ  S SKKJLrLJMrMJNrNJOrOJPrPJQrQ  S SKRJSrSJTrTJUrU  S SKVJWrW  S SKXJYrYJZrZ  S SK[J\r\J]r]  S SK^J_r_J`r`  S SKaJbrb  S SKcJdrd  S SKeJfrf  S SK[Jgrg  S SKhJiri  S SKjJkrkJlrl  S SKmJnrnJoro  S S KpJqrqJrrrJsrsJtrt  \" S!S"S"S#9ruS$ rvS% rwS& rxS' ryS( rzS) r{S* r|S+ r}S, r~S- rS. rS/ rS0 rS1 rS2 rS3 rS4 rS5 rS6 rS7 rS8 rS9 rS: rS; rS< r\kS= 5       rS> rS? rS@ rSA rSB rSC rSD rSE rSF rSG rSH rSI rSJ rSK rSL r\kSM 5       rSN rSO rSP rSQ rSR rSS rST rSU r\kSV 5       rSW rSX rSY rSZ rS[ rS\ rS] rS^ rS_ rS` rSa rSb rSc rSd rSe rSf rSg rSh rSi rSj rSk rSl rSm rSn rSo rSp rSq rSr rSs rSt rSu rSv rSw rSx rSy rSz rS{ rS| rS} rS~ rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS Gr S GrS GrS GrS GrS GrS GrS GrS GrS Gr	S Gr
S GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS Gr S Gr!S Gr"S Gr#S Gr$S Gr%g)    )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            	         [        [        [        [        5      [        L d   e[        [        [        [        * 5      [        * L d   e[        [        * [        [        5      [        * L d   e[        [        S-  [        [        * 5      [        L d   e[        [        S-  * [        [        5      [        * L d   e[        [        [        [        5      -  [        SSS9S:X  d   e[        S[        -  [        [        5      S:X  d   e[        [	        [        5      [        [        5      [        L d   e[        [	        [        5      * [        [        5      [        * L d   e[        [	        [        5      [        -  [        [        5      [        L d   e[        S[        -  [	        [        * 5      -
  [        [        5      S:X  d   e[        [        S[        -  -   [        [        5      [        L d   e[        [        [        S-  -
  [        [        5      [        * L d   e[        S[        -   S[        S5      -   -  [        S5      S:X  d   e[        S[        -   [        -  [        S5      [        [        S-   [        -  [        S5      :X  d   e[        S[        -   [        -  [        SSS9[        [        S-   [        -  [        SSS9:X  d   e[        S[        -   [        -   [        -  [        SSS9[        S[        -   [        -   [        -  [        SSS9:X  d   e[        [        [        -  [        [        5      -  [        S5      [        * [        [        5      -  :X  d   e[        [        [        [        -   5      [        -  [        S5      [        [        [        5      5      [        -  :X  d   e[        [        S[        -  S-   5      [        [        5      S:X  d   e[        [        R                  [        [        * 5      [        R                  L d   e[        [        S5      [        -  [        [        R                  5      [        R                  L d   e[        S[        S-
  -  [        SSS9[        L d   e[        S[        S-
  -  [        SSS9[        * L d   e[        SS[        -
  S-  -  [        SSS9[        * L d   e[        SS[        -
  S-  -  [        SSS9[        L d   e[        S[        [        5      -  [        [        SS9[        * L d   e[        S[        [        5      -  [        [        SS9[        L d   e[        S[        [        5      -  [        [        S-  SS9[        * L d   e[        S[        [        5      -  [        [        S-  SS9[        L d   e[        S[!        [        S-  5      -  [        S[        -  [#        SS5      -  SS9[        L d   e[        S[!        [        S-  5      -  [        S[        -  [#        SS5      -  SS9[        * L d   e[        S[%        [        5      S-  -  [        [        [#        SS5      -  SS9[        * L d   e[        S[%        [        5      S-  -  [        [        [#        SS5      -  SS9[        L d   e[        [!        [        5      [        [        5      ['        [        R(                  [        R*                  5      :X  d   e[        [%        [        5      [        [        5      ['        [        R(                  [        R*                  5      :X  d   e[        [-        [        5      [        [        5      ['        [        R(                  [        R*                  5      :X  d   e[        [/        [        5      [        [        5      ['        [        R(                  [        R*                  5      :X  d   e[        [        [        5      [        -  [        SS	S9S:X  d   e[        [        S-  [        SS	S9S:X  d   e[        S[        S-  -  [        SS	S9[        L d   e[        S[        -  [        SS	S9[0        L d   e[        SS[        -  -   [        S5      [        L d   e[        SS[        -  -   [        SSS9[        * L d   e[        [        S
-  [        SSS9[        L d   e[        [        S-  [        SSS9[        * L d   e[        S[        [        5      -  [        SSS9[        * [2        -  :X  d   e[        [        S-  [        SSS9S:X  d   e[        [        [        5      [        SSS9S:X  d   e[        [        [        * -  [        SSS9[        * SS[        -
  -  -  :X  d   e[        S[        [        5      -   [        -  [        S5      [        [        [        5      S-   [        -  [        S5      :X  d   e[        S[5        [        5      -  [        SSS9[        :X  d   e[        S[5        [        5      -  [        SSS9[        * :X  d   e[        S[7        [        5      -  [        SSS9[        :X  d   e[        S[7        [        5      -  [        SSS9[        * :X  d   e[        [        S[        -  5      S[        [        5      -  -   [        SSS9[        :X  d   e[        [        S[        -  5      S[        -  -   [        SSS9[        :X  d   eg )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$        V/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_limits.pytest_basic1rp   )   s\   Ar?b   Ass"""!Qs"""Aq2#"$$$!Q$22#%%%3q61aS)Q...1a!!!QB2%%%#a&!R RC'''Q1b!R'''1sA2w2&!+++QqS!R B&&&QT1b!bS(((!a%1tAw;'A.!333!a%"a#ua!eb[!Q'????!a%"a,q1urk1aS0QQQQ!a%!)b!QC0E1q519r/1aUX4YYYY1SVQ"rc$q'k111QUAq!$SVR777qsQwB'1,,,B3155(((q!Q&!%%///AEAqc*b000AEAqc*rc111AEA:q!-"444AEA:q!-3333q61bc*rc1113q61bc*b0003q61bd,3333q61bd,2223q!t9a!B$!Q!7SARGGG3q!t9a!B$!Q!7SAbSHHH3q619a"Xa^"3#>2#EEE3q619a"Xa^"3#>"DDDQB;q/A/A1::#NNNNQB;q/A/A1::#NNNNQB;q/A/A1::#NNNNQB;q/A/A1::#NNNN Q1aT*a///Aq!&!+++1a4A4(B... 1a%,,, QqS!Q2%%% QqS!QC(RC///R!QC(B...R!QC(RC///47Aqc*sAg555Aq!%***a!QC(A---RCA3'B3a"f~+====!c!f*r!1a(E3q6A:2BAq,IIII 47Aq,22247Aq,33347Aq,22247Aq,333QqSAc!fH$a#6"<<<QqSAaCAS1R777rn   c                     [        [        [        -  [        SSS9S:X  d   e[        [        [        5      S-
  [        -  [        S5      S:X  d   e[        SS[        -  -   [        [        5      S:X  d   e[        [        S[        -  5      * [        [        5      S:X  d   e[        [        [        [        * 5      -   [        [        5      [        L d   e[        [        [        [        S-  * 5      -   [        [        5      [        L d   e[        [        [        [        [        5      * 5      -   [        [        5      [        L d   e[        SS[        -  -   [        [        * 5      -
  [        [        5      S:X  d   eg )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!Wa$***S!Q$ZB'2---S#a&\!1b)R///acCG#Q+r111rn   c                      [        S[        -  [        SSS9[        L d   e[        S[        -  [        SSS9[        * L d   eg )Nrb   r   r_   r`   rc   rI   rU   r   rm   rn   ro   test_basic3rw   {   s>    1a$***1a$+++rn   c                  0   [        S[        -  [        [        -  -   [        S5      S:X  d   e[        S[        -  [        [        -  -   [        S5      S[        -   :X  d   e[        S[        S-  -  [        [        S-  -  -   [        S5      S[        S-  -
  :X  d   e[        [        [        S-   5      [        [        5      -
  [        [        5      S:X  d   e[        S[        S-  S-   -  [        S[        45      S[        -  [        S5      -  S	-  :X  d   eg )
Nr^   r   rb      rh   rg   i   rd   	   )rI   rU   rV   r*   r   rG   r   rm   rn   ro   test_basic4r{      s    1qsAq!Q&&&1qsAq!QU***1a4!AG)#Q+sQqSy888a!etAw&2.!333Q1q\Aq":.!B$tAw,q.@@@rn   c            	      J   [        SSS9u  pn[        X-  5      [        U 5      [        U5      -
  -
  nUR                  U [        5      S:X  d   eX2-  R                  U [        5      S:X  d   e[        SSS9u  pEUS-  US-
  US-   -  [        US-   5      -  US-  S-   S-  -  SUS-  S-   US-   -  -  -   SU-  [	        XT-  5      -  US-  S-  S	-
  [        US-  US-  -   5      -  -   US-  S-   S-  -  -
  -  n[        Xe[        5      [
        US
-  -  US-  S-   S-  -  :X  d   eg )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      sa   g-GA!ACCFSVO$A771b>QE==B1$$$Wt,FC6C!GcAg&s1q5z136A:/AAQIa%H E VDK/36!8c>3sAvdH D 3 1fqj1_%% &D "CFCFQJ?!::::rn   c                      [        [        [        S-
  S5      S-   [        S-   -  [        SS5      [        SS5      :X  d   eg )N   rd   r^   rg   r_   rb      )rI   r)   rU   r   rm   rn   ro   test_piecewiser      s:    )AE1%)AE2Ar3?8Ar?RRRrn   c                     S[        [        5      -  [        S[        -  S-
  [        [        SSS[        -  S-
  S-  -  -
  5      5      -  S[        -  S-
  S:  4SS[        -  -
  [        [        SSS[        -  S-
  S-  -  -
  5      5      -  S45      -  n [        [        S-  S-  [        S:*  4[        S-  S-
  S45      n[        [        S-
  S	-  [        S
:  4[        S-
  S	-  [        S:  4[        [        [        S-
  5      5      S45      n[	        U [        S5      S:X  d   e[	        U[        S5      S:X  d   e[	        U[        S
5      S:X  d   eg )Nr^      rb   r   Tr~   g      ?rz   re   ri   rd   )r*   rU   r+   r   rI   )func1func2func3s      ro   test_piecewise2r      sK   d1gIi!A#'3tA1Q37Q,4F/G+H!H!A#PQ'K !1Wc$q1acAg\>'9":;;TBD DEq!tAvqCx(1Q3;*=>EA{AF+q1uk1q5-ADQQRUDTVZC[\E1"""1"""2!###rn   c                       " S S[         5      n [        U " [        5      [        [        5      [	        U " [        5      [        [        5      :X  d   eg )Nc                   $    \ rS rSr\S 5       rSrg)test_basic5.<locals>.my   c                 J    U[         R                  L a  [         R                  $ g N)r   rl   rj   )clsargs     ro   evaltest_basic5.<locals>.my.eval   s    ajj uu !rn   rm   N)__name__
__module____qualname____firstlineno__classmethodr   __static_attributes__rm   rn   ro   myr      s    		 
	rn   r   )r   rI   rU   r   rH   )r   s    ro   test_basic5r      s8    X 
 A2%1q""5555rn   c                      [        [        [        -  [        [        -  -   [        S5      [        [        -  S[        -  -   :X  d   eg Nr^   )rI   rU   rV   rW   rm   rn   ro   test_issue_3885r      s1    1qsAq!QqS1Q3Y...rn   c                  >   [        [        [        5      [        -  [        S5      S:w  d   e[        [        [        5      [        -  [        S5      R                  5       S:X  d   e[        [        [        SSS9R                  [        [        S[        S5      4:X  d   eg )Nr   rb   rf   r`   )rH   r6   rU   doitargsr   rm   rn   ro   
test_Limitr      su    Q1a A%%%Q1a %%'1,,,Aqd#((Q1fTl,CCCCrn   c                  @   [        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        S	S5      S	:X  d   e[        [        [        5      [        S	S5      S
:X  d   e[        [        [        S[        -  5      -  S-  [        SS5      [        SS5      :X  d   e[        [        [        S-   5      [        [        5      -
  [        [        5      [        [        R                  * [        S5      S-  5      :X  d   e[        [        [        [        5      5      [        [        5      S:X  d   e[        [        [        [        5      5      [        [        * 5      S:X  d   e[        [        [        [        5      5      [        [        5      S:X  d   e[        [        [        [        5      5      [        [        * 5      S:X  d   eg )Nrg   r_   rc   rh   ri   r   rb   r^         rd   r~   )
rI   r&   rU   r   r   rM   r   Halfr1   r%   rm   rn   ro   
test_floorr      sQ   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2k166'1Q4PQ66RRRR tAwB'1,,,tAwRC(B...a!1b)Q...a!1rc*b000rn   c                     [        [        [        [        5      5      [        SS5      S:X  d   e[        [        [        [        5      5      [        SS5      S:X  d   e[        [        [	        [        5      5      [        SS5      S:X  d   e[        [        [	        [        5      5      [        SS5      S:X  d   e[        [        S[        [        5      -   5      [        SS5      S:X  d   e[        [        S[        [        5      -   5      [        SS5      S:X  d   e[        [        S[	        [        5      -   5      [        SS5      S:X  d   e[        [        S[	        [        5      -   5      [        SS5      S:X  d   eg )Nr   r_   rc   ri   re   r   )rI   r&   r6   rU   r2   rm   rn   ro   &test_floor_requires_robust_assumptionsr      s   s1v1c*a///s1v1c*b000s1v1c*a///s1v1c*a///q3q6z"Aq#.!333q3q6z"Aq#.!333q3q6z"Aq#.!333q3q6z"Aq#.!333rn   c                     [        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        SS5      S:X  d   e[        [        [        5      [        S	S5      S
:X  d   e[        [        [        5      [        S	S5      S	:X  d   e[        [        [        S[        -  5      -  S-  [        SS5      [        SS5      :X  d   e[        [        [        S-   5      [        [        5      -
  [        [        5      [        [        R                  * [        S5      S-  5      :X  d   eg )Nrg   r_   ri   rc   r   rb   r^   rd   r      r~   )rI   r%   rU   r   r   rM   r   r   rm   rn   ro   test_ceilingr      s   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QS)S000 71Q3<!1a-!Q???S!GAJ.26+qvvgqQRtTUv:VVVVrn   c                     [        [        [        [        5      5      [        SS5      S:X  d   e[        [        [        [        5      5      [        SS5      S:X  d   e[        [        [	        [        5      5      [        SS5      S:X  d   e[        [        [	        [        5      5      [        SS5      S:X  d   e[        [        S[        [        5      -   5      [        SS5      S:X  d   e[        [        S[        [        5      -   5      [        SS5      S:X  d   e[        [        S[	        [        5      -   5      [        SS5      S:X  d   e[        [        S[	        [        5      -   5      [        SS5      S:X  d   eg )Nr   r_   rb   rc   re   r   )rI   r%   r6   rU   r2   rm   rn   ro   (test_ceiling_requires_robust_assumptionsr      s   Q!Q,111Q!Q,111Q!Q,111Q!Q,111SV$aC0A555SV$aC0A555SV$aC0A555SV$aC0A555rn   c                     [        [        [        5      [        [        5      [	        SS5      :X  d   e[        [        [        5      S[        -  -  [        [        5      [	        SS5      :X  d   e[        [        [        5      S[        -  -  [        [        * 5      [	        S[        5      :X  d   e[        [        [        5      [        -  [        [        5      [	        S[        5      :X  d   e[        [        [        [        5      5      [        SS5      S:X  d   e[        [        [        [        5      5      [        SS5      S:X  d   e[        [        [        [        5      5      [        SS5      S:X  d   e[        [        [        S-  5      [        SS5      S:X  d   e[        [        S 5        [        [        S[        -  S-   5      [        SS5      S:X  d   e[        [        S[        -  S-   5      [        SS5      S:X  d   e[        [        [        [        R                  -   5      [        SS5      [        S5      S-  :X  d   e[        [        S[        -  5      [        S5      [	        SS5      :X  d   eg )	Nr   rb   r_   rc   rf   r^   c                  @    [        [        [        5      [        SS5      $ Nr   rf   )rI   r'   rU   rm   rn   ro   <lambda>test_frac.<locals>.<lambda>  s    uT!WaD9rn   rg   )rI   r'   rU   r   rM   r6   r2   rR   
ValueErrorr   r   rm   rn   ro   	test_fracr      s   a!R K1$5555a1Q3B';q!+<<<<a1Q3RC(K2,>>>>a!Q#{1b'9999c!fq!S)Q...c!fq!S)Q...c!fq!T*a///adQ4(A---
:9:bdQhAs+q000bdQhAs+q000a!&&j!1a.!A$q&888acAq![A%6666rn   c                     [        [        [        [        5      [        -  5      [        SS5      S:X  d   e[        [        [        [        5      [        -  5      [        SS5      S:X  d   e[        [        [	        [        5      * [        -  5      [        SS5      S:X  d   e[        [        [	        [        5      * [        -  5      [        SS5      S:X  d   eg )Nr   r_   rc   rg   )rI   r&   r6   rU   r7   rm   rn   ro   test_issue_14355r     s    s1vax!Q,111s1vax!Q,111Awqy!1a-333Awqy!1a-333rn   c                      [        SSS9n [        [        U 5      [        SU -  5      -  U S5      S:X  d   e[        [        U 5      [	        U S-   5      -   [	        U 5      -
  U [
        5      [        S-  :X  d   eg )NrU   Trealrb   r   r^   )r   rI   r1   r6   r*   r   r   rU   s    ro   	test_atanr     sk    sAaQqS!1a(A---a4A;&a0!R8BqD@@@rn   c            
      $   [        [        [        5      [        S5      S:X  d   e[        [        [        [        5      5      [        S5      S:X  d   e[        [        [	        [        5      5      [        S5      S:X  d   e[        [        [        [        S-   5      5      [        S5      [        S5      :X  d   e[        [        [        [        -   5      [        [        [        -
  5      -
  S[        -  -  [        S5      [        [        5      :X  d   e[        [        [        [        5      [        S-  -  5      [        [        5      S:X  d   e[        [        [        [        [        5      [        S-  -  5      [        [        [        S-   5      [        S-   S-  -  5      -  S-
  -  [        [        5      S:X  d   e[        [        [        [        S-
  5      S-  S-
  5      [        SS5      [        :X  d   e[        [        [        [        5      5      [        S5      [        :X  d   e[        [        [        [        [        5      5      5      [        S5      [        :X  d   e[        SSS9n [        [        [        U 5      S-   5      [        U 5      -  U [        5      S:X  d   e[        U [        SU -  [        -   5      [        [        SU -  -
  5      -
  -  S-  U S5      S:X  d   e[        [	        U 5      [        U 5      -  U [        S	5      S
:X  d   eg )Nr   rb   r^   rd   r_   rW   Tr}   rc   ri   )rI   absrU   r6   r2   r   rV   r   r   r   r   r   rW   s    ro   test_set_signsr     sP   QA!###SVa#q(((SVa#q(((SQZ!Q'3q6111 #a!e*s1q5z)AaC0!Q747BBB SVAqD[!1b)Q...CAq!t$SQUQUQJ)>%??!CDaLPQQQQ SQZ]Q&'As3r999 SVa#r)))SQ[!1a(B... 	sT"ASVaZQ'B/1444 C!aL3q1Q3w</02Aq9Q>>> QQB,222rn   c                  (   [        SSS9n [        [        SU -  5      [        U 5      -   U SS5      [	        SS5      :X  d   e[        [        S[        [        U 5      5      [        [        SU -  5      5      -  -   5      U S5      [        S5      :X  d   eg )	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#ha(!Q4B8JJJJQd1gtC!H~5561=QGGGrn   c                      [        SSS9n SU -  [        U * [        -  5      -  n[        U[        [        5      S:X  d   eUR                  [        [        5      S:X  d   eg )NrW   Tr}   ri   r   )r   r   rU   rI   r   )rW   fs     ro   test_issue_3871r   >  sS    sT"A
1S!AYAAr?a771b>Qrn   c                  v   [        S5      n [        SSS9n[        SX-  -   U -  U [        5      [        U5      :X  d   e[        SUSU -  -  -   U -  U [        5      [        US-  5      :X  d   e[        SUSU -  S-   -  -   U -  U [        5      [        US-  5      :X  d   e[        US-
  US-   -  U-  U[        5      [        S5      :X  d   e[        SSSU-  -   U-  -   U[        5      S[        R
                  -   :X  d   e[        SSU-  -   U-  SU-  U-  -  U[        5      [        [	        S	5      5      :X  d   eg )
NrY   rU   Tr   rb   r^   rg   r   z1/3)r   rI   r   r   r   Exp1rY   rU   s     ro   test_exponentialr   E  s4   sAsA!ac'Aq"%Q///!a1g+!1b)S1X555!a1qk/A%q"-QqS9991q51q5/A%q"-R888a!A#g\!1b)QZ777!ac'AqsQh&2.#ah-???rn   c                      [        S5      n [        S[        U [        U 5      -   -  -   U -  U [        5      [        [        5      :X  d   eg )NrY   rb   )r   rI   rU   r6   r   r   )rY   s    ro   test_exponential2r   P  s<    sA!aSVn$q(!R0CF:::rn   c                      [        S[        -  [        5      n [        U [        [        5      nUR	                  5       [        L d   eg r   rF   rU   rH   r   r   r   ls     ro   	test_doitr   U  s1    QAaBA668r>>rn   c            
         [        [        [        5      [        [        S-   5      -
  [        [        5      [	        SS5      :X  d   e[        [        [        5      [        [        S-   5      -
  S-   [        [        5      [	        SS5      :X  d   e[        [        [        5      [        [        5      [        [        5      -  -
  [        [        5      [	        SS5      :X  d   eS[        S5      -   S-  n S[        S5      -   S-  n[        [	        X5      SS[        S5      -   -  SS9n[        [        [        [        [        5      R                  [        5      [        S	[        45      R                  5       R                  [        5      5      [        [        5      U:X  d   e[        [	        S[        S5      S-  -   [        S5      S-  S-   5      SS[        S5      -
  -  5      n[        [        [        [        [        5      R                  [        5      [        S	[        45      R                  5       R                  [        5      5      [        [        5      U:X  d   e[        [        [        5      S-   S-  [        -  [        [        5      [	        S	[        5      :X  d   eS[        * -  [        [        5      S-   [        -  -  n[        U[        [        5      [	        S	[        5      :X  d   eg )
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0BBBBQ#a!e*$q(!R0KA4FFFF Q#a&Q-'B/;r13EEEE s1v+qB
c!f*aB	[ !R#a&[/E	BB#c!fnnS1Aq!9=BBDLLSQRTUWYZ^````	[c!fQhAq15q!c!f*~	FB#c!fnnS1Aq!9=BBDLLSQRTUWYZ^````3q6A:q.1$a,Ar0BBBB 	
QBQ!aAAr?k!R0000rn   c                  b   [        [        S[        5      [        [        5      S:X  d   e[        [        S[        5      [        [        * 5      S:X  d   e[        [        S[        5      [        [        [        -  5      [        [        -  :X  d   e[        [        S[        5      [        [        * [        -  5      [        * [        -  :X  d   e[        [        S[        5      [        [        5      S:X  d   e[        [        S[        5      [        [        * 5      S:X  d   e[        [        S[        5      [        [        [        -  5      [        * :X  d   e[        [        S[        5      [        [        * [        -  5      [        * :X  d   e[        [        S[        5      [        [        5      [        :X  d   e[        [        S[        5      [        [        * 5      [        * :X  d   e[        [        S[        5      [        [        [        -  5      S:X  d   e[        [        S[        5      [        [        * [        -  5      S:X  d   e[        [        S[        5      [        [        5      S:X  d   e[        [        S[        5      [        [        * 5      [        * [        -  :X  d   e[        [        S[        5      [        [        [        -  5      S:X  d   e[        [        S[        5      [        [        * [        -  5      S:X  d   e[        [        S[        5      [        [        5      S:X  d   eg Nrb   r   )rI   r:   rU   r   r   r9   r8   r;   rm   rn   ro   !test_bessel_functions_at_infinityr   r  s9    A2&!+++AB3'1,,,A1R4(BqD000AA2b5)bSU222A2&!+++AB3'1,,,A1R4(RC///AA2b5)bS000A2&",,,AB3'B3...A1R4(A---AA2b5)Q...A2&!+++AB3'B3q5000A1R4(A---AA2b5)Q... A2&!+++rn   c                      [        S[        -  [        5      n [        U [        [        5      nUR	                  SS9U:X  d   eg )Nr^   Fdeepr   r   s     ro   
test_doit2r     s8    QAaBA66u6"""rn   c                      [        [        [        [        5      -  [        [        5      S-
  -  [        [        * 5      S:X  d   eg r   rs   rm   rn   ro   test_issue_2929r     s0    !c!f*s1vz*As3q888rn   c                     [        S[        [        5      -
  [        S-  -  [        [        R                  5      SS[        [        R                  5      -  -
  :X  d   e[        [        [        [        S-   5      S-   5      [        S5      [        S[        S5      -   5      :X  d   e[        [        [        [        S-   5      S-   5      [        S5      S[        S5      -   :X  d   eg )Nrb   r^   r   r   )rI   r2   rU   r   r   r6   r   rm   rn   ro   test_issue_3792r     s    !c!f*ad"Aqvv.!aAFFm2CCCCSQZ!^$a+s1s1v:>>>SQZ!^$a+q3q6z999rn   c                     [        S[        S-   -  [        S5      [        SS5      :X  d   e[        S[        [        -   -  [        S5      [        R
                  S[        -   -  :X  d   e[        [        [        5      [        S-  S-   -  [        S5      [        S5      S-  :X  d   e[        [        [        5      [        S-  [        -   -  [        S5      [        S5      S[        -   -  :X  d   eg )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AFQ"aeeQVn444QA"Aq)SVAX555QA#Q*c!fa"fo===rn   c                      [        [        [        5      [        SSS9[        L d   e[        [        [        5      [        [        S-  SS9S:X  d   eg )Nr   r_   r`   r^   )rI   r3   rU   r   r   rm   rn   ro   test_issue_4547r     s@    QA3'2---QBqDc*a///rn   c                     [        [        S-  [        [        5      [        S-  s=:X  a
  [        L d   e   e[        [        S-  [        S5      S:X  d   e[        [        S-  [        S5      S:X  d   e[        [        S-  [        [        5      S:X  d   e[        [        S-  [        S5      [        R                  :X  d   eg )Nr~      r   r   g      )rI   rU   r   r   r   rm   rn   ro   test_issue_5164r     s    CB2s70b00000CB1$$$CA!###TAr"a'''TAq!QVV+++rn   c                  f    SS[         -  -   S[         -  -  n [        U [         S5      [        :X  d   eg )N      ?r   )rU   rI   r
   )funcs    ro   test_issue_5383r     s0    cAg1-Dq!!!!rn   c                  H   [         [        S5      S-  -   [        [         5      -  [         -
  [        S[        -  5      S-  -   [        [	        [         5      5      -
  [        S5      S[         -  -  -   [         S-  -  n [        U [         [        5      [        S5      S-  :X  d   eg )Nrb   r^   r   rd   ih  )rU   r   r   r   r   rI   r   r   s    ro   test_issue_14793r     s    1aZ3q6!A%AbD	!3IaLaD"Q$K()*A.Dq"1c)))rn   c                     [        [        [        [        * /SS/SS[        R                  [        SS5      /SS/5      5      n / [        P[        P[        * P[        P[        * [        -  P[        P[        * S[        SS5      -  -  P[        PSPSPSPSPSPSPSPSP[        P[        P[        P[        * P[        P[        * [        -  P[        P[        * S[        SS5      -  -  PSPSPSPSPSPSPSPSP7n[        U 5      [        U5      :X  d   e[        [        X5      5       H+  u  nu  p4Uu  pVpxXVU-  -  n	 [        U	[        SUS9U:X  d   eM-     g ! [         a      ef = f)	Nri   rb   r^   rd   rc   r_   r   r`   )listr   rU   r   r   r   r   r   len	enumerateziprI   AssertionErrorprint)
testsresultsir   resrV   sr   deqs
             ro   test_issue_5183r	    s   !aRaQA7s% &E'r '2 's 'B 'A 'r 'B3Xa^/C+C 'R '''''''!"'$%''''3' "'%'CE'+-'02sB!Q3G/G' ' ' ' ' '  ' "#' %&'G u:W%%%#C$78;D
a1X	Qq)S000	 9
  	 t	s   =EE&c                  J   [        [        [        5      [        -  [        [        5      S:X  d   e[        [	        [        5      [        [        5      [
        S-  :X  d   e[        [        [        5      [        [        5      [        L d   e[        [        [        5      [        -  [        [        5      S:X  d   e[        [        [        5      [        [        R                  5      [        [
        5      :X  d   e[        SSS9n [        U [        SU -  5      -  U S5      S:X  d   eg )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1aff%b111sA3qs8Q"a'''rn   c                  v    [        S[        -   S[        -  -  [        R                  -
  [        S5      S:X  d   eg r   )rI   rV   r   r   rm   rn   ro   test_issue_5229r    s.    !a%1Q3!&&(!Q/1444rn   c                     [        [        [        [        /[        * S-  S[        S-  [        [        [        SS5      -  /SS/5      5      n SS[        * [        SS[        * [        SS[        [        * SS[        [        * SS[        [        * 4n[        U 5      [        U5      :X  d   e[        [        X5      5       H/  u  nu  p4Uu  pVnU" [        5      n [        U[        XgS9U:X  d   eM1     g ! [         a      ef = f)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    s    #s#a%BqD"b!Q.?@s% &E !bS"aRCQB31b2#q!R"6Gu:W%%%#C$78;DaqT	Q)S000	 9
  	 t	s   C11C?c                      [        S[        [        S5      -  -   S[        -  -  [        S5      S:X  d   e[        SS[        -  -  SS[        -  -  -   [        -  [        S5      S:X  d   eg )Nrb   rd   r   re   )rI   rU   r   rm   rn   ro   test_issue_3934r    s_    !aQi-1Q3'A.!333!ac(Q1X%)1a0A555rn   c                     [        [        S-  S[        S-  -   -  [        [        5      S:X  d   e[        [        S-  S[        S-  -   -  [        [        5      S:X  d   e[        [        S-  S[        S-  -   -  [        [        5      S:X  d   e[        [        S-  [        S-   S-  [        [        * 5      -   -  [        [        5      S:X  d   eg )Nr   rb   d   i]    rI   rU   r   r   rm   rn   ro   test_issue_5955r    s    !R%!ae)$a,111!S&1q#v:&2.!333!T'A4K(!R0A555!T'AED=3r723a<AAArn   c                      [        [        S[        [        5      -  5      [        [	        [        5      5      -  [        S5      S:X  d   eg r   )rI   r   r6   rU   r3   rm   rn   ro   test_newissuer    s2    Qs1vXs3q6{*Aq1Q666rn   c                     [        [        [        -
  [        [        5      [        [        [        -
  [        [        5      :X  d   e[        S[        [	        [        5      -   -  [        -
  [        S5      [        S[        [	        [        5      -   -  [        -
  [        S5      :X  d   e[        [        [        -  [        [        5      [        [        [        -  [        [        5      :X  d   e[        [        [        -
  S[        -  -   [        [        5      [        [        [        -
  S[        -  -   [        [        5      :X  d   eg r   )rI   rU   r   rH   r6   rm   rn   ro   test_extended_real_liner    s    RB5RB#7777AAJ"$a+uQCF
^b5H!Q/OOOOAq"r!tQ!3333R!A#q"%q2v!|Q)CCCCrn   c                      [        SSS9n [        U 5      [        -  [        SU 5      :w  d   e[        [        U S-  S-
  -  U [        5      [        L d   eg )NrU   Tr}   rb   r^   r   )r   rP   r   rI   r   s    ro   test_order_oor    sM    sT"A8B;%1+%%%QTAX2&",,,rn   c                  H    [        [        S 5        [        [        S 5        g )Nc                  T    [        [        [        [        -  5      [        [        5      $ r   rI   r   rU   rV   r   rm   rn   ro   r   !test_issue_5436.<locals>.<lambda>  s    c!A#h2(>rn   c                  V    [        [        [        * [        -  5      [        [        5      $ r   r!  rm   rn   ro   r   r"    s    c1"Q$iB(?rn   rR   NotImplementedErrorrm   rn   ro   test_issue_5436r&    s    
 >?
 ?@rn   c                  H    [        [        S 5        [        [        S 5        g )Nc                  *    [        [        [        SSS9$ )Nr   r`   rH   rU   rm   rn   ro   r    test_Limit_dir.<locals>.<lambda>  s    eAq!3rn   c                  *    [        [        [        SSS9$ )Nr   0r`   r)  rm   rn   ro   r   r*    s    uQ1#6rn   )rR   	TypeErrorr   rm   rn   ro   test_Limit_dirr.    s    
934
:67rn   c            	         [        [        S-   S-  [        S-   S-  S-   -  [        [        5      S:X  d   e[        [        S-   S-  [        S-   S-  S-   -  [        [        * 5      S:X  d   e[        [        [        SS5      -  S[        [        SS5      -  -   -  [        [        5      S:X  d   e[        [        S-  S[        S-  -   -  [        [        5      S:X  d   eg )Nrb   r  M   rd   gfffffFY@rI   rU   r   r   rm   rn   ro   test_polynomialr2     s    !a%$Q 12Ar:a???!a%$Q 12As;q@@@hr1o%Q(2q/-A)ABArJaOOOeq1:~.26!;;;rn   c                     [        S[        -  S[        [        -   -  [        [        [        -   -  [        -  -   [        -  -
  [        [        5      [        S-
  [        [        -  -  :X  d   e[        S[        -  S[        [        -   -  [        [        [        -   -  [        -  -   [        -  -
  [        [        * 5      [        S-
  [        [        -  -  :X  d   eg Nrb   )rI   rV   rU   rW   r   rm   rn   ro   test_rationalr5  '  s    11q5	Aq1uIaK/22Ar:q1uqsmKKK11q5	Aq1uIaK/22As;A!}LLLrn   c                      [        [        [        5      [        -  [        S[        -  5      [        -  -
  [        S5      [
        [        [        [        -
  5      -  :X  d   eg Nr^   r   )rI   r   rU   rW   rV   r   r   rm   rn   ro   test_issue_5740r8  ,  s>    QC!HQJ&1-DQK???rn   c                      [        SSSS9n U S-   [        U S-   -  -  [        U S-   -  S-
  -  [        [        S-
  -  -
  n[        U[        S5      R                  5       U S-  :X  d   eg )NrY   TrZ   rb   r^   )r   rU   rI   cancel)rY   r  s     ro   test_issue_6366r;  0  sg    sD40A	
QAE
AAJN+aQi7AAq>  "ac)))rn   c                     [        [        5      n [        U [        [        5      [        L d   e[        [        U -  [        [        5      S:X  d   e[        U [	        S[
        -  [        -  5      [        [        -  [        -  -  -  [        [        5      S:X  d   e[        U [        [        * 5      [        [        * 5      :X  d   eg )Nr   r^   rb   )r   rU   rI   r   r*   r   r
   rC   r   s    ro   test_factorialr>  6  s    !AAr?b   1a!!! D2aL!A#)*Ar2a777AsubSz)))rn   c                     S[         S-  -  S-  [         [        SS5      -  -
  [        S[         S-  -  S-  [        R                  -
  -  S[         S-  -  S-  -   S[         S-  -  S-  -
  [        SS5      -   S[        S-   -  -  -   n [        U [        [        5      S[         S-  -  S-  S[         S-  -  S-  -   S[         -  S-  -
  [        SS5      -
  :X  d   eg )	Nre   rd   r   r^   #   ry      rb   )rU   r   rV   r   r   rI   r   r   s    ro   test_issue_6560rC  @  s    	
1a4Ahq!n$	$1QT6!8aff+<(=1WQY)')+AqD)35=a^)DFGQi(Q 
QAAr?a1fQh1a41AaCE9HQNJJJJrn   c                  F  ^^ [        S5      m[        SSS9n [        S5      n[        SSS9n[        SSS9nS	T-  TU -
  S
-   -  TU TU -
  S
-   -  -   -  U-  U S
-
  TTU -
  S	-   -  TU TU -
  S
-   -  -   -  U-  -  -   T-
  TU-  T-
  -  mTR                  XS
-   5      m[        [        UU4S j5        [	        TR                  X5      T[
        5      S
:X  d   e[	        TR                  X5      T[
        5      R                  5       S	US
-   -  U -   S
-
  U S
-   US
-   -  -  :X  d   eg )NrY   r  Tr}   r   pmnegativer^   rb   c                  &   > [        T T[        5      $ r   )rI   r   )r   rY   s   ro   r   !test_issue_5172.<locals>.<lambda>O  s    dAr(:rn   )r   subsrR   r%  rI   r   rK   )r  r   rE  rF  r   rY   s       @@ro   test_issue_5172rL  E  sI   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99QAD
 :;1!R(A---1!R(113	
QUa!	a!eq1u--. . .rn   c                  ~    [        S5      n [        [        [        [        U -   -  5      [        [        5      S:X  d   eg )Nr   rb   )r   rI   r*   rU   r   r   s    ro   test_issue_7088rO  U  s.    sAaQi!R(A---rn   c                  \   [        [        [        [        -  S-   5      [        S5      [        [        S5      -
  :X  d   e[        [        [        [        -  S-   5      [        SS5      [        S5      :X  d   e[        [        [        [        -  S-
  5      [        S5      [        S5      * :X  d   e[        [        [        [        -  S-
  5      [        SS5      [        * [        S5      -   :X  d   e[        [        [        [        -  S-   5      [        S5      [        S5      * :X  d   e[        [        [        [        -  S-   5      [        SS5      [        S5      :X  d   e[        [        [        [        -  S-
  5      [        S5      [        S5      :X  d   e[        [        [        [        -  S-
  5      [        SS5      S[        -  [        S5      -
  :X  d   e[        [        [        S[        -  -   5      [        S5      [        [        S5      -  :X  d   e[        [        [        S[        -  -   5      [        SS5      [        * [        [        S5      -  -   :X  d   e[        [        [        S[        -  -
  5      [        S5      [        [        [        S5      -  -
  :X  d   e[        [        [        S[        -  -
  5      [        SS5      [        * [        S5      -  :X  d   e[        [        S[        -  5      [        S5      [        S-  :X  d   e[        [        S[        -  5      [        SS5      [        * S-  :X  d   e[        [        [        5      [        [        5      [        S-  :X  d   e[        [        [        5      [        [        * 5      [        * S-  :X  d   e[        [        [        [        S5      S-  [        -  -   5      [        S5      [        [        [        [        S5      S-  5      -  -
  :X  d   e[        [        [        [        S5      S-  [        -  -   5      [        SS5      [        * [        [        S5      S-  5      -  :X  d   e[        [        [        [        S5      S-  [        -  -
  5      [        S5      [        [        [        S5      S-  5      -  :X  d   e[        [        [        [        S5      S-  [        -  -
  5      [        SS5      [        * [        [        [        S5      S-  5      -  -   :X  d   e[        [        [        5      [        S5      [        S-  :X  d   e[        [        [        5      [        SS5      [        * S-  :X  d   e[        [        [        [        -  [        S5      S-  -   5      [        S5      [        [        S5      S-  5      :X  d   e[        [        [        [        -  [        S5      S-  -   5      [        SS5      [        [        S5      S-  5      * :X  d   e[        [        [        [        -  [        S5      S-  -
  5      [        S5      S[        -  [        [        S5      * S-  5      -
  :X  d   e[        [        [        [        -  [        S5      S-  -
  5      [        SS5      [        [        S5      * S-  5      :X  d   e[        [        [        [        -  [        S5      S-  -   5      [        S5      [        [        S5      S-  5      :X  d   e[        [        [        [        -  [        S5      S-  -   5      [        SS5      [        [        [        S5      S-  5      -
  :X  d   e[        [        [        [        -  [        S5      S-  -
  5      [        S5      [        * [        [        S5      S-  5      -   :X  d   e[        [        [        [        -  [        S5      S-  -
  5      [        SS5      [        [        S5      S-  5      * :X  d   e[        [        [        [        -  S-
  5      [        S5      [        [        -  :X  d   e[        [        [        [        -  S-
  5      [        SS5      [        * [        -  :X  d   e[        [        [        * [        -  S-
  5      [        S5      [        * [        -  :X  d   e[        [        [        * [        -  S-
  5      [        SS5      [        [        -  :X  d   e[        [        [        [        -  S-
  5      [        S5      [        :X  d   e[        [        [        [        -  S-
  5      [        SS5      [        * :X  d   e[        [        [        * [        -  S-
  5      [        S5      [        * :X  d   e[        [        [        * [        -  S-
  5      [        SS5      [        :X  d   e[        [!        [        [        -  S-
  5      [        S5      S[        S5      S-  -  :X  d   e[        [!        [        [        -  S-
  5      [        SS5      S[        S5      S-  -  * :X  d   e[        [!        [        * [        -  S-
  5      [        S5      S[        S5      S-  -  * :X  d   e[        [!        [        * [        -  S-
  5      [        SS5      S[        S5      S-  -  :X  d   eg )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_cutsrQ  Z  s   acAg1%d1g555acAg1c*d1g555acAg1%$q'111acAg1c*rcDGm;;;acAg1%$q'111acAg1c*d1g555acAg1%b111acAg1c*adT"Xo===a!A#g1%58333a!A#g1c*rcAeAhJ.>>>>a!A#g1%aaj888a!A#g1c*qbqk999acAq!RT)))acAq#&2#a%///a!R BqD(((a!bS!bSU***a!A$q&(l#Q*b1U1Q46]?.BBBBa!A$q&(l#Q3/A2eAaDFm3CCCCa!A$q&(l#Q*aad1fo===a!A$q&(l#Q3/B351a=3HHHHa!Q2a4'''a!Q$A---acAaDFl#Q*d1Q46l:::acAaDFl#Q3/D1aL=@@@acAaDFl#Q*adT1Q4%'].BBBBacAaDFl#Q3/41a=@@@acAaDFl#Q*d1Q46l:::acAaDFl#Q3/2QqT!V3DDDDacAaDFl#Q*rcD1aL.@@@@acAaDFl#Q3/D1aL=@@@QqS1Wq!$",,,QqS1Wq!S)aRU222aRTAX1%!B...aRTAX1c*ad222acAg1%***acAg1c*qb000qbdQhA&1",,,qbdQhAs+q000acAg1%"!Q777acAg1c*ad1f~o===qbdQhA&B!A$q&>/999qbdQhAs+ad1f~===rn   c                  "   [        S5      n [        S[        S[        -   5      [        U 5      S-  -  -
  [        S[        -
  5      [	        U 5      S-  -  -
  -  n[        U[        S5      S[	        U 5      S-  [        R                  -
  -  :X  d   eg )Nr   rb   r^   r   )r   rW   r*   r6   r2   rI   r   r   )r   r   s     ro   test_issue_6364rS    su    sA	1tAE{3q619$$tAE{3q619'<<=AAq>QA	AFF 23333rn   c                      [        [        S[        [        * 5      -  5      [        S-  -  [        S5      [        S[        -  5      :X  d   eg r7  )rI   r   r<   rU   r   rm   rn   ro   test_issue_6682rU    s9    Qr1"vXq!t#Q*c!J,.????rn   c                     [        S5      n [        U [        -  [        S5      [        [	        U 5      -  :X  d   e[        U * [        -  [        S5      [        * [	        U 5      -  :X  d   e[        U * [        -  [        [        5      [        * [	        U 5      -  :X  d   e[        U [        -  [        [        5      [        [	        U 5      -  :X  d   eg )Nr   r   )r   rI   rU   r   r   rN  s    ro   test_issue_4099rW    s    sA1ar$q'z)))!Aq!DG+++!Aq""T!W,,,1a47
***rn   c            	         [        S5      n [        [        S[        [        U -   5      -   5      [        S[        [        5      -   5      -
  U -  U S5      [        [        5      S[        [        [        5      S-   5      -  -  :X  d   eg )Ndxrb   r   r^   )r   rI   r*   r   rU   )rY  s    ro   test_issue_4503rZ    sl    	B$q3q2v;'$q3q6z*::B>AFA$s1vz""#$ $ $rn   c                      [        SSSS[        * 5      n [        U 5      n[        U[        SS5      S:X  d   e[        U[        [        5      [        * :X  d   eg )Nrm   )rb   )r   r   rf   )rE   rU   rL   rI   r   )Ggs     ro   test_issue_6052r^    sP    BdQB'AAAAq$1$$$Ar?rc!!!rn   c                  H   [        [        5      [        S[        S[        -  5      5      -  n [        [        [	        U [        [        5      -  U -  [        S5      S:X  d   e[        [        [	        U [        [        5      -  U -  [        S5      R                  5       S:X  d   eg )Nrb   ry   r   r^   g       @)r*   rU   r8   rI   r   evalfr   s    ro   test_issue_7224ra    s|    771T!A#Y''D4a##D(!Q/14444a##D(!Q/5573>>>rn   c                     [        S5      n [        U " [        5      [        S5      [        U " [        5      [        SSS9:X  d   e[        [        U " [        5      S-  -  [        S-  U " [        5      S-  -   -  [        S5      [        [        U " [        5      S-  -  [        S-  U " [        5      S-  -   -  [        SSS9:X  d   eg )Nr   r   r_   r`   r^   r   )r   rI   rU   rH   r=  s    ro   test_issue_7391_8166rc    s    A1q!adAqc ::::1Q47AqD1Q47N+Q2eAadAgIq!taPQdTUg~<VXY[\be6ffffrn   c                  b    [        [        [        SS5      S-
  -  [        [        5      S:X  d   eg )Nrb   g    eAr   )rI   rY   r   r   rm   rn   ro   test_issue_8208re    s*    Xa%)*Ar2a777rn   c                      [        [        [        SS5      -  S-
  [        [        5      S-
  [        SS5      -  -  [        S5      S:X  d   eg )Nrb   r   r^   rd   r   r   )rI   rU   r   r*   rm   rn   ro   test_issue_8229rg    sB    !Xa^#a'$q'A+A)FF2NRSSSSrn   c                  f    [        SSS9u  p[        [        SX-  -
  5      U[        5      S:X  d   eg )Nzd tTr}   rb   ri   )r   rI   r=   r   )r  ts     ro   test_issue_8433rj    s1    54(DAQWq"%+++rn   c                      [        SSSS9n [        SSS9n[        X-  [        U* 5      -  [        U 5      -  U [        5      S:X  d   eg )NrX   T)r[   nonnegativelamdar}   r   )r   rI   r   r   r   )rX   rm  s     ro   test_issue_8481rn    sI    sDd3A7T*ECK')A,62>!CCCrn   c                      [        [        [        [        S-  5      [        [        5      [        :X  d   e[        [        [        [        S-  5      S[        * -  -  [        [        5      S:X  d   eg )Nr^   rd   r   )rI   r   rY   r   rm   rn   ro   test_issue_8462rp    sQ    !QqS!1b)R///!QqS!A1"I-q"5:::rn   c                      [        SSSS9n [        S5      n[        X-  U[        * 5      [        [        SU -  5      -  :X  d   eg )NrY   TrZ   rU   ri   )r   rI   r   r   r   s     ro   test_issue_8634rr    sA    sD40AsAq2#"T2']"2222rn   c                  t   [        SSS9n [        SSS9n[        U [        -  U [        S-
  -  -
  U [        5      S:X  d   e[        U [        -  U [        S-
  -  -
  U [        5      [        :X  d   e[        U [        -  U [        S-
  -  -
  U [        5      [        :X  d   e[        U [        -  U [        U-
  S	-
  -  -
  U [        5      [        :X  d   e[        SSS9n [        U [        -  U [        S	-
  -  -
  U [        5      [        :X  d   e[        U [        -  U [        S
-   -  -
  U [        5      [        * :X  d   eg )NrU   Tr   rX   r}   r   re   g      @rb   r^   )r   rI   rY   r   )rU   rX   s     ro   test_issue_8635_18176rt    s   sAsT"AAAE
"Ar*a///AAE
"Ar*b000AAG$a,222AAEAI&2."444sT"AAAE
"Ar*b000AAE
"Ar*rc111rn   c                  Z    [        [        [        5      [        [        5      [        L d   eg r   )rI   r   rU   r   rm   rn   ro   test_issue_8730rv    s    a!R(B...rn   c                     ^ ^ [        SSS9m[        SSS9m [        [        T5      T[        T5      -  -  ST -   T-  -  T[        5      S:X  d   e[	        [
        U U4S j5        g )	NrY   Tr[   r   r}   rb   r   c                  b   > [        [        T5      T[        T5      -  -  T T-  -  T[        5      $ r   )rI   r   r   r   rY   s   ro   r   !test_issue_9252.<locals>.<lambda>  s(    s1v3q6.BQT.I1b(Qrn   )r   rI   r   r   rR   r%  rz  s   @@ro   test_issue_9252r|    s\    sD!AsT"A#a&Ac!fH%Q
2Ar:a???
 QRrn   c                  T    [        [        [        5      S-  [        SS5      S:X  d   eg )NrA  r   rc   )rI   r6   rU   rm   rn   ro   test_issue_9558r~    s#    QQ3'1,,,rn   c                      [        S[        -  [        [        S[        -  [        5      S-  -  -  [        [        5      [        :X  d   eg )Nr   r^   )rI   rX   r   r   r   rm   rn   ro   test_issue_10801r    s7    Q!hqsA.112Ar:b@@@rn   c                  p    [        SSS9u  p[        [        X-  5      [        U 5      -  U S5      U:X  d   eg )Nzs xTr   r   )r   rI   r=   )r  rU   s     ro   test_issue_10976r    s5    5t$DAQS#a&!Q'1,,,rn   c                      [        [        [        5      [        [        S5      -  [        -  [	        S[
        -  [        -  5      -  -  [        [        5      S:X  d   eg Nrb   r^   )rI   r   rY   r   r*   r   r   rm   rn   ro   test_issue_9041r    s?    1!CF(Qad1f!=>2F!KKKrn   c                  *   [        S5      u  pn[        X U5      R                  U1:X  d   e[        X US5      R                  U1:X  d   e[        X-   X-   U5      R                  U1:X  d   e[        U S-  * U-   U S-  U5      R                  X1:X  d   eg )Nzx, y, arc   r^   )r   rH   free_symbols)rU   rV   r   s      ro   test_issue_9205r    s    i GA!q>&&1#---q#++s222q!..1#555!Q$AqD!$11aV;;;rn   c                      [        S[        [        S5      -  [        S-  -  [        [        5      S:X  d   e[        S[        [        S5      S-   -  [        S-  -  [        [        5      S:X  d   eg )N   rd   rb   )rI   r   rY   r   rm   rn   ro   test_issue_9471r    s[    2Aa>1a4'2.!3332Aa
#QT)1R0B666rn   c                      [        [        [        S-   5      [        [        5      -  [        [        5      [        :X  d   eg r4  )rI   r   rY   r   r   rm   rn   ro   test_issue_10382r    s+    1q5!)A,.26+EEErn   c                  l    [        [        [        S[        -  5      5      [        [        5      S:X  d   eg r  )rI   r>   r   rU   r   rm   rn   ro   test_issue_11496r    s%    c!A#hB'1,,,rn   c                      [        [        [        [        -   [        -  [        [        -  -
  [        -  [        S5      5      [        [        [        S-
  -  -  :X  d   eg Nr   rb   )rK   rI   rU   rV   rY   rm   rn   ro   test_issue_11879r    s?    EAaC!8AqD=!+Q23qQqSzAAArn   c                      [        S5      n [        SU -  U [        5      S:X  d   e[        SSU -  -  U [        5      [        SS5      :X  d   eg )NrX   r   rb   g333333?rd   
   )r   rI   r   r   )rX   s    ro   test_limit_with_Floatr    sK    A1b!Q&&&S!VQ#x2666rn   c                      [        S[        -  S[        * S-
  -  -  [        S-   S-  -  [        S-  -  [        [        5      [        SS5      :X  d   eg Nrd   rb   r^   r1  rm   rn   ro   test_issue_10610r    sH    Aa1"q&k!1q51*,QT11b9Xa^KKKrn   c                  B   [        [        [        5      [        [        5      -   [        SS5      [        S5      :X  d   e[        [        [        5      [        [        5      -   [        SS5      [        S5      S[        -  [
        -  -   :X  d   e[        [        S 5        [        [        [        5      [        [        5      -   [        [        5      [        :X  d   e[        [        [        5      [        [        5      -   [        SS5      [        S5      :X  d   e[        [        [        5      [        [        5      -   [        SS5      [        * :X  d   e[        [        S 5        [        [        [        5      [        [        5      -   [        [        5      [        :X  d   eg )Nr   r_   r^   rc   c                  `    [        [        [        5      [        [        5      -   [        SS5      $ r   )rI   r   rU   r"   rm   rn   ro   r   "test_issue_10868.<locals>.<lambda>$      uSVeAh%61dCrn   c                  `    [        [        [        5      [        [        5      -   [        SS5      $ r   )rI   r   rU   r!   rm   rn   ro   r   r  (  r  rn   )
rI   r   rU   r"   r   r   rR   r   r   r!   rm   rn   ro   test_issue_10868r  !  s   Q%("Aq#.#a&888Q%("Aq#.#a&1Q3r6/AAA
:CDQ%("Ar*b000Q%("Aq#.#a&888Q%("Aq#.2#555
:CDQ%("Ar*b000rn   c                  p    [        [        [        [        5      -   [        -  [        [        5      S:X  d   eg r4  )rI   rY   r2   r   rm   rn   ro   test_issue_6599r  ,  s%    !c!f*aB'1,,,rn   c                  0   [        S[        -  S[        S-  -  -   [        S-  [        [        5      -   -  [        [        * 5      S:X  d   e[        S[        -  S[        S-  -  -   [        S-  [        [        5      -   -  [        [        5      [        L d   eg )Nrd   r^   r  rs   rm   rn   ro   test_issue_12555r  0  st    !Q$ArE/aec!fn5q2#>!CCC!Q$ArE/aec!fn5q"=CCCrn   c                     [        SSS9u  pn[        SSSS9u  p4pVpxn	Xt-  Xd-  -  U -  U-  [        US-  USU-  -  -  US-  -  US-
  -  USU-  -  US-  -  US-  -  US-
  -  -   USU-  -  USU-  -  -  US-  -  US-
  -  US-  SU-  -
  S-   -  -   SUSU-  -  -  XdS-   -  -  U-  U -  U-  US-  SU-  -
  S-   -  -
  SXtS-   -  -  USU-  -  -  U-  U -  U-  US-  SU-  -
  S-   -  -   SXtS-   -  -  XdS-   -  -  US-  -  US-
  -  -
  US-
  US-  SU-  -
  S-   -  -  5      -
  X@-  U-
  U -
  S-   -  n
U
R                  Xg5      R                  SS9[	        XU5      R                  SS9:X  d   eg )	Nzr z xTr   za b s0 K F0 s T)r\   r   r^   rb   r   )r   r*   rK  factorrI   )r  rW   rU   r   r   s0KF0r  Tfxs              ro   test_issue_12769r  5  s   gD)GA!#$54PA"
%*Q,r/D"a%AaC.A"5q1u"=
QqS	!Q$q!tQU##$&(1Q3iAaC&8Q&>A&F1qQRs
UV&W#X	"qs)AAJq "2%q!taczQ7#8 	
"1u+a!A#hq "2%q!taczA~6#7 	
"1u+aa%j A%q1u-	#. 23QA!a0H	"J K K NOSTUXXY\\]M]	
_B 771>  d +uRB/?/F/FD/F/QQQQrn   c                  N   [        [        S5      SS[        -  S-
  -  -  S[        -  [        -  -  S[        -  S-   S[        -  S[        R                  -  -   -  -  S[        -  S-   S[        -  S[        R                  -  -
  -  -  [        [
        5      [        S	S
5      :X  d   eg )N   re   rb   i@  r^   r   i   $   )rI   r*   rU   r   r   r   r   rm   rn   ro   test_issue_13332r  A  s    b!bdQh-'q14acAg1qx5PP1qBqD1QVV8O,-./58@R8HI I Irn   c                  R   [        [        S-  [        [        [        5      -  -   [        [        5      -   [        [        * 5      [        L d   e[        [        S-  [        [        [        5      -  -   [        [        5      -   [        [        5      [        L d   e[        [        [        [        5      -   S-  R                  5       [        [        5      [        L d   e[        [        [        [        5      -   S-  R                  5       [        [        5      [        L d   e[        [        [        [        5      -   S-  R                  5       [        [        * 5      [        L d   e[        [        [        [        5      -   S-  R                  5       [        [        * 5      [        L d   eg r   )rI   rU   r6   r2   r   expandrm   rn   ro   test_issue_12564r  F  s   A#a&3q6)1rc2b888A#a&3q6)1b1R7771s1v:/))+Q3r9991s1v:/))+Q3r9991s1v:/))+Q4:::1s1v:/))+Q4:::rn   c                  H    [        [        S 5        [        [        S 5        g )Nc                  b    [        [        [        5      [        [        5      R	                  5       $ r   )rH   r   rU   r   r   rm   rn   ro   r   "test_issue_14456.<locals>.<lambda>P  s    c!fa(=(B(B(Drn   c                  j    [        [        S-  [        S-   -  [        [        5      R                  5       $ )Nr^   rb   )rH   rU   r   r   rm   rn   ro   r   r  Q  s"    adAaCj!S(A(F(F(Hrn   r$  rm   rn   ro   test_issue_14456r  O  s    
 DE
 HIrn   c                      [        S[        S[        -  [        -  [        S-  -
  5      -  [        S[        -  S[        -  S-
  -  5      [        * L d   eg )Nrd   r      r^   )rI   r5   r   rU   r   rm   rn   ro   test_issue_14411r  T  sF    3qtAv!|$$a2r"uqy)9:rcAAArn   c                      [        [        [        S-   S-  S-   [        S-  S-   -  S-
  -  [        [        5      S:X  d   eg r  rv   rm   rn   ro   test_issue_13382r  X  s<    a!eaZ!^adQh/!34a<AAArn   c            	          [        [        S[        [        [        S-   5      -   S-   [        [        [        5      -   -  -   -  [        [        5      S:X  d   eg )Nri   rb   rI   rU   r   r   rm   rn   ro   test_issue_13403r  \  sA    B!c!a%j.1,q3q6z::;QCqHHHrn   c                     [        [        S-  * [        [        5      S-  -  [        S-
  [        S-   S-  -  [        [        S-   5      S-  -  -   [        S-  [        [        5      S-  -  -  [        [        5      S:X  d   eg r  r  rm   rn   ro   test_issue_13416r  `  sl    1a4%A	/QUQUQJ$6s1q5z1}$DDq!tCPQFTUI~VXY[]^bccccrn   c                      [        [        S-  S[        -  SSS[        -  -  -
  [        -  * S-   -  [        -
  [        S-  * S-  [        S-  -   [        -  -
  -  [        [        5      [        S-  S-  [        S-  S-  -
  [        S-  -   :X  d   eg )Nr^   rb   r   rd   r  ry   r   )rI   rY   rU   r   rm   rn   ro   test_issue_13462r  d  s    Aqsa!QqS'kA--12Q61a4%'AaC-9JJKQPRSWXZ[W[\^W^abdeaefgagWgjklnjnWnnnnrn   c                      [        S5      n [        [        U [        -
  5      [        [        5      S:X  d   e[        [        [        [        5      [        -
  5      [        [        5      S:X  d   eg )Nr   ri   )r   rI   r=   rU   r   r*   rN  s    ro   test_issue_13750r  h  sN    sAQUQ#r)))T!Wq[!1b)R///rn   c                  L   [        [        [        [        5      [	        [        5      -  [        [
        5      [        5      (       d   e[        [        [        [        5      [        [        5      -  [        [
        5      [        5      (       d   e[        [        [        [	        [        [        5      5      5      [        [
        5      [        5      (       d   e[        SS[        S-  [        [        5      -   -  -   [        S-  [        -   -  [        [
        5      [        :X  d   eg r  )	
isinstancerI   r6   rU   r   r   rH   r2   r
   rm   rn   ro   test_issue_14276r  n  s    eCFCFNAr2E::::eCFCFNAr2E::::eCCF,a4e<<<<!aAA''1a4!84a<AAArn   c                      [        S[        [        5      [        [        5      -  -  S[        -  -  [        [        5      S:X  d   eg r4  )rI   r   rU   r   rm   rn   ro   test_issue_14514r  u  s3    !SVSV^$!,a4999rn   c                      [        [        [        5      S-  [        [        5      -
  [	        [        5      [        [        5      -  -   [        [        5      [        [        R                  [        R                  5      :X  d   e[        [        [        5      S-  [        [        5      -
  [        [        5      [        [        5      -  -   [        [        5      [        [        R                  [        R                  5      :X  d   e[        [        [        5      [	        [        5      S-  -
  [        [        5      [        [        R                  [        R                  5      :X  d   e[        [        [        5      [	        [        5      S-  -
  [        [        5      [        [        R                  [        R                  5      :X  d   e[        [        [        5      [	        [        5      S-  -
  [        [        5      [        [        R                  [        R                  5      :X  d   e[        [        [        5      S-  [	        [        5      S-  -
  [        [        5      [        [        R                  [        R                  5      :X  d   e[        [	        [        5      S-  [        [        5      S-  -   [        [        5      -
  [        [        5      [        [        R                  * [        R                  5      :X  d   eg r   )rI   r6   rU   r2   r7   r4   r   rM   r   rk   rl   r3   r   rm   rn   ro   test_issues_14525r  y  s   QSV#c!fSVm3Q;{1K]K]_`_i_i?jjjjQSV#c!fSVm3Q;{1K]K]_`_i_i?jjjjQ#a&!)#Q+{1;M;Mqzz/ZZZZQ#a&!)#Q+{1;M;Mquu/UUUUQ#a&!)#Q+{1;M;Mquu/UUUUQSVQY&2.+a>P>PRSRWRW2XXXXQSVQY&Q/B7;vqzz;ZZZZrn   c                      [        [        [        5      [        [        [        S-  -
  5      -  [        S-   -  [        [        5      S:X  d   eg Nr^   rb   r   )rI   r*   rU   r2   r   rm   rn   ro   test_issue_14574r    s7    aQAX&!a%0!R8A===rn   c                  |   [        [        [        5      [        [        5      [        R
                  :X  d   e[        S[        [        5      -   [        [        5      S[        R
                  -   :X  d   e[        S[        [        5      -  [        [        5      [        SS5      :X  d   e[        [        [        5      [        [        5      [        R
                  :X  d   e[        [        [        5      [        [        * 5      [        SS5      :X  d   e[        S[        [        5      -  [        [        * 5      S:X  d   eg )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8A;2&(1a.888!a$...!a"%"a8888A;B3'2---rn   c                  &    [        [        S 5        g )Nc                      [        [        [        [        -  5      [	        [
        [        -  5      -  [        [        5      $ r   )rI   r   r   rU   r6   r   r   rm   rn   ro   r   "test_issue_14377.<locals>.<lambda>  s"    c!A#hs2a4y.@!R(Hrn   r$  rm   rn   ro   test_issue_14377r    s    
 HIrn   c                  `   [         S-  S[         S-  -  S[         S-  S-
  -  [         S-  -  [        [         S-  S-   5      -  -
  S[         S-  S-
  -  [         S-  -  [        [         S-  [         -   S-   5      -  -   [         -   S-   -  n [        U [         [        5      [	        S5      S-  :X  d   eg )Nr^   rg   rd   rb   )rU   rB   rI   r   r   rB  s    ro   test_issue_15146r    s    	
1AqD1adQh<!Q$.A1BBB	1a4!8q!tgadQhl334678:;< 	=AAr?ad1f$$$rn   c                     S[         -  SS[         * -  SS[         -  -  [         -   S-   -  -   -  [         S-   -  [         S-   -  n [        U [         [        5      [        S5      :X  d   e[	        [         S5      S-  S[         -  [        [         5      -  -   S[         -  -   [        [         S-   5      S[        [         5      -  -   S[         -  -   -  n [        U [         [        5      S:X  d   eg )Nr^   rg   rb   r   r  re   rd   )rU   rI   r   r   r   r   rB  s    ro   test_issue_15202r    s    	
Aq1r7Bq!tGaK!O,,	-q1u	5Q?AAr?c!f$$$	QA1Yq\)	)AqD	0Yq1u5E)TU,5VY[]^Y^5^_AAr?b   rn   c                  v    [        [        S-  [        S-   S-  -
  [        S-  -  [        [        5      S:X  d   eg )Ni  rb   i  i0rv   rm   rn   ro   test_issue_15282r    s3    !T'QUTM)QW4a<EEErn   c                      [        [        * [        [        [        5      S-   5      -   [        -  [        [        SS9S:X  d   eg )Nrb   rc   r`   r   )rI   rU   r   r   r   rm   rn   ro   test_issue_15984r    s3    1"s3q6A:&)1bc:a???rn   c                  v    [        [        [        S5      [        [        5      -  [        [        5      S:X  d   eg r4  )rI   rD   rU   rC   r   rm   rn   ro   test_issue_13571r    s)    Aq!E!H,a4999rn   c                      [        [        [        [        5      5      [        S5      [        [        [        R
                  5      5      :X  d   eg r4  )rI   r,   r?   rU   r   r   rm   rn   ro   test_issue_13575r    s.    d1g1%d155k)::::rn   c                     [        [        [        5      [        -  [        SSS9R                  5       S:X  d   e[        [        S-  [        SSS9R                  5       S:X  d   e[        S[        S-  -  [        SSS9R                  5       [        L d   e[        S[        -  [        SSS9R                  5       [
        L d   eg )Nr   rf   r`   rb   r^   )rH   r6   rU   r   r   r   rm   rn   ro   test_issue_17325r    s    Q1aT*//1Q666Aq!&++-2221a4A4(--/25551a%**,333rn   c                  V    [        [        5      R                  [        S5      S:X  d   eg Nr   )r   rU   rI   rm   rn   ro   test_issue_10978r    s!    A;Q"a'''rn   c                  `    [        [        [        S-  5      [        [        5      [        L d   eg r   )rI   r&   rY   r   rm   rn   ro   test_issue_14313_commentr    s!    qsQ#r)))rn   c                  |    SS[         -  -
  [         -  R                  [         5      n [        U [         SSS9S:X  d   eg Nrb   r_   r`   )rU   r   rI   )r  s    ro   test_issue_15323r    s7    
ac'AAAAqc"a'''rn   c                      [        [        [        [        5      * 5      * [        [        5      -  [        S5      S:X  d   eg r4  )rI   r   r   rU   rm   rn   ro   test_issue_12571r    s0    (CF7##CF*Aq1Q666rn   c                      [        [        S-  [        S-   [        -  [        -  -  [        S-   [        S-   -  [        S-   -  -  [        [        5      [        S5      :X  d   eg r  r  rm   rn   ro   test_issue_14590r    sM    !Q$Q	A~%QQQ(?@!RHCPQFRRRrn   c                      [        S5      u  p[        [        U-  [        U-  -
  [        U -  [        U -  -
  -  [        [        5      U[        U * U-   -  -  U -  :X  d   eg )Na b)r   rI   rU   rV   r   r   s     ro   test_issue_14393r    sS    5>DA!Q$A+1q!t,a3qaR!V}QFFFrn   c                      [        [        [        S-   5      S[        S-   -  -  [        [        5      S[        -  -  -
  [        [        5      [	        S5      :X  d   eg )Nrb   ri   )rI   r   rY   r   r   rm   rn   ro   test_issue_14556r    sH    1q5!Aq1uI.1!1DDaLPSTVPWWWWrn   c                      [        S[        S5      S-  [        S-   -  -   S[        -  -  S[        S5      S-  [        S-
  -  -  -  [        [        5      [        :X  d   eg )Nrb   r^   rd   r   rI   r   rU   r   rm   rn   ro   test_issue_14811r    sU    11a1q5)*ad3a1Q46QU:K6LMqRTUY[[[[rn   c                  ^    [        [        [        5      [        S5      [        S5      :X  d   eg )Ni ʚ;)rI   r   rU   rm   rn   ro   test_issue_16222r    s!    QJ'3z?:::rn   c                      [        [        [        S-   -  [        S-   [        -  -   [        [        S-   -  -  [        -  [        [        5      [        [        S5      5      :X  d   eg r4  r  rm   rn   ro   test_issue_16714r    sI    1q1u:Q
*a!a%j81<aDCPQFSSSrn   c                  V   [        SSS9n [        [        [        U -   [        5      [        U * -  -  [        [        5      S[        U S-   5      -  :X  d   e[        SSSS9n [        [        [        U -   [        5      [        U * -  -  [        [        5      S[        U S-   5      -  :X  d   eg )NrW   Tr}   rb   )r\   r[   )r   rI   r   rY   r   rC   r   s    ro   test_issue_16722r    s    d#A!a%#ArE)1b1QuQU|^CCCdD1A!a%#ArE)1b1QuQU|^CCCrn   c                  &   [        [        S-   S-   [        S-   S-   [        [        S-   5      -  -  [        S-   -  [        [        5      -  [        S-   -  [        [        5      S:X  d   e[        [        S-   S-  [        [        5      -  [        S-   [        S-   -  [        [        S-   5      -  -  [        [        5      S:X  d   e[        [        S-   [        [        5      -  [        [        [        S-   5      -  -  [        [        5      S:X  d   eg )Nrb   r^   r   rd   )rI   rY   r   r   rm   rn   ro   test_issue_17431r    s    1q5A+AEQ;)AE2B"BCa%$Q<(+,q5234b:=>? ? ?!a%!IaL(1q51q5/)AE:J*JKb  !a%9Q<'1yQ/?+?@!RHAMMMrn   c                      [        [        [        [        5      * 5      [        [        [        5      5      [        -  -
  [        S5      [        :X  d   eg r4  )rI   r<   r   rU   r   rm   rn   ro   test_issue_17671r    s4    SVGs3q6{1},a3zAAArn   c                      [        SSS9u  pp#[        U S-   U-  [        U S-   S-  US-  -  X-  -   U-   5      -
  U[        5      U* SU -  S-   -  :X  d   eg )Nza b c xTr}   rb   r^   )r   rI   r*   r   )r   r   r   rU   s       ro   test_issue_17751r    sf    T2JA!!a%T1q51*QT/AC"7!";<<aDAaCRSGTTTrn   c                      [        [        [        5      [        [        5      -  [	        S5      [        -  [        -  -  [        [
        5      [        S5      [        [        5      -  :X  d   eg r  )rI   r   rY   r*   r   r   r   rm   rn   ro   test_issue_17792r    sD    1d1g%s1vax!m3Q;tAwtBx?OOOOrn   c                      [        [        [        [        5      5      [        SS5      S:X  d   e[        [        [        [        5      5      [        SS5      S:X  d   eg )Nr   rc   ri   r_   rb   )rI   r   r6   rU   rm   rn   ro   test_issue_18118r	    sD    c!fq!S)R///c!fq!S)Q...rn   c                      [        [        [        [        5      5      [        [        [        5      5      -  [        SS5      S:X  d   eg )Nr   r_   rb   )rI   r6   r*   rU   rm   rn   ro   test_issue_18306r    s0    T!Wd3q6l*Aq#6!;;;rn   c                      [        [        [        S[        -  5      [        -   5      [        [        [        5      [        S-  -   5      -  [        [        5      S:X  d   eg )Nrd   r  )rI   r   r   rU   r   rm   rn   ro   test_issue_18378r    s@    S1X\"3s1v3#77B?1DDDrn   c                      [        S[        S5      S-  [        -  -
  S[        -  -  [        [        5      [        L d   e[        [        * [        -  [        [        5      [        L d   eg )Nrb   r^   rd   )rI   r   rU   r   r   rm   rn   ro   test_issue_18399r    sO    !ad1fQh,!A#&2.#5551"q!R C'''rn   c                      [        [        [        5      S[        [        5      -  -  [        [
        SS9[        [        [        5      S[        [        5      -  -  [        [
        SS9:X  d   eg )Nr^   rc   r`   )rI   r7   rU   r*   r   r   rH   rm   rn   ro   test_issue_18442r    sN    Q!d2h-(!RS9U3q6APTUWPXMCZ\]_agj=kkkkrn   c                      [        [        [        [        5      5      [        -  [        S5      S:X  d   e[        [        [        [        5      5      [        -  [        SS5      S:X  d   eg )Nr   rb   rc   )rI   r   r   rU   rm   rn   ro   test_issue_18452r    sJ    SVaA&!+++SVaAs+q000rn   c                     [        [        [        5      S[        -  -  [        [        5      [	        [        [        5      S[        -  -  [        [        SS9:X  d   e[        [        [        5      S[        -  -  [        [        5      [	        [        [        5      S[        -  -  [        [        SS9:X  d   e[        [        [        5      S[        -  -  [        [        5      [	        [        [        5      S[        -  -  [        [        SS9:X  d   e[        [        [        5      S-   S[        -  -  [        [        5      S:X  d   e[        [        [        5      S-   S[        -  -  [        [        5      S:X  d   e[        [        [        5      S-
  S[        -  -  [        [        5      [	        [        [        5      S-
  S[        -  -  [        [        SS9:X  d   e[        [        [        5      S-   S[        -  -  [        [        5      [        SS5      :X  d   e[        [        [        5      S-  S[        -  -  [        [        5      [        S[        5      :X  d   e[        [        [        5      S-  S[        -  -  [        [        5      [        SS5      :X  d   e[        [        [        5      S-   S[        -  -  [        [        * 5      [        S[        5      :X  d   e[        [        [        5      S-  S[        -  -  [        [        * 5      [        S[        5      :X  d   e[        [        [        5      S-  S[        -  -  [        [        * 5      [        S[        5      :X  d   eg )Nrb   rc   r`   r^   r  r   )rI   r6   rU   r   rH   r2   r7   rM   rm   rn   ro   test_issue_18473r    se   Q!A#2&%A1q"#*NNNNQ!A#2&%A1q"#*NNNNQ!A#2&%A1q"#*NNNN#a&1*!$a,111#a&2+1%q"-222#a&1*!$a,s1vzQqS6I1bVY0ZZZZ#a&1*!$a,Aq0AAAA#a&!)qs#a,Ar0BBBB#a&!)qs#Q+{1a/@@@@#a&1*!$a"-Q1CCCC#a&!)qs#Q,Ar0BBBB#a&!)qs#a"-Q1CCCCrn   c                      [        S[        S[        -  5      -  [        S[        -  5      S-   -  S[        -  -  [        [        5      [        S5      :X  d   eg Nr^   rd   rb   )rI   r   rU   r   rm   rn   ro   test_issue_18482r  *  sC    !C!H*c!A#hl+qs3Q;s1vEEErn   c            	         [        [        [        5      [        S[	        [        5      -
  5      -  [        S5      [        S5      :X  d   e[        [        [        5      [        S[	        [        5      -
  5      -  [        SSS9[        S5      :X  d   e[        [        [        5      [        S[	        [        5      -
  5      -  [        SSS9[        S5      * :X  d   eg )Nrb   r   r^   r_   r`   rc   )rI   r6   rU   r*   r2   rm   rn   ro   test_issue_18508r  .  s    QQs1vX&1-a888QQs1vX&1#6$q'AAAQQs1vX&1#647(BBBrn   c                  &    [        [        S 5        g )Nc                  Z    [        [        S[        -
  [        -  5      [        [        5      $ r   )rI   r   rY   rU   r   rm   rn   ro   r   "test_issue_18521.<locals>.<lambda>5  s    c1q5A+.>2(Frn   r$  rm   rn   ro   test_issue_18521r  4  s    
 FGrn   c                      [        SSS9u  p[        [        U 5      X5      [        U5      :X  d   e[        [        [        U 5      5      X5      [        [        U5      5      :X  d   eg )Nr  Tr}   )r   rI   r   r   r  s     ro   test_issue_18969r   8  sT    54(DA!a#x{222Xa[!1(C,<<<<rn   c                      [        [        [        [        5      S[        -  -  -  [        [        5      [	        S5      :X  d   eg r4  )rI   rY   r   r   r   rm   rn   ro   test_issue_18992r"  >  s/    IaL1Q3'(!R0CF:::rn   c                      [        S5      n [        [        U 5      [        U S-
  5      [        U S-   5      -  -  U S5      S:X  d   eg )NrU   rb   r^   r   ri   )r   rI   rC   r   s    ro   test_issue_19067r$  B  s@    sAq5Q<a!e45q!<BBBrn   c                  l    [        [        S[        -  S[        * -  -  -  [        [        5      S:X  d   eg r  rv   rm   rn   ro   test_issue_19586r&  G  s,    QT!qb'\"Ar*a///rn   c                  X    [        S5      n [        SSS9n[        X-   U S5      S:X  d   eg )NrY   rE  T)zeror   )r   rI   )rY   rE  s     ro   test_issue_13715r)  K  s0    sAsA1"""rn   c            
          [        [        S-  [        * S-
  [        S[        -  5      -  [        S-   [        S[        S-   -  5      -  -   -  [        * S-   -  [        [        5      S:X  d   eg r  )rI   rY   r6   r   rm   rn   ro   test_issue_15055r+  Q  s\    AQAaC(AE3q!a%y>+AABQBFKQPRSWXXXXrn   c            
          [        SSS9u  p[        S5      u  p#n[        X#-  U-  [        U 5      [        SU-  U-  U-  XS-  -  -   5      -  -
  X-  -   X!-  -  US5      XCU-  -   U-  :X  d   eg )Nzm viTr}   zB ti drg   r^   r   )r   rI   r*   )rF  viBtir  s        ro   test_issue_16708r0  U  s    FT*EAx HA1!$r'DGDAaQQwY)>$???!$FNPQSTUZ[ac^cZcegYggggrn   c                  z   [        [        SS[        -  5      [        [        S[        5      S-  -  -  [        [        5      S[	        S5      -  [
        -  S-  :X  d   e[        [        SS[        -  5      [        [        S[        5      S-  -  -  [        [        * 5      S[	        S5      -  [
        -  S-  :X  d   eg )Nrb   rd   r^   rg   )rI   r8   rU   r   r*   r   rm   rn   ro   test_issue_19154r2  [  s    AqD!1gamQ&6#67R@Ad1gIbLQRNRRRAqD!1gamQ&6#67bSARQZPR]ST_TTTrn   c                  D   [        SSS9n [        SSS9n[        SSS9n[        SSS9n[        SSS9n[        S5      nS	US
-  -  U -  U-  USU-  U -  U-  -  -  nUS
-  US
-  -  nXQU -  U-  -  S-
  nU* SU-  U-  -  US
U-  US
-  -  -  -
  XeX-  U-  -  S-   -  S
U-  US	-  -  -  -
  USU-  U -  U-  -  U-  -   n	[        [        U	5      U 5      * n
[	        U
SU-  U-  -
  U [
        5      S:X  d   e[	        U
R                  " 5       SU-  U-  -
  U [
        5      S:X  d   eg )NbetaTr}   hrF  omegar]  rb   rd   r^   r~   r   r   )r   r   r   r   rI   r   rK   )r4  r5  rF  wr]  r   qrE  r  Zr
   s              ro   test_issue_19453r:  `  se   &4(DsT"AsT"Aw&AsT"AAA	!Q$tAa#a%*Q,''A	1QT	A	dF1HA	
AaCE
Q!AqD\!A16!8}q'8$91Q3q!t8$DD#a%*Q,!	"A	c!fd	ASU1WdB'1,,,Aa'r2a777rn   c                  b    [        [        S5      * S-  [        -  [        [        5      S:X  d   eg )Nrb   r   r   r  rm   rn   ro   test_issue_19739r<  s  s'    1Q4%'Aq"%***rn   c                  |    [        S[        * -  [        S[        S-   -  S-   5      -  [        [        5      S:X  d   eg )Nr^   r   rb   )rI   rU   r*   r   rm   rn   ro   test_issue_19766r>  w  s5    aRa!a%j1n--q"5:::rn   c                  |   [        S5      n [        [        U [        -  5      [        -  [        [        5      [        [        U [        -  5      [        -  [        [        SS9:X  d   e[        SSS9n [        [        U [        -  5      [        -  [        [        5      [        [        U [        -  5      [        -  [        [        SS9:X  d   e[        SSS9n [        [        U [        -  5      [        [        5      [        SS5      :X  d   e[        [        U [        -  5      [        -  [        [        5      S	:X  d   eg )
NrF  rc   r`   Tr   )nonzerori   rb   r   )r   rI   r2   rU   r   rH   rM   )rF  s    ro   test_issue_19770rA  {  s    sAQqS!Q#uS1XaZBC'HHHHsAQqS!Q#uS1XaZBC'HHHHsD!AQqS1b![Q%7777QqS!Q#q(((rn   c            	         [        [        [        5      [        [        [        5      5      -  [        [        S-  5      [        [        [        5      [        [        [        5      5      -  [        [        S-  SS9:X  d   e[        [        [        5      [        [        [        5      5      -  [        [        S-  SS9[        [        [        5      [        [        [        5      5      -  [        [        S-  SS9:X  d   e[        [        [        5      [        [        [        5      5      -  [        [        S-  SS9[        [        [        5      [        [        [        5      5      -  [        [        S-  SS9:X  d   e[        [        [        [        5      5      [        [        S-  5      [        SS5      :X  d   e[        * S[        [        * 5      -  -  [        [        * [        5      :X  d   e[        S[        [        5      -  -  [        [        * [        5      :X  d   e[        S[        [        * 5      -  -  [        [        * [        5      :X  d   e[        * S[        [        5      -  -  [        [        * [        5      :X  d   eg )Nr^   r_   r`   rc   rf   ri   rb   )rI   r7   rU   r6   r   rH   rM   r   rm   rn   ro   test_issue_7535rC    s   QCF#Q1-s1vc#a&k7I1bQRdX[1\\\\QCF#Q1#6%As3q6{@RTUWYZ[W[ad:eeeeQCF#Q1$75QCPQFASUVXZ[\X\bf;ggggSVQr!t$B(::::3#rc(
{B33333qRy>["b1111qbSz?k2#r22223#b'	?k2#r2222rn   c                      [        [        S-   S[        -  -  [        -
  [        -  [        S5      [        * S-  :X  d   eg )Nrb   r   r^   )rI   rU   r
   rm   rn   ro   test_issue_20365rE    s5    1q5AaC.1$a'A.1"Q$666rn   c                      [        S[        -   S[        -  -  SS[        -  -   SS[        -  -  -  -
  [        [        5      -  [        S5      [        S-  :X  d   eg )Nrb   r^   r   )rI   rU   r0   r
   rm   rn   ro   test_issue_21031rG    sL    1q5AaC.A!Gq!A#w#77a@!QG1Q3NNNrn   c                      [        [        [        [        -  5      S[        -  S-
  -  [        S5      [        S-  :X  d   eg )Nrd   r   r   )rI   r6   r   rU   rm   rn   ro   test_issue_21038rI    s2    RTAaC"H%q!,1444rn   c                      [        [        5      [        S[        -  5      -  n [        U [        SS5      S:X  d   e[        U [        SS5      S:X  d   e[        U [        SS5      S:X  d   eg )Nrb   r   r_   rc   rf   )r   rU   r6   rI   r   s    ro   test_issue_20578rK    sc    q6C!HDa#!###a#!###a$1$$$rn   c                     [        [        5      n U R                  [        [        S9[        :X  d   eU R                  [        [        * S9[        * :X  d   e[        [        [        5      * 5      n U R                  [        [        S9[        [        * 5      :X  d   eU R                  [        [        * S9[        [        5      :X  d   e[        [        [        5      5      n U R                  [        [        S9[        [        5      :X  d   eU R                  [        [        * S9[        [        * 5      :X  d   eU R                  [        [        S9[        [        5      :X  d   e[        [        [        S[        -  5      5      5      n U R                  [        [        S9[        [        [        * 5      5      :X  d   eU R                  [        [        * S9[        [        [        5      5      :X  d   eU R                  [        [        S9[        [        [        * 5      5      :X  d   eU R                  [        [        * S9[        [        [        5      5      :X  d   eg )N)logxrb   )r   rU   nseriesrV   r=  s    ro   test_issue_21227rO    s   AA99QQ91$$$99QaR9 QB&&&SVGA99QQ93r7***99QaR9 CF***CFA99QQ93q6)))99QaR9 CG+++99QQ93q6)))CAaCMA99QQ93sA2w<///99QaR9 CAK///99QQ93sA2w<///99QaR9 CAK///rn   c                      [         S-
  [        S[         S-
  -  5      -  n U R                  " [         S5      S:X  d   eU R                  " 5       R                  [         S5      S:X  d   eg r   )rU   r2   rI   r  )r   s    ro   test_issue_21415rQ    sU    Q3AqsG
C99Qq>Q::<a"a'''rn   c                      [        [        [        S-   5      [        [        5      -  [        [        5      [        :X  d   eg r4  )rI   r$   rY   r   r
   rm   rn   ro   test_issue_21530rS    s*    a!eT!W$a,111rn   c                      [        S5      S-
  S-  n [        [        U -
  [        S-  [        -   S-
  -  [        U 5      [        S5      S-  :X  d   eg )Nre   rb   r^   )r*   rI   rU   r  s    ro   test_issue_21550rU    sG    	a1aA!a%!Q$(Q,'A.$q'!);;;rn   c                      [        [        [        S-   -  [        [        5      S-   -  S-   [        -  [        S5      n U [        S5      S-  S[        S5      -  -   :X  d   eg )Nrb      l   qjl   S[	)rI   rU   r   r   )outs    ro   test_issue_21661rY    sU    
QUs1vz*Q.!3Q
;C!M"2%SW(<<<<<rn   c                      [        [        [        [        5      [        [        -  -  R	                  [        S5      [        S5      [        S5      S-  :X  d   eg )Nr   r   rb   i 	 )rI   r:   rW   rU   rK  r   rm   rn   ro   test_issue_21701r[    s=    '!Q-1$**1a0!Q71Q4;FFFrn   c                      [        SSS9n [        S[        S[        U -
  S-  -   -  -  [        5      nUR                  " [        [
        5      [        R                  :X  d   eg )Nr   Tr   rb   r^   )r   rG   r   rU   rI   r   r   r   )r   r   s     ro   test_issue_21721r]    sL    sA!Ra!eaZ()1-A771b>QVV###rn   c                     S[        S[        -  [        -  [        -  5      -
  S[        S[        -  [        -  [        -  S-  5      -
  -  n U R	                  [        S5      S:X  d   e[        U 5      R	                  [        S5      S:X  d   eg )Nrb   rg   re   r   )r   r   r   rW   rI   r   )terms    ro   test_issue_21756r`    sq    BqDGAISAb1%5!56D::aq   d8>>!Q1$$$rn   c                      [        S5      n [        U S-  * [        S-  -   S[        S-  -
  -  5      R                  U SS5      [        :X  d   eg )Nr   r^   rb   rc   )r   r*   rU   rI   r   rN  s    ro   test_issue_21785rb    sH    sA!Q$AAqD)*00As;q@@@rn   c                  ^    [        S[        -  S[        * -  -  [        [        5      S:X  d   eg )Nri   r^   r   rv   rm   rn   ro   test_issue_22181rd    s(    "q1r7"Ar*a///rn   c            	         [        S5      [        [        S5      [        [        S-  5      -  S-  5      -  S-  n [        S5      [        -  [        [        S5      [        [        S-  5      -  S[        S5      -  [        -  S-  -
  5      * [        [        S5      [        [        S-  5      -  S[        S5      -  [        -  S-  -   5      7-   -  S-  n[        U [        [        * 5      [        S5      * [        -  S-  :X  d   e[        U[        [        * 5      [        S5      * [        -  S-  :X  d   e[        U [        [        * S5      [        S5      [        -  S-  :X  d   e[        U[        [        * S5      S:X  d   e[        [        [        -
  5      [        [        * [        -
  5      -
  n[        US	S
9n[        U[        [        5      [        U[        [        5      s=:X  a  [        [        -  :X  d   e   e[        [        [        S-  5      [        -
  5      * [        [        [        S-  5      [        -   5      -   n[        U[        [        S5      S[        -  [        -  :X  d   e[        U[        [        S5      S:X  d   eg )Nr  r^   r   rA  re   <   rc   r   T)forcer_   )
r*   r1   r7   rU   r   r   rI   r   rJ   r   )e1e2r   expr2s       ro   test_issue_22220rk    s   	b$tBxAaC(*+	+B	.B	b!c$q'#ac(*QtBxZ\!^;<<$q'#ac(*QtBxZ\!^;<<= 
>>@
AB Qb	"R///Qb	"R///QS!T"Xb[^333QS!Q&&& q1u:QBF#Dt4(Eq"ua!4<"<<<<< AaC1%%s3qs8a<'884q"c"ac"f,,,q"c"a'''rn   c                     [        SSS9u  p[        US-   U -  US-   U S-   -  XS-   -  -
  -  U[        5      SU S-   -  :X  d   e[        US-   U -  US-   U S-   -  XS-   -  -
  R                  5       -  U[        5      SU S-   -  :X  d   e[        US-   U -  XU -  * US-   U -  -   -  US-   U -  -   -  U[        5      SU S-   -  :X  d   eg )Nzk, nTr}   rb   )r   rI   r   r  )rX   rY   s     ro   test_issue_22334rm    s    FT*DA!A#AaC1Q3<1!*45q"=AEJJJ!A#AaC1Q3<1!*4<<>>2F!QQRU)SSS!A#1!teq1uqj01QUQJ>?BG1aRSe9TTTrn   c                      [        SS[        -  -  [        S[        -  5      -  [        S5      [        R                  :X  d   eg r  )rI   rU   r   r   Zerorm   rn   ro   test_issue_22836_limitrp    s3    QqS)AqE**Aq1QVV;;;rn   c                      [        [        SS[        -  -   5      [        [        5      -  [        [        5      [        S5      :X  d   eg r  )rI   r   rU   r*   r   rm   rn   ro   test_sympyissue_22986rr    s2    q1Q3wQ'B/47:::rn   c                      S[         -  S[         * -  -
  S[         -  S[         * -  -   -  n [        U [         [        * 5      S:X  d   eg )Nr^   ri   )rU   rI   r   r=  s    ro   test_issue_23231rt    sA    	
AQB!Q$aR.)AAsr!!!rn   c                      [        S[        -   [        S-  -  [        S[        -  5      -  [        S[        45      [        :X  d   eg )Nrb   r^   ri   r   )rG   rU   r   r   rm   rn   ro   test_issue_23596rv    s6    q1uadlC1I-1bz:b@@@rn   c                     [        [        * [        S-  -  [        -   S-
  5      n [        [        * [        S-  -  [        [        -  -   S-
  5      n[        U [        SS5      [        S5      * [        -  :X  d   e[        U [        SS5      [        S5      * [        -  :X  d   e[        U[        SS5      [        S5      [        -  :X  d   e[        U[        SS5      [        S5      * [        -  :X  d   eg )Nr^   rd   r   r_   rc   )r*   r   rU   rI   )expr1rj  s     ro   test_issue_23752ry    s    !AqD1q!E!AqD1Q3"#E1c"tAwhqj0001c"tAwhqj0001c"d1gai///1c"tAwhqj000rn   c                     [        [        [        S-  [        [        5      -  5      5      R                  [        5      n U R                  [        [        5      S:X  d   eU R                  5       R                  [        [        5      S:X  d   eU R                  [        5      R                  [        [        5      S:X  d   eU R                  [        5      R                  5       R                  [        [        5      S:X  d   eg r   )r   r7   r   r#   rU   r   rI   r   rK   r   r6   )r  s    ro   test_issue_24276r{  "  s    	SAd1g		$	$Q	'B88Ar?a;;=q"%***::c?  B'1,,,::c?##%++Ar2a777rn   c                    ^ [        SSS9m[        SSS9n [        SSS9n[        SSS	9n[        [        U4S
 j5        [        [	        [
        U 5      [
        X -  S5      S:X  d   e[        [	        [
        U 5      [
        X -  S5      U :X  d   e[        [	        [
        U5      [
        X!-  S5      U:X  d   e[        [	        [
        U5      [
        X!-  S5      S:X  d   eg )Nr   Tr   r   r}   r   rG  rY   rx  c                  B   > [        [        [        T 5      [        T 5      $ r   )rI   r	   rU   rN  s   ro   r   "test_issue_25230.<locals>.<lambda>.  s    c!QiA(>rn   r_   r   rc   )r   rR   r%  rI   r	   rU   )r   r   rY   r   s      @ro   test_issue_25230r  )  s    s4 Ast$Ast$Asd#A
 >?QAqsC(A---QAqsC(A---QAqsC(A---QAqsC(A---rn   c                     [        [        [        [        5      5      [        [        S5      [        * [
        -  :X  d   e[        [        [        [        5      5      [        [        S5      [        [
        -  :X  d   e[        [        [        [        5      5      [        [        S5      [        S-  :X  d   e[        [        [        [        5      5      [        [        S5      S:X  d   e[        [        [        [        5      5      [        [        S5      [        S-  :X  d   e[        [        [        [        5      5      [        [        S5      S:X  d   eg )Nrc   r^   r   )rI   r0   r   rU   r   r   r,   r1   r   r-   r/   r.   rm   rn   ro   test_issue_25582r  5  s    c!fq"c*rc!e333c!fq"c*bd222c!fq"c*bd222c!fq"c*a///c!fq"c*bd222c!fq"c*a///rn   c                     [        [        [        [        5      [        -  5      [        SS5      [        S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      [        S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      S:X  d   e[        [        [        [        5      [        -  5      [        SS5      [        S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      [        * [        -  :X  d   e[        [        [        S[        -  5      5      [        SS5      S:X  d   e[        [        [        [        5      [        -  5      [        SS5      S:X  d   e[        [        [        S[        -  5      5      [        SS5      [        [        -  :X  d   e[        [        [        S[        -  5      5      [        SS5      [        S-  :X  d   e[        [        [        [        5      [        -  5      [        SS5      [        S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      S:X  d   e[        [        [        S[        -  5      5      [        SS5      [        S-  :X  d   e[        [        [        [        5      [        -  5      [        SS5      S:X  d   e[        [        [        S[        -  5      5      [        SS5      [        S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      [        [        -  :X  d   e[        [        [        [        5      [        -  5      [        SS5      [        S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      S:X  d   e[        [        [        S[        -  5      5      [        SS5      [        * [        -  :X  d   e[        [        [        [        5      [        -  5      [        SS5      [        :X  d   e[        [        [        S[        -  5      5      [        SS5      [        * [        -  S-  :X  d   e[        [        [        S[        -  5      5      [        SS5      S:X  d   e[        [        [        [        5      [        -  5      [        SS5      [        S[!        S5      -   5      :X  d   e[        [        [        S[        -  5      5      [        SS5      [        :X  d   e[        [        [        S[        -  5      5      [        SS5      S:X  d   e[        [#        [        [        5      [        -  5      [        SS5      S:X  d   e[        [#        [        S[        -  5      5      [        SS5      [        :X  d   e[        [#        [        S[        -  5      5      [        SS5      [        [        -  S-  :X  d   e[        [%        [        [        5      [        -  5      [        SS5      [        :X  d   e[        [%        [        S[        -  5      5      [        SS5      S:X  d   e[        [%        [        S[        -  5      5      [        SS5      [        * [        -  S-  :X  d   e[        ['        [        [        5      [        -  5      [        SS5      S:X  d   e[        ['        [        S[        -  5      5      [        SS5      [        [        -  S-  :X  d   e[        ['        [        S[        -  5      5      [        SS5      [        :X  d   e[        [)        [        [        5      [        -  5      [        SS5      [        S[!        S5      -   5      :X  d   e[        [)        [        S[        -  5      5      [        SS5      S:X  d   e[        [)        [        S[        -  5      5      [        SS5      [        :X  d   eg )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_25847r  ?  s   c!fQhAt,1444c!A#hAs+r!t333c!A#hAs+q000 c!fQhAt,1444c!A#hAs+s1u444c!A#hAs+q000 c!fQhAt,111c!A#hAs+r!t333c!A#hAs+r!t333 c!fQhAt,1444c!A#hAs+q000c!A#hAs+r!t333 c!fQhAt,111c!A#hAs+r!t333c!A#hAs+r!t333 c!fQhAt,1444c!A#hAs+q000c!A#hAs+s1u444 s1vax!Q-333s1Q3x!Q,2a777s1Q3x!Q,111 s1vax!Q-Qa[1AAAAs1Q3x!Q,222s1Q3x!Q,111 s1vax!Q-222s1Q3x!Q,222s1Q3x!Q,"Q666 s1vax!Q-333s1Q3x!Q,111s1Q3x!Q,2a777 s1vax!Q-222s1Q3x!Q,"Q666s1Q3x!Q,222 s1vax!Q-Qa[1AAAAs1Q3x!Q,111s1Q3x!Q,222rn   c                      [        [        S[        S-   5      [        S[        5      -  [        [        5      [        R
                  :X  d   eg r  )rI   r8   rU   r   r   r   rm   rn   ro   test_issue_26040r  }  s3    AE"71a=0!R8AFFBBBrn   c                     [        S[        -  [        S-  S[        -  -   S-   -  5      n [        S[        -  [        S-  S[        -  -   S-   -  5      nSS[        S-  -  -
  U S-  -  S-  [        S-  S[        -  -
  S-   U -  U-  S-  -
  n[        S-  [        S-  S[        S-  -  -
  [        S-  -
  S[        S-  -  -   [        S-  -
  S[        S-  -  -
  [        S-  -   -  n[	        X#-  [        S	5      [        S5      * S-  :X  d   eg )
Nr   r^   rb   rd   ry   r   r   re   r   )rS   rU   rT   r   rI   r   )r   rX   rh  ri  s       ro   test_issue_26250r    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$qAv-14qAv=1D	EB1!A$q(((rn   c                     [        [        [        * [        S-   -  [        -  5      [        [        5      [	        S5      :X  d   e[        [        [        S-   -  [        -  [        [        5      [	        S5      :X  d   e[        [        S 5        g )Nrb   ri   c                  X    [        [        * [        S-   -  [        -  [        [        5      $ r4  rv   rm   rn   ro   r   "test_issue_26513.<locals>.<lambda>  s    AaC1}a)Drn   )rI   r   rU   r   r   rR   r%  rm   rn   ro   test_issue_26513r    sc    qb!A#h]#Q+s2w666!QU)aB'3r7222
!DErn   c                      [        [        [        5      [        [        * 5      -  [        [        75      S:X  d   e[        [        [        5      [        [        * 5      -  [        [        * 5      S:X  d   eg r  )rI   r<   rU   r   r   rm   rn   ro   test_issue_26916r    sP    AsA2wB3'1,,,AsA2wB3'1,,,rn   c            	         [        [        [        S[        -  -   5      S-
  S[	        [        S[        -  -   5      -
  -  [        [
        5      [
        :X  d   e[        SS[        -  -
  [        -  [        SS[        -  -
  5      S[        SS[        -  -
  -  -  -   -  [        SSS9S:X  d   e[        [        [        S[        -  -   5      S[	        [        S[        -  -   5      -
  -  [        [
        5      S:X  d   e[        [        [        S[        -  -   5      S-
  [	        [        S[        -  -   5      * -  [        [
        5      [
        :X  d   eg r  )rI   r   r
   rU   r*   r   rm   rn   ro   test_issue_22982_15323r    s    #a!A#g,"a$q1Q3w-&78!R@BFFF!ac'As1qs7|aA!Go=>1#NRSSSS#a!A#g,1tA!G}#45q"=BBB#a!A#g,"Q1Wo62>"DDDrn   c            
          [        [        [        S-
  [        [        S[        -  5      5      -  [        [        5      -   S-
  -  [        [        5      S[        S5      -  :X  d   eg )Nr   gQ?r~   rb   )rI   rU   r$   r#   r   rm   rn   ro   test_issue_26991r    sK    QUDd1f..a83>?BG1TRSW9TTTrn   c                      S[         [        [         S-   [         -  5      -  -  [         -  [         S-   [        [         S-   [         S-   -  5      -  [         S-   -  -  S-  n [        U [         [        5      S:X  d   eg )Nrb   rd   r   )rU   r   rI   r   r   s    ro   test_issue_27278r    sf    qa!eQY 1$q1uc1q51q5/.B&Ba!e%LLQNDq""""rn   N(&  	itertoolsr   sympy.concrete.summationsr   sympy.core.functionr   r   
sympy.corer   r   sympy.core.modr	   sympy.core.numbersr
   r   r   r   r   r   sympy.core.singletonr   sympy.core.symbolr   r   %sympy.functions.combinatorial.numbersr   (sympy.functions.combinatorial.factorialsr   r   r   $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.  r2  r5  r8  r;  r>  rC  rL  rO  rQ  rS  rU  rW  rZ  r^  ra  rc  re  rg  rj  rn  rp  rr  rt  rv  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$  r&  r)  r+  r0  r2  r:  r<  r>  rA  rC  rE  rG  rI  rK  rO  rQ  rS  rU  rY  r[  r]  r`  rb  rd  rk  rm  rp  rr  rt  rv  ry  r{  r  r  r  r  r  r  r  r  r  r  rm   rn   ro   <module>r     s    ) 0 .  < < " / ; X X @ @ G G h h h F F L L :Z Z Z Z O O ] ] P P 1 ; . : 2 9  * $ . (    
3t,D8N2,
A;S
$6/D124W&67 4A3>H@;
1.,2 # #9:>0
,"
*0(5*6
B7D - -A
8
<M
@**K
 . ..
->`4@+$"?g8T,
D;
3	2/S-A
-
L<7
F-B7L1-D
	RI
;J
BBIdo0B:[>.J%!F@:;4(*(
7SG
X\;TDNBU
P/
<E(
l1
D FCH=;C
0#YhU
8&+;	)37O5%02(2<
=
G$%A
0(,U<;"
A18	.0;3|C)F-
EU#rn   