
    \h(=                    ,	   S SK r S SKJrJr  S SKJr  S SKJr  S SKJ	r	  S SK
JrJrJrJr  S SKJr  S SKJrJrJrJrJrJrJrJr  S S	KJrJr  S S
KJr  S SKJ r J!r!  S SK"J#r#  S SK$J%r%J&r&J'r'J(r(J)r)  S SK*J+r+J,r,J-r-J.r.  S SK/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7  S SK8J9r9J:r:J;r;  S SK<J=r=  S SK>J?r?J@r@JArAJBrBJCrCJDrDJErEJFrF  S SKGJHrHJIrI  S SKJJKrKJLrLJMrMJNrNJOrOJPrPJQrQJRrR  S SKSJTrTJUrU  S SKVJWrWJXrX  S SKYJZrZ  S SK[J\r\  S SK]J^r^  S SK_J`r`  S SKaJbrb  S SKcJdrdJere  S SKfJgrg  S SKhJiri  S SKjJkrk  S S KlJmrm  S S!KnJoro  S S"KpJqrq  S S#KrJsrsJtrt  S S$KJuru  S S%KvJwrw  S S&K]Jxrx  S S'KyJzrz  S S(K{J|r|  S S)K}J~r~JrJrJr  S S*KJr  S S+KJr  \!" S,5      u  rrrrrrrrrrrr\ " S-S.S/9r\" S05      rGS S1 jrS2 r\S3 5       rS4 rS5 rS6 rS7 rS8 rS9 rS: 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] r\S^ 5       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 Gr S GrS GrS GrS GrS GrS Gr\S 5       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 5       Gr\S 5       GrS GrS GrS Gr\S 5       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$S Gr%S Gr&\S 5       Gr'S Gr(S Gr)S Gr*S Gr+S Gr,S Gr-S Gr.S Gr/S Gr0S Gr1S Gr2S Gr3S Gr4S Gr5S Gr6S Gr7S Gr8\S 5       Gr9S Gr:S Gr;S Gr<S Gr=S Gr>S Gr?S Gr@S GrAS GrBS GrCS GrDS GrES GrFS GrG\S 5       GrH\S 5       GrIS GrJS GrKS GrLS GrMS GrNS GrOS GrPS GrQS GrRS GrSS GrTS GrUS GrVS GrWS GrXS GrYS GrZS Gr[\S 5       Gr\S Gr]S Gr^S Gr_S Gr`S GraS Grbg(      N)Sum	summation)Add)Tuple)Expr)
DerivativeFunctionLambdadiff)
EulerGamma)EIRationalnanoopizoo	all_close)EqNe)S)Symbolsymbols)sympify)Absim
polar_liftresign)LambertWexp	exp_polarlog)acoshasinhcoshcothcschsinhtanhsech)MaxMinsqrt)	Piecewise)acosasinatancossinsinctansec)
DiracDelta	Heaviside)CiEiSierferfcerfifresnelcli)gamma	polygamma)hypermeijerg)SingularityFunction)lerchphi	integrate)And)Matrix)Polyfactor)sstr)O)Interval)	gammasimp)simplify)trigsimp)IdxIndexedBase)	unchanged)floor)Integral)NonElementaryIntegral)units)raisesslowwarns_deprecated_sympywarns)SymPyDeprecationWarning)verify_numericallyzx y z a b c d e s t x_1 x_2nTintegerfc                 J    [        [        U 5      R                  " U40 UD6SS9$ )NT)	full_prec)rN   r   evalf)era   optionss      \/var/www/auris/envauris/lib/python3.13/site-packages/sympy/integrals/tests/test_integrals.pyNSrk   3   s#    
  .g.$??    c                  r   [        S[        -  [        5      n U R                  [        5      [        [        S-  [        SS9:X  d   e[        [        SS9   [        U [        5        S S S 5        [        [        SS9   [        U [        45        S S S 5        g ! , (       d  f       N7= f! , (       d  f       g = f)N   QQ)domainFtest_stacklevel)rL   xrI   r^   r_   rX   ps    rj   test_poly_deprecatedrv   7   s|    QqS!A;;q>T!Q$$7777	&	>!Q 
?	&	>QD 
?	> 
?	>	>	>s   B<B(
B%(
B6c                    ^^ S[         -  m[        T[         [        * [        45      R                  5       S:X  d   e[        T[        [        * [        45      R                  5       [        [        S[         -  5      -  :X  d   e[        [        U4S j5        [        [        U4S j5        S[         S-  S-
  -  m[        T[         [        * [        45      R                  5       R                  5       [        S5      * [        -  S-  :X  d   e[        [        U4S j5        S[         S-  S-
  -  n [        U [         [        * [        45      R                  5       S:X  d   e[        U [         SS45      R                  5       [        S5      * :X  d   e[         [         S-  S-
  -  n[        U[         [        * [        45      R                  5       S:X  d   e[        U[         SS45      R                  5       S:X  d   e[         S-  [         S-  S-
  -  n[        U[         [        * [        45      R                  5       [        L d   e[        U[         SS45      R                  5       [        S5      * S	-   :X  d   eS[         S-  S-
  S[         S-  -   -  -  n[        U[         [        * [        45      R                  5       [        * S-  :X  d   e[        U[         SS45      R                  5       [        S5      * [        S5      S-  -
  :X  d   eg )
N   r   c                  @   > [        T [        5      R                  5       $ N)rX   rs   principal_valuegs   rj   <lambda>&test_principal_value.<locals>.<lambda>F   s    xA/??Arl   c                  6   > [        T 5      R                  5       $ rz   )rX   r{   r|   s   rj   r~   r   G   s    x{::<rl      c                  P   > [        T [        [        * S45      R                  5       $ Nrx   )rX   rs   r   r{   )ls   rj   r~   r   K   s    xAsA;7GGIrl   rn      )rs   rX   r   r{   yr   r[   
ValueErrortogetherr.   r   r#   r2   )dvsrd   r}   r   s       @@rj   test_principal_valuer   A   s   	AAAB3|$446!;;;AB3|$446"tAE{:JJJJ
:AB
:<=	a1f\AAB3|$446??Ad1gXb[QR]RRR
:IJ	Q!VaZAAB3|$446!;;;A2qz"224Q???	Q!VaZAAB3|$446!;;;A2qz"224999	Q!q&1*AAB3|$446"<<<A2qz"224Q!CCC	a1fqjQaZ()AAB3|$4462#'AAAA2qz"224a3q6A:8MMMMrl   c                     U R                   nU HV  nU R                  U5      R                  5       U R                  5       R                  U5      -
  R                  5       S:X  a  MV   e   U$ )zReturn the set of symbols, s, which were used in testing that
i.diff(s) agrees with i.doit().diff(s). If there is an error then
the assertion will fail, causing the test to fail.r   )free_symbolsr   doitexpand)isymsr   s      rj   	diff_testr   ^   sV     >>Dq	 1668==#33;;=BBB Krl   c                  
   [        [        [        5      [        SS45      S:X  d   e[        [        S-  [        S[        45      S:X  d   e[        SS[	        [        5      -   -  [        S[        45      [        S5      :X  d   eg )Nr   rx   r   rn   )rI   r#   rs   r   r!    rl   rj   test_improper_integralr   h   sk    SVaAY'2---QWq!Rj)Q...QCF
^aBZ0CF:::rl   c                  \   [        [        [        5      n U R                  [        [        5      4:X  d   e[        [        [        45      nUR                  [        [        5      4:X  d   e[        [	        [
        [
        S[        45      5      nUR                  [        [        5      4:X  d   e[        [        [        [        5      5      nUR                  [        [        5      4:X  d   e[        [        [        [        SS5      45      nUR                  [        [        SS5      4:X  d   e[        [        [        S:  5      nUR                  [        [        S[        5      4:X  d   e[        [        [        S:  [        S:  -  5      nUR                  [        [        SS5      4:X  d   eg )Nrx   rn   
      )	rX   ra   limitsr   r   rs   r   rP   r   )s1s2s3s4s5s6s7s          rj   test_constructorr   n   s>    
!QB99q###	!aT	B99q###	#a!Q#	$B99q###	!U1Y	B99q###	!a!Q(	)B99q!Q)))) 
!QV	B99q"b)++++	!a!eA&	'B99q!Q))))rl   c            	      &   [        S[        5      S:w  d   e[        [        [        SS45      S:w  d   e[        [        [        5      [        :w  d   e[        [        R                  [        5      [        R                  L d   e[        [        [        [        5      [        5      S:X  d   e[        [        [        [        SS45      [        5      S:X  d   e[        [        [        [        5      [        5      [        :X  d   e[        [        [        [        S[        45      [        5      [        :X  d   e[        S-   S-  n [        [        U [        S[        45      [        5      [        [        U [        S[        45      [        5      R                  5       R                  5       s=:X  a  S[        -   S-  R                  5       :X  d   e   e[        [        U [        S[        45      [        5      [        [        U [        S[        45      [        5      s=:X  a  S:X  d   e   e[        [        U [        S[        45      [        5      [        [        U [        S[        45      [        5      s=:X  a  S:X  d   e   e[        [        U [        5      [        5      [        [        U [        5      [        5      s=:X  a  S:X  d   e   e[        U [        [        [        45      R                  [        5      [        U [        [        [        45      R                  [        5      R                  5       R                  5       :X  d   e[        U [        [        [        45      R                  [        5      R                  5       S[        -   S-  :X  d   e[        U [        [        [        45      R                  [        5      R                  5       S[        -   S-  * R                  5       :X  d   e[        [        S-  [        [        S[        -  45      R                  [        5      S[        S-  -  :X  d   e[        [        [        5      R                  5       [        1:X  d   e[        [        [        5      [        SS45      R                  5       [        R                  [        R                  [        1:X  d   e[!        [        [        [        S[        -  45      5      [        1:X  d   e[!        [        [        [        S[        -  45      5      [        [        1:X  d   e[        [        [        [        [        45      S:X  d   e[        [        [        [        * [        * 45      S:X  d   e[        [        [        -   [#        [        5      -   [        5      [        [        -  [        S-  S-  -   [#        [        5      -   :X  d   e[        [        5      R$                  (       d   e['        SSS9n[        U[        -   [        5      R$                  SL d   eg )	Nr   rx   rn      r   ra   Fcommutative)rX   rs   r   r   NaNr   r   trI   r   r   aatomsrd   ZeroOner   r!   is_commutativer   rh   ra   s     rj   test_basicsr      s   Aq>QA1ay!Q&&&B?b   AEE1&&&A"a'''Q1I&*a///A"a'''Q1I&*a///	
Q
A	!aAY'+Xa!Q#Q',,.557
a%!     	!aAY'+Xa!Q#Q'-+,- - - - -	!aAY'+Xa!Q#Q'-+,- - - - -	!Q#tHQNA'>C!CCCCCQAq	"''*Q1I##A&++-4467 7 7A1ay!&&q)..0a!eaZ@@@QAq	"''*//1Azk5I5I5KKKKQTAq!A#;',,Q/1QT6999Aq>!aS(((AaD1a)$**,0BBBBXa!QqS*+s222Xa!QqS*+1v555QB$)))QRC"&!+++ QUSV^Q'1Q3Aa<#a&+@@@@A;%%%%s&AAE1,,555rl   c                       " S S[         5      n U " 5       n[        US-   U5      US-  S-  U-   :X  d   e[        US-   USS45      [        SS5      :X  d   e[        [        S 5        [        [        S 5        g )	Nc                       \ rS rSrSrSrSrg)test_diff_wrt.<locals>.Test   Tr   N)__name__
__module____qualname____firstlineno__	_diff_wrtr   __static_attributes__r   rl   rj   Testr      s    	rl   r   rx   rn   r   r   c                  6    [        [        S-   [        S-   5      $ r   rI   rs   r   rl   rj   r~   test_diff_wrt.<locals>.<lambda>   s    yQA6rl   c                  <    [        [        S-   [        S-   SS45      $ )Nrx   r   r   r   rl   rj   r~   r      s    yQQ1>rl   )r   rI   r   r[   r   )r   r   s     rj   test_diff_wrtr      sw    t  	AQUA!Q$q&1*,,,QUQ1I&(1a.888
:67
:>?rl   c            
         [        [        [        [        S[        -  S[        -  4[        [        S[        -  45      5      [        1:X  d   e[        [        [        [        S[        -  4[        [        S[        -  45      5      [        1:X  d   e[        [        [        [        S[        -  4[        [        S[        -  45      5      [        [        1:X  d   e[        [        [        [        [        5      5      [        [        1:X  d   e[        [        [        [        -  [        [        5      5      [        [        1:X  d   e[        [        [        [        -   [        [        S[        45      5      [        1:X  d   e[        [        [        [        -   [        [        [        4[        [        [        45      5      [        [        1:X  d   eg )Nr   r   rn   rx   )r   rX   rs   r   r   rl   rj   test_basics_multipler      s6   Xa!QqS!A#Aqs<=!DDDXa!QqSAq!A#;78QC???Xa!QqSAq!A#;78QFBBBXaA&'Aq6111Xac1a()aV333Xa!eQAq	23s:::Xa!eaAYAq	:;1vEEErl   c                     [        SSS9u  p[        SSS9n[        X-  U45      nUR                  5       R	                  5       UR	                  5       R                  5       :X  d   eUR                  5       R	                  5       UR	                  5       R                  5       :X  d   eUR                  5       R	                  5       UR	                  5       R                  5       :X  d   e[        SSS9n[        X-  U45      nUR                  5       R	                  5       UR	                  5       R                  5       :X  d   eUR                  5       R	                  5       UR	                  5       R                  5       :X  d   eUR                  5       R	                  5       UR	                  5       R                  5       :X  d   eg )NzA BFr   rs   T)complexreal)r   r   rX   adjointr   	conjugate	transpose)ABrs   ru   s       rj   test_conjugate_transposer      sP   5e,DAsD!AqdA99;!1!1!3333;;=1668#5#5#7777;;=1668#5#5#7777sAqdA99;!1!1!3333;;=1668#5#5#7777;;=1668#5#5#7777rl   c                     [        S[        S[        45      S:X  d   e[        S[        S[        45      S[        -  :X  d   e[        [        [        S[        45      [        S-  S-  :X  d   e[        S[        -  [        S[        45      S[        S-  -  S-  :X  d   e[        S[        S-  -  [        S[        45      [        S-  :X  d   e[        S[        -  [        S[        45      [        [        5      :X  d   e[        S[        S-  -  [        S[        45      S[        -  S-
  :X  d   e[        [        S-  S[        -  -   S-
  [        S[        45      [        S-  S-  S[        S-  -  S-  -   S[        -  -
  :X  d   e[        [        S-  [        5      [        S-  S-  :X  d   e[        S[        -  [        -  S-  [        5      S[        -  S-  [        S-  -  S-  :X  d   e[	        S	5      n [	        S
5      n[        [
        [        -  [        S[        45      [
        [        S-  -  S-  :X  d   e[        [
        [        S-  -  [        S[        45      [
        [        S-  -  S-  :X  d   e[        [
        [        S-  -  U [        -  -   U-   [        S[        45      [
        [        S-  -  S-  U [        S-  -  S-  -   U[        -  -   :X  d   eg )Nr   r   rn   rx   r   r         bcr   )rI   r   rs   r#   r   r   )r   r   s     rj   test_integrationr      se   QAq	"a'''QAq	"ac)))QAq	"ad1f,,,QqS1a)$!Q$q000Qq!tVaAY'1a4///QqS1a)$A...R1Wq!Qi(AaC!G333QTAaCZ!^aAY/1a46AadF1H3Dqs3JJJJQT1Aa'''ac!eaZ#!ax!Q$'::::sAsAQqS1a)$!Q$q000Qq!tVaAY'1QT6!8333Qq!tVac\A%1ay1Qq!tVAX!Q$q5H1Q35NNNNrl   c                     [        [        S-  [        S-  -  [        SS4[        SS45      [        S5      :X  d   e[        [        S-  [        S-  -  [        [        5      [        SS5      [        S-  -  [        S-  -  :X  d   e[        S[        S-   -  S[        -   S-  -  [        5      [	        S[        -   5      [        SS5      -  [	        S[        -   5      [        SS5      -  -   [        SS[        -  -   S[        S-  -  -   -  -   :X  d   e[        [        [        [        -  5      [        -  [        SS4[        SS45      [        S5      * S-   :X  d   eg )	Nrn   r   rx   r   	   r   r   r   )rI   rs   r   r   r#   r4   r   rl   rj   test_multiple_integrationr      s*   adQT]Q1I2qz:hqkIIIadQT]Aq)Xa^QT-BAqD-IIIIQAYAz)1-AE
8B?"SQZA%>>A!GaPQSTPTfDTAUUV V VS1XaZ!QQ1I63q6'A+EEErl   c                  Z    [        [        [        * 5      [        S[        45      S:X  d   eg Nr   rx   )rI   r!   rs   r   r   rl   rj   test_issue_3532r      s#    S!Wq!Rj)Q...rl   c                  `   [        [        [        5      S-  [        5      S[        [        5      S-  -  S-  :X  d   e[        [        [        5      [        5      S[        [        5      S-  -  S-  :X  d   e[        S[        [        5      S-  -  [        5      S[        [        5      -  :X  d   eg )Nr   rn   r   rx   r   )rI   r.   rs   r   rl   rj   test_issue_3560r      s    T!WaZ#qa!|A~555T!Wa Ad1gqjLN222QtAwz\1%DG333rl   c                  &    [        [        S 5        g )Nc                  ,    [        [        [        45      $ rz   r   r   rl   rj   r~   "test_issue_18038.<locals>.<lambda>   s    9aV#4rl   )r[   AttributeErrorr   rl   rj   test_issue_18038r      s    
>45rl   c                     [        [        [        S-  [        -  -   [        S-  -   [        [        5      n [        5          [	        U [        5      nS S S 5        [        [        SS9   [        U [        5      nS S S 5        [        [        SS9   [        U [        5      nS S S 5        [        W[         5      SL d   e[        W[         5      SL d   eUR                  [        [        4:X  d   eUR                  [        [        4:X  d   eUR                  5       [        S-  S-  [        S-  [        -  S-  -   [        [        S-  -  -   :X  d   eUR                  5       [        [        -  [        S-  [        S-  -  S-  -   [        S-  S-  -   :X  d   eg ! , (       d  f       GNJ= f! , (       d  f       GN5= f! , (       d  f       GN = f)Nrn   r   Frq   Tr   )rL   rs   r   r]   rX   r^   r_   rI   
isinstancegensas_expr)ru   qxqys      rj   test_integrate_polyr     sV   QAaZ!Q$1%A 
 	!a^ 
"	&	>q!_ 
?	&	>q!_ 
? b$4'''b$4'''77q!f77q!f::<1a46AqDF1H,qAv5555::<1Q3Aad1,q!tAv5555 
"	!	>	>	>	>s#   F&F%F7
F"%
F47
Gc                  ~   [        [        [        S-  [        -  -   [        S-  -   [        [        5      n [        5          [	        U [        SS45      nS S S 5        [        [        SS9   [        U [        SS45      nS S S 5        [        [        SS9   [        U [        S[        45      nS S S 5        [        W[         5      SL d   e[        W[         5      SL d   eUR                  [        4:X  d   eUR                  [        4:X  d   eUR                  5       [        R                  [        S-  -   [        S-  -   :X  d   eUR                  5       [        S-  S-  [        [        -  -   [        S-  [        S-  -  S-  -   :X  d   eg ! , (       d  f       GN== f! , (       d  f       GN%= f! , (       d  f       GN	= f)	Nrn   r   r   rx   Frq   Tr   )rL   rs   r   r]   rX   r^   r_   rI   r   r   r   r   r   Half)ru   QxQys      rj   test_integrate_poly_definiter     sO   QAaZ!Q$1%A		!a!Q# 
"	&	>q1a)$ 
?	&	>q1a*% 
? b$4'''b$4'''77qd??77qd??::<166AaC<!Q$....::<2q57RT>BE!Q$JqL8888 
"	!	>	>	>	>s#   F	)FF-	
F
F*-
F<c                     ^  [        S5      m [        [        5      [        S-  S-  :X  d   e[        [        S 5        [        [        U 4S j5        g )Nr   rn   c                      [        S5      $ Nrn   rH   r   rl   rj   r~   )test_integrate_omit_var.<locals>.<lambda>0  s    y|rl   c                  (   > [        [        T -  5      $ rz   r   r   s   rj   r~   r   1  s    y1~rl   )r   rI   rs   r[   r   r   s   @rj   test_integrate_omit_varr   +  s<    sAQ<1a46!!!
:+,
:-.rl   c                     [        S5      n [        [        [        U 5      -  [        5      [        S-  [        U 5      -  S-  :X  d   e[        [        S-  [        U 5      -  [        5      [        S-  [        U 5      -  S-  :X  d   eg )Nr   rn   i  i  )r   rI   rs   r4   r   s    rj   test_integrate_poly_accuratelyr   4  sl    sAQs1vXq!QT#a&[]222 QWSV^Q'1d73q6>$+>>>>rl   c                      [        S5      n [        [        S-  U 5      [        S-  U -  :X  d   e[        [        S-  U SS45      S[        S-  -  :X  d   eg )Nr   rn   r   rx   )r   rI   rs   r   s    rj   test_issue_3635r   =  sS    sAQT1Aa'''QTAr1:&!AqD&000rl   c                  f   [        SSS9n [        [        U -  [        SS9[        U S-   -  U S-   -  :X  d   e[        [        U 5      [        -  SU -  -   S[	        U 5      -   -  [        SS9[        U * 5      [        U 5      [        -  SU -  -   S[	        U 5      -   -  -  S[	        U 5      -   -  :X  d   eg )Nr   Tpositivenonecondsrx   rn   )r   rI   rs   r!   r4   r   s    rj   test_integrate_linearterm_powr   E  s    sT"AQT1F+q1q5z1q5/AAAAc!fQh1nCF
3QfEQBQAaC1s1v:..!c!f*=> > >rl   c                     [        [        [        [        5      -  [        5      S[        -  [        [        5      S-  -  S-  :X  d   e[        [        [        [        5      -  [        [        [        5      S-  -  -   [        5      S[        -  [        [        5      S-  -  S-  S[        -  [        [        5      S-  -  S-  -   :X  d   eg )Nrn   r   r   )rI   r   r.   rs   r   r   rl   rj   test_issue_3618r   N  s    RQZ#qtDGQJq'8888RQZ!DGQJ,.2	"T!WaZAaCa!OA--. . .rl   c            	      l   [        [        [        S-   [        -  5      [        5      [	        [        [        [        S-   -  5      [        S-   -  [        [        S-   S5      4[        S45      :X  d   e[        [        [        S-
  [        -  5      [        5      [	        [        [        [        S-
  -  5      [        S-
  -  [        [        S-
  S5      4[        S45      :X  d   e[        [        [        S-   [        -  5      [        [        S-
  [        -  5      -   [        5      [	        [        [        [        S-
  -  5      [        S-
  -  [        [        S-
  S5      4[        S45      [	        [        [        [        S-   -  5      [        S-   -  [        [        S-   S5      4[        S45      -   :X  d   eg )Nrx   r   T)rI   r3   ra   rs   r/   r4   r   r   rl   rj   test_issue_3623r  T  sW   S!a%^Q'9	QAYQ	AE1.D	,; ; ; ;S!a%^Q'9	QAYQ	AE1.D	,; ; ; ;S!a%^c1q5!)n4a83q!a%y>1q5)2a!eQ<81d)D3q!a%y>1q5)2a!eQ<81d)D	EE E Erl   c                     [        SSSS9n [        S[        -  [        U [        -  [        -  S-  5      -  [        SS/5      S[        [        U -  5      -  [        U -  -  :X  d   e[        [        [        U [        -  [        -  S-  5      -  [        S	S5      -  [        SS/5      S[        [        U -  5      -  [        U -  -  :X  d   eg )
Nra   T)rc   nonzerog      rn   r   r          @r   )r   rI   rs   r4   r   r3   r   ra   s    rj   test_issue_3664r  ^  s    sD$/AUQYQVaZ\!22QAJ?C1Ir!t  QQVaZ\**Xb!_<q"ajI	#bd)RT  rl   c                  v    [        [        S[        S-  S[        -  -
  S-   -  [        SS45      5      S:X  d   eg )Nrx   rn   r      r   z1.10714871779409)rk   rX   rs   r   rl   rj   test_issue_3679r
  f  s8    hq!Q$1*r/*Q1I67;MMMMrl   c                      SSK Jn   SSKJn  U " [	        [        [        S-  5      [        5      5      [        S5      [        [        5      -  U" [        S5      [        -  [        [        5      -  5      -  S-  :X  d   eg )Nr   expand_func)fresnelsrn   )	sympy.core.functionr  'sympy.functions.special.error_functionsr  rI   r4   rs   r.   r   )r  r  s     rj   test_issue_3686r  k  s^    /@yQTA./QR$q'!)DH"455a78 8 8rl   c                      [         R                  n [         R                  n[        [        U -  U-  [        SU-  SU-  45      SU -  U-  :X  d   eg )Nrx   r      )rZ   mr   rI   rs   )r  r   s     rj   test_integrate_unitsr  r  sG    AAQU1Wq!A#qsm,1Q666rl   c                      [        [        S[        -  5      [        5      [        * [        [        S[        -  5      -  -   [        [        S[        -  5      -  -   :X  d   eg r   )rI   r    rs   r   rl   rj   test_transcendental_functionsr  x  sJ    Xac]A&	
Qx!}_q!A#./ / /rl   c                      [        [        S[        -
  5      [        -  [        SS45      [        S-  * S-  :X  d   e[        [        [        5      S[        -
  S-  -  [        SS45      [        S-  * S-  :X  d   eg )Nrx   r   rn   r   r   )rI   r#   rs   r   r   rl   rj   test_log_polylogr  }  si    SQZ\Aq!9-"a%999SVQUbM)Aq!95"a%AAArl   c                  @   S[        [        5      -  S[        [        5      S-  -  -
  n [        [        U [        5      [        5      n[	        U R                  [        S5      R                  5       UR                  [        S5      R                  5       -
  5      S:  d   eg )Nr   rn   *   g|=)r#   rs   r   rI   abssubsrg   )rd   fids     rj   test_issue_3740r    sp    	#a&1SVQY;A
yA
"Cqvva}""$sxx2'<'<'>>?%GGGrl   c                  d    [        SS[        S-  -   -  [        5      [        [        5      :X  d   eg Nrx   rn   )rI   rs   r2   r   rl   rj   test_issue_3788r"    s'    QAqD\1%a000rl   c                     ^  [        [        5      m [        T [        5      [        [        5      * :X  d   e[	        [
        U 4S j5        g )Nc                  *   > [        T S[        -  5      $ r   r   rd   s   rj   r~   !test_issue_3952.<locals>.<lambda>  s    yAaC0rl   )r4   rs   rI   r3   r[   r   r%  s   @rj   test_issue_3952r'    s1    AAQ?s1vg%%%
:01rl   c                      [        S[        -  S[        -  -
  [        5      S[        -  [        S5      -  [        S-  -
  :X  d   eg r   rI   rs   r#   r   rl   rj   test_issue_4516r*    s8    QTAaCZ#q!tCF{QT'9999rl   c                      [        [        S[        -   * [        -  5      [        S[        45      n [        U 5      [        R                  :X  a  [        U 5      [        SS5      :X  d   eg )Nrx   r   r   rn   )
rI   r!   r   rs   r   r   r   r   r   r   )anss    rj   test_issue_7450r-    sL    
C!a%
OaBZ
0Cc7affCHRO!;;;!;rl   c            
         [        S[        S[        -  5      -   SS[        S[        -  5      -  -
  -  [        S[        45      [        * S-  [	        S5      [        -  S-  -   :X  d   e[        S[        S[        -  5      -   SS[        S[        -  5      -  -
  -  5      [        * S-  [	        S5      [        [	        S5      [        [        5      -  5      [        [        [        [        S-  -
  [        -  5      -  -   -  S-  -   :X  d   eg )Nrx   rn   r   r   r   rI   r3   rs   r   r.   r2   r6   rW   r   rl   rj   test_issue_8623r0    s    a#ac(lq1S1X:~6Ar
Cs1utTUwWYzZ[|G[[[[a#ac(lQ3qs8^45!AQdSTgVYZ[V\nI]
5!bd(BJ  A!!"A# :# # # #rl   c            	         [        SS[        [        5      -
  -  [        S[        45      [        [	        S5      -  :X  d   e[        SS[        [        5      -
  -  5      S[	        S5      -  [        [	        S5      [        [        S-  5      -  5      [        [        [        S-  [        S-  -
  [        -  5      -  -   -  S-  :X  d   eg Nrx   rn   r   r   r/  r   rl   rj   test_issue_9569r3    s    Q!c!f*%1bz2baj@@@QCF
^$$q'	4QAaC8H3IBuVWXYVY\^_`\`V`bdUdOeLe3e(fgh(hhhhrl   c                     [        SSS9n [        [        [        -
  S-  * SU -  U -  -  5      [	        S[
        -  U -  U -  5      -  n[        U[        [        [        45      n[        U[        S[        45      [	        S5      U -  [        [        S-  * SU S-  -  -  5      -  S[	        [
        5      -  -  [        [        [	        S5      [        -  SU -  -  5      -  S-  -   [        S-  -   :X  d   eg )Nr   Tr   rn   r   )
r   r!   zr   r.   r   rI   rs   r   r=   )r   pzpzgxs      rj   test_issue_13733r8    s    sT"A	q1uqj[!A#a% 	!$qtAvax.	0BR!Q$DTAq":&$q'!)CAqAv4G*G4PR8*T	#d1gai1o
q +!#$Q3+' ' ' 'rl   c            	         [        SS[        [        5      -   -  [        S[        45      [        [	        S5      -  :X  d   e[        SS[        [        5      -   -  5      S[	        S5      -  [        [	        S5      [        [        S-  5      -  S-  5      [        [        [        S-  [        S-  -
  [        -  5      -  -   -  S-  :X  d   eg r2  r/  r   rl   rj   test_issue_13749r:    s    Q!c!f*%1bz2baj@@@QCF
^$$q'	4QAaC8H8J3KbQVXYZ[X[^`ab^bXbdfWfQgNg3g(hij(jjjjrl   c                      [        [        [        5      S[        -   S-  -  [        5      [        [        [        5      [        S-   S-  -  [        5      :X  d   eg r!  )rI   r!   rs   rY   r   rl   rj   test_issue_18133r<    sD    SVQUQJ&*.CCFAPQETU:DUWX.YYYYrl   c                     Sn Sn[        U[        -  [        U * [        -  [        -  [        -  [
        -  5      -  [        U * [        -  [        -  [        -  [        -  5      -  [        [        -  -  [        [        S5      4[        [        U * [        -  [        -  [        -  [
        -  5      -  S45      n[        S[        -  [        -  [        [        -  [        [
        -  -   -  S-  -  n[        [        U[        5      U5      (       d   eg )Ng    NAgƐ>r   Tr   gƠ>)r/   r   r!   r   r   r   rs   r5  r   r   r   rI   )r   r   rfuns       rj   test_issue_21741r@    s    AA1Q3sA2a4719Q;''QBqDGAIaK(88"Q$?AqJS!Ab1%%t,	.A
r!tBw!AaC <0
1CYsA&****rl   c            	          [        SSS 5      n [        U [        5      [        [        [        5      * [        S[        -  5      * /[        S[        -  5      * [        S[        -  5      * //5      :X  d   eg )Nrn   c                 @    X-   S-   [        X-   S-   [        -  5      -  $ r   )r4   rs   )r   js     rj   r~   test_matrices.<locals>.<lambda>  s    1519c1519a-.@"@rl   r   )rK   rI   rs   r3   )Ms    rj   test_matricesrF    si    q!@AAQ?f
a&3qs8)
ac(S1XI&    rl   c                  ^   [        [        [        5      [        5      [        [        [        5      [        5      :X  d   e[        [        [        5      [        SS45      [        [        [        5      [        SS45      :X  d   e[        [        [        5      [	        [        [        5      [        5      -  [        5      [        [        5      S-  S-  :X  d   e[        [	        [        [        5      [        5      [        [        5      -  [        5      [        [        [        5      5      :X  d   eg Nr   rx   rn   )rI   rd   rs   rX   r   r#   r   rl   rj   test_integrate_functionsrI    s    QqT1!A$!2222QqTAq!9%!A$Aq	)BBBBQqT$qtQ-'+qtQwqy888T!A$]QqT)1-QqT:::rl   c                     [        [        [        [        5      [        5      [        5      [        [        5      :X  d   e[        [        [        [        5      [        5      [        5      [        [        [        [        5      [        5      -  :X  d   e[        [        [        [        5      [        5      S-  [        5      [        [        [        [        5      [        5      S-  [        5      :X  d   eg r   )rI   r   rd   rs   r   rX   r   rl   rj   test_integrate_derivativesrK    s    Z!a(!,!444Z!a(!,*QqT12E0EEEEZ!a(!+Q/AaD!$a'+, , ,rl   c            	      N  ^ [        [        S-  S-   [        SS45      n [        nS[        -  S-   nU R                  5       U R	                  X5      R                  5       :X  d   eU R	                  X5      R	                  X!5      U :X  d   eS[        -  S-   n[        nU R	                  X5      R	                  X!5      U :X  d   e[        [        S[        -  5      [        SS45      n U R	                  [        S[        -  5      [        [        [        5      [        S-  -  [        S[        45      :X  d   eU R	                  [        S[        -  5      R	                  [        S[        -  5      U :X  d   e[        [        [        S-  * 5      [        [        * [        45      n U R	                  [        S[        -  5      [        S[        S[        S-  -  5      -  [        [        * [        45      :X  d   e[        [        [        5      R	                  [        U [        -  5      R                  5       [        [        U S-  -  [        5      R                  5       :X  d   e[        S5      n[        [        [        SU* 45      R	                  [        S[        -  5      R                  5       [        S[        S-  -  [        [        * SU-  45      R                  5       :X  d   e[        [        [        SU45      R	                  [        S[        -  5      [        [        S-  [        SU-  [        45      :X  d   e[        [        [        -   [        SS4[        SS45      mTR	                  [        [        S[        -  -   [        45      R                  5       TR	                  [        [        S[        -  -   [        45      R                  5       s=:X  a  S:X  d   e   e[        [        [        U [        45      mTR	                  [        S[        -  5      [        S[        -  [        U S-  [        S-  45      :X  d   e[        [        U4S	 j5        [        [        U4S
 j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        S-  [        SS45      m[        [        U4S j5        [        SSS9n[        SSS9n[        [        [        XT45      mTR	                  [        S[        -  5        TR	                  [        S[        -  5      [        S[        -  [        US-  US-  45      :X  d   e[        [        [        U 45      mTR	                  [        S[        -  5      [        S[        -  [        U S-  45      :X  d   eg )Nrn   rx   r   r   r   r   c                  0   > T R                  [        S5      $ r   )	transformrs   r   s   rj   r~    test_transform.<locals>.<lambda>  s    q{{1a0rl   c                  F   > T R                  [        [        [        -  5      $ rz   rP  rs   r   r   rQ  s   rj   r~   rR    s    q{{1ac2rl   c                  :   > T R                  [        [        * 5      $ rz   rP  rs   r   rQ  s   rj   r~   rR    s    q{{1qb1rl   c                  D   > T R                  [        [        [        45      $ rz   rT  rQ  s   rj   r~   rR    s    q{{1q!f5rl   c                  D   > T R                  S[        -  S[        -  5      $ r   rV  rQ  s   rj   r~   rR    s    q{{1Q3!4rl   c                  >   > T R                  [        S-  [        5      $ r   rV  rQ  s   rj   r~   rR    s    q{{1a43rl   r   T)negativer   r   )rX   rs   r   r   rP  r4   r   r!   r   r5  r   r   r[   r   r   )r   fxfy_3ambpr   s         @rj   test_transformr`    s\   AAr1:&A	
B	
1qB668q{{2*//1111;;r((0A555	
1qB	
B;;r((0A555QqSAq!9%A;;q!A#(3q6!Q$;Ar
"CCCC;;q!A#((AaC0A555adUa"b\*A;;q!A#(1SAqD\>AsB<"HHHHAq>##Aqs+0021a4  "# # #	
1BA1rc{#--a15::<AqD1rc2b5/*//12 2 2A1bz",,Q!4R1adB-() ) ) 	QAq	Aq!9-A;;q1qs7A,',,.	AAaC|$))+1/01 1 1 1 1 	Q1IA;;q!A#(1Q3AaC1">>>>
:01
:23
:12
:56
:45A1ay!A
:34	d	#B	d	#BQK AKK1Q3;;q!A#(2a4!RT2a4"AAAAQFA;;q!A#(1Q3AaC"9999rl   c                  4   [         R                  [        [        5      -  [        [	        S[        S-  -
  5      -  S-  -   n [        [        [        [        5      5      [        5      U :X  d   e[        [        [        [        5      5      [        5      U :X  d   eg r!  )	r   r   r1   rs   r.   rI   r3   r4   r0   r%  s    rj   test_issue_4052rb    sh    	tAw4AqD>)!++ASa\1%***Sa\1%***rl   c                  &   [        [        [        [        SS45      S5      S:X  d   e[        [        [        S-  * 5      [        [        * [        45      n [        U S5      S:X  d   e[        U S-  [
        -
  [        [        SS5      -  -   S5      S;   d   e[        S	5      nS
[        S5      -  SSUS-  -  -   -  nS[        S5      -  SU-  S-   -  [        SUS-  -  U-   S-   5      S-  -  nSUS-  -  S-   SUS-  -  SU-  -   S-   S-  -  n[        S5      SUS-  -  SU-  -   S-   -  SUS-  -  SU-  -   S-   S-  -  nX#U-  -
  U-
  n[        [        XaSS45      S5      [        S[        S5      -  S[
        -  -
  S[        [        S5      5      -  -   S-  S5      :X  d   e[        [        [        [        S[        -  5      5      S[        -   [        S-  -   -  [        SS45      S5      [        SS5      :X  d   e[        [        [        [        [        S-  S-   5      5      [        [        S-  S-   5      [        S-  S-   -  -  [        SS45      S5      [        S[
        S-  -  S-  S5      :X  d   e[        [        [        [        [
        [        -  5      [        [
        * [        -  5      -
  [        S-  S-   -  -  [        S[        45      S5      [        SS5      :X  d   e[        [        [        [        [        [        5      [        [        5      -  5      5      [        [
        S-  [
        S-  45      SSS9[        SS5      :X  d   e[        S[        [        S[        [        S-  5      -  5      [        [
        * [
        45      -   SSS9[        SS5      :X  d   e[        S[        [        S[        [        S-  5      -  5      [        [
        * [
        45      -   SSS9[        SS5      :X  d   e[        S[        [        S[        [        S-  5      -  5      [        [
        * [
        45      -   SSS9[        SS5      :X  d   e[        [
        S[        S [        SS45      -  -
  SS!SS"9S#;   d   e[        [        [        5      [        S-  -  [        S[        45      R                  SS$9nS%Us=:  a  S&:  d   e   e[        [        [        [        5      [        S-  -  [        S[        45      S'S(9S):X  d   e[        [        [        [
        [        -  S-   5      [        -  [        [        * S*45      S'S(9S+:X  d   e[        [        [        [        5      5      S,:X  d   e[        [        [        [        [        45      5      S-:X  d   eg ).Nrn   r      z10.5000000000000z1.77245385090552rx   l      Fx:^V )z2.71828182845904e-20z2.71828182845905e-20r   r   r      r         6   A   r   2   1      r  z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))`   zlog(2)/2-1/4Tchopzpi/4*log(4*pi**3/gamma(1/4)**4)r	        zsqrt(1-x**2)   )maxnro  )z0.00)rs  g\(\?gRQ?osc)quadz0.504067061906928r   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rk   rX   rs   r!   r   r   r   r   r   r.   r2   r#   r4   r3   rg   r   )gaussr   r   r   r   r   rd   s          rj   test_evalf_integralsrx    s   hq1a)$b)-????S!Q$Z!bS".EeR=....eQhma	6!  KL L L 	sA	$q'	1qAv:A
47
AaC!GT!AqD&1*q.1144A	
1a4!bAg!ma'!++AQQTBqD2%&1a4!A#(9A'==A	aC!Ahqa)$b)
Ad1gI2DaM 1125r:; ; ; hs3qs8}a!eadl3aAY?D
7<= = = htDAN+T!Q$(^QTAX-FG!J "a%
B/0 0 0 hq3r!t9s	A( A BZ)*,.13NB1GH H H hs3s1vc!f}-.BqD"Q$@"4P
,b12 2 2 	HS3qs8_q2#rl33RdDGI!RyQ Q Q	HS3qs8_q2#rl33RdDGI!RyQ Q Q	HS3qs8_q2#rl33RdDGI!RyQ Q Q b1XAq	# # #$&Rd<?KL L L 	Q1q!Rj)//R/8A!?d???Q1q!Rj)7:MN N NhBqD1Ha!bS"'-247JK K K hq!n!1111hq1a&!"&;;;;rl   c                  <   [        [        S[        S-  S-   -  [        5      R                  [        S5      SS9S;   d   e[        [	        S[        S-  S-   -  [        SS45      5      S:X  d   e[        [        S[        S-  S-   -  [        SS45      SS9S:X  d   eg )	Nrx   r   r   Trn  )z-0.000976138910649103z0.965906660135753z1.93278945918216rn   z0.0144361088886740)rk   rI   rs   r  rX   r   rl   rj   test_evalf_issue_939rz  C  s     i1a4!8a(--a3$?JK K K hq!Q$(|aAY/04HHHH!QTAX,Aq	*7:NO O Orl   c                  n   [        [        [        5      [        [        -  -   [        SS4[        SS45      n [	        U S5      S:X  d   eU [        SS5      S[        S5      -  S-  -   :X  d   e[        [        [        [        [        -  -   5      [        SS4[        SS45      [        R                  L d   eg )	Nrx   rn   r   rd  z2.43790283299492rM  r   r   )	rI   r.   rs   r   rk   r   r4   r   r   ress    rj   (test_double_previously_failing_integralsr~  R  s    
DGacMAq!9q"aj
9Cc2;,,,,(2q/Ad1gIaK////SQqS\Ar1:2qz:affDDDrl   c                     [        [        [        S5      [        [        SS5      -   n [        [        [        S5      S-  [        [        SS5      -   n[        U [        5      U:X  d   eS[        [        SS5      -  S[        [        SS5      -  -
  nS[        [        SS	5      -  S[        [        SS5      -  -
  n[        U[        5      U:X  d   eS
[        S
-  -  [        -  S[        [        SS5      -  -
  S
[        [        SS5      -  -
  nS
[        S-  -  [        -  S-  S
[        -  [        [        SS5      -  -
  S[        [        SS5      -  S-  -
  n[        S
-  [        S
-  -  S[        -  [        [        SS5      -  -
  S
[        [        SS5      -  -
  n[        U[        5      U:X  d   e[        U[        5      U:X  d   e[        [        U[        45      (       d   e[        U[        5      [        U[        45      :X  d   e[        U[        5      R                  5       U:X  d   eS[        [        SS5      -  S
[        [        SS5      -  -
  nS[        [        SS5      -  S-  S
[        [        SS5      -  -
  n[        U[        [        * [        45      U:X  d   e[        [        [        SS5      [        5      [        [        SS5      :X  d   e[        [        [        SS5      [        [        * [        45      S	:X  d   e[        S[        [        SS5      -  [        [        * [        45      S:X  d   e[        [        [        SS5      [        [        5      -  [        [        * [        45      [        S5      :X  d   eg )Nr   r   r   r   r   r   ir   rx   rn   rM  r   r   )
rF   rs   r   rI   r   rV   rX   r   r   rd   )	in_1out_1in_2out_2in_3out_3_1out_3_2in_4out_4s	            rj   "test_integrate_SingularityFunctionr  ]  s!   q!Q'*=aB*GGD1a(*-@Aq-IIET1&&&!!Q**Q/B1b"/M-MMD"1a++a0CAr20N.NNET1&&&QT6!8R+Ar1555:MaQSUW:X8XXD1fQhqj1Q321b"===BUVWY[]^B_@_`a@aaGd1a4i"Q$21b!<<<qATUVXZ\^A_?__GT1(((T1(((XtaT****D!t 4444D!!!#w...!!R++a0CAr20N.NND!!R++A-2EaR2P0PPETAsA;'5000(Ar2A6:MaQRTU:VVVV(Ar2QRLAQFFFQ*1a44q2#rlCqHHH(Ar2QqT9AsB<HAaDPPPrl   c            	         [        [        [        5      [        [        5      -  [        [        * [        45      [        S5      :X  d   e[        [        [        5      S-  [        [        * [        45      [        S5      :X  d   e[        [        SS[        -  -
  [        [
        -  -   S[
        -  -
  [        [        5      -  [        [
        S-
  5      -  [        SS45      [
        SS45      S:X  d   e[        [        S-  [
        S-  -   * 5      [        -  n [        U [        [        S[
        -  -
  5      -  [        [        * [        4[
        [        * [        45      [        U [        [        S[
        -  -
  5      -  [
        [        * [        4[        [        * [        45      s=:X  a  [        U [        S[        -  [
        -
  5      -  [        [        * [        4[
        [        * [        45      s=:X  af  [        U [        S[        -  [
        -
  5      -  [
        [        * [        4[        [        * [        45      s=:X  a  S[        S[        -  5      -  :X  d   e   eg )Nr   rn   r   rx   r   e   )	rI   r8   rs   rd   r   r   r!   r   r.   rt   s    rj   test_integrate_DiracDeltar  z  s    Z]QqT)AsB<8AaD@@@Z]A%B3|4
1EEEYAaC!A#! 31  Q' (*+Q467AY@CDE E E 	adQTkNBAQz!bd(++a"b\AsB<H!Jq2a4x((1rc2,RCE!Jr!tax((1rc2,RCE 	!Jr!tax((1rc2,RCE 	
$s2v,	    rl   c                  x   [        [        [        -  [        5      [        [        [        S-   -  [        S-   -  [	        [        S5      4[        [        5      S45      :X  d   e[        [        [        -  [        5      [        [        [        -  [        [        5      -  [	        [        [        5      S5      4[        S45      :X  d   e[        [        [        [        -  5      [        5      [        [        [        [        -  5      [        -  [	        [        S5      4[        S45      :X  d   e[        [        [        [        [        -  5      -  [        5      [        [        [        -  S-
  [        [        [        -  5      -  [        S-  -  [	        [        S-  S5      4[        S-  S-  S45      :X  d   e[        [        [        [        -  -  [        5      [        [        [        [        -  S-   -  [        [        -  S-   -  [	        [        [        -  S5      4[        [        5      S45      :X  d   e[        [        [        [        -  -  [        5      [        [        [        [        -  -  [        [        [        5      -  -  [	        [        [        [        5      -  S5      4[        S45      :X  d   e[        [        [        [        -  5      [        5      [        [        [        [        -  5      [        -  [	        [        S5      4[        S45      :X  d   e[        [        [        [        -  5      S-  [        5      [        [        [        -  S-  [        [        [        -  5      [        [        [        -  5      -  S-  -   [        -  [	        [        S5      4[        S45      :X  d   e[        [        [        [        [        -  5      -  [        5      [        [        [        [        [        -  5      -  [        -  [        [        [        -  5      [        S-  -  -   [	        [        S5      4[        S-  S-  S45      :X  d   e[        [        [        [        -  5      [        5      [        [        [        [        -  5      * [        -  [	        [        S5      4S5      :X  d   e[        [        [        [        -  5      S-  [        5      [        [        [        -  S-  [        [        [        -  5      [        [        [        -  5      -  S-  -
  [        -  [	        [        S5      4S5      :X  d   e[        [        [        [        [        -  5      -  [        5      [        [        * [        [        [        -  5      -  [        -  [        [        [        -  5      [        S-  -  -   [	        [        S5      4S5      :X  d   e[        [        [        [        -  5      [        S[        45      [        [        [        [        -  5      [        -  S[        -  -
  [        [        * :  [        [        :  -  [	        [        S5      -  4[        S45      :X  d   e[        [        [        5      [        [        * [        [        [        -
  5      -  5      -  [        5      [        [        [        5      * [        [        [        -
  5      [        [        [        [        [        -
  5      -  5      -  [        [        [        [        [        -
  5      -  5      -
  -  [	        [        [        S-   5      4[        S45      :X  d   eg )Nrx   r   Tr   rn   r   T)rI   rs   r   r/   r   r#   r!   ra   r3   r4   r5  r   r   r.   r   rl   rj    test_integrate_returns_piecewiser    sI   QT1	
QUQU	R2Y'#a&$"9 9 9 9QT1	
Ac!fbQm$q$i"1 1 1 1S1Xq!Y	QqS!R1XD	&+ + + +Qs1Q3xZ#y
A#'3qs8	AqD	 "QT1+.Aa(@ @ @ @Q1Xq!Y	
QqS1WqsQw	AaC-A~&? ? ? ?Q1Xq!Y	
QqS1SV8	b3q61o.D	&; ; ; ;S1Xq!Y	QqS!R1XD	&+ + + +S1Xq[!$	
A#a%#ac(3qs8#A%
%q	("Q(3aY)@ @ @ @Qs1Q3xZ#y	
3qs8AAaCA	%r!Qx01a464.(B B B BS1Xq!Y
ac(1bAh&, , , ,S1Xq[!$	
A#a%#ac(3qs8#A%
%q	("Q(3Y)@ @ @ @Qs1Q3xZ#y
C!HQQqS!Q$	&1a19(> > > >S1X1ay)Y	QqS!ac	AGB/"Q(:;aY.H H H H SVC4A;//3y
a&$q1u+c!DQK-003qa!e}3EE	F
1a!e	4y8" " " "rl   c            	      6   [        SSS9n [        [        U S5      U SS45      S:X  d   e[        [        U S-  U S-  5      U SS45      [	        SS	5      :X  d   e[        [        [        U 5      [        U * 5      5      S-  U 5      [        [        SU -  5      S-  U S:*  4S
[        SU -  5      S-  -
  S45      :X  d   e[        SSS9n[        [        X5      [        U S-  * 5      -  U [        * [        45      n[        U[        U S-  * 5      -  U [        * U45      n[        U [        U S-  * 5      -  X[        45      nX#U-   s=:X  aO  [        [        5      U-  [        U5      -  S-  [        [        5      U-  S-  -   [        US-  * 5      S-  -   :X  d   e   eg )Nrs   Tr   rn   r   r   r   rk  r  rx   r   r   )extended_real)r   rI   r-   r,   r   r!   r/   r   r.   r   r=   )rs   r   int1int2int3s        rj   test_integrate_max_minr    s   $ASAYAq	*a///SAq!t_q!Qi0HR4DDDDSQaR)1,a0I	QqS!Q!Vq3r!t9Q;557 7 7 7 	4(ASYsAqD5z)AsB<8DQsAqD5z\AsA;/DQsAqD5z\A":.D$; $$r(1*SV"3A"5R
1#AqD5z!|#$ $ $ $ $ $rl   c                     [        [        [        5      [        SS45      [        SS5      :X  d   e[        [        [        5      [        SS45      [        R
                  :X  d   e[        [        [        S-   5      [        SS45      [        SS5      :X  d   e[        [        [        S-  S-
  5      [        SS45      S:X  d   e[        [        [        S-  S[        -  -
  5      [        SS	45      S
:X  d   e[        [        [        5      [        SS45      S:X  d   e[        [        [        5      [        [        5      -  [        [        * [        45      S:X  d   e[        [        [        S-
  5      [        S-  -  [        SS45      [        SS5      :X  d   e[        SSS9u  p[        [        U 5      U 5      [        U S-  * S-  U S:*  4U S-  S-  S45      :X  d   e[        [        SU -  S-
  5      U 5      [        U S-  * SU -  -   U S:*  4U S-  SU -  -
  S-   S45      :X  d   e[        [        XS-  -
  5      U SS45      SUS-  -  [        SUS-  5      -  SUS-  -  -
  [        SUS-  5      S-  -
  S-   :X  d   e[        [        [        U 5      * 5      U 5      [        [        U 5      U S:*  4S[        U * 5      -
  S45      :X  d   e[        [        SU -  S-
  5      U 5      [        U * U S:  4U S-
  S45      :X  d   e[        SU -  [        U S-  S-
  5      -  U 5      [        U S-  U S:  4U S-  * S-   U S:  4U S-  S45      :X  d   e[        [        U 5      XS-   45      [        US-   US-   S:  4U* S-
  US-   S:  4S5      :X  d   eg )Nr   rx   r   rn   r   r   r   rd  i  r   rf  zt sTr   r      r  )rI   r   rs   r   r   r   r   r4   r   r   r/   r  r-   r!   )r   r   s     rj   test_integrate_Abs_signr    s   SVaQZ(HQN:::SVaAY'166111SQZ!Q+x1~===SA]QAJ/1444SA!_q#rl3t;;;T!Wq"aj)Q...T!WSV^a"b\2a777T!a%[1a4'!Q3xAFFF5t$DASVQ9
Q$q!q&AqDFD>$+ + + +S1q\1%
Q$1a1f1qs
R6*8 8 8 8c!d(maAY/	!Q$s1ad|a1f$s1ad|Q6:; < ;S#a&\1%	Qa1sA2w;-*/ / / /T!A#']A&)
QUa!eT]+$ $ $ $QqSadQh'+y	
Aq2v!Q$AE*QT4L0: : : :T!Wqa%j)Y	
QA	aR!VQUQY/.< < < <rl   c                     [        [        [        [        -
  5      [        5      n U R	                  [        S5      [        [        [        S-
  5      [        5      :X  d   e[        [        [        [        -
  5      [        SS45      n U R	                  [        S5      [        [        [        S-
  5      [        SS45      :X  d   e[        [        [        [        S-  * 5      5      n[        U" [        [        -
  5      U" [        5      -  [        [        * [        45      nUR	                  [        S05      [        [        S[        S-  -  5      [        [        * [        45      :X  d   eg Nr   r   rx   rn   r   )rX   r!   rs   r   r  r
   r   rh   rd   convs      rj   
test_subs1r    s    QUQA66!Q<8CAJ2222QUaAY'A66!Q<8CAJAq	::::q#q!te*AAa!eHQqTMAsB<0D99aVR1WB3| DDDDrl   c                  &   [        [        [        [        -
  5      [        [        5      n U R                  [        S5      [        [        [        S-
  5      [        [        5      :X  d   e[        [        [        [        -
  5      [        SS4[        SS45      n U R                  [        S5      [        [        [        S-
  5      [        SS4[        SS45      :X  d   e[        [        [        [        S-  * 5      5      n[        U" [        [        -
  5      U" [        5      -  [        [        * [        4[        SS45      nUR                  [        S05      [        [        S[        S-  -  5      [        [        * [        4[        SS45      :X  d   eg r  rX   r!   rs   r   r   r  r
   r   r  s      rj   
test_subs2r    s   QUQ"A66!Q<8CAJ15555QUaAYAq	2A66!Q<8CAJAq	Aq!9EEEEq#q!te*AAa!eHQqTMAsB<!Q;D99aVR1WB3|aAY OOOOrl   c                  n   [        [        [        [        -
  5      [        S[        4[        [        S45      n U R                  [        S5      [        [        [        S-
  5      [        SS4[        SS45      :X  d   e[        [        [        [        S-  * 5      5      n[        U" [        [        -
  5      U" [        5      -  [        [        * [        4[        [        S45      nUR                  [        S05      [        [        S[        S-  -  5      [        [        * [        4[        SS45      :X  d   eg Nr   rx   r   rn   r   r  r  s      rj   
test_subs3r    s    QUaAYAq	2A66!Q<8CAJAq	Aq!9EEEEq#q!te*AAa!eHQqTMAsB<!Q;D99aVR1WB3|aAY OOOOrl   c                  L   [        [        [        5      [        S[        4[        [        S45      n U R                  [        S5      [        [        [        5      [        SS4[        SS45      :X  d   e[        [        [        [        S-  * 5      5      n[        U" [        5      U" [        5      -  [        [        * [        4[        [        S45      nUR                  [        S05      [        [        S[        S-  -  5      [        [        * [        4[        SS45      :X  d   eg r  r  r  s      rj   
test_subs4r    s    Q!QQ1I.A66!Q<8CFQ1I1ayAAAAq#q!te*AAaD1IB3|aAY7D99aVR1WB3|aAY OOOOrl   c                     [        [        [        S-  * 5      [        [        * [        45      n U R	                  [        S5      U :X  d   e[        [        [        S-  * [
        -   5      [        5      n U R	                  [
        S5      [        [        [        S-  * S-   5      [        5      :X  d   e[        [        [        S-  * [
        -   5      [        [        45      n U R	                  [        S5      [        [        [
        [        S-  -
  5      [        S45      :X  d   eU R	                  [
        S5      [        [        [        S-  * S-   5      [        5      :X  d   e[        [        [        S-  * [
        -   5      [
        [        * [        4[        [        * [        45      n U R	                  [        S5      U :X  d   eU R	                  [
        S5      U :X  d   e[        [        [        S-  * 5      [        [        45      n U R	                  [        S5      [        [        [        S-  * 5      [        S45      :X  d   e[        [        [        5      [        5      n U R	                  [        S5      U R	                  [        S5      -
  [        [        [        5      [        SS45      -
  R                  5       R                  (       d   eg )Nrn   r   rx   r   )rX   r!   rs   r   r  r   r   is_zerorh   s    rj   
test_subs5r    s   adUa"b\*A66!Q<1adUQY#A66!Q<8CA	NA6666adUQY!Q(A66!Q<8CAqDMAq6::::66!Q<8CA	NA6666adUQY!bS"B3|<A66!Q<166!Q<1adUaV$A66!Q<8CAJA7777QAFF1QK!&&1+%Q!Q(CC
$&  rl   c            
         [        S5      u  p[        [        [        -  [        [	        [        5      [	        [        5      45      nUR                  [        S5      [        [        [        -  [        [	        S5      [	        [        5      45      :X  d   eUR                  [        S5      [        [        [        [	        [        5      [	        S5      45      :X  d   e[        [        [        -  [        [	        [        5      [	        [        5      4[        [	        [        5      [	        [        5      45      nUR                  [        S5      [        [        [        -  [        [	        S5      [	        [        5      4[        [	        S5      [	        [        5      45      :X  d   eUR                  [        S5      [        [        [        -  [        [	        [        5      [	        [        5      4[        [	        [        5      [	        S5      45      :X  d   e[        [        [        -  [        [	        [        5      [	        U 5      4[        [	        [        5      [	        U 5      45      nUR                  U S5      [        [        [        -  [        [	        [        5      [	        S5      4[        [	        [        5      [	        S5      45      :X  d   eg )Nza brx   )r   rX   rs   r   rd   r  )r   r   rh   s      rj   
test_subs6r    s   5>DA1q!A$!o&A66!Q<8AaC!QqT1Q4999966!Q<8A1Q4177771q!A$!o1Q417A66!Q<8AaC!QqT1Q41adAaD/JJJJ66!Q<8AaC!QqT1Q41adAaD/JJJJ1q!A$!o1Q417A66!Q<8AaC!QqT1Q41adAaD/JJJJrl   c            	      N   [        [        [        S[        4[        SS45      n U R                  [        S[        S05      U :X  d   e[        [	        [        5      [	        [        5      -   [        [	        [        5      [	        [        5      4[        SS45      n U R                  [	        [        5      S5      U :X  d   eU R                  [	        [        5      S5      [        [	        [        5      [	        [        5      -   [        S[	        [        5      4[        SS45      :X  d   eg r!  )rX   rs   r   r  r4   r  s    rj   
test_subs7r    s    Q1I1ay)A661aA,1$$$Q#a&1c!fc!f"5#$a)	-A66#a&!!!!66#a&!Q#a&1aQ.*+Q!4 4 4 4rl   c                     [        [        [        5      [        [        S-  5      -   [        S[        45      n U R	                  5       [        [        [        5      [        S[        45      [        [        [        S-  5      [        S[        45      -   :X  d   e[        [        [        5      [        [        S-  5      -   [        S[
        45      n U R	                  5       U :X  d   eU R	                  SS9[        [        [        5      [        S[
        45      [        [        [        S-  5      [        S[
        45      -   :X  d   eg )Nrn   rx   T)force)rX   rd   rs   r   r   r   r  s    rj   test_expandr  "  s    1a1g1ay)A88:!A$Aq	2Xa1g1ay5QQQQQ1a1g1bz*A88:??88$88AaD1a*#=AadGaBZ($) ) ) )rl   c                  H    [        [        S 5        [        [        S 5        g )Nc                  <    [        [        [        S-  * 5      S5      $ Nrn   r   )rX   r!   rs   r   rl   rj   r~   +test_integration_variable.<locals>.<lambda>,  s    xQTE
A6rl   c                  T    [        [        [        S-  * 5      S[        * [        45      $ r  )rX   r!   rs   r   r   rl   rj   r~   r  -  s    xQTE
QRLArl   )r[   r   r   rl   rj   test_integration_variabler  +  s    
:67
:ABrl   c                     [        [        [        S-  5      [        [        S-  5      S-   -  [        SS45      R	                  5       [        [        [        S-  5      [        [        S-  5      -  [        SS45      [        [        [        S-  5      [        SS45      -   :X  d   e[        [        [        S-  5      [        [        S-  5      S-   -  [        5      R	                  5       [        [        [        S-  5      [        [        S-  5      -  [        5      [        [        [        S-  5      [        5      -   :X  d   eg )Nrn   rx   r   )rX   r3   rs   r4   r   r   rl   rj   test_expand_integralr  0  s    C1Is1a4y1}-1ay9@@BQT3q!t9$q!Qi0QTQ1I&	'' ' ' C1Is1a4y1}-q188:QT3q!t9$a(QTA	  rl   c                  6  ^  [        [        [        S-  S-   5      [        SS45      m T R                  SSS9S[        S5      -  :X  d   eT R                  SSS9S	[        S
5      -  S[        S5      -  -   :X  d   eT R                  SSS9S[        S5      -  S-  S[        S5      -  S-  -   S[        S5      -  S-  -   :X  d   eT R                  S	SS9S[        S5      -  S	[        S5      -  -   S	[        S5      -  -   S[        S5      -  -   :X  d   e[	        T R                  S	SS9R                  5       T R                  5       -
  5      S:  d   e[        [        [        S-  [        S-  -   5      [        SS4[        SS45      m [        [        U 4S j5        g )Nr   rx   rn   r   midpointmethodr      r   ri  r  9   i	     iI  i  r   V   r      g      ?r   c                  &   > T R                  S5      $ )Nr   as_sumr  s   rj   r~   'test_as_sum_midpoint1.<locals>.<lambda>D  s    rl   )	rX   r.   rs   r  r  ra   r   r[   NotImplementedErrorr  s   @rj   test_as_sum_midpoint1r  9  s   adQh!Q,A88Aj8)QtCy[88888Aj8)QtBxZ"T"X+-EEEE88Aj8)QtCy[]	$t*R.DK-*.+ + + +88Aj8)QtCy[	$q'	.d2hJ.!"48., , , ,qxx*x-//1ACCE9:S@@@adQTk"Q2JAr
;A
 34rl   c                     [        [        [        -   S-  [        SS45      n [        SSSS9nU R	                  SSS9R                  5       [        SS	5      [        -   [        S-  -   :X  d   eU R	                  SSS9R                  5       [        S
S5      [        -   [        S-  -   :X  d   eU R	                  SSS9R                  5       [        SS5      [        -   [        S-  -   :X  d   eU R	                  S	SS9R                  5       [        SS5      [        -   [        S-  -   :X  d   eU R	                  USS9R                  5       [        S-  [        -   [        SS5      -   SSUS-  -  -  -
  :X  d   eg )Nrn   r   rx   ra   Tr   rc   r  r  r   r   re  r   #   l      @   r  )rX   rs   r   r   r  r   r   r   s     rj   test_as_sum_midpoint2r  G  s]   !a%!aAY'AsT40A88Aj8)002hq!nq6H1a46OOOO88Aj8)002hq"o6IAqD6PPPP88Aj8)002hr36G!6KaQRd6RRRR88Aj8)002hr26F6JQPQT6QQQQ88Aj8)002	1q8Aq>!Ar!Q$wK/0 0 0rl   c                     [        [        [        -   S-  [        SS45      n U R                  SSS9R	                  5       [        S-  :X  d   eU R                  SSS9R	                  5       [        SS5      [        S-  -   [        S-  -   :X  d   eU R                  SSS9R	                  5       [        SS	5      [        [        SS5      -  -   [        S-  -   :X  d   eU R                  S
SS9R	                  5       [        SS5      [        [        SS
5      -  -   [        S-  -   :X  d   eU R                  [        SS9R	                  5       [        S-  [        -   [        SS5      -   [        [        -  -
  SS[        -  -  -
  SS[        S-  -  -  -   :X  d   eU R                  SSSS9R                  [        5      (       d   eg )Nrn   r   rx   leftr  r   r   r   r  r   r       r   r   F)r  evaluate)	rX   rs   r   r  r   r   ra   hasr   r  s    rj   test_as_sum_leftr  R  s   !a%!aAY'A88Af8%,,.!Q$66688Af8%,,.(1a.1Q32FA2MMMM88Af8%,,.(1b/AhqRSnDT2TWXZ[W[2[[[[88Af8%,,.(1b/AhqRSnDT2TWXZ[W[2[[[[88Af8%,,.	1q8Aq>!AaC'!QqS'1AqAvJ>? ? ?88Bv86::3????rl   c                  Z   [        [        [        -   S-  [        SS45      n U R                  SSS9R	                  5       SS[        -  -   [        S-  -   :X  d   eU R                  SSS9R	                  5       [        SS5      [        [        SS5      -  -   [        S-  -   :X  d   eU R                  SSS9R	                  5       [        S	S
5      [        [        SS5      -  -   [        S-  -   :X  d   eU R                  SSS9R	                  5       [        SS5      [        [        SS5      -  -   [        S-  -   :X  d   eU R                  [        SS9R	                  5       [        S-  [        -   [        SS5      -   [        [        -  -   SS[        -  -  -   SS[        S-  -  -  -   :X  d   eg )Nrn   r   rx   rightr  r   r   r   r  r  r   rd  r  r   )rX   rs   r   r  r   r   ra   r  s    rj   test_as_sum_rightr  ]  s   !a%!aAY'A88Ag8&--/1qs7QT>AAA88Ag8&--/8Aq>AhqRSnDT3TWXZ[W[3[[[[88Ag8&--/8B3CaQRTUFV3VYZ\]Y]3]]]]88Ag8&--/8B3CaQRTUFV3VYZ\]Y]3]]]]88Ag8&--/	1q8Aq>!AaC'!QqS'1AqAvJ>? ? ?rl   c                  t   [        [        [        -   S-  [        SS45      n U R                  SSS9R	                  5       [        S-  [        -   [
        R                  -   :X  d   eU R                  SSS9R	                  5       [        S-  [        -   [        SS5      -   :X  d   eU R                  SSS9R	                  5       [        S-  [        -   [        SS	5      -   :X  d   eU R                  S
SS9R	                  5       [        S-  [        -   [        SS5      -   :X  d   eU R                  [        SS9R	                  5       [        S-  [        -   [        SS5      -   SS[        S-  -  -  -   :X  d   e[        [        [        5      [        SS45      R                  SS5      [
        R                  :X  d   eg )Nrn   r   rx   	trapezoidr  r   r      rh  r   rf  r  r   )
rX   rs   r   r  r   r   r   r   ra   r   r  s    rj   test_as_sum_trapezoidr  g  sw   !a%!aAY'A88Ak8*113q!tax!&&7HHHH88Ak8*113q!tax(1a.7PPPP88Ak8*113q!tax(2rBR7RRRR88Ak8*113q!tax(2rBR7RRRR88Ak8*113	1q8Aq>!AqAvJ./ / /DGaAY'..q+>!&&HHHrl   c                  
  ^  [        [        [        -   S-  [        SS45      m [        [        U 4S j5        [        [        U 4S j5        [        [        S 5        [        [        U 4S j5        [        [        U 4S j5        g )	Nrn   r   rx   c                  &   > T R                  S5      $ )Nr   r  r  s   rj   r~   $test_as_sum_raises.<locals>.<lambda>t  s    qxx|rl   c                  &   > T R                  S5      $ Nr   r  r  s   rj   r~   r  u  s    qxx{rl   c                  >    [        [        5      R                  S5      $ )Nr   )rX   rs   r  r   rl   rj   r~   r  v  s    x{11!4rl   c                  .   > T R                  [        5      $ rz   )r  r   r  s   rj   r~   r  w  s    qxx|rl   c                  $   > T R                  SSS9$ )Nr   xxxx2r  r  r  s   rj   r~   r  x  s    qxx'x:rl   )rX   rs   r   r[   r   r  s   @rj   test_as_sum_raisesr  r  sT    !a%!aAY'A
:+,
:*+
:45
:+,
::;rl   c                      [        [        [        [        5      [        5      n [        [        [        [        5      nU R                  5       UR                  5       :X  d   eg rz   )rX   rs   r   rh   rd   s     rj   test_nested_doitr  {  s<    !Q#AAqA668qvvxrl   c                  L   [        [        S-  [        S S45      n [        [        S-  [        SS 45      nU R                  5       [        SS5      :X  d   eUR                  5       [        SS5      :X  d   e[        [        [        -  [        S [        45      R                  [        [        5      [        [        [        -  [        S [        45      :X  d   e[        [        [        -  [        [        S 45      R                  [        [        5      [        [        [        -  [        [        S 45      :X  d   e[        [        S-  [        S S45      [        SS5      :X  d   e[        [        S-  [        SS 45      [        SS5      :X  d   e[        SS5      [        SS5      :X  d   eg )Nrn   rx   r   r   zx**2)rs   1N)rX   rs   r   r   r   r  r   rI   r  s     rj   test_issue_4665r    sB   A4|$AA1d|$A668x1~%%%668xA&&&AaC!T1&++Aq1XacAtQ<5PPPPAaC!Q&++Aq1XacAq$<5PPPPQTAtQ<(HQN:::QTAq$<(HRO;;;V-.(2q/AAArl   c                  h    [        [        S-  [        SS45      n U [        U R                  6 :X  d   eg )Nrn   r   rx   )rX   rs   argsr  s    rj   test_integral_reconstructr    s/    A2qz"A!&&!!!!rl   c            
         [        [        S[        -  5      [        SS45      n U R                  5       [        SS5      :X  d   eU R                  SS9[        SS5      :X  d   e[	        S5      n[        U" [        5      [        SS45      R                  5       S:X  d   e[        S[        S[        U" [        5      [        5      45      R                  5       S:X  d   e[        [        [
        S45      R                  5       S:X  d   e[
        S[        [        5      4[        S44n[        [
        /UQ76 R                  5       [        SS5      :X  d   e[        [
        /[        [        U5      5      Q76 R                  5       S:X  d   eg )	Nrn   r   rx   r   Fdeeprd   r   )	rX   rs   r   r   r	   r   r!   listreversed)rh   rd   r   s      rj   test_doit_integralsr    sB   !A#Aq	*A668x1~%%%66u6!Q///AAaD1a)$))+q000A1hqtQ/01668A===A1v##%***!SVnq!f%FA$$&(1a.888A/Xf-./446!;;;rl   c            	         [        [        [        5      S[        -   -  5      [        S[        [        5      -  [        S-   S-  -  S-  S[        [        5      -  [        S-   -  S-  -
  S[        [        5      -  S-  -
  [	        [        S-   5      S:  4S[
        -  [        [        * 5      -  [        S-   S-  -  S-  S[
        -  [        [        * 5      -  [        S-   -  S-  -
  S[
        -  [        [        * 5      -  S-  -
  S45      :X  d   e[        [        [        -  S[        [        5      -   -  5      [        [        -  :X  d   eg )Nrx   rn   r   rd  r   T)rI   r.   rs   r/   r   r   r#   r   rl   rj   test_issue_4884r    s   T!Wa!e_%tAwYAz!!#aQiQ&7&::QtAwYr\IAJNqSqb\1q51*$Q&1T1"Xq1u)=b)@@aCaRLO!#	$$ $ $ QT1s1v:&'1a4///rl   c                     [        [        [        -  [        [        5      -  [        5      [	        [        [        -  [        [        -  -  [        [        5      -  [        S-  S[        -  -   S-   -  [        [        [        -  -  [        [        5      -  [        S-  S[        -  -   S-   -  -   [        [        [        -  -  [        S-  S[        -  -   S-   -  -
  [        [        S5      4[        [        5      S-  S-  S45      :X  d   eg )Nrn   rx   r   T)rI   rs   ra   r#   r/   r   r   rl   rj   test_issue_18153r    s    QT#a&[#	
1QT#a&!Q$1*q.	)adF3q6M1a4!A#:>"
#%&q!tVQTAaCZ!^%<
=Bi	q619Q;%  rl   c                     SSK Jn JnJn  [	        U 5      R
                  SL d   e[	        SU 5      R
                  SL d   e[	        SU S45      R
                  SL d   e[	        SU SS45      R
                  SL d   e[	        SU SU45      R
                  SL d   e[	        SX45      R
                  SL d   e[	        X5      R
                  SL d   e[	        XSU 45      R
                  SL d   e[	        XSS45      R
                  SL d   e[	        X SS45      R
                  SL d   e[	        XSS45      nUR
                  SL a  UR                  5       S:X  d   e[	        XX"45      nUR
                  SL a  UR                  5       S:X  d   e[	        SXUS-   45      nUR
                  SL a  UR                  5       S:X  d   e[	        X-  U SS4USS45      R
                  SL d   e[	        X-  U SS4USU45      R
                  SL d   e[	        X S45      R
                  SL d   e[	        X S[	        XSS45      45      R
                  SL d   e[	        [        X"SS45      U SS45      R
                  SL d   e[	        [        U 5      S-  [        U 5      S-  -   S-
  U 5      R
                  SL d   e[	        [        U 5      U SS45      R
                  SL d   eg )	Nr   rs   r   r5  Frx   Trn   r  r   )	sympy.abcrs   r   r5  rX   	is_numberra   r   r4   r3   rd   )rs   r   r5  r   s       rj   test_is_numberr    s   !!A;  E)))Aq>##u,,,A1v((D000A1ay!++t333A1ay!++u444Av((E111A>##u,,,A1ay!++u444A1ay!++u444A1ay!++t333 	1IA;;%ACCEQJ..IA;;%ACCEQJ..Q1q5M"A;;%ACCESL00AC!QQ1I.88D@@@AC!QQ1I.88EAAAA1v((D000A1hqa)456@@DHHHCq!9%1ay1;;tCCC CFAIA	)A-q1;;uDDDAaD1a)$..$666rl   c                     SSK Jn JnJn  [	        SU 5      R
                  U 1:X  d   e[	        U 5      R
                  U 1:X  d   e[	        X S U45      R
                  U1:X  d   e[	        X US 45      R
                  U1:X  d   e[	        X SU45      R
                  U1:X  d   e[	        X US45      R
                  U1:X  d   e[	        X X45      R
                  X1:X  d   e[	        X U5      R
                  X1:X  d   e[	        X SS45      R
                  [        5       :X  d   e[	        XSS45      R
                  U 1:X  d   e[	        XX"45      R
                  X1:X  d   e[	        XSS4US S 45      R
                  X1:X  d   e[	        XSS4U SU45      R
                  U1:X  d   e[	        SUSS4USU 4U SS45      R
                  [        5       :X  d   e[	        SXS4USU 4U SS45      R
                  [        5       :X  d   e[	        SU SS4XS4USS45      R
                  U 1:X  d   e[	        [        U 5      [        U 5      SU45      R
                  U1:X  d   e[	        [        U 5      [        U 5      SU 45      R
                  U 1:X  d   eg )Nr   r  rx   rn   )r  rs   r   r5  rX   r   setrd   r  s      rj   test_free_symbolsr    s   !!Aq>&&1#---A;##s***A4|$11aS888A1d|$11aS888A1ay!..1#555A1ay!..1#555A1y!..1&888A!))aV333A1ay!..#%777A1ay!..1#555A1y!..1&888A1ay1dD/ 

,1&! ! !A1ay1a) 

,1#  A1ay1a)aAY 

,#%     Aay1a)aAY 

,#%     A1ay1)aAY 

,1#  AaD1Q4A,'44;;;AaD1Q4A,'44;;;rl   c            	         SSK Jn Jn  [        SU SU 45      R                  (       d   e[        SU SS45      R                  (       d   e[        SU SS4[
        S45      R                  SL d   e[        XS45      R                  (       d   e[        X-   US45      R                  b   e[        XS[        U 5      4U S45      nUR                  b   e[        XS4US[        U 5      45      R                  SL d   e[        X [        [        45      R                  (       d   e[        X [        * [        * 45      R                  (       d   e[        [        U 5      U SS[        -  45      R                  b   eg )Nr   )rs   r  rx   rn   FT)
r  rs   r  rX   r  r   r!   r   r4   r   )rs   r  r   s      rj   test_is_zeror    sO   A1ay!))))A1ay!))))A1ay1a&)11U:::A1v&&&&AEAq6"**2223q6NQF+A99A1v1c!f~.66$>>>A2r{#++++AB3}%---- CFQ1R4L)11999rl   c            	         SSK Jn   [        [        U 5      X 45      nUR	                  U 5      nUR                  U SS9R                  5       [        [        S5       Vs/ s H  n[        U5      PM     sn6 :X  d   eg s  snf )Nr   rs   r   r  r   )
r  rs   rX   r3   lseriesnseriesremoveOr   rangenext)rs   r   rh   rC  s       rj   test_seriesr    sg    Q! A			!A99Q!9$$&#q/JAQ/J*KKKK/Js   A<
c                      [        S5      n [        S[        U 5      -   U -  U 5      [        U 5      [	        U 5      -   :X  d   e[        [        U 5      S-   U -  U 5      R                  [        5      (       d   eg )Nrs   rx   rn   )r   rI   r4   r#   r<   r3   r  r:   r  s    rj   !test_trig_nonelementary_integralsr  
  sd    sAa#a&j!^Q'3q6BqE>999 c!fqj!^Q'++B////rl   c                  f   [        S5      n [        S5      n[        SSS9n[        [        U S-  US-  -   5      U 5      US-  [        X-  5      -  S-  U [        U S-  US-  -   5      -  S-  -   :X  d   e[        [        U S-  US-  -
  5      U 5      U [        U S-  US-  -
  5      -  S-  US-  [	        U [        U S-  US-  -
  5      -   5      -  S-  -
  :X  d   e[        SSS9n [        SSS9n[        SU S-  US-  -   [        S	5      -  -  U 5      XS-  [        U S-  US-  -   5      -  -  :X  d   eg )
Nrs   r   r5  Tr   rn   r   rx   z3/2)r   rI   r.   r%   r#   r   r  s      rj   test_issue_4403r    sf   sAsAsT"AT!Q$A+&*	1U13ZAd1a4!Q$;//112 2 2T!Q$A+&*	$q!tad{
A1ST!Q$A+->)>%? ? AAB B B 	sAsT"AQ1q!tah..2	a4QTAqD[!!"# # #rl   c            
          [        [        [        S-  * S-
  5      [        5      S[        [        [        S[        S-  -
  5      -  5      -  [        [        S[        S-  -
  5      -  S-  -   :X  d   eg )Nrn   r   r   rM  )rI   r.   rs   r2   r   rl   rj   test_issue_4403_2r  #  sb    T1a4%!)_a(
4$rAqDy/!""QtBAI%6q%889 9 9rl   c                      [        SSS9n [        [        U S-  [        S-  -
  5      [        SU 45      [        U S-  -  S-  :X  d   eg )NRTr   rn   r   r   )r   rI   r.   rs   r   )r  s    rj   test_issue_4100r  (  sF    sT"AT!Q$A+&Aq	2bAgai???rl   c            	         SSK Jn JnJnJn  [        S5      n[        [        U" U5      U5      U5      [        U" U5      X5      :X  d   e[        U" U5      5      R                  U" U5      [        U5      4:X  d   e[        [        U" U5      5      5      R                  U" U5      [        U5      [        U5      4:X  d   e[        [        U" U5      5      U5      R                  U" U5      [        U5      [        U5      4:X  d   e[        [        U" U5      U5      U5      R                  U" U5      [        U5      [        U5      4:X  d   e[        [        [        U" U5      U5      U5      U5      R                  U" U5      [        U5      [        U5      [        U5      4:X  d   e[        [        U" U5      U5      U5      [        U" U5      X5      :X  d   e[        [        U" U5      U5      U5      U[        U" U5      U5      -  :X  d   e[        [        U" U5      U5      U5      [        X$" U5      -  U5      U[        U" U5      U5      -  4;   d   e[        [        SU5      U5      US-  :X  d   e[        [        SU5      U5      SU-  U-  :X  d   e[        SX5      R                  [        SX!5      R                  :w  d   e[        U" U5      X!X!5      R                  5       US-  [        U" U5      X5      -  S-  :X  d   e[        U" U5      USS4U SU4USU45      R                  5       X!S-
  -  [        U" U5      USS45      -  US-
  [        U" U5      USS45      -  -
  :X  d   eg )Nr   )wrs   r   r5  rd   rn   rx   )r  r  rs   r   r5  r	   rX   r  r   rI   r   )r  rs   r   r5  rd   s        rj   test_issue_5167r  -  s   $$AHQqT1%q)XadA-AAAAAaD>1Q4q"2222HQqTN#((QqT58U1X,FFFFHQqTNA&++!eAha/IIIIHQqT1%q)..1Q4q582LLLLHXadA.2A6;;	
1uQxq58,- - -XadA&*hqtQ.BBBBXadA&*a1q0A.AAAAXadA&*x!A$/BAhqQRtUVFWDW.XXXXXa^Q'1a4///Xa^Q'1Q3q5000Aq!!Xa%6%;%;;;;AaD!%**,1XadA5I0I!0KKKKAaD1a)aAYAq	:??A	q5	(1Q4!Q++q1uhqtaAY6O.OOP P Prl   c            
      F   [        SSS9n [        [        [        [        5      S-  * 5      [        5      [        [        5      [        [        SS5      5      -  [        [        [        5      [        R                  -
  5      -  S-  :X  d   e[        [        [        [        5      S-  5      [        5      [        [        5      [        [        SS5      5      -  [        [        [        5      [        R                  -   5      -  S-  :X  d   e[        [        U * [        [        5      S-  -  5      [        5      [        [        5      [        SSU -  -  5      -  [        [        U 5      [        [        5      -  SS[        U 5      -  -  -
  5      -  S[        U 5      -  -  :X  d   eg )Nr5  Tr   rn   rx   r   r   )r   rI   r!   r#   rs   r.   r   r   r=   r   r   r?   r5  s    rj   test_issue_4890r  D  s9   sT"AS#a&!)_a(RXa^$$SQ!&&%99!;< < <SQ^Q'RXb!_%%d3q6!&&=&99!;< < <S!CFAI&*RQ!Wc$q'#a&.1aQi="@AA1T!W9MN N Nrl   c            	          [        S[        [        S[        S-  -
  5      -  -  [        5      R                  [        5      (       a   eg r!  )rI   rs   r.   r  rX   r   rl   rj   test_issue_4551r  N  s9    Ad1q!t8n,-q155h?????rl   c            
         [        SSSS9n [        [        U [        SU -  -  S-
  -  [        S[        R
                  45      U S-  SSU -  -  U S-  -  -
  U SSU -  -  -  -
  SSSU -  -   -  U SSSU -  -   -  -  -   -  -
  5      S:X  d   eg )Nra   Trc   r   rx   r   rn   )r   rR   rI   rs   r   r   r  s    rj   test_issue_4376r  R  s    sD40AIaQqSA.Aqvv?AAaCA%!ac(
2QQqS\Aa!aPQc'lN5RST UXYZ Z Zrl   c                      [        [        [        5      [        S-  -
  [        [        SS5      -  -  [        5      S[        [        SS5      -  -  S-  S[        [        SS5      -  -  S-  -
  :X  d   eg )Nr   rx   r   r   rf  )rI   r.   rs   r   r   rl   rj   test_issue_4517r!  X  si    d1g1na!Q&77;	!Xa^
A!Xb!_"4 4R 778 8 8rl   c                  (   [        SSS9u  p[        [        U [        -  5      [        U[        -  5      -  [        S[        45      R                  5       [        S[        U S5      [        US5      -  4[        * S-  [        X* 5      [        U S5      [        US5      -  -  4[        S-  [        X5      [        U S5      [        US5      -  -  4S5      :X  d   e[        [        U [        -  5      [        U[        -  5      -  [        45      [        S[        [        U S5      [        US5      5      4[        * [        U[        -  5      S-  -  S-  [        [        U[        -  5      S-  -  S-  -
  [        U[        -  5      [        U[        -  5      -  SU-  -  -   [        X* 5      4[        [        U[        -  5      S-  -  S-  [        [        U[        -  5      S-  -  S-  -   [        U[        -  5      [        U[        -  5      -  SU-  -  -
  [        X5      4U[        U [        -  5      -  [        U[        -  5      -  U S-  US-  -
  -  U [        U[        -  5      -  [        U [        -  5      -  U S-  US-  -
  -  -
  S45      :X  d   eg )Nzk mTrb   r   rn   r  )
r   rI   r4   rs   r   rR   r/   r   rJ   r3   )kr  s     rj   test_issue_4527r$  ]  s8   5$'DAS1Xc!A#h&Ar
3<<>1bAhAq)*3q5"Q)r!Qx"Q(':;<a4AR1X1a%89:	   S1Xc!A#h&-	
C1a"Q(#$
C!HaK	Ac!A#hkM!O	+c!A#hs1Q3x.?1.E	Er!RyQ	
3qs8Q;q1S1Xq[=?	*S1Xc!A#h->!-D	DbhO	
3qs8C!H	adQTk	*	
3qs8C!H	adQTk	*
+,0	2	23 3 3 3rl   c                  2   [        SSS9n [        [        [        * S-  [        -  U -  [
        -  5      [
        -  [
        [        * [        4SS9[        [        [        * S-  [        -  U -  [
        -  5      [
        -  [
        [        * [        45      :X  d   eg )Nr   Tr   rn   r   r   )r   rI   r!   r   r   rs   r   rX   )yposs    rj   test_issue_4199r'  r  s{    #%DS!Aba(*QRLGaRT"WT\!^$Q&RC56 6 6rl   c            
      P   [        SSS9u  pp#[        [        [        S-  * [        U-  [        -  -   5      [        5      [        [        5      * [        US-  * S-  5      -  [        [        U-  S-  [        -
  5      -  S-  :X  d   e[        [        U [        S-  -  U[        -  -   U-   5      [        5      R                  [        [        5      [        X!S-  SU -  -  -
  5      -  [        SU -  [        -  U-   S[        U 5      -  -  5      -  S[        U 5      -  -  5      (       d   eSSK
Jn  SSKJn  U" [        [        [        S-  * 5      [        [        U-  [        -  5      -  [        [        * [        45      5      [        [        5      [        US-  * S-  5      -  :X  d   e[        S	SS9u  pU" [        [        U * [        S-  -  SU-  [        -  -   5      [        [        * [        45      5      [        [        5      [        US-  U -  5      -  [        U 5      -  :X  d   eg )
Nza:dTr   rn   r   r   )
expand_mul)r#  za d)r   rI   r!   rs   r   r.   r   r=   equalsr?   r  r)  r  r#  r   )r   r   r   r   r)  r#  s         rj   test_issue_3940r+  y  s   .JA!S!Q$1Q'+	b	#q!teAg,s1Q3q519~-a/0 0 0S1a4!A#)*A.55RQAqs^$$T1Q3q519qay*A%BBAd1gINP P P P /iQTE
3qs1u: 5B3|DERadU1W  54(DAiQBq!tGac!eO 4q2#rlCDRQT!VT!W$% % %rl   c                      [        [        * [        S-  [        S-  -   -  [        5      [        [	        [        * [        -  [        -   5      -  S-  [        [	        [        [        -  [        -   5      -  S-  -
  :X  d   eg r   )rI   r   rs   r   r#   r   rl   rj   test_issue_5413r-    s^     aRA1%q)QsA2a4!8}_Q->3qsQw<PQAQ-QQQQrl   c                     [        S5      u  p[        SSS9nU * [        U* 5      -  nU * U[        -  -  [	        [
        5      S-  [        [        5      S-  -   -  n[	        [
        5      S-  * [        [        5      S-  -
  n[	        [
        5      S-  * [	        [        5      S-  -   S-
  n[        X$U-
  -  [        5      X * U* -  [        U[        -  5      -  U-  U [        -  [        U* 5      -  -   -  X * U* -  [        U[        -  5      -  U-  U [        -  [        U* 5      -  -   -  X U-  [        U[        -  5      -  U-  U [        -  [        U* 5      -  -   -  X U-  [        U[        -  5      -  U-  U [        -  [        U* 5      -  -   -  X-  [        -  X* -  [        [        5      -  [        U5      -  -
  [        U* 5      -  X-  [        -  X* -  [        [        5      -  [        U5      -  -
  [        U* 5      -  4;   d   eg )NzA zr   T)r  rn   rx   )
r   r   r!   r   r4   rs   r3   r   rI   r#   )r   r5  r   P1P2h1h2s          rj   test_issue_4892ar3    s   5>DAsD!A
CGB
QqS3q619s1vqy(	)B
a&!)c!fai	B
a&!)c!fai	!	#B QR[!$	2s8C!HQ1S!W,-	2s8C!HQ1S!W,-	rE3qs8OA!CG+,	rE3qs8OA!CG+,	
QCQA&	&QB/	
QCQA&	&QB/)   rl   c                     [        [        5      [        S-  -  S[        [        5      -  [        S-  -  -   S-   [        S-  S-   -  n [	        [        [        U [        5      R                  [        5      U -
  5      5      S:X  d   eg )Nr   rn   r  r   )r4   r   rs   r3   rS   rM   rI   r   )exprs    rj   test_issue_4892br6    sk     F1a4K!CF(1a4-'",q!tax8DF9T1-2215<=>!CCCrl   c            	         [        [        [        5      [        [        [
        5      -  [        S[        4[        S[        4[
        S[        45      S[        [        [        [
        5      [        S[        4[
        S[        45      -  :X  d   eg Nr   rn   )rI   r4   rs   rd   r   r5  r   rX   r   rl   rj   test_issue_5178r9    sb    SVAaG^aBZ!QaBZH	(1Q7Q2JAr

334 4 4rl   c                     [        [        5      R                  [        SS5      n [        S-  S-  [        S-  S-  -
  [        S-  S-  -   [        S-  S	-  -
  [        S-  S
-  -   [        [        S-  5      -   n[	        U [        5      U:X  d   e[        [	        U [        5      [        5      U :X  d   e[	        [        [        S-  5      [        5      [        [        S-  5      :X  d   eg )Nr   r   rn   r      r   i  r   i  i _7 rf  r   )r4   rs   seriesrO   rI   r   rd   r}   s     rj   test_integrate_seriesr>    s    AaBA	1QAb1a48#ad5j01b5=@1QU8KAQ?a	!Q#q(((Qq!tWa AadG+++rl   c            	      T    SSK Jn   U " [        / / S// [        5      [        5      b   eg )Nr   heurischrx   )sympy.integrals.heurischrA  rE   rs   r@  s    rj   test_atom_bugrC    s'    1GBQCQ/3;;;rl   c                  ,   [        SSS9n [        [        [        [        -  U -  5      [        S[
        4[        S[
        45      R                  5       [        U 5      [        [
        S-  U -  5      -
  [        -   S[        [
        5      -  -   U -  :X  d   eg )Nr5  Fzeror   rn   )
r   rI   r4   rs   r   r   r   r#   r:   r   r  s    rj   test_limit_bugrG    sy    sAS1QZ!QaBZ8AAC	Q"RU1W+	
	*Qs2wY	69: : :rl   c                      [        S5      n [        [        [        5      U " [        5      -  [        5      R	                  [
        5      (       d   eg )Nr}   )r	   rI   r!   rs   r  rX   r|   s    rj   test_issue_4703rI    s5    ASVAaD[!$((2222rl   c                      [        S5      n [        U " [        5      R                  [        5      S-  [        5      R	                  [
        5      (       d   eg )Nrd   rn   )r	   rI   rs   r   r  rX   r%  s    rj   test_issue_1888rK    s9    AQqTYYq\1_a(,,X6666rl   c                      [        [        [        [        -  5      [        [        * S-  [        S-  4[        S[        45      S[        [        S-  S-  5      -  :X  d   eg )Nrn   r   )rI   r3   rs   r   r   r<   r   rl   rj   test_issue_3558rM    sH    S1XB3q5"Q$/!Q<"RU1W+MMMrl   c            	          [        S[        SS[        S-  -  -   5      -  [        5      [        [        S-  5      S-  :X  d   eg )Nrx   re  r   rn   )rI   r.   rs   r%   r   rl   rj   test_issue_4422rO    s9    QtB1a4K((!,ac
Q>>>rl   c            
          [        [        [        [        SS[        -  -   5      -  [        5      5      [        S[        -  S-   5      S[        S-  -  [        -   S-
  -  S-  :X  d   eg )Nrx   rn   r   rd  )rR   rI   rs   r.   r   rl   rj   test_issue_4493rQ    sY    IaQ1Woq12QqS1WqAvzA~&r)* * *rl   c                  V   [        [        [        5      [        -  [        [        * [        45      [        :X  d   e[        [        [        5      [        -  [        S[        45      [        S-  :X  d   e[        [        [        5      [        -  [        5      [        [        5      :X  d   eg r8  )rI   r4   rs   r   r   r<   r   rl   rj   test_issue_4737rS    so    SVAXB3|,222SVAX1bz*bd222SVAXq!RU***rl   c            
         SSK Jn   [        SSS9n[        U " [	        [        [        * 5      [        [        5      -  [        U-  -  [        S[        45      5      5      U[        SU5      -  S-   [        U5      -  :X  d   eg )Nr   r  r   Tr   rx   )r  r  r   rR   rI   r!   rs   r#   r   rC   rB   )r  r   s     rj   test_issue_4992rU    sm    /sT"AK	#qb'#a&.A*=1bz JKL	
9Q?	Q	a() ) )rl   c                      SSK Jn   [        [        [	        [
        * 5      [
        [        -  -  [
        5      5      U " [        S-   [
        5      :X  d   eg )Nr   
lowergammarx   )'sympy.functions.special.gamma_functionsrX  rR   rI   r!   rs   r   rW  s    rj   test_issue_4487rZ    s8    BIc1"gadlA./:a!eQ3GGGGrl   c                  V    [        S5      n [        SU S-  -  U SS45      [        L d   eg )Nrs   rx   rn   r   )r   rI   r   r  s    rj   test_issue_4215r\    s.    sAQ1X2qz*b000rl   c                  t   [        SSSS9n [        [        U -  [        [        5      -  [        5      U [        -  [        U -  -  [        [        5      -  U S-  SU -  -   S-   -  [        [        U -  -  [        [        5      -  U S-  SU -  -   S-   -  -   [        [        U -  -  U S-  SU -  -   S-   -  -
  :X  d   eg )Nra   Tr  rn   rx   )r   rI   rs   r#   r  s    rj   test_issue_4400r^    s    sD40AadCF]A&	!AqDQA!a(1QT6#a&=!Q$1*q.+II	!Q$1qs
Q	      rl   c                      [        [        S[        -
  5      [        S[        -   5      -   S-  [        -  [        SS9[        [        [        * S-   5      [        [        S-   5      -   S-  [        -  [        5      :X  d   eg )Nrx   rn   TrE   )rI   r.   rs   rX   r   rl   rj   test_issue_6253ra    si     d1q5kDQK/!3A5q$G$rAv,a!e,q02A67 7 7rl   c            	          [        SS[        -   [        -   [        -   -  [        SS4[        SS4[        SS45      S[	        S5      -  S[	        S5      -  S-  -
  S[	        S5      -  S-  -   S[	        S5      -  -   S	[	        S
5      -  -   S[	        S5      -  S[	        S
5      -  -   S[	        S5      -  S-  -
  S[	        S5      -  S[	        S5      -  S-  -
  S[	        S5      -  S[	        S5      -  S-  -
  S[	        S5      -  S-  -   4;   d   eg )Nrx   r   ir   r   rn   r   r   r   r   r  rq  /   rI   rs   r   r5  r#   r   rl   rj   test_issue_4153re  
  s    QA	A&Aq	Aq!9q!QiHCF
Qs1vXaZ!CF(1*,qQx7!CF(B	#a&1SV8bQik)2c!f9r#a&y{+BCF
Qs1vXaZ"SV)A+-M/ / / /rl   c                     [        S5      u  pn[        U[        U -
  U-   -  U-  [        U S-  [        S-  -
  5      -  [        X-
  U 45      nUR	                  [
        5      (       a   eUR	                  [        5      (       a   eg )NzR b hrn   )r   rI   rs   r.   r  r   rX   )r  r   hrh   s       rj   test_issue_4326rh    st    gGA! 	Aq1uqyM1$d1a4!Q$;&77!QUAGAuuSzz>uuXrl   c                      [        S[        -  S[        -  -   [        5      S[        -  [        S5      -  S[        -  [        S5      -  -   :X  d   eg r  r)  r   rl   rj   test_powersrj    s@    QTAqD[!$1SVad3q6k(AAAArl   c                      [        [        S 5        [        [        S[        -   5      [        -  [        SS4SS9R                  [        5      (       d   eg )Nc                  0    [        S[        -  [        SSS9$ )Nrx   T)manualrE   r   r   rl   rj   r~   $test_manual_option.<locals>.<lambda>   s    y1adKrl   rx   r   Trm  )r[   r   rI   r#   rs   r  rX   r   rl   rj   test_manual_optionrp    s?    
:KLS1XaZ!Q48<<XFFFFrl   c                      [        [        S 5        [        [        [        5      [        SS9[        [        [        5      [        5      :X  d   eg )Nc                  0    [        S[        -  [        SSS9$ )Nrx   T)rE   rischr   r   rl   rj   r~   %test_meijerg_option.<locals>.<lambda>&  s    y1aTJrl   Tr`  )r[   r   rI   r6   rs   rX   r   rl   rj   test_meijerg_optionru  %  s3    
:JKSVQ-#a&!1DDDDrl   c                     [        [        S 5        [        [        [        S-  * 5      [        SS9[        [        [        S-  * 5      [        5      :X  d   e[        [        S[        -  5      [        -  [        [        SS9[        S-  [        [        S[        -  5      -  S-  [        S-  -   -  :X  d   e[        [        [        5      [        SS9[        [        [        5      [        5      :X  d   eg )Nc                  N    [        S[        [        5      -  [        S[        4SS9$ )Nrx   r   Trs  )rI   r#   rs   r   r   rl   rj   r~   #test_risch_option.<locals>.<lambda>-  s    y3q6Aq":TJrl   rn   Trx  rx   )
r[   r   rI   r!   rs   rY   r#   r   r=   rX   r   rl   rj   test_risch_optionrz  +  s    
:JKS!Q$Z$/3HaQRdUUV3WWWWS1XaZAT2adAc!A#hJqL1Q3<N6OOOOSVQd+xA/BBBBrl   c            	         [        [        S 5        [        [        [        S-  5      [        SS9[        [        5      [        [        5      -  S-  :X  d   e[        [        [        5      [        -  [        SS9[        [        [        5      [        -  [        5      :X  d   e[        [        [        5      [        [        [        5      5      -  [        [        SS5      -  -  [        SS9S[        [        S	S5      -  -  [        [        [        5      5      -  S
-  S[        [        S	S5      -  -  [        [        [        5      5      -  S
-  -   S[        [        S	S5      -  -  [        [        [        5      5      -  S-  S[        [        S	S5      -  -  [        [        [        5      5      -  S-  -   [        [        5      -  -   :X  d   eg )Nc                  0    [        S[        -  [        SSS9$ )Nrx   T)rs  rA  r   r   rl   rj   r~   &test_heurisch_option.<locals>.<lambda>6  s    y1atdKrl   rn   Tr@  r   r   Firx   i!     re  r	  )r[   r   rI   r!   rs   r.   r   r?   rX   r#   r3   r   r4   r   rl   rj   test_heurisch_optionr  4  sV   
:KLSAYD1T"Xd1g5Ea5GGGGSVAXq40HSVAXq4IIIISVCAK'8Aq>(991uMQAs3q6{*3.QA5F1Fs3q6{1RSV1VV	Ax1~	c#a&k	)"	,qHQN1B/B3s1v;/Nr/Q	QSVWXSYY	Z[ [ [rl   c                      SS[         S-  -  S-
  -  n [        U [         5      R                  [         5      n[        XSS9(       d   eg )Nrx   gHzG?rn   g333333@g-q=)tol)rs   rI   r   r`   r=  s     rj   test_issue_6828r  A  s>    	419s?A!QQAa...rl   c            	          [        S5      n [        [        [        -  [	        U [
        -
  * [        [        5      -  5      -  [
        5      [        [	        [
        U -
  [        [        5      -  5      -  [        [        5      -  [        -  :X  d   eg )Nx_max)r   rI   r   r   r!   rs   r3   r   )r  s    rj   test_issue_4803r  G  si    7OEQrT#	l3q6122A6	#q5y#a& 
!!#a&(+, , ,rl   c            	          [        S[        S[        [        5      S-  -   5      -  5      [        [        5      [        S[        [        5      S-  -   5      -  :X  d   eg r!  )rI   r.   r6   rs   r   rl   rj   test_issue_4234r  M  sE    QtAA	M**+s1vd1s1vqy=6I/IIIIrl   c                     [        [        [        S-  [        S[        S-  -
  5      -  [        5      5      R	                  SS9[        [        S[        S-  -  S[        S-  -  -
  S[        -  -   S[        [        S-  S-
  5      -  [        [        S5      [        -  S-  5      -  -
  -  S[        [        S-  S-
  5      -  -  [        [        S5      :  [        [        S5      * :  -  4S[        S-  -  S[        S-  -  -
  S[        -  -   S[        S[        S-  -
  5      -  [        [        S5      [        -  S-  5      -  -
  S	[        [        S-  * S-   5      -  -  S45      :X  d   eg )
Nrn   r   Tr  rd  r      r   i)	rR   rI   rs   r.   rM   r/   r   r$   r1   r   rl   rj   test_issue_4492r  Q  sL   IadT!ad(^3Q78?? @ 	
AadFR1Wr!t#badQh&7d1gaik8J&JJ	KtAqD1H~
!"T!Wd1gX >	@
AqD&2ad7
RT
!BtA1H~$5d4719Q;6G$G
GadUQY
!"&	()) ) )rl   c            	      &   S[         [        -   [        [        5      -   -  n [        U [        SS45      n[	        U [        SS45      R                  5       U:X  d   e[        U [        [        5      -   [        SS45      U[        S5      -
  [        S5      -   :X  d   e[        SU -  [        [        5      -   [        SS45      SU-  [        S5      -
  [        S5      -   :X  d   e[        [        S[        -  [        -  [        -  [        * [        -   -  [        -  5      [        S[        45      [        [        S[        -  [        -  [        -  5      [        S[        -  [        -  [        S-  -  [        -  5      -  [        S[        45      :X  d   eg )Nrx   rn   r   g333333?r   g333333)r   r5  r#   rY   rX   r   rI   r!   ra   r   r   rs   )rd   
integral_fs     rj   test_issue_2708r  Z  sJ    	
1q53q6>A&q1a)4JA1ay!&&(J666QQZ!Q+zCF/BSV/KKKKQqS3q6\Aq!9-	*s1vA&' ' 'SQqQBF+A-.Aq	:c$q&(1*oc#a%'!Q$,q..AA#$a)	-- - -rl   c                      S[         -  S[        -  -   S-   [        S[         -  5      -  n [        U [         SS45      n[	        U5      S:X  d   eg )NgJ  @gD @g      $@g?g?z%1.86831064982608*y + 2.16387491480008)rs   r   r!   rI   str)rd   rh   s     rj   test_issue_2884r  h  sM    		N1,	,~	=s46{JA!ac]#Aq6<<<<rl   c                     SSK Jn Jn  [        [	        [
        * [        -  5      [        [        5      -  [        S[        45      [        [        [        [
        * [        [
        S-  * S-   -  -  U" [
        S-  5      S:  4S[        [
        -  SS[
        S-  -  -
  -  -  U" [
        S-  5      S:  4[        [        R                  4S4S[        R                  4S4[        [
        5      S-  5      S45      -  [
        S-  S:  4[        [	        [
        * [        -  5      [        [        5      -  [        S[        45      S45      :X  d   e[        [	        [
        * [        -  5      [!        [        5      -  [        S[        45      [        S	[
        S-   -  S-  S[
        * S-   -  S-  -
  [#        U" [
        5      S:  U" U " [
        5      5      [        S-  :  U" U " [
        5      5      [        S-  :*  5      4[        [	        [
        * [        -  5      [!        [        5      -  [        S[        45      S45      :X  d   eg )
Nr   argr   rn   rx   r   )r   r   )r   Tr   )$sympy.functions.elementary.complexesr  r   rI   r!   r   rs   r&   r   r/   r   rE   r   r   r   rX   r)   rJ   r  s     rj   test_issue_8368ir  n  s   =S!AYtAw&Ar
39BA	N+AqD	A'2a4Qq!tV,-AGq(*ffY/[$/&qM1,. 	
 
 1q aRT47*Q2J7	  $ S!AYtAw&Ar
3AE
1q1"q&z!|+FQJAK"Q$&AK2a4' aRT47*Q2J7		 	 	rl   c            	      |   [        [        S[        -  5      5      S[        S[        -  5      -  :X  d   e[        [	        S[        -  5      5      S[        -  S[        [	        S[        -  5      S-   5      -  -
  :X  d   e[        [	        [        5      5      [        [        [	        [        5      S-   5      -
  :X  d   eg )N      ?rx   )rI   r)   rs   r&   r*   r#   r   rl   rj   test_issue_8901r    s    T#a%[!Sc!e_444T#a%[!SUST#a%[1_1E-E%EEEET!WSa1%5!5555rl   c                     [        [        [        5      S-  [        -  [        SS45      [        S5      * S-  S[        S5      -  S-  -   :X  d   e[        [        [        5      S-  [        -  [        S[        45      [
        S-  :X  d   e[        [        [        5      S-  [        S-  -  [        5      [        S[        -  5      * [        S[        -  5      S[        -  -  -
  SS[        -  -  -
  :X  d   eg )Nr   r   rx   r   rn   )rI   r4   rs   r<   r   r   r3   r   rl   rj   test_issue_8945r    s    SVQYq[1a),Aq1RU7190DDDDSVQYq[1a*-A555SVQYq!t^Q'BqsG8c!A#h!n+Dq!A#w+NNNNrl   c                      [        S5      u  pp#[        [        U -  [        -  U-  5      S-  X#[        -  -   -  R	                  [
        5      n[        [        U[        SU45      R                  ;  d   eg )Nzi L a brn   r   )r   r3   r   rs   rewriter!   rI   r   )r   Lr   r   	integrands        rj   test_issue_7130r    sa    #JA!RT!VAX!Q1W-66s;IIi!Q3@@@@@rl   c                      [        S5      u  pp#[        X-  X/5      n[        XC5      [        XC5      R	                  5       :X  d   e[        XC5      [        XS-  -  S-  /X-  /X#-  //5      :X  d   eg )Nza b c trn   )r   rK   rI   rX   r   )r   r   r   r   vts        rj   test_issue_10567r    ss    #JA!	a	BRx335555RvQ$qzAC513%&@AAAArl   c                      [        [        [        S-  * S[        -  -   S-   5      [        SS45      S[        -  :X  d   eg )Nrn   r   0   r   r  re  )rI   r.   rs   r   r   rl   rj   test_issue_11742r    s9    T1a4%!A#+*+aBZ8BrEAAArl   c                      [        S5      n [        [        [        U -  5      U 5      [	        [        U -  5      [        -  :X  d   eg )Nr   )r   rI   r5   r   r<   )r   s    rj   test_issue_11856r    s4    AT"Q$Z#r"Q$x{222rl   c                      [        [        [        S[        -  5      5      [        SS45      [        [        5      S-  :X  d   eg Nrx   r   rn   )rI   r.   r#   rs   r   r   rl   rj   test_issue_11876r    s1    T#ac(^aAY/48A:===rl   c                      [        S[        [        5      -  S[        S[        -  5      -  -
  [        S[        -  5      -  [        5      S[        S[        -  5      -  S[        S[        -  5      -  -
  :X  d   eg )Nig3333333@r   g333333r   g      (@r   )rI   r!   rs   r   rl   rj   test_issue_4950r    sa    c#a&j4AaC=0#ac(:A>S1XS1X%& & &rl   c            	          [        [        [        [        S-  5      5      5      [        [        [        [        S-  5      5      -  S-  S[        -  [	        [        [        S-  5      5      -  S-  -
  :X  d   eg )Nrn   r   )rI   r4   r#   rs   r3   r   rl   rj   test_issue_4968r    sW    SQT^$#c!Q$i.(8(:QqSSAY=OPQ=Q(QQQQrl   c                     [        S[        S-  -  [        [        * [        45      [        L d   e[        S[        S-  -  [        SS45      [        L d   e[        S[        S-
  S-  -  [        SS45      [        L d   e[        S[        S-  -  [        SS45      [        * L d   e[        S[        S-
  S-  -  [        SS45      [        * L d   eg )Nrx   rn   r   r   )rI   rs   r   r   rl   rj   test_singularitiesr    s    Qq!tVa"b\*b000Qq!tVaQZ(B...QAz\Ar1:."444Qq!tVaBZ(RC///QAz\Aq":.2#555rl   c            
         [        SSS9u  p[        [        X -  U -  X-  -   5      U [        [        X-  -
  5      * [        [        X-  -
  5      4U[        [        5      * [        [        5      45      [        [        U S-  US-  -   5      U [        US-  * [        -   5      * [        US-  * [        -   5      4U[        [        5      * [        [        5      45      :X  d   eg )Nzx yTr   r   rn   )r   rI   r4   r.   r   rX   )rs   r   s     rj   test_issue_12645r    s    5t$DAc!#a%!#+&4QS>/4QS>:48)T"X.0 C1q!t,q!tebj!1 14A
3CDb	48466 7 6rl   c                      [        [        [        5      [        [        5      S-  -  [        S[        S-  45      [        SS5      :X  d   eg )Nr   r   r   rx   )rI   r4   rs   r3   r   r   r   rl   rj   test_issue_12677r    s8    SVs1vqy)Aq"Q$<8HQNJJJrl   c                      [        [        S[        -  5      [        [        5      -
  [        -  [        S[        45      [	        S5      * :X  d   eg )Nr   r   )rI   r3   rs   r   r#   r   rl   rj   test_issue_14078r    s8    c!A#hs1voq(1a*5#a&@@@rl   c                  l    [        S[        [        5      -  [        S[        45      [        S-  :X  d   eg r  )rI   r&   rs   r   r   r   rl   rj   test_issue_14064r    s)    QtAwYAr
+r!t333rl   c                     [        SS[        [        [        R                  -
  5      S[        [        5      -   -  -   -  [        5      [        [        [        R                  5      [        [        [        5      [        [        R                  5      S[        [        R                  5      -   -  -   5      -  [        [        R                  5      [        -   -  -
  :X  d   eg r   )rI   r!   rs   r   r   r#   r   r   rl   rj   test_issue_14027r    s    QCAFF
OQQZ8891=	CKCFS[!c!&&k/%BBCCS[ST_UUV V Vrl   c                  x    [        [        [        5      [        S[        S-  45      [        R
                  L d   eg r8  )rI   r6   rs   r   r   Infinityr   rl   rj   test_issue_8170r    s)    SVaBqD\*ajj888rl   c                      [        S[        -  [        SS45      [        R                  L d   e[        S[        S-   -  [        SS45      [        R                  L d   eg )Nrx   r   r   r   )rI   rs   r   r   r   rl   rj   test_issue_8440_14040r    sL    QqS1b!*%...QAYB
+quu444rl   c                  \   [        S[        [        -   S-  -  [        SS45      S[        S-   -  S[        -  -   :X  d   e[        SS[        -   [        -   [        -   S-  -  [        SS4[        SS4[        SS45      S[	        S5      -  S[	        S5      -  -
  S[	        S	5      -  -   :X  d   eg )
Nrx   rn   r   r   rM  r   r   r   r   rd  r   rl   rj   test_issue_14096r    s    QAz\Aq!9-QUac1AAAAQA	A))Aq!9q!Qi!QK
3q6	Ac!fHqQx'( ( (rl   c            
      "   [        [        S[        S[        S-  -
  5      -  [        SS45      R	                  5       S-
  5      S:  d   e[        [        [        S[        S-  -
  5      [        SS45      R	                  5       S-
  5      S:  d   eg )Nrx   r   r   gQdVo?gư>g) ?)r   rI   r.   rs   ra   r   rl   rj   test_issue_14144r    s{    y4AqD>)Aq!95779HDELLLya!Q$h!Q3557(BCdJJJrl   c                      [        [        [        [        -  5      [	        [        5      -  [        5      R                  [        5      (       d   eg rz   )rI   r!   r   rs   r#   r  r;   r   rl   rj   test_issue_14375r    s2     S1Xc!f_a(,,R0000rl   c            	          [        S5      " [        [        [        5      n [	        U [        SS4[        SS4[        SS45      [        U [        SS4[        SS4[        SS45      :X  d   eg )Nrd   r   rx   rn   r   )r	   rs   r   r5  rI   rX   r%  s    rj   test_issue_14437r    sc    aAAQAq	Aq!9q!Qi8Q1I1ay1a)<= = =rl   c            	         [        S[        [        [        5      S-   5      -  [        5      [	        [        [        [        5      S-   5      S-
  5      [	        [        [        [        5      S-   5      S-   5      -
  :X  d   eg r   rI   r.   r!   rs   r#   r   rl   rj   test_issue_14470r    sb    QtCFQJ''+s4A
3Ca3G/H3tTWXYTZ]^T^O_bcOcKd/ddddrl   c            	         [        S[        [        S-  5      [        -  -
  S[        S-  -  -   5      S[        S-  -  [        -   -  S[        [        S-  5      [        -  -
  S-  -  n [        U [        5      [        S[        S-  -  [        [        [        S-  5      -  -
  S-   5      * [        [        S[        S-  -  5      -  [        S[        S-  -  5      -
  -  :X  d   eg Nrx   rn   r   )r!   rs   rI   r%  s    rj   test_issue_14877r    s    AAqD	!Oa1f$%qAvz2AAqD	!Oa3GGAQ?	Qq!tVaAqD	k!A%	&&#a1f+AadF(CDE E Erl   c                      [        [        S-  * S-   5      [        S-  * [        -   -  n [        U [        SS/5      [        * S-  :X  d   eg )Nrn   rx   r   r   )r.   rs   rI   r   r%  s    rj   test_issue_14782r    sE    adUQY!Q$#AQB
#tax///rl   c                      [        [        S-  * S-   5      [        S-  * [        -   -  n [        U [        SS/5      [        R                  S-  [
        S-  -
  :X  d   eg )Nrn   rx   r   r   re  )r.   rs   rI   r   r   r   r%  s    rj   test_issue_14782_slowr    sP    adUQY!Q$#AQAq	"aeeai"r'&9999rl   c                      [         [        SS5      -  [        [         * 5      -  n [        U [         S[        /5      [        L d   eg )NrN  rn   r   )rs   r   r!   rI   r   r%  s    rj   test_issue_12081r    s8    	HROS!W$AQAr
#r)))rl   c                      S[         -  S-
  n SU -  [        SU -  5      -  [         S-  -  n[        U[         SS/5      S:X  d   eg )Nrx   r   r   rn   r   )rs   r!   rI   )r   rd   s     rj   test_issue_15285r    sH    	!aA	!C1IadAQAq	"a'''rl   c            
         [        [        [        -  [        [        * 5      -  [	        [        5      -  [        S[
        45      R                  5       [        [        [        S-   5      [        S[        5      -  [        [        S-   5      [        -  -   [        [        5      S-   S:  4[        [        [        -  [        [        * 5      -  [	        [        5      -  [        S[
        45      S45      :X  d   eg )Nr   rx   T)rI   rs   ra   r!   r#   r   rQ   r/   rB   rC   r   rX   r   rl   rj   test_issue_15432r  $  s    QTCG^c!f,q!Rj9CCE	q1ui1o	%a!eQ	61	AF	!Q$sA2w,s1v%1bz	2D9J; ; ; ;rl   c                  .   [        S5      n [        S[        S9u  p[        [	        [
        [        -  X   X   -   -  5      [
        SS9[        * [	        [        [
        -  X   -  5      -  [	        [        [
        -  X   -  5      -  X   X   -   -  :X  d   eg )Nomegazm p)clsr   r   )rU   r   rT   rI   r!   rs   r   )r  r  ru   s      rj   test_issue_15124r  *  s     E5c"DAS1eh123QfE	
3qs58|S1UX..580CDE E Erl   c            	         [        5          [        [        [        [        5      5        S S S 5        [        5          [        [        [        [        5      [        5      [        [        [        [        5      [        [        [        5      5      :X  d   e S S S 5        [        5          [        [        [        [        5      [        5      R                  5       [        [        S-  S-  [        [        -  5      :X  d   e S S S 5        [        [        SS9   [        [        [        5      R                  [        5      [        [        S-  S-  [        [        -  5      :X  d   e S S S 5        [        [        [        [        5      [        SS45      [        [        R                  [        5      :X  d   e[        [        [        5      R                  [        SS45      [        [        R                  [        5      :X  d   eg ! , (       d  f       GN= f! , (       d  f       GN= f! , (       d  f       GN+= f! , (       d  f       N= f)Nrn   Frq   r   rx   )r]   rX   r   rs   r   r   r^   r_   rI   r   r   r   rl   rj   test_issue_15218r  1  sR   		!Aq 
"		!1a!$8Aq>8Aq>(JJJJ 
"		!1a!$))+r!Q$q&!A#>>> 
"	&	> !Qx!!!$1a461Q3777 
? R1X1ay)R]:::a8q!Qi(BqvvqM999 
"	!	!	!	!	!	>	>s1   G<AH%AH AH2<
H
H 
H/2
I c            
         [        [        [        S-  * [        S[        -  5      -  5      [        [        S-  [        S[        -  5      -  5      -  [        S[        45      n [        U [        5      (       d   e[        U [        [        5      S-  [        [        5      -  -
  R                  [        [        S-  5      5      S:X  d   eg )Nrn   r   r   )rI   r!   rs   r3   r   r4   r   r   r/   rQ   r.   r   r  r|  s    rj   test_issue_15292r  B  s    
CAc!A#h'#ad3qs8m*<<q!Rj
ICc9%%%%cDHQJQ//55aA>?1DDDrl   c                      [        [        S[        -  5      [        [        5      -  [        5      S[        [        5      -  :X  d   eg r   )rI   r4   rs   r   rl   rj   test_issue_4514r  H  s/    S1Xc!f_a(Ac!fH444rl   c                  >   [        SSS9u  pn[        [        [        U S-
  5      5      XU45      n[        [        [        U S-
  5      5      U 5      nUR	                  USUS05      SS[
        -  -   :X  d   eUR	                  U S5      UR	                  U S5      -
  SS[
        -  -   :X  d   eUR	                  USUS	05      [        S5      * [        S
5      -   :X  d   eUR	                  U S	5      UR	                  U S5      -
  [        S5      * [        S
5      -   :X  d   eg )Nzx a bTr   rn   rx   r   r   rN  r   r   )r   rI   r!   r   r  r   )rs   r   r   definite
indefinites        rj   test_issue_15457r  L  s   gD)GA!S1Xq	2H3s1Q3x=!,J==!Q1&"qs(222??1a :??1a#88B1HDDD==!RB(SVGc!f,<<<<??1b!JOOAr$::s1vgA>NNNNrl   c                      [        [        [        [        5      -  [        [        5      -  [        5      [        [        [        5      -  [        [        5      -
  [        [        5      -  [        [        5      -
  [	        [        5      -   :X  d   eg rz   )rI   rs   r!   r#   r;   r   rl   rj   test_issue_15431r  V  sZ    Qs1vXc!f_a(	
3q6CF	CF"SV+be34 4 4rl   c                     [         [        [         5      -  n [        S[        [         5      -  5      n[        U [         5      U:X  a  UR	                  [         5      U :X  d   e[         S-  [        [         5      S-  -  n [         S-  * [        [         5      -  S[        S[        [         5      -  5      -  -   n[        U [         5      U:X  a  UR	                  [         5      U :X  d   e[        [        [         5      5      [         S-  -  n [        [        5      * [        [        [        [         5      5      5      -  S-  [        [        [         5      5      [         -  -
  n[        U [         5      U:X  a  UR	                  [         5      U :X  d   eg )Nrn   r   r   )rs   r#   r;   rI   r   r.   r   r>   )rd   Fs     rj   "test_issue_15640_log_substitutionsr  [  s   	#a&A
1SV8AQ?aAFF1IN22	1SVQYA	
Ac!fqAc!fH~%AQ?aAFF1IN22SVQTA	b	$tCF|$$Q&c!fa7AQ?aAFF1IN22Nrl   c            	         SSK Jn   U " S5      nUR                  n[        [	        [
        U-  [        -   5      U[        [        4SS9[        [        [
        [        -  [        -   5      * [
        -  [        [
        [        -  [        -   5      [
        -  -   [
        [        * :  [
        [        :  -  [        [
        S5      -  4[        * [	        [        5      -  [        [	        [        5      -  -   S45      :X  d   eg )Nr   )
CoordSys3DNTr@  )sympy.vectorr  rs   rI   r3   r   r   x_1x_2r/   r4   r   r   )r  r  rs   s      rj   test_issue_15509r  g  s    '3A	AS1q\AsC=4@I
aeai.	S3^A-	-RCAF/CbAh/NOT#a&[3s1v:%t,E. . . .rl   c            	         [        SSS9n [        U [        SU S-  -
  5      -  U 5      [        U S-  S-  SU S-  -  S-  -
  U S:*  4U S-  * S-  SU S-  -  S-  -   [	        SS5      -
  U S	:*  4U S-  S-  SU S-  -  S-  -
  S45      :X  d   eg )
Nrs   Tr   r   rn   r   rN  Q   r   )r   rI   r  r/   r   r  s    rj   test_issue_4311_fastr  p  s    $AQs1QT6{]A&)	
Aa!AqD&(	AG$
Q$q1QT6!8	hr1o	-qAv6	
Aa!AqD&(	D!+# # # #rl   c                     [        SSS9n [        SSS9n[        SSS9n[        SSS9n[        [        [        * U -  US-  -  X!-  -   5      U5      [	        [
        5      [        [        * US-  -  S	U -  -  5      -  [        S
[        -  U -  U-  U-   S[	        U 5      -  [	        [        * 5      -  -  5      -  S[	        U 5      -  [	        [        * 5      -  -  :X  d   e[        SS[        US-  -  -   -  U5      [        * [	        [        * 5      [        U[        [	        [        * 5      -  -
  5      -  S-  [	        [        * 5      [        U[        [	        [        * 5      -  -   5      -  S-  -
  -  :X  d   e[        [        [        * US-  -  5      U5      [	        [
        5      [        [	        [        5      U-  5      -  S[	        [        5      -  -  :X  d   e[        S[        [        U-  5      S-
  -  U5      U* S-  [        [        [        [        U-  5      S-
  5      -  S-  -
  :X  d   e[        S[        [        U-  5      S-
  -  USS[
        -  45      [
        * :X  d   eg )NKTr   rs   r   r  r   rn   r   r   rx   r   )	r   rI   r!   r   r.   r   r?   r#   r=   )r  rs   r  r   s       rj   %test_integrate_with_complex_constantsr  x  s*   sT"AsAsAsAS!Aad13'+tBxQBq!tGc= 9 0 "Q$q&(Q,47481C!DE0FGHayQUWXVXQYGY0[ [ [ [QAadF
^Q'QBaRQ48^9L0LQ0NA2hs1qqbz>**1,1- -. / / /S!AqD\1%b#d1gai.)@!DG))LLLLaQqS!nq)aRTAc#ac(Q,6G4G4I-IIIIaQqS!n1ad|4;;;rl   c            	          [        S5      n [        SSSS9n[        XUS-
  -  -  U S-   -  U 5      US-  X-  -  [        U [        [        [
        -  5      -  SU5      -  [        U5      -  [        US-   5      -  :X  d   eg )Nrs   ra   Tr  rx   rn   )r   rI   rG   r"   r   r   rB   )rs   ra   s     rj   test_issue_14241r    s    sAsT40AQq1u%Q/3a49Xa	!B$/A66uQx?a!eLM M Mrl   c                      [        [        [        5      S-  SS[        [        5      -  -
  -  [        SS[        -  /5      [        S-  :X  d   eg )Nrn   r   r   r   )rI   r4   r   r3   r   r   rl   rj   test_issue_13112r    s>    SVQY!aAh,/!Q">"q&HHHrl   c                      [        SSS9n [        [        [        SS[        -  U -  -
  5      -  [        SU 45      nUSU S-  -  [        -  S-  :X  d   eg )	Nrg  Tr   rx   rn   r   r   re  )r   rI   rs   r0   r   )rg  r   s     rj   test_issue_14709br    sS    sT"A!DQqSUO#aAY/A!Q$r	"rl   c                  
   [        S5      n [        S5      n[        [        U5      U-  U[        * U 45      [	        U 5      :X  d   e[        [        U * 5      [        SU -  5      -
  U -  U S[        45      [        S5      :X  d   eg )Nrs   r   r   r   rn   )r   rI   r!   r   r;   r#   )rs   r   s     rj   test_issue_8614r    st    sAsASVAXB3{+r!u444c1"gBqD	)1,q!Rj9SVCCCrl   c                  :   [        SSS9n [        U S-  5      S[        SU -  5      -  -
  [        U 5      -   [        U 5      -  n[        X5      nU[        R                  :w  d   e[        UR                  U S5      S-
  5      S::  d   e[        U S-  5      S[        [        S	5      S
-  U -  5      -  -
  [        U 5      -   [        U 5      -  n[        X5      S[        SU -  S
-  5      -  S-  S[        SU -  S-  5      -  S-  -   [        SU -  5      S-  -   :X  d   eg )Nr   Tr   rn   g?rx   gRt?,e:0yE>r   r   i   r   )r   r!   rI   r   r   r  r  )r   r  solutions      rj   test_issue_15494r    s   d#AQqSAc#a%jL(3q613q69I&Hquu x}}Q"&789TAAAQqSAc!A$q&(mO+c!f4c!f<IY"c#bd1f+ob&81S1QZ<>&ICPQRSPSHUVJ&VVVVrl   c                  l   [        S5      n [        [        U [        S-  -  5      [        5      R	                  5       [        [        [        [        S-  U -  5      -  [        [        S[        [        S-  U -  5      -  S-  5      -  [        [        S-  U -  5      -  -
  [        U S5      4S5      :X  d   eg )Nr   rn   r   r   r  )
r   rX   rA   rs   r   r/   r;   r#   r.   r   r   s    rj   test_li_integralr    s    sABqAvJ"'')Y"QT!V*	"Qs1a46{]1_
d1a46l*9+
1a8.   rl   c                     [        S5      n [        S5      n[        R                  nXS-   -  [        X"U-  -   5      -  [	        X"U-  -   4SU-  SU-  X!-  -   4U SU-  -  * S-  5      -  SU-  [        SU-  X!-  -   5      -  -  n[        [        X-  5      U 5      nXC:X  d   e[        SSS9nX0n[        [        XQ-  5      U5      UR                  U5      R                  5       :X  d   eg )	Nrs   ra   rx   r   rn   r   FrE  )	r   r   r   rB   rD   rI   r4   xreplacer   )rs   ra   rg  r,  got_xrepss          rj   test_issue_17473r    s    sAsA	A
!e*U1s7^
#E1s7*	
1acACi1qs8)A+%' '()!E!A#),<(<>C
CIq
!C::	%	 B7DSZ$T(:(A(A(CCCCrl   c                     [        [        [        [        5      5      [        S-  -  [        S[        /5      [        * :X  d   e[        [        [        [        5      5      [        S-  -  [        S[        /5      [        S5      * S-  [        S-  -
  :X  d   e[        [        [        [        5      5      [        S-  -  [        S[        /5      [        S5      * S-  [        S-  -
  :X  d   eg )Nrn   rx   r   r   r   )rI   r#   rs   r   r   r   rl   rj   test_issue_17671r    s    SQ[1a4'!Q4CCCSQ[1a4'!Q4Q	JqL8PPPPSQ[1b5(1a*5#a&ZPQ\9QQQQrl   c            	          [        S5      n [        S5      n[        S5      n[        SUS-  U-   [        S5      S-  -  -  X * S-  U S-  45      X[        S5      S-  -  [        SU S-  SU-  -  -   5      -  -  :X  d   eg )Nr  Cr   rx   rn   r   r   )r   rI   r   r.   )r  r  r   s      rj   test_issue_2975r    s    sAsAsAQ1Q!A$q&))Ar!tQqS>:aQqT!VTRSVWYZVZ\]^_\_V`R`MaAa>bbbbrl   c                    ^^ [        S5      u  mmn [        SSS9n[        [        TT-  TSU45      T5      TS-  US-  S-  US-  -   -  :X  d   e[        [        T[	        T5      -  TSU45      T5      [        TS-  [	        T5      -  S-  TSU45      :X  d   e[        [        [	        TT-  5      TSU45      T5      [        [        [        TT-  5      * T-  [        TS5      4S	5      TSU45      :X  d   e[        [        [        [	        TT-  5      TSU45      T5      T5      [        [        [        [	        TT-  5      * TS-  -  [        TS5      4T* T-  S45      TSU45      T[        * :  T[        :  -  [        TS5      -  4S	5      :X  d   e[        [        TTSU 45      T5      U TS-  -  S-  :X  d   e[        [        UU4S
 j5        [        [        UU4S j5        [        [        U4S j5        g )Nzx n Mr  Trb   rx   rn   r   r   r  c                  F   > [        [        TT[        T 45      [        5      $ rz   rI   r   r   ra   rs   s   rj   r~   !test_issue_7827.<locals>.<lambda>  s    yQAq	):A>rl   c                  6   > [        [        TTST 45      T 5      $ r   )rI   r   r  s   rj   r~   r    s    yQAq	):A>rl   c                  >   > [        [        T T S[        45      T 5      $ r   r  r  s   rj   r~   r    s    yQAq	):A>rl   )r   r   rI   r   r4   r   r/   r3   r   r   r[   r   )rE  r  ra   rs   s     @@rj   test_issue_7827r    s   gGAq!sD!AYqsQ1I.2adAqDFQqSL6IIIIYqQx!Aa115AqDQKMAq!9%& & &Ys1Q3x!Aa115IAaCy{Bq!H-y9Aq!9EF F FYyQqSAa7;Q?C3y3qs8)AqD."Q(!;qbdD\J	
Aq	"WR(2a8356?	AA A A SQ1I&*a1fQh666
:>?
:>?
:>?rl   c                     SS[         -  -   [        [         [        [         5      -   5      SS[         -  -   -  -   [         S-  -   [         [         [        [         [        [         5      -   5      -   -  [        [         [        [         5      -   5      -  -  n [        U [         5      S[        [         [        [         5      -   5      -  S[        [         [        [         [        [         5      -   5      -   5      -  -   :X  d   eg r  )rs   r.   r#   rI   r%  s    rj   test_issue_4231r    s    	
QqS4CF
#Q1W-	-1	4q!d1s1v:>N:N7OPTUVY\]^Y_U_P`7`aAQ?aQQZ 001ST!c!f*=M9M5N3NNNNNrl   c                      [        S[        S-  [        -   [        -   -  [        5      n [        U [        5      S[        S-  [        -   [        -   -  :X  d   eg r!  )r   rs   r   rI   r%  s    rj   test_issue_17841r    sC    Q1Qq\1AQ?aAA....rl   c                     [        SSSS9n X S-  * [        S5      S-  -  U [        U [        [        S5      5      -   5      -  -
  S-   -  nU [	        [        S5      5      -   X SSU -  -  -   -  -  n[        X5      U S-  * S[        S5      S-  -  -  U S	-  [	        U [        [        S5      5      -   5      -  -
  SU S	-  -  S	-  -   S	U -  [        U [        [        S5      5      -   5      -  -   S	[	        U [        [        S5      5      -   5      -  -
  :X  d   e[        X 5      [        U S	-  [        S5      S-  -   5      S	-  S	[        S
5      -  [	        [        S5      5      -  [        S	[        S
5      -  U -  5      -  -   :X  d   eg )Nrs   Tr   r  r   r   rx   r  r   rn   r   )
r   r1   r)   r#   r&   r3   rI   r   r.   r2   )rs   f1f2s      rj   test_issue_21034r"    s   st,A	
TE$q'1*qa#d1g,&6!777!;	<B
d3q6l
QAr!tH-	.BR	
Aqa!|q!tDSa\)9$:::Qq!tVAXE!DQRUXY]^_Y`UaQaLbHbbefgklmpstxyzt{p|l|g}e}}~ ~ ~ RAqD1Q47NA$q'	$s1v, 6tAd1gIaK7H HHI I Irl   c                  J   [        [        [        5      [        [        * 5      -  [        5      [	        [        * 5      [        [        * 5      [        [        5      -  -
  :X  d   e[        [        [        5      [        [        * 5      -  [        S[
        45      [        * :X  d   eg r  )rI   r#   rs   r!   r;   r   r   r   rl   rj   test_issue_4187r$    si    SVCG^Q'2qb6CGCFN+BBBBSVCG^aBZ0ZK???rl   c                     [        S5      n [        S5      n[        S5      n[        S5      n[        US-  [        U5      S-  -  X* S-  U S-  45      US-  * U * S-  [        U S-  5      [        U S-  5      -  S-  -
  -  US-  U S-  [        U S-  5      [        U S-  5      -  S-  -   -  -   :X  d   e[        US-  [        X1-  5      S-  -  X* S-  U S-  45      [	        US-  * U * U-  S-  [        X-  S-  5      [        X-  S-  5      -  S-  -
  -  U-  US-  X-  S-  [        X-  S-  5      [        X-  S-  5      -  S-  -   -  U-  -   U[
        * :  U[
        :  -  [        US5      -  4XS-  -  S45      :X  d   eS[        -  U-  U -  n[        S5      [        U 5      -  US-  -  [        [        S5      [        U 5      -  5      -  [        [        R                  S-  5      -  S	[        [        S
5      S-  5      -  -  XS-  -  S-  -   n[        US-  [        XA-  5      S-  -  X* S-  U S-  45      U:X  d   eg )Nr  r5  r0R0rn   r   r   Tre  r   )r   rI   r3   r4   r/   r   r   r   r.   r@   rB   r   r   )r  r5  r&  r'  r  sols         rj   test_issue_5547r)    s}   sAsA	B	BRU3q619_q"Q$!n5"a%!A!HS1X%a'B( :)+-q5!A#AaCQqS8I!8K2K+L:M M M M RU3rt9a<'!RT1Q38I
a%!Bq3qtAv;s146{2144	5b	8	QQQT!VSa[022	3B	6
79;rcb2g8NQSTVXYQZ8Z	\	
q5$=   
 	
"QqA
q'$q'/"a%
aa 9
9%a.
H"USTUVSWXYSY]JZ
[^_de`e^efg^g
gCRU3qs8Q;&BqD!A#73>>>rl   c                  x    [        SSS[        -  S-  -  S-   -  [        S[        45      [        SS5      :X  d   eg )Nrx   rn   r   r   )rI   rs   r   r   r   rl   rj   test_issue_15810r+    s8    QAaCE
Q'!Q4AFFFrl   c                     [        SSSS9n [        U 5      [        SU -  5      -  [        SU -  [        S5      -   5      -   nU [        U 5      S-  -  U [        SU -  [        S5      -   5      -  -   U SS[        S5      -  -
  -  -   SU -  SU -  [        S5      -  -   [        U 5      -  -   [        S5      [        SU -  [        S5      -   5      -  S-  -   nU[        X5      :X  d   eU [        S5      -   U S-  -  n[        U 5      [        S5      U -  -
  nU[        X5      :X  d   eU S-  [        S	5      -   U -  nU S-  S-  [        S	5      [        U 5      -  -   nU[        X5      :X  d   eU SU -  [	        S5      -   -  nU S-  [        SU -  [	        S5      -   5      [	        S5      -  S-  -
  nU[        X5      :X  d   eU [        S5      U -  -
  nU S-  S-  [        U 5      [        S5      -  -
  nU[        X5      :X  d   e[        U [        S	5      U -  -   5      nU [        U [        S	5      U -  -   5      -  U -
  S[        [        S	S5      5      -  [        U [        [        S
S5      5      -  5      -  -   nU[        X5      :X  d   eU S	-  U [        -   -  nU S	-  S	-  [        U S-  -  S-  -
  U S-  [        S5      -  S-  -   U S-  [        S5      -  S-  -
  U [        S5      -  -   [        S	5      [        U [        -   5      -  -
  nU[        X5      :X  d   eSU -  U [        S	5      -   -  nSU -  S[        U [        S	5      -   5      -  [        S	5      -  -
  nU[        X5      :X  d   eU S-  SU -  [        S5      -   -  nU S-  S-  U [        S5      -  S-  -
  [        SU -  [        S5      -   5      [        S5      S-  -  S-  -   nU[        X5      :X  d   eU S-  * U [        -   -  nU S-  * S-  [        U -  -   [        S5      [        U [        -   5      -  -
  nU[        X5      :X  d   eSU -  S-   [        S	5      -  U -  nSU -  [        S	5      -  S[        S	5      -  [        U 5      -  -   nU[        X5      :X  d   eU S-   [        S5      U -  -   nU S-  S-  SU -  -   [        U 5      [        S5      -  -   nU[        X5      :X  d   eU [	        S5      U S-  -  -
  nU S-  S-  [	        S5      SU S-  -  -  -   nU[        X5      :X  d   eSU -  [        S5      -
  U -  nSU -  [        S5      [        U 5      -  -
  nU[        X5      :X  d   eU S-  U [        S	5      -   S-  -  U -   nU S-  S-  U S-  [        SS5      [        S	5      -
  -  -   SU -  [        S5      -  -   S[        S5      -  [        U [        S	5      -   5      -  -
  [        S5      U [        S	5      -   -  -
  nU[        X5      :X  d   eX [        S5      U S-  -  -   -  U -   nU S-  S-  U S-  S-  -   [        S5      [        U 5      -  -   nU[        X5      :X  d   eX S	U -  [        S5      -   -  -   nU S-  S-  U S	-  -   [        S	U -  [        S5      -   5      [        S5      -  S-  -
  nU[        X5      :X  d   eU [        S5      -   SU S-  -  SU -  -   -  n[        S5      [        U 5      -  S-  [        S5      [        U S-   5      -  S-  -
  [        U S-   5      S-  -   nU[        X5      R                  5       :X  d   e[        U S[        S5      -  -   5      nU [        U S[        S5      -  -   5      -  U -
  S[        U S[        S5      -  -   5      -  [        S5      -  -   nU[        X5      :X  d   eU * S[        S
5      [        S5      U -  -
  S-  -  [        S5      -  U -  -   nU S-  * [        S5      -  S-  S[        U 5      -  [        S5      -  -   SU S-  -  [        S	5      -  [        S5      -  [        S5      -  SU -  [        S5      -  [        S5      -  [        S5      S-  -  -   S[        S5      -  [        S5      -  [        S5      S-  -  -
  SU S-  -  -  -
  [        S5      -  nU[        X5      :X  d   eSU S-  -  [        S5      -  SU -  -   nSU S-  -  S-  S[        S5      -  [        U 5      -  -   [        S5      -  nU[        X5      :X  d   eg )Nrs   Tr  r   r   rn   rx   r   r   r   r   r   rd  rp  r  iLZ   r  rM  )r   r#   r!   rI   r*   r)   r   r2   r   r&   r   r4   )rs   rd   r  F_trues       rj   test_issue_21024r0    s	   st,AAs1Q3x#acCFl++A	#a&!)aAaC#a&L)))Aq1SV8|,<<	A!CF
	CF"	#%(VC!c!f,=%=a%?	@A	!	
SVQTAAQA	!	
AAA	1QQAA	!	1Q3a=A	!c!A#Q- a(**A	!	DGAIA	1QQQA	!AAqLA	#a#a&(l
a!CA$7"7Qs8BPQ??S=S8T"TTA	!	1a!eA	1Q1a4AqDQKM)AqDQKM9Ac!fHDs1vcRSVWRWjGXXA	!	!Qa[A	!aAQK  a((A	!	1acDGmA	1Q471s1Q3a=1$q'1*<Q>>A	!	
Aq1uA	
Aa!A#As1q5z))A	!	
1q#a&A	!CF
Qs1vXc!f_$A	!	AQ	A	1Q1s1vd1g~%A	!	DGAqDLA	1Qa!AqD&!!A	!	
1s1vqA	!c!fSVmA	!	1a#a&j1_q A	1QAx1~A.//!A#c"g+=#b'	#aRUVWRXj/@YY\_`b\cefilmnioeo\ppA	!	s2wq!t|q A	1QAa#b'#a&.(A	!	qsT!W}A	1Q1s1Q3a=)$q'1"44A	!	
SVa1fqsl#AAs1va#a&QU+A--AE
1<A	!&&((((A$q'	MA	#a!DG)m
q 1SQtAwY%7#7Q#??A	!	
RR4719$q((Q/11A
Q$s2wq2c!f9SV+	+tAqDyQ/?A/FtAw/NQSTUQUVYZ\V]Q]^abc^dQdeijkelnoeoQo/o
3r7
3q6$q'1*$0%'(Av// 
/03C	9A	!	!Q$s2w1A1fQh3q6#a&(#b'1FYq_$$$rl   c                     [        S5      n [        S[        S[        U -
  S-  -   -  -  [        [        * [        45      R                  5       [        [        U 5      S-
  S5      * [        [        U 5      S-   S5      -   :X  d   eg )Nr   rx   rn   r   )r   rI   r   rs   r   r   r9   r   r   s    rj   test_issue_21721r3  n  ss    sAQAqsQhJ(!RC4;;=r!uqy!yAA667 7 7rl   c                      [        S5      n [        [        SU -  5      SS[        U 5      -  -
  -  U SS[        -  45      [        S-  :X  d   e[        SU -  5      SS[        U 5      -  -
  -  n[        XSS[        -  45      [        S-  :X  d   eg )	Nthetar   r   r   r   rn   r  r   )r   rI   r3   r   )r5  r  s     rj   test_issue_21831r6  t  s    GES5\1Qs5z\>2UAqt4DEBNNNAeGa!CJ,./IY1R4 01RT999rl   c                      [        [        S-  [        SS5      -
  S-  [        S[        S-  -
  5      -  [        SS45      [        S-  :X  d   eg )Nrn   rx   r   r   r  )rI   rs   r   r.   r   r   rl   rj   test_issue_22033_integralr8  {  sI    adXa^+a/$q1a4x.@1b!*MQSTVQVVVVrl   c                     [        S[        [        S-  [        S-  -   S[        S-  -
  [        S-  -
  4[        [	        S[        S-  -
  5      * [	        S[        S-  -
  5      4[        SS45      [
        :X  d   e[        SS[        S-  -
  [        S5      S-  -  -  S-  S[	        S[        S-  -
  5      -  SS[        S-  -  -
  -  -   [        SS45      [
        :X  d   eg )Nrx   rn   r   rM  r   )rI   r5  rs   r   r.   r   r   r   rl   rj   test_issue_21671r:    s    Q!Q$q!t)AadF1a4K0!T!AqD&\M$qAv,1OQRSUVWPXY]____RQTQqT!V,,Q.4AqD>1A1qAv:1NNQRTVXYPZ[_aaaarl   c                  "   [        SSS9n [        [        5      S[        [        5      S-  -   -  n[	        UR                  [        U 5      U SS9R                  U [        5      n[	        U[        SS9Us=:X  a  [        U[        5      :X  d   e   eg )NxrTr   r   rn   ro  )r   r3   rs   r4   rI   r  rX   )r<  r5  res_reals      rj   test_issue_18527r>    sy     
D	!BFAs1vkM"D1b)2d;@@QGHT1T*hK(4:KKKKKKrl   c                  |   S[         [        [        5      -  [        [	        [        5      -  -   -  n [        [        * [         -  [        [        S-  5      -   [        [        S-  [         S-  -   5      [         -  -
  5      * [        [        S-  [         S-  -   5      -  [        [        * [         -  [        [        S-  5      -   [        [        S-  [         S-  -   5      [         -  -   5      [        [        S-  [         S-  -   5      -  -   n[        [        [        [        [        S-  5      S-
  5      * [        [        [        S-  5      S-   5      -   -  [        [        S5      [        [         S5      -  4[        [        [        S-  5      5      [        -  [        [         S5      4[        * [        * [         -  [	        [        5      -  [         [        [        5      -  -   -  [        [        [        * [         -  5      4[        [        [         -  [	        [        5      -  [         [        [        5      -  -   -  [        [        [        [         -  5      4US45      n[        U [        5      U:X  d   e[        SSS9u  p4[        U[         U0n[        U R                  U5      [        5      UR                  U5      :X  d   eg )Nrx   rn   r   Tza, br   )r   r3   rs   r   r4   r#   r6   r.   r/   r   r   r   rI   r   r  )rd   Fposr  apr_  reps         rj   test_issue_23718rC    s   	1SV8aAhA!AAaC41q!t#4Q#6677QTAqD[8II!AAaC41q!t#4Q#667QTAqD[8IIJD 
s3qs8a<  3s1Q3x!|#44	51a2a88KL	S1Xq1aA
aRT#a&[1SV8#	$1qbdD	
AaCAJ3q6!	"1qsD	=		A Q?aVd+FBb!R.CQVVC[!$		#666rl   c                      [        S[        [        S-  S-
  5      -  [        SS45      n U [        S[        S5      -
  5      * :X  d   e[        R
                  " U R                  5       S5      (       d   eg )Nrx   rn   r   r   r   gCqB?)rI   r.   rs   r#   mathisclosera   rQ  s    rj   test_issue_23566rG    s`    !DAaL.1b"+.AQa[!!!!!<</0000rl   c            	         [        S[        [        [        -
  S-  S-
  5      -  5      [	        [        [        [        -
  5      [        [        [        -
  S-  5      S:  4[        * [        [        [        -
  5      -  S45      :X  d   eg )Nrx   rn   T)rI   r.   rs   r   r/   r$   r   r1   r   rl   rj   test_pr_23583rI    so    QtQUQJqL))*iq1usAPQETU:YZGZ8[_`^`aefgjkfkal^lnr]s.ttttrl   c            
         [        [        [        5      [        S[        S[        -  5      -   5      -  5      [        [        S[        -  5      S-   5      [        [        5      -  S-  [	        [        [        5      5      S-  -   :X  d   eg r!  )rI   r!   rs   r.   r%   r   rl   rj   test_issue_7264rK    sf    SVDS1X../4AaC13Ec!f3LQ3NQVWZ[\W]Q^_`Q`3````rl   c                      [        [        [        5      [        SS45      S[        [	        [
        R                  5      5      -  :X  d   eg rH  )rI   r+   rs   r2   r*   r   r   r   rl   rj   test_issue_11254arM    s3    T!Wq!Qi(Ad4<.@,@@@@rl   c                      [        [        [        5      [        5      [        [	        [        S-  5      5      :X  d   e[        [        [        5      [        SS45      [
        :X  d   eg )Nrn   r   rx   )rI   r(   rs   r#   r*   r   r   rl   rj   test_issue_11254brO    sF    T!Wa CQqS	N222T!Wq!Qi(B...rl   c                  F   [        S[        [        [        [        -  S-  -   SS9S-  -  [        5      S[        S[        -  5      S-   -  :X  d   e[        [        [        5      S-  [        5      S[        [        S-  5      -  [        [        S-  5      S-  S-   -  :X  d   eg )Nr   rn   Fr  r   rx   )rI   r)   rs   r   r   r!   r&   r*   r   rl   rj   test_issue_11254drR    s    RQ2aZ%8!;;Q?2s1Q3xRS|CTTTTT!Wr]A&!D1I+tAaCy!|a7G*HHHHrl   c            
      t   [        S[        S-  -  [        S-  -
  S[        -  -   S-
  [        [        S-  S[        -  -
  S-   5      -  [        SS45      n U S[        S5      -  S-  S[        SS[        S5      -  -
  5      -  S	-  -
  :X  d   e[        R
                  " U R                  5       S
5      (       d   eg )Nr   rn   r   r   rx   ir      re  g2{)rI   rs   r.   r#   rE  rF  ra   rQ  s    rj   test_issue_22863rU    s    1QT6!Q$;qs?1$d1a4!8A:&66Aq	BAT!WQSQtAwY%7!7!:::::<<01111rl   c                  (   [        [        [        [        [        5      -   5      5      S[        [        [        5      [        -   5      -  [        [        5      S-  [        S-  -   [        S5      S-  -
  -  [	        S[        [        5      -  S[        [        [        5      [        -   5      -  -   S-   5      S-  -   :X  d   e[        [        S[        -  S-   [        S[        -  S-   5      -   5      S-  5      [        S[        -  [        S[        -  S-   5      -   S-   5      S[        -  S	-  S
S[        -  S-   [        S5      S-  -  -  S-  -   [        S[        -  S-   5      S-  -   S[        -  S-   S-  S	-  -   [        S
5      S	-  -   -  S-  :X  d   eg )Nrn   r  r   rx   r   r   r   r   r   rf  (   rI   r.   rs   r   r#   r   rl   rj   test_issue_9723rY    sv   T!d1g+&'	$tAw{
T!WRZ!A#-!Q67#aQi!DQUVWQX[\Q\L]J]>]`a>a:bcd:dde e eT!A#a%QqSU+,a/0QqS4!a= 1$%aCFR1qAaDF++B..acAgr1AAQqS1WqLQSOSVWXZV[\^V^^	``a	bb b brl   c                  D   [        [        [        5      [        S-  -  [        [        S-  -  [        [        -  -   [
        -   -  [        SS9[        [        [        5      [
        [        S-  -  [        [        S-  -  -   [        [        S-  -  -   -  [        5      :X  d   eg )Nrn   Trx  r   r   )rI   r#   rs   r   r   r   rY   r   rl   rj   test_issue_23704r[    s{     c!fQTk1QT6!A#:a<0$? Q1a4!AqD&1QT6)A!BAFG H Grl   c                     [        S[        S[        S[        -  5      -
  5      -  5      [	        [        S[        S[        -  5      -
  5      S-
  5      S-  [	        [        S[        S[        -  5      -
  5      S-   5      S-  -
  :X  d   eg r!  r  r   rl   rj   test_exp_substitutionr]    sz    QtAc!A#hJ''(CQQqS\0BQ0F,G,ICPTUVY\]^_`]`YaUaPbefPfLghiLi,iiiirl   c                     [        [        [        5      5      [        [        [	        [        5      S-   5      -
  [        [	        [        5      5      -   :X  d   e[        [        [        5      5      S[        [	        [        S-  5      5      -  :X  d   e[        [        [        5      5      [        [	        [        S-  5      5      :X  d   eg r!  )rI   r'   rs   r#   r*   r+   r2   r(   r   rl   rj   test_hyperbolicr_    s    T!WSa1%5!5DG!DDDDT!W4QqS	?!2222T!WT!A#Y///rl   c                  `   [        [        [        S-  5      5      [        [        [        S-  5      -  S-  :X  d   e[        [        [        [        S5      S-  -  5      5      S[        -  [        [        [        S5      S-  -  5      -  S-  :X  d   e[        S[        [        S-  5      -  5      [        [	        [        5      -  [        [        S-  5      -  :X  d   e[        [        [        [        S-  5      -  5      [        S-  [        [        S-  5      -  [	        [        5      -  :X  d   eg )Nrn   r   r   r   rf  rx   rM  rX  r   rl   rj   test_nested_powra    s    T!Q$Z Ad1a4jLN222T!ad1f+&'1Q3tA!QK/@+@+CCCCQtAqDz\"aAhtAqDz&9999QtAG}_%Ad1b5k)9#a&)@@@@rl   c                  
   [        S[        S[        S-  -  S[        -  -   S-   5      -  5      [        S5      [        S[        S5      -  [        [	        S5      S-  -   -  S-  5      -  S-  :X  d   e[        S[        S[        S-  -  S[        -  -   S-   5      -  5      [        S5      [        S[        S5      -  [        [	        S5      S-  -
  -  S-  5      -  S-  :X  d   e[        S[        S[        S-  -  S[        -  -   S-
  5      -  5      [        S5      [        S	[        -  S[        S5      -  [        S[        S-  -  S[        -  -   S-
  5      -  -   S-   5      -  S-  :X  d   e[        S[        S[        S-  -  S[        -  -
  S-   5      -  5      [        [        R                  -
  [        [        [        R                  -
  5      -  S[        [        [        R                  -
  S-  5      -  -  :X  d   e[        S[        [        [        [        -  -   [        [        S-  -  -   5      -  [        5      [        [        [        S[        [        5      -  [        [        [        [        -  -   [        [        S-  -  -   5      -  -   S[        -  [        -  -   5      [        [        5      -  [        [        S
5      [        [        [        S-  S[        -  -  -
  S
5      -  4[        S[        -  -  [        -   [        [        S[        -  -  [        -   5      -  [        [        [        S[        -  -  [        -   S-  -  5      -  [        [        S
5      4S[        [        [        [        -  -   5      -  [        -  [        [        S
5      4[        [        [        5      -  S45      :X  d   e[        S[        -  S	-   [        S[        S-  -  S[        -  -   S-   5      -  5      S[        S[        S-  -  S[        -  -   S-   5      -  S-  S[        S5      -  [        S[        S5      -  [        [	        S5      S-  -   -  S-  5      -  S-  -   :X  d   e[        S[        -  S	-   [        S[        S-  -  S[        -  -   S-   5      -  5      S[        S[        S-  -  S[        -  -   S-   5      -  S-  S[        S5      -  [        S[        S5      -  [        [	        S5      S-  -
  -  S-  5      -  S-  -   :X  d   e[        S[        -  S	-   [        S[        S-  -  S[        -  -   S-
  5      -  5      S[        S[        S-  -  S[        -  -   S-
  5      -  S-  S[        S5      -  [        S	[        -  S[        S5      -  [        S[        S-  -  S[        -  -   S-
  5      -  -   S-   5      -  S-  -   :X  d   e[        [        [        [        -  -   [        [        [        [        -  -   [        [        S-  -  -   5      -  [        5      [        [        * [        -  S[        -  -  [        -   [        [        [        S[        [        5      -  [        [        [        [        -  -   [        [        S-  -  -   5      -  -   S[        -  [        -  -   5      [        [        5      -  [        [        [        S-  S[        -  -  -
  S
5      4[        S[        -  -  [        -   [        [        S[        -  -  [        -   5      -  [        [        [        S[        -  -  [        -   S-  -  5      -  S45      -  [        [        [        [        [        -  -   [        [        S-  -  -   5      -  [        -  -   [        [        S
5      4S[        -  [        [        [        [        -  -   5      -  S[        -  [        * [        [        [        [        -  -   5      -  [        [        [        -  -   [	        S5      S-  -  S-  -   -  [        -  -   [        -  [        [        S
5      4[        [        -  [        [        S-  -  S-  -   [        [        5      -  S45      :X  d   e[        S[        S-  -  [        S-  -
  S[        -  -   S-
  [        [        S-  S[        -  -
  S-   5      -  5      [        [        S-  S[        -  -
  S-   5      [        S-  S[        -  S-  -   [	        S5      S-  -   -  S[        S[        -  S[        [        S-  S[        -  -
  S-   5      -  -   S-
  5      -  S-  -   :X  d   e[        [        S[        S-  -  S[        -  -
  S-   5      5      [        S-  [	        S5      S-  -
  [        S[        S-  -  S[        -  -
  S-   5      -  S[        S5      -  [        S[        -  S-  [	        S5      S-  -
  5      -  S-  -   :X  d   e[        [        [        [        [        -  -   [        [        S-  -  -   5      [        5      [        [        S-  [        S-  S[        -  -  -
  [        [        [        S[        [        5      -  [        [        [        [        -  -   [        [        S-  -  -   5      -  -   S[        -  [        -  -   5      [        [        5      -  [        [        [        S-  S[        -  -  -
  S
5      4[        S[        -  -  [        -   [        [        S[        -  -  [        -   5      -  [        [        [        S[        -  -  [        -   S-  -  5      -  S45      -  [        S[        -  -  [        S-  -   [        [        [        [        -  -   [        [        S-  -  -   5      -  -   [        [        S
5      4S[        [        [        -  -   [	        S5      S-  -  -  S[        -  -  [        [        S
5      4[        [        5      [        -  S45      :X  d   e[        [        [        [        S-  S[        -  -   S-   5      -  5      [        S-  S-  [        S	-  -   [	        S5      S	-  -   [        [        S-  S[        -  -   S-   5      -  S[        [        S5      [        S-   -  S-  5      -  S-  -
  :X  d   eg )Nrx   r   rn   r   r   rf  rN  r  r   r   Tr   r   ir  r  r  r   rT  re  i  i iY  i+A  iiQ  iC)  ir+  i  i:C)rI   r.   rs   r%   r   r1   r#   r   r   r   r   r/   r   r   rh   r   rl   rj   test_sqrt_quadraticrc    s
   QtAadF1Q3JqL))*d1geAd2hJAaDQRF
<STV<V6W.WXY.YYYYQtBq!tGAaCKM**+tAwtAd2hJAaDQRF
<STV<V7W/WXY/YYYYQtAadF1Q3JqL))*d1gc!A#$q'	$qQRTUQUvXYZ[X[|^_O_J`@`:`cd:d6e.efg.ggggQtAadF1Q3JqL))*q166z3q166z?.JAdTUXYX^X^T^abSbNcLc.ddddQtAacE!AqD&L))1-3q1T!W9T!ac'AadF*:%;;;ac!eCDT!WLbQRTUhY[\]`acd`dfghifi`j\jlmYnNnoqsGaKQ!Wq[!11$q!QqS'A+9I7I2JJBqRSHUT!ac']?1$bAh/!DG)T1B	DD D D
 ac!eT!AqD&1*Q,//0T!AqD&1Q3,"##A%$q'	%$r(
A!QJ8OPR8R2S(STU(UUV V Vac!eT"QT'!A#+a-001d2ad7QqS=1$%%a'"T!W*T!DH*a!A$q&j:QRT:T5U*UVW*WWX X Xac!eT!AqD&1*Q,//0T!AqD&1Q3,"##A%$q'	#acAd1gId1QPQT6TUVWTW<Z[K[F\<\6\_`6`2a(abc(ccd d da!eT!AaC%!Q$,//3QBqD!A#JNc!aQiQ1WqAv5E0F&F"F1Q"NOPTUVPWWY[\]`acd`dfghifi`j\jlmYno !A#w{C1Q3!,<<T!Q!Wq[STDTBT=UUW[\^^ T!ac'AadF*++A-. 02!Qx9 aCQ1W%!aRQ1W-=QqSAaDQRF@STU@U-U(VWX(XXZ[[]_`acd]efaC!AqD&(NDG+T2	44 4 4 a1fQTk!A#oa'ad1Q3hqj)99:1qs
QA1Q3!9:SQqS1TRSUVRVYZ[\Y\R\_`R`MaKaEadeEeAf=fgi=iij j j T%1*U1W,U234aC!E(5. $uQTzE!G';e'C"DDT$ZeAgemahtm&C DDZOPP P P T!AaC%!Q$,'+AaC!Q$!*$c!aQiQ1WqAv5E0F&F"F1Q"NOPTUVPWWY[\]`acd`dfghifi`j\jlmYno !A#w{C1Q3!,<<T!Q!Wq[STDTBT=UUW[\^^ qsGacM4AaC!AqD&(8#99: <>a8E a!A#g1a((!A#.1a9719d#	%% % % QtAqD1HQJ''(	
Aa!A#!Q	QTAaCZ!^ 44qtAwAq?P9Q7QRS7SST T Trl   c                  *   [        [        [        [        5      -  [        [        5      -  5      [        [        [        5      -  [	        [        [        5      [        [        5      -   5      -
  :X  d   e[        [        [        [        5      S-  -  [        5      [        [        [        5      -  [	        [        [        5      5      -   :X  d   e[        [        S-  [        [        [        5      [        S45      -  5      [        S-  [        [        [        5      [        S45      -  S[        S-  -  [        [        [        5      [        S45      -  -
  S[        -  [        [        [        5      [        5      -  -   S[        [        5      -  -
  :X  d   eg )Nrn   r   r   r   )rI   rs   r7   r6   r#   r3   r   rd   r   rl   rj   test_mul_pow_derivativere    s   Qs1vXc!f_%3q6CAQ4H)HHHHQs1vqy[!$#a&3s1v;(>>>>QT*QqTAq6223a4
1Q4!Q((1QT6*QqTAq62J+JJQqSQ[\]^_\`bcQdMddghijklimgmmn n nrl   c                  `   [        S[        S:  4S5      n [        S[        S:  4S5      * nX-   n[        [        S5      * S4n[        X5      S:X  d   e[        X5      S:X  d   e[        U * U5      S:X  d   e[        U* U5      S:X  d   e[        X#5      S:X  d   e[        U* U5      S:X  d   eg )	Nr   g        )rx   Tr  Infrx   r   g      )r/   rs   floatrI   )fun1fun2fun_sumr  s       rj   test_issue_20782rl    s    aS\9-Dq!c'lI..DkG	
U5\M1AT"""T"""dUA"$$$dUA!###W B&&&gXq!S(((rl   c                  n  ^ S mU4S jn [         [        S5      * [         4n[        U " S5      U5      nUS[         -  [        S[         5      -
  [        [         [	        SSSS95      -
  :X  d   e[        U " S	5      [         [        S5      * [         45      S[         -  S[        S	[         5      -  -
  :X  d   eg )
Nc                 >    [        S[        U :  4S[        U :  45      $ r   )r/   rs   r2  s    rj   r~   "test_issue_20781.<locals>.<lambda>)  s    )QAJAF4rl   c                 J   > T" [        U 5      5      T" [        U 5      5      -   $ rz   )intrh  )r   Ps    rj   r~   ro  *  s    !CF)aak)rl   rg  rx   rn   r  FrQ  r   )rs   rh  rI   r-   r,   )rd   r  r   rr  s      @rj   test_issue_20781rs  (  s    4A)A	
U5\M1A	1Q4	B1s3{"SCQ,G%HHHHH QqTAe}a0 
qS1SAY;  rl   c                     [        S5      n [        U S-  [        SU S-  -
  5      -  U SS45      [        S-  :X  d   e[        SU S-  -  [        SU S-  -
  5      -  U SS45      [        * S-  :X  d   e[        S[        SU S-  -
  5      -  U SS45      [        S-  :X  d   e[        U S-  SU S-  -  -
  S-   [        SU S-  -
  5      -  U SS45      S[        -  S-  :X  d   eg )	Nrs   r   rx   rn   r   re  r   r   )r   rI   r.   r   r  s    rj   test_issue_19427ru  4  s    	sA a1fQaZ 001b!*=bHHHb16kT!a1f*%552qzBrcAgMMMa4AF
++aQZ8BFBBB a1fq16z)A-a!q&j1AAAr1:NRSVXRX[]R]]]]rl   c            
         [        S[        [        S[        -   S-  -  S[        -   S-  -   5      -  [        S[        45      n U R                  [        SSS9[        S[        [        S-  S[        S-  -  -   S[        -  -   S-   5      -  [        S[        45      [        [        S-
  [        S45      -   :X  d   e[        S[        [        S[        -
  S-  -  S[        -   S-  -   5      -  [        S[        45      nUR                  [        SSS9[        S[        S[        S-  -  S[        S-  -  -
  S	[        S-  -  -   S
[        -  -
  S-   5      -  [        S[        45      [        [        S-
  [        S45      -   :X  d   eg )Nrx   r   rn   r   r  r   r   r     i  i  )rX   r.   r   rs   r5  r<  rO   )I1I2s     rj   test_issue_23942rz  B  sb   	!DAEA:Q
233aAY	?B99QQ98Ad1a4!AqD&=1Q33F3J.K,KaQRTUY#WZ[\]`a\adeghciZj#jjjj	!DAEA:Q
233aAY	?B99QQ98Ad1QT6Bq!tG3Cc!Q$h3NQTUVQV3VY\3\.],]`acdfg_h#ilmnorsnsvwyzu{l|#||||rl   c                  X   S[         -
  [        S[         -  5      -  n SS[        -  [        -  S-   S[        -  -   -  [        S[        -  [        -  5      -  S[        S[        -  5      -  -
  n[	        U [         [        S45      nUR                  U[        R                  5      (       d   eg )Nrx   y        >T?r  gzg	
T8?gz?g>T?)rs   r!   r   r   rI   is_samerE  rF  )rd   F_expr  s      rj   test_issue_25886r~  I  s    	
1c,q.!!A"1$Q& q ! ""%k!mAo"67 s;q=112E 	!aC[!A99UDLL))))rl   c                     [        [        [        [        S-  5      5      [        -  5      n U [	        [        [        S-  5      5      S-  :X  d   e[        S[        S-  [
        S-  -   [        SS5      -  -  [        5      nU[        [
        S-  [        [        S-  [
        S-  -  S-   5      -  -  :X  d   e[        S[        [        5      S-   -  [        SS[        -  45      nUS[        S5      -  [        -  S-  :X  d   eg )Nrn   rx   r   r   )	rI   r3   r#   rs   r4   r   r   r.   r   )rx  ry  I3s      rj   test_old_issuesr  T  s    	3s1a4y>!#	$BSAY!!!!	1ad1a4i8Aa=11!	4BAqDad1a4i!m,,----	1c!fQh<1QrT
	+B472arl   c                  ,   [        SSS9n [        SSSS9n[        X[        -   -  5      S-  n[        X [        * [        * S-  45      n[        S-  nSnUR	                  X5      R                  5       nUR                  5       n[        Xg-
  5      S	:X  d   eg )
Nrs   Tr   r   )r   r   rn   r   rx   r   )r   r4   r   rI   r  rg   rR   )rs   r   integral_exprsymbolic_resultcorrect_resulta_valuenumeric_symbolic_resultnumeric_correct_results           rj   test_integral_issue_26566r  `  s    $A$.A V%q(MB3A?O !VN G-221>DDF+113 +DEJJJrl   c                      [        SSS9n [        SSU S-   S-  -  -
  5      n[        XSS45      nUR                  5       n[        S	5      S
-  S[        -  S-  -   n[        X4R                  5       -
  5      S:  d   eg )Nrs   Tr   rx   g      ?gOUUUUU?rn   r   r   r   r   r   r  )r   r.   rI   rg   r   r  )rs   r  result_symbolicresult_numericexpected_results        rj   .test_definite_integral_with_floats_issue_27231r  u  s    $AVq+<'<&BBBCM  2qz:O$**,N 1gkAFQJ.O ~ 5 5 7784???rl   c                     [        [        S-  [        S-  -   5      n [        [        U -  [        S5      -  5      U -  n[        U[        [        5      R                  [        [        [        [        -  [        [        -  -
  5      4/5      nS[        S5      -  [        -  [        S-  -  [        [        S-  * [        S-  -  S-  5      -  S[        [        5      -  -  n[        [        U[        [        * [        45      5      U:X  d   eg )Nrn   r   r   )r.   rs   r5  r=   r   r   r  r   r!   r   rR   rI   )r>  uEcr  s       rj   test_issue_27374r    s    QTAqD[AAaCQKA	aA		aac!A#g/0	1Bajl1a4'QTE!Q$JqL(991T"X:FOIb1qb!*-./AAArl   )rd  (c  rE  sympy.concrete.summationsr   r   sympy.core.addr   sympy.core.containersr   sympy.core.exprr   r  r   r	   r
   r   
sympy.corer   sympy.core.numbersr   r   r   r   r   r   r   r   sympy.core.relationalr   r   sympy.core.singletonr   sympy.core.symbolr   r   sympy.core.sympifyr   r  r   r   r   r   r   &sympy.functions.elementary.exponentialr    r!   r"   r#   %sympy.functions.elementary.hyperbolicr$   r%   r&   r'   r(   r)   r*   r+   (sympy.functions.elementary.miscellaneousr,   r-   r.   $sympy.functions.elementary.piecewiser/   (sympy.functions.elementary.trigonometricr0   r1   r2   r3   r4   r5   r6   r7   'sympy.functions.special.delta_functionsr8   r9   r  r:   r;   r<   r=   r>   r?   r@   rA   rY  rB   rC   sympy.functions.special.hyperrD   rE   -sympy.functions.special.singularity_functionsrF   &sympy.functions.special.zeta_functionsrG   sympy.integrals.integralsrI   sympy.logic.boolalgrJ   sympy.matrices.denserK   sympy.polys.polytoolsrL   rM   sympy.printing.strrN   sympy.series.orderrO   sympy.sets.setsrP   sympy.simplify.gammasimprQ   sympy.simplify.simplifyrR   sympy.simplify.trigsimprS   sympy.tensor.indexedrT   rU   rV   #sympy.functions.elementary.integersrW   rX   sympy.integrals.rischrY   sympy.physicsrZ   sympy.testing.pytestr[   r\   r]   r^   sympy.utilities.exceptionsr_   sympy.core.randomr`   rs   r   r5  r   r   r   r   rh   r   r   r  r  ra   rd   rk   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-  r0  r3  r8  r:  r<  r@  rF  rI  rK  r`  rb  rx  rz  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$  r'  r+  r-  r3  r6  r9  r>  rC  rG  rI  rK  rM  rO  rQ  rS  rU  rZ  r\  r^  ra  re  rh  rj  rp  ru  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r$  r)  r+  r0  r3  r6  r8  r:  r>  rC  rG  rI  rK  rM  rO  rR  rU  rY  r[  r]  r_  ra  rc  re  rl  rs  ru  rz  r~  r  r  r  r  r   rl   rj   <module>r     s    6  '   D D ! L L L * " / & P P R R d d d E E : a a a I _ _ _ F : M ; / # ' 0 #   $ . , , 3 % 5 . 7  L L > 0 *11N)O &1aAq!Q1c3
3SM@ N N8;*,+6\
@F8 O&F/466*9(/?1>.EN
87/
B
H12:<
#i
'k
Z+;,-:`+ 0< 0<fOEQ:""B$<6EPPP&	K4)C
50@?I< 
B"
<07@<8:&L0#"9
@
P.N@Z8
3*6% R*
D4
,<
:3
7N?*
+)H
1
 7/BGEC 	[ 	[/,J)-=@6 O O A ABB3
 > >&
R67KA4V
95
(K
1=eE0
 : :
*
(;E:"E5O4
	3.#<MID W W
DRc@"O
/
	I@
?*GV%r7: W W b b
L7*1u
aA/
I2bHj0A'TTn)	 
^ 
^}*	 K*@ Brl   