
    sgv4                     P   d dl mZ d dlmZ d dlmZmZmZ d dlm	Z	m
Z
mZ d dlmZmZ d dlmZmZ d dlmZmZmZ d dlmZmZmZmZ d d	lmZ d d
lmZ d dlm Z m!Z!m"Z"m#Z#m$Z$m%Z% d dl&m'Z'm(Z(m)Z)m*Z* d dl+m,Z, d dl-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4 d dl5m6Z6 d dl7m8Z8m9Z9m:Z: d dl;m<Z<m=Z= d dl-m>Z>  ed      \  Z?Z@ZAZB ed      ZCd ZDd ZEd ZFd ZGd ZHd ZId ZJd ZKd  ZLd! ZMd" ZNd# ZOd$ ZPd% ZQd& ZRd' ZSe<d(        ZTd) ZUd* ZVd+ ZWd, ZXd- ZYd. ZZd/ Z[d0 Z\e=d1        Z]d2 Z^d3 Z_d4 Z`d5 Zad6 Zby7)8    )Sum)Add)
DerivativeFunctiondiff)IRationalpi)EqNe)Symbolsymbols)LambertWexplog)asinhcoshsinhtanhsqrt)	Piecewise)acosasinatancossintan)besseljbesselkbesselyjn)erf)Integral)And)Matrix)ratsimp)simplify)
componentsheurischheurisch_wrapper)XFAILslow)	integratezx,y,z,nufc            	         t        t        t        z  t              t        hk(  sJ t        dt        t        z   z  t              t        hk(  sJ t        t        t              t              t        t              t        hk(  sJ t        t        t              t	        t        t                    z  t              t        t              t        t              t	        t        t                    t        hk(  sJ t        t        t        t        t              t        z        z  t              t        t        t        t              z        t        t        t              hk(  sJ t        t        t        dd      z  t	        t        t                    z  t              t        t              t        t        dd      z  t	        t        t                    t        hk(  sJ t        t        t              t              t        t        t              hk(  sJ t        t        t        t              t              t              t        t        t              t        t        t              t              hk(  sJ t        t        t              t        t        t              t              z  t              t        t        t              t        t        t              t              t        t        t              t              hk(  sJ y )N      6   )r)   xyr   r   r   r   r	   r/   r   r        V/var/www/html/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_heurisch.pytest_componentsr9      s   ac1!$$$aQi#s***c!fa SVQK///c!fT#a&\)1-	QQc!fq)* * *aCF1Hoq)	Qs1vX3q6"# # #a"b))$s1v,6:	QHQO#T#a&\156 6 6 adA	
AaD	  j1q)1-	
AaD*QqT1%&' ' 'ad4!a=(!,	
AaD*QqT1%z!A$':;< < <r7   c                      t        t        t        t        t        t        t        t        t              z        z        z  t              t              sJ y N)
isinstancer.   r4   r   r$   r6   r7   r8   test_issue_10680r=   -   s4    i3q#aQi.'8#9 9!<hGGGr7   c            
          t        t        t        t        t	        t                    z        t        ddf      dk(  sJ y )Nr1   r   )r.   r   r4   r   absr6   r7   r8   test_issue_21166rA   1   s.    S4A<(1b!*5:::r7   c                     t        dt              t        k(  sJ t        t        t              t        dz  dz  k(  sJ t        t        dz  t              t        dz  dz  k(  sJ t        t        t              t        t        z  k(  sJ y )Nr1      r2      )r*   r4   r+   r5   r6   r7   r8   test_heurisch_polynomialsrE   5   sl    Aq>QAq>QT!V###ArE1Br)))Aq!QqS(((r7   c                  P   t        dt        z  t              t        t              k(  sJ t        ddt        z   z  t              t        t        dz         k(  sJ t        dt        t        t              z   z  t              t        t        t        t              z         k(  sJ t        dt        dz  z  dt        dz  z  dz
  z  t              dt        dt        dz  z  dz
        z  dz  dt        dt        dz  z  dz         z  dz  fv sJ t        dt        dz  z  dt        dz  z  dz   z  t              dt        dt        dz  z  dz         z  dz  k(  sJ t        dt        dz  z  t              dt        z  k(  sJ t        dt        dz  z  t              ddt        dz  z  z  k(  sJ y )	Nr1   rC            r?      )r*   r4   r   r   r5   r6   r7   r8   test_heurisch_fractionsrL   =   s}   AaCs1v%%%Aq1uIq!SQZ///Aq3q6zNA&#a#a&j/999 AadF	!Q$
c!AqD&1*o-2Ac"QT'A+6F4F4KLM M MAadFAadFQJ'+qQq!tVaZ/@2/EEEEAadFA"Q$&&&Bq!tGQ1a1f:---r7   c                     t        t        t              t              t        t        t              z  t        z
  k(  sJ t        t        dt        z        t              t         t        t        d      z  z   t        t        t              z  z   k(  sJ t        t        t        dz        t              t        t        t        dz        z  dt        z  z
  dt        z  t        t              z  dt        z  z
  fv sJ y )N   rC   )r*   r   r4   r6   r7   r8   test_heurisch_logrO   N   s    CFA!CF(Q,...C!Ha QB3q6MAc!fH$<<<<C1Iq!aAqD	kAaC&71SVac9I%JJJJr7   c            
         t        t        t              t              t        t              k(  sJ t        t        t               t              t        t                k(  sJ t        t        dt        z        t              t        dt        z        dz  k(  sJ t        t        t        t              z  t              t        t        t              z  t        t              z
  k(  sJ t        t        t        t        dz        z  t              t        t        dz        dz  k(  sJ t        t        t        dz         t              J t        dt        z  t              dt        z  t        d      z  k(  sJ t        t        dt        z  z  t              t        dt        z  z  t        d      z  dt        z  t        d      dz  z  z
  k(  sJ t        t	        t        t
        z  t        z  t        ddft
        ddf      j                  t              t        t        t
        z  z  t        z  t
        dz   z  k(  sJ t        t        t        t
        z  t
        ddf      j                  t
              t        t
        z  t        t              z  k(  sJ t        t
               t        t        t        z
        t        t
        t        t        t        z
        z        z  t        t
        t        t        t        z
        z        z
  z  } t        t        t
              t        t
         t        t        t        z
        z        z  t
              | k(  sJ y )Nr2   rC   rJ   r1   rN   )
r*   r   r4   r   r$   zr5   functionr   r   )antis    r8   test_heurisch_exprT   T   sL   CFA#a&(((CGQCG8+++C1Iq!SAY^333Ac!fHa Ac!fHs1v$5555Ac!Q$iK#s1a4y1}444CAJ"***AqD!1SV+++AadFA!AqD&Q-!Q$s1v|2C"CCCCHQT!VaAYAq	:CCQGAaQRdFSTHWXYZWZK[[[[C1q!Qi(1115Ac!fDDD F7DQKAd1q5kM 22S4A;5GGHDCF3r$q1u+~..2d:::r7   c            	      b   t        t        t              t              t        t               k(  sJ t        t        t        t              z  dz   t              t        t        t        t              z  z
  k(  sJ t        t        t              t              t        t              k(  sJ t        t        t              t              t        dt        t              dz  z         dz  t        t        t              t        z         t        t        z  z   t        t        t              t        z
        t        t        z  z
  fv sJ t        t        t              t        t              z  t              t        t               t        t              z  k(  sJ t        t        t              t        t              z  t              t        t               t        t              z  k(  sJ t        t        t              t        t              z  t              t        t              dz  dz  t        t              dz   dz  fv sJ t        t        t              t        t              z  t              t        t        t                    k(  sJ t        t        t        dt        z        z  t              t        dt        z        dz  t        t        dt        z        z  dz  z
  k(  sJ t        dt        z  dz  t        dz  z  t        t              z  t              dt        z  dz  t        dz  t        t              z  dt        t              z  z
  dt        z  t        t              z  z   z  k(  sJ t        t        t        dz        t        t        dz        z  t              dt        z  t        dt        dz  z
        t        t        dz        z  z
  t        dt        dz  z
        t        t        dz        z  z   t        t        t        dz        z  t        t        dz        z  z   k(  sJ t        t        t              t        t              dz  dz   z  t              t        t        t                     k(  sJ t        dt        t              dz   z  t              dt        d      z  t        t        d      t        t        dz        z  dz        z  dz  k(  sJ t        dt        t              z  t        t              z  t        t              dz  dz   z  t              t        t        d      t        t              z  dz
        t        t        d      t        t              z  dz         z
  k(  sJ t        dt        t              z  t              dt        t        t        dz              z  k(  sJ y )Nr1   rC      1   rK      rN   )r*   r   r4   r   r
   r   r   r   r5   r   r   r   r   r   r   r6   r7   r8   test_heurisch_trigonometricrY   h   s   CFA3q6')))Bs1vIM1%RAY666CFA#a&(((CFAAA	M1CFQJ!A#CFQJ!A##    CF3q6M1%#a&Q777CF3q6M1%#a&Q777 CF3q6M1%#a&!)a-#a&!)a)HHHHCF3q6M1%SV444Ac!A#hJ"c!A#hmaAaCj1n&DDDDAbDFQTM#a&(!,"Q1SVc!fH9 s3q6z9* 1+ + + + D1IQqS	)1-1R!Q$YaPQc7R1RQT	?D1I
%2&()$qs)D1I(=2> > > > CFCFAIaK(!,c!f===As1vaxL!$$q'	$tAws1Q3x7G7I2J(J1(LLLLAc!fHSVOSVQY]3Q74QA
A <DGCFNQ&'<( ( ( ( Ad1gIq!QtD1I%6666r7   c                     t        t        t              t              t        t              k(  sJ t        t        t              t              t        t              k(  sJ t        t        t        t              z  t              t        t        t              z  t        t              z
  k(  sJ t        t        t        t              z  t              t        t        t              z  t        t              z
  k(  sJ t        t        t	        t        dz        z  t              t        dz  t	        t        dz        z  dz  t	        t        dz        z   t        t        dt        dz  z         z  dz  z
  k(  sJ y NrC   rK   )r*   r   r4   r   r   r   r6   r7   r8   test_heurisch_hyperbolicr\      s   DGQ47***DGQ47***Ad1gIq!QtAwYa%8888Ad1gIq!QtAwYa%8888	%!*aqDqsOA-ac
:QtA1H~=Ma=OOP P Pr7   c            	         t        t        t              t        t              z  t              t        t              t        t              z  dz  t        t              t	        t              z  dz  z
  k(  sJ t        t        t        t        t               z        t              dt        z  t	        t        t        t               z        z  t        t               z  dt        t        t        t               z        z  z
  k(  sJ y NrC   )r*   r   r4   r   r   r   r6   r7   r8   test_heurisch_mixedr_      s    CF3q6M1%QAq3q6#a&=?)JJJJC$r(
OQ'1Q3s1T1"X:+>tQBx+G!CPQRVXYWYRZPZOJ[+[[[[r7   c            
      p   t        dt        t              z  t              dt        t              z  k(  sJ t        dt        t              dz  z  t              dt        t              z  k(  sJ t        t        t              dz  t              dt        t              dz  z  dz  k(  sJ t        t        t              t        t	        t                    z  t              dt        t	        t                    dz  z  dz  k(  sJ t        d      } t        t        | t        t              z        t              d| dz  z  t        | t        t              z        z  dt        t              z  t	        | t        t              z        z  | z  z
  k(  sJ t        t        | t        t              z        t              t        dt        t              z  t	        t        t              | z        z  | z  dt        t        t              | z        z  | dz  z  z   t        | d      fd      k(  sJ t        dd	
      } t        t        | t        t              z        t              d| dz  z  t        | t        t              z        z  dt        t              z  t	        | t        t              z        z  | z  z
  k(  sJ y )Nr1   rC   rN   rJ   rG   r5   r   )r   TTpositive)	r*   r   r4   r   r   r   r+   r   r   r5   s    r8   test_heurisch_radicalsrd      s   Ad1gIq!QtAwY...Ad1gqjL!$47
222DGQJ"aQ
l1n444CF4A<'+r$s1v,//A!/CCCCsAC$q'	NA&!AqD&QtAwY*?	$q'	#aQi. "+# # # #C$q'	NA.)	DGCQ	N	"1	$qT!WQY'71'<	<bAhG3    	sT"AC$q'	NA.!AqD&QtAwY2G	$q'	#aQi. "3# # # #r7   c                  j   t        t        t              t              t        t        t              z  t        t        dz         t	        t
              z  z   k(  sJ t        t        t        dz         t        t              z  t              t	        t
              t        t              dz  z  dz  k(  sJ y r[   )r*   r#   r4   r   r   r
   r6   r7   r8   test_heurisch_specialrf      sy    CFA!CF(S!Q$ZR-@"@@@@CAJs1v%q)T"Xc!fai-?!-CCCCr7   c            
         t        dt        t        z   z  t              t        t        t        z         k(  sJ t        dt        t	        d      z   z  t              t        t        t	        d      z         k(  sJ t        t        t        t        t        t        z   t        z         t              t                    t        t        t        z   t        z         k(  sJ y Nr1   rC   )r*   r4   r5   r   r   r(   r   rQ   r6   r7   r8   test_heurisch_symbolic_coeffsri      s    Aq1uIq!SQZ///Aq47{OQ'3q47{+;;;;D#a!eai.!4a89SQ^KKKr7   c            
         t        d      } t        dt        dz  | z   z  t              t        t	        t        t        |        z
        dt        |        z  z  t	        t        t        |        z         dt        |        z  z  z
  t        | d      fdt        z  df      k(  sJ t        dd      } t        dt        dz  | z   z  t              t        t        t        |       z        t        |       z  k(  sJ y )Nr5   r1   rC   r   r?   Tra   )r   r+   r4   r   r   r   r   r   rc   s    r8   "test_heurisch_symbolic_coeffs_1130rk      s    sAAq!taxL!,	T1"X$r(
#c!dA2h,&748&DDq!H1d|1    	sT"AAq!taxL!,aQia1HIIIr7   c                     t        t        ddt        dz  z  z         t        g       t        t        ddt        dz  z  z         z  dz  t        d      t        t        d      t        z        z  dz  z   k(  sJ t        t        ddt        dz  z  z
        t        g       t        t        ddt        dz  z  z
        z  dz  t        d      t	        t        d      t        z        z  dz  z   k(  sJ t        dt        ddt        dz  z  z         z  t        g       t        d      t        t        d      t        z        z  dz  k(  sJ t        dt        ddt        dz  z  z
        z  t        g       t        d      t	        t        d      t        z        z  dz  k(  sJ t        t        dt        dz  z        t        g       t        dt        z        t        t        d      t        z        z  dz  k(  sJ t        dt        ddt        dz  z  z
        z  t        g       t	        t        t        dd	      z        dz  k(  sJ t        dt        ddt        dz  z  z         z  t        g       t        t        t        dd	      z        dz  k(  sJ t        dt        d	t        dz  z  dz
        z  t        g       t        d	      t        d	t        z  t        d	      t        d	t        dz  z  dz
        z  z         z  d	z  k(  sJ y )
Nr1   rV   rC   hints   i	   rK   rN   )
r*   r   r4   r   r   r   r
   r#   r	   r   r6   r7   r8   test_heurisch_hackingrq      s   DQq!tV$ar2	$q1QT6z
1tAwuT!WQY'77::; ; ;DQq!tV$ar2	$q1QT6z
1tAwtDGAI6r99: : : Ad1qAv:&&4Qd1gai  "# # #Ad1qAv:&&4QT!WQY!" " " C1a4L!2.QrT
3tAwqy>!"$% % % Ad1qAv:&&4Qx1~q ! ! ! Ad1qAv:&&4aA!" " " Ad1QT6!8n$ar273qsT!WT!AqD&1*%55566q89 9 9r7   c                  B    t        t        t              t              J y r;   )r*   r/   r4   r6   r7   r8   test_heurisch_functionrs      s    AaD!$$$r7   c                     t        t        t              t              } t        t        t              | z  t              t        t              dz  dz  k(  sJ t        t        t              dz  | z  t              t        t              dz  dz  k(  sJ t        | t        t              z  t              t	        t        t                    k(  sJ y )NrC   rN   )r   r/   r4   r*   r   )dfs    r8   !test_heurisch_function_derivativerv      s     
adABAaDGQ1Q4719,,,AaD!GBJ"adAgai///BqtGQ3qt9,,,r7   c            	      f   dt         t        z   z  } t        | t              t        t        t         z         k(  sJ dt         t        z
  z  } t        | t              t        t        t         z
         k(  sJ dt         t        z
  t         t        z   z  z  } t        | t              t	        t        t        t         z
         dt         z  z  t        t        t         z         dt         z  z  z   t        t         d      fdt        z  df      k(  sJ t        t        dz  t         t        z
  t         t        z   z  z        } t        | t              t        t        t        dz   t        dz  t         dz  z
  z        z  t         dz  t        t        dz   t        dz  t         dz  z
  z        z  t        z  z
  k(  sJ y )Nr1   rC   r   T)r5   r4   r+   r   r   r   r   )r/   s    r8   test_heurisch_wrapperrx      sb   	1q5	AAq!SQZ///	1q5	AAq!c!a%j[000	AEAE?AAq!Y
a!e*ac	SQZ1-	-r!Qx81Q3+&G G G G 	QTAEAE?#$AAq!QtQTE1a4!Q$;,?'@%@d4Aq!tad{#$$Q&&' ' ' 'r7   c                      t        dt        dt        t              dz  z   z  z  t              t        t        t                    k(  sJ y rh   )r*   r4   r   r   r6   r7   r8   test_issue_3609rz      s5    AqAA	M*+Q/4A<???r7   c                     d } t         dz  dt         dz  z  z
  dt         dz  z  z
  dt         z  z   dz
  t         dz  dt         dz  z  z   dt         dz  z  z   dt         dz  z  z   z  }ddt         dz  z  z   dt         z  z   d	t         d	z  z  z   t         d
z  dt         d	z  z  z   dt         z  z   z  t        t               z   } | t        t        |t                     t               |k(  sJ y )Nc                     | j                   r2t        | j                  D cg c]  }|j                  |      s| c} S | S c c}w r;   )is_Addr   argshas)exprr4   args      r8   
drop_constz"test_pmint_rat.<locals>.drop_const   s8    ;;B#cggaj#BCCK Cs
   AArV      rK   rC      rH   rI   rN   rG   )r4   r   r'   r*   )r   r/   gs      r8   test_pmint_ratr      s     
A1a4!AqD&	 1Q3	&	*QTAadF]R1W-DqAv-MNA	
Qq!tVac	AadF	"QTAadF]QqS%89CFBAghq!n-q1Q666r7   c                  ,   t         t        t               z
  t        t               dz  z  t        t               z   } t         dz   dz  t         t        t               z  z
  t        t        t               dz  dz         dz  z   }t        | t               |k(  sJ y )NrC   r1   )r4   r   r   r*   r/   r   s     r8   test_pmint_trigr     sp    	
SVs1vqy 3q6)A	
Aa!CF(SQQ/11AAq>Qr7   c                     dt         z   t         t        t               z  z   t         t        t               z   t        t               z   dz
  z  t         t        t               z   t        t               z   dz  z  t         z  } t        t         t        t               z   t        t               z         dt         t        t               z   t        t               z   z  z   }t        t	        | t                     |k(  sJ y rh   )r4   r   r   r'   r*   r   s     r8   test_pmint_logexpr     s    	
Q3q6	AAJQ/!34a#a&j3q66IA5MMaOAAAJQ 1a#a&j3q6&9#::A8Aq>"a'''r7   c                     t        t        dz         t        t              z  t        t              dz  t        t              dz  z
  t        t              z
  dz   z  } t        t              t        t        t              dz
        z  dz  t        t              t        t        t              dz         z  dz  z
  t        t              dt        t              z  dz
  z  z
  }t        t        | t                    |k(  sJ y )NrC   rN   r1   r   rK   )r   r4   r#   r   r
   r   r'   r*   r   s     r8   test_pmint_erfr     s    QTE
3q63q619s1vqy03q69A=>ARSVaZ "T"Xc#a&1*o%=a%??$r(AcRSfHWXLBYYA8Aq>"a'''r7   c                      t        t              } t        t        t              z  t        z
  t        t        t              z  z   }t        | t              |k(  sJ y r;   )r   r4   r*   r   s     r8   test_pmint_LambertWr      s>    A	(1+AhqkM)AAq>Qr7   c                     t        t        dz   t              t        t        t              z  } t        t        t              z  t        t        t        t                    z
  }t	        | t              |k(  sJ t        t        t        t              z  t        t        t        dz   t              z  z
  t        z  } t        t        t              }t	        | t              |k(  sJ t        t        dz   t              t        t        t              z  } t        t        t              z  t        t        t        t                    z
  }t	        | t              |k(  sJ y )Nr1   )r   nur4   r   r*   r"   r   s     r8   test_pmint_besseljr   '  s    Q72q>)A
3q6	CA''AAq>Q	GBN	QwrAvq11	114AAAAq>Q
261bQiA
3q6	C2q	N"AAq>Qr7   c                     t         t        t        t               z  t        t        dt         z        z  } dt         z  t        t        t               z  t        t        dz
  dt         z        z  dz  t         t        t        dz
  t               z  t        t        dt         z        z  dz  z   }t	        | t               |k(  sJ t         t        t        t               z  t        t        dt         z        z  } dt         z  t        t        t               z  t        t        dz
  dt         z        z  dz  t         t        t        dz
  t               z  t        t        dt         z        z  dz  z
  }t	        | t               |k(  sJ y )NrC   rJ   r1   rN   rG   )r4   r   r   r!   r*   r    r   s     r8   test_pmint_bessel_productsr   8  s"   	'"a.QqS))A
1WR^GBFAaC002QwrAvq7I5I'RTVWXYVYJZ5Z[\5\\AAq>Q	'"a.QqS))A
1WR^GBFAaC002QwrAvq7I5I'RTVWXYVYJZ5Z[\5\\AAq>Qr7   c                     d } d | t               dt         | t                     t          | t               z   z  z   z  z   d | t               z   z  t          | t               z   z  }t        t         t        t	        t                     z         t        t        t	        t                           z   }t        |t               |k(  sJ y )Nc                 *    t        t        |             S r;   )r   r   )r4   s    r8   omegaz%test_pmint_WrightOmega.<locals>.omegaF  s    Ar7   r1   rC   )r4   r   r   r   r   r   r*   )r   r/   r   s      r8   test_pmint_WrightOmegar   E  s      
U1XSq]a%(l;;<	<q58|LaRWXYRZl[AAQ  !CQ(8$99AAq>Qr7   c                      t        t        ddt        dz  z  z         t        g       dt        z  t        dt        dz  z  dz         z  dt        dt        z        z  z   k(  sJ y )Nr1   g      ?rC   rm         ?g      ?)r*   r   r4   r   r6   r7   r8   test_RRr   O  s_     DT!Q$Y'"5Ad419q=!!Cc!e$445 5 5r7   c                      t        d      \  }  t        d      |       }fd}t         ||      |      }t         ||       |       }||j                  ||       k(  sJ y )Nzt RrQ   c                 2    | t        dz  | dz  z
        z  S r^   r   )r4   Rs    r8   r/   ztest_issue_22527.<locals>.fc  s    tAqD1a4K   r7   )r   r   r.   subs)trQ   r/   UzUtr   s        @r8   test_issue_22527r   `  s]    6?DAqaA!	1Q4	B	1Q4	BAr7   c                  n   t        dd      } t        | dz   ddt        z
  dz  z  z        }t        || g       J t	        t
              t        dt        z   dz        z  dz  }t        t        t         | dz  z  dz        | ddf      |t        |z  z
  k(  sJ t        t        dz   ddt        z
  dz  z  z        }t        |t        g       J t	        t
              t        dt        z   dz        z  dz  }t        t        t         t        dz  z  dz        t        ddf      |t        |z  z
  k(  sJ y )NrT)realrC   rm   r1   r   )	r   r   r   r*   r   r
   r#   r.   r4   )r   as     r8   %test_heurisch_complex_erf_issue_26338r   j  s"   $AQTE1a!eaZ< !AAq#+++Ra!eQY!AS!AqD^aAY/1qs7:::QTE1a!eaZ< !AAq#+++Ra!eQY!AS!AqD^aAY/1qs7:::r7   c            	      J   t        d      } t        ddd      \  }}}}t        t        | |z        gg      }t	        dd      }dd|dd	d
dg\  }}}	}
}}}||
|z  dt        ||z
   |z        z
  z  ||z  dt        ||z
   |z        z
  z  z   z  }||
|z  t        ||z
   |z        z  t        |	|z
  |z        dz
  z  ||z  t        ||z
   |z        z  t        |	|z
  |z        dz
  z  z   z  }t        d||k  f|t        ||k  ||	k        f||	|k  f      }t         | |      |      }t        | | |      z  gg      }||j                  ||      dz  z  |j                  |j                  |j                        j                  ||      z  }t        |d   |d|f      }|J y )NZ0zk01 k10 t sT)r   rb   S   d   r   2   g333333?rC   x   r1   r   r?   )r   r   r&   r   r	   r   r%   r   r   lhsrhsr.   )r   k01k10r   sm_83r   bcder/   r   AIF_btfAIF_atfAIF_symaif_eqf_vec	integrandsolutions                        r8   test_issue_15498r   w  s   	$BMtDNCacT!VA
2s
C #sBQ<Q1aAq1a#Ahqj/)*QqS!cAE(1*o2E-FFGG1S1q5!_$c1q5!)nq&8 
aCa!eHQJa!eQY!!345 6GAE
Wc!q&!a%.@$AGQRSVCTUG1wFSAYK=!E!&&A,""5::fjj&**#E#J#J1a#PPI11ay1Hr7   N)csympy.concrete.summationsr   sympy.core.addr   sympy.core.functionr   r   r   sympy.core.numbersr   r	   r
   sympy.core.relationalr   r   sympy.core.symbolr   r   &sympy.functions.elementary.exponentialr   r   r   %sympy.functions.elementary.hyperbolicr   r   r   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr   r   r   r   r   r   sympy.functions.special.besselr   r    r!   r"   'sympy.functions.special.error_functionsr#   sympy.integrals.integralsr$   sympy.logic.boolalgr%   sympy.matricesr&   sympy.simplify.ratsimpr'   sympy.simplify.simplifyr(   sympy.integrals.heurischr)   r*   r+   sympy.testing.pytestr,   r-   r.   r4   r5   rQ   r   r/   r9   r=   rA   rE   rL   rO   rT   rY   r\   r_   rd   rf   ri   rk   rq   rs   rv   rx   rz   r   r   r   r   r   r   r   r   r   r   r   r   r6   r7   r8   <module>r      s6   )  < < 0 0 ( / G G K K 9 : V V J J 7 . # ! * , K K , /j!1aSM<&H;)."K;(7BP\
#"D
LJ90% 	- 	-'@7 ((" 	 	5"
; r7   