
    \h7                     r   S SK Jr  S SKJr  S SKJrJrJr  S SKJ	r	J
r
Jr  S SKJrJr  S SKJrJr  S SKJrJrJr  S SKJrJrJrJr  S S	KJr  S S
KJr  S SKJ r J!r!J"r"J#r#J$r$J%r%  S SK&J'r'J(r(J)r)J*r*  S SK+J,r,  S SK-J.r.  S SK/J0r0  S SK1J2r2  S SK3J4r4  S SK5J6r6  S SK7J8r8J9r9J:r:  S SK;J<r<J=r=  S SK-J>r>  S SK?J@r@  \" S5      u  rArBrCrD\" S5      rES rFS rGS rHS rIS rJS rKS rLS  rMS! rNS" rOS# rPS$ rQS% rRS& rSS' rTS( rU\<S) 5       rVS* rWS+ rXS, rYS- rZS. r[S/ r\S0 r]S1 r^\=S2 5       r_S3 r`S4 raS5 rbS6 rcS7 rd\=S8 5       reS9 rfg:);    )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)	integrate)Szx,y,z,nufc            	         [        [        [        -  [        5      [        1:X  d   e[        S[        [        -   -  [        5      [        1:X  d   e[        [        [        5      [        5      [        [        5      [        1:X  d   e[        [        [        5      [	        [        [        5      5      -  [        5      [        [        5      [        [        5      [	        [        [        5      5      [        1:X  d   e[        [        [        [        [        5      [        -  5      -  [        5      [        [        [        [        5      -  5      [        [        [        5      1:X  d   e[        [        [        SS5      -  [	        [        [        5      5      -  [        5      [        [        5      [        [        SS5      -  [	        [        [        5      5      [        1:X  d   e[        [        [        5      [        5      [        [        [        5      1:X  d   e[        [        [        [        5      [        5      [        5      [        [        [        5      [        [        [        5      [        5      1:X  d   e[        [        [        5      [        [        [        5      [        5      -  [        5      [        [        [        5      [        [        [        5      [        5      [        [        [        5      [        5      1:X  d   eg )N      6   )r)   xyr   r   r   r   r	   r0   r   r        [/var/www/auris/envauris/lib/python3.13/site-packages/sympy/integrals/tests/test_heurisch.pytest_componentsr:      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))$s1v,6:	QHQO#T#a&\156 6 6 adA	
AaD	  j1q)1-	
AaD*QqT1%&' ' 'ad4!a=(!,	
AaD*QqT1%z!A$':;< < <r8   c                      [        [        [        [        [        [        [        [        [        5      -  5      -  5      -  [        5      [        5      (       d   eg N)
isinstancer.   r5   r   r$   r7   r8   r9   test_issue_10680r>   /   s7    i3q#aQi.'8#9 9!<hGGGGr8   c            
          [        [        [        [        [	        [        5      5      -  5      [        SS45      S:X  d   eg )Nr2   r   )r.   r   r5   r   absr7   r8   r9   test_issue_21166rB   3   s.    S4A<(1b!*5:::r8   c                     [        S[        5      [        :X  d   e[        [        [        5      [        S-  S-  :X  d   e[        [        S-  [        5      [        S-  S-  :X  d   e[        [        [        5      [        [        -  :X  d   eg )Nr2      r3      )r*   r5   r+   r6   r7   r8   r9   test_heurisch_polynomialsrF   7   sl    Aq>QAq>QT!V###ArE1Br)))Aq!QqS(((r8   c                  `   [        S[        -  [        5      [        [        5      :X  d   e[        SS[        -   -  [        5      [        [        S-   5      :X  d   e[        S[        [        [        5      -   -  [        5      [        [        [        [        5      -   5      :X  d   e[        S[        S-  -  S[        S-  -  S-
  -  [        5      S[        S[        S-  -  S-
  5      -  S-  S[        S[        S-  -  S-   5      -  S-  4;   d   e[        S[        S-  -  S[        S-  -  S-   -  [        5      S[        S[        S-  -  S-   5      -  S-  :X  d   e[        S[        S-  -  [        5      S[        -  :X  d   e[        S[        S-  -  [        5      SS[        S-  -  -  :X  d   eg )	Nr2   rD            r@      )r*   r5   r   r   r6   r7   r8   r9   test_heurisch_fractionsrM   ?   s}   AaCs1v%%%Aq1uIq!SQZ///Aq3q6zNA&#a#a&j/999 AadF	!Q$
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:---r8   c                     [        [        [        5      [        5      [        [        [        5      -  [        -
  :X  d   e[        [        S[        -  5      [        5      [        * [        [        S5      -  -   [        [        [        5      -  -   :X  d   e[        [        [        S-  5      [        5      [        [        [        S-  5      -  S[        -  -
  S[        -  [        [        5      -  S[        -  -
  4;   d   eg )N   rD   )r*   r   r5   r7   r8   r9   test_heurisch_logrP   P   s    CFA!CF(Q,...C!Ha QB3q6MAc!fH$<<<<C1Iq!aAqD	kAaC&71SVac9I%JJJJr8   c            
         [        [        [        5      [        5      [        [        5      :X  d   e[        [        [        * 5      [        5      [        [        * 5      * :X  d   e[        [        S[        -  5      [        5      [        S[        -  5      S-  :X  d   e[        [        [        [        5      -  [        5      [        [        [        5      -  [        [        5      -
  :X  d   e[        [        [        [        S-  5      -  [        5      [        [        S-  5      S-  :X  d   e[        [        [        S-  * 5      [        5      b   e[        S[        -  [        5      S[        -  [        S5      -  :X  d   e[        [        S[        -  -  [        5      [        S[        -  -  [        S5      -  S[        -  [        S5      S-  -  -
  :X  d   e[        [	        [        [
        -  [        -  [        SS4[
        SS45      R                  [        5      [        [        [
        -  -  [        -  [
        S-   -  :X  d   e[        [        [        [
        -  [
        SS45      R                  [
        5      [        [
        -  [        [        5      -  :X  d   e[        [
        5      * [        [        [        -
  5      [        [
        [        [        [        -
  5      -  5      -  [        [
        [        [        [        -
  5      -  5      -
  -  n [        [        [
        5      [        [
        * [        [        [        -
  5      -  5      -  [
        5      U :X  d   eg )Nr3   rD   rK   r2   rO   )
r*   r   r5   r   r$   zr6   functionr   r   )antis    r9   test_heurisch_exprU   V   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:::r8   c            	         [        [        [        5      [        5      [        [        5      * :X  d   e[        [        [        [        5      -  S-   [        5      [        [        [        [        5      -  -
  :X  d   e[        [        [        5      [        5      [        [        5      :X  d   e[        [        [        5      [        5      [        S[        [        5      S-  -   5      S-  [        [        [        5      [        -   5      [        [        -  -   [        [        [        5      [        -
  5      [        [        -  -
  4;   d   e[        [        [        5      [        [        5      -  [        5      [        [        5      * [        [        5      -  :X  d   e[        [        [        5      [        [        5      -  [        5      [        [        5      * [        [        5      -  :X  d   e[        [        [        5      [        [        5      -  [        5      [        [        5      S-  S-  [        [        5      S-  * S-  4;   d   e[        [        [        5      [        [        5      -  [        5      [        [        [        5      5      :X  d   e[        [        [        S[        -  5      -  [        5      [        S[        -  5      S-  [        [        S[        -  5      -  S-  -
  :X  d   e[        S[        -  S-  [        S-  -  [        [        5      -  [        5      S[        -  S-  [        S-  [        [        5      -  S[        [        5      -  -
  S[        -  [        [        5      -  -   -  :X  d   e[        [        [        S-  5      [        [        S-  5      -  [        5      S[        -  [        S[        S-  -
  5      [        [        S-  5      -  -
  [        S[        S-  -
  5      [        [        S-  5      -  -   [        [        [        S-  5      -  [        [        S-  5      -  -   :X  d   e[        [        [        5      [        [        5      S-  S-   -  [        5      [        [        [        5      5      * :X  d   e[        S[        [        5      S-   -  [        5      S[        S5      -  [        [        S5      [        [        S-  5      -  S-  5      -  S-  :X  d   e[        S[        [        5      -  [        [        5      -  [        [        5      S-  S-   -  [        5      [        [        S5      [        [        5      -  S-
  5      [        [        S5      [        [        5      -  S-   5      -
  :X  d   e[        S[        [        5      -  [        5      S[        [        [        S-  5      5      -  :X  d   eg )Nr2   rD      1   rL      rO   )r*   r   r5   r   r
   r   r   r   r6   r   r   r   r   r   r   r7   r8   r9   test_heurisch_trigonometricrZ   j   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'	$tAws1Q3x7G7I2J(J1(LLLLAc!fHSVOSVQY]3Q74QA
A <DGCFNQ&'<( ( ( ( Ad1gIq!QtD1I%6666r8   c                     [        [        [        5      [        5      [        [        5      :X  d   e[        [        [        5      [        5      [        [        5      :X  d   e[        [        [        [        5      -  [        5      [        [        [        5      -  [        [        5      -
  :X  d   e[        [        [        [        5      -  [        5      [        [        [        5      -  [        [        5      -
  :X  d   e[        [        [	        [        S-  5      -  [        5      [        S-  [	        [        S-  5      -  S-  [	        [        S-  5      -   [        [        S[        S-  -   5      -  S-  -
  :X  d   eg NrD   rL   )r*   r   r5   r   r   r   r7   r8   r9   test_heurisch_hyperbolicr]      s   DGQ47***DGQ47***Ad1gIq!QtAwYa%8888Ad1gIq!QtAwYa%8888	%!*aqDqsOA-ac
:QtA1H~=Ma=OOP P Pr8   c            	         [        [        [        5      [        [        5      -  [        5      [        [        5      [        [        5      -  S-  [        [        5      [	        [        5      -  S-  -
  :X  d   e[        [        [        [        [        * 5      -  5      [        5      S[        -  [	        [        [        [        * 5      -  5      -  [        [        * 5      -  S[        [        [        [        * 5      -  5      -  -
  :X  d   eg NrD   )r*   r   r5   r   r   r   r7   r8   r9   test_heurisch_mixedr`      s    CF3q6M1%QAq3q6#a&=?)JJJJC$r(
OQ'1Q3s1T1"X:+>tQBx+G!CPQRVXYWYRZPZOJ[+[[[[r8   c            
      x   [        S[        [        5      -  [        5      S[        [        5      -  :X  d   e[        S[        [        5      S-  -  [        5      S[        [        5      -  :X  d   e[        [        [        5      S-  [        5      S[        [        5      S-  -  S-  :X  d   e[        [        [        5      [        [	        [        5      5      -  [        5      S[        [	        [        5      5      S-  -  S-  :X  d   e[        S5      n [        [        U [        [        5      -  5      [        5      SU S-  -  [        U [        [        5      -  5      -  S[        [        5      -  [	        U [        [        5      -  5      -  U -  -
  :X  d   e[        [        U [        [        5      -  5      [        5      [        S[        [        5      -  [	        [        [        5      U -  5      -  U -  S[        [        [        5      U -  5      -  U S-  -  -   [        U S5      4S5      :X  d   e[        SS	S
9n [        [        U [        [        5      -  5      [        5      SU S-  -  [        U [        [        5      -  5      -  S[        [        5      -  [	        U [        [        5      -  5      -  U -  -
  :X  d   eg )Nr2   rD   rO   rK   rH   r6   r   )r   TTpositive)	r*   r   r5   r   r   r   r+   r   r   r6   s    r9   test_heurisch_radicalsre      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	$q'	#aQi. "3# # # #r8   c                  n   [        [        [        5      [        5      [        [        [        5      -  [        [        S-  * 5      [	        [
        5      -  -   :X  d   e[        [        [        S-  * 5      [        [        5      -  [        5      [	        [
        5      [        [        5      S-  -  S-  :X  d   eg r\   )r*   r#   r5   r   r   r
   r7   r8   r9   test_heurisch_specialrg      sy    CFA!CF(S!Q$ZR-@"@@@@CAJs1v%q)T"Xc!fai-?!-CCCCr8   c            
         [        S[        [        -   -  [        5      [        [        [        -   5      :X  d   e[        S[        [	        S5      -   -  [        5      [        [        [	        S5      -   5      :X  d   e[        [        [        [        [        [        -   [        -   5      [        5      [        5      5      [        [        [        -   [        -   5      :X  d   eg Nr2   rD   )r*   r5   r6   r   r   r(   r   rR   r7   r8   r9   test_heurisch_symbolic_coeffsrj      s    Aq1uIq!SQZ///Aq47{OQ'3q47{+;;;;D#a!eai.!4a89SQ^KKKr8   c            
         [        S5      n [        S[        S-  U -   -  [        5      [        [	        [        [        U * 5      -
  5      S[        U * 5      -  -  [	        [        [        U * 5      -   5      S[        U * 5      -  -  -
  [        U S5      4S[        -  S45      :X  d   e[        SSS9n [        S[        S-  U -   -  [        5      [        [        [        U 5      -  5      [        U 5      -  :X  d   eg )Nr6   r2   rD   r   r@   Trb   )r   r+   r5   r   r   r   r   r   rd   s    r9   "test_heurisch_symbolic_coeffs_1130rl      s    sAAq!taxL!,	T1"X$r(
#c!dA2h,&748&DDq!H1d|1    	sT"AAq!taxL!,aQia1HIIIr8   c                     [        [        SS[        S-  -  -   5      [        / S9[        [        SS[        S-  -  -   5      -  S-  [        S5      [        [        S5      [        -  5      -  S-  -   :X  d   e[        [        SS[        S-  -  -
  5      [        / S9[        [        SS[        S-  -  -
  5      -  S-  [        S5      [	        [        S5      [        -  5      -  S-  -   :X  d   e[        S[        SS[        S-  -  -   5      -  [        / S9[        S5      [        [        S5      [        -  5      -  S-  :X  d   e[        S[        SS[        S-  -  -
  5      -  [        / S9[        S5      [	        [        S5      [        -  5      -  S-  :X  d   e[        [        S[        S-  -  5      [        / S9[        S[        -  5      [        [        S5      [        -  5      -  S-  :X  d   e[        S[        SS[        S-  -  -
  5      -  [        / S9[	        [        [        SS	5      -  5      S-  :X  d   e[        S[        SS[        S-  -  -   5      -  [        / S9[        [        [        SS	5      -  5      S-  :X  d   e[        S[        S	[        S-  -  S-
  5      -  [        / S9[        S	5      [        S	[        -  [        S	5      [        S	[        S-  -  S-
  5      -  -   5      -  S	-  :X  d   eg )
Nr2   rW   rD   hints   i	   rL   rO   )
r*   r   r5   r   r   r   r
   r#   r	   r   r7   r8   r9   test_heurisch_hackingrr      s   DQq!tV$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 9r8   c                  D    [        [        [        5      [        5      b   eg r<   )r*   r0   r5   r7   r8   r9   test_heurisch_functionrt      s    AaD!$$$r8   c                     [        [        [        5      [        5      n [        [        [        5      U -  [        5      [        [        5      S-  S-  :X  d   e[        [        [        5      S-  U -  [        5      [        [        5      S-  S-  :X  d   e[        U [        [        5      -  [        5      [	        [        [        5      5      :X  d   eg )NrD   rO   )r   r0   r5   r*   r   )dfs    r9   !test_heurisch_function_derivativerw      s     
adABAaDGQ1Q4719,,,AaD!GBJ"adAgai///BqtGQ3qt9,,,r8   c            	      n   S[         [        -   -  n [        U [        5      [        [        [         -   5      :X  d   eS[         [        -
  -  n [        U [        5      [        [        [         -
  5      * :X  d   eS[         [        -
  [         [        -   -  -  n [        U [        5      [	        [        [        [         -
  5      * S[         -  -  [        [        [         -   5      S[         -  -  -   [        [         S5      4S[        -  S45      :X  d   e[        [        S-  [         [        -
  [         [        -   -  -  5      n [        U [        5      [        [        [        S-  * [        S-  [         S-  -
  -  5      -  [         S-  [        [        S-  * [        S-  [         S-  -
  -  5      -  [        -  -
  :X  d   eg )Nr2   rD   r   T)r6   r5   r+   r   r   r   r   )r0   s    r9   test_heurisch_wrapperry      sb   	1q5	AAq!SQZ///	1q5	AAq!c!a%j[000	AEAE?AAq!Y
a!e*ac	SQZ1-	-r!Qx81Q3+&G G G G 	QTAEAE?#$AAq!QtQTE1a4!Q$;,?'@%@d4Aq!tad{#$$Q&&' ' ' 'r8   c                      [        S[        S[        [        5      S-  -   -  -  [        5      [        [        [        5      5      :X  d   eg ri   )r*   r5   r   r   r7   r8   r9   test_issue_3609r{      s5    AqAA	M*+Q/4A<???r8   c                     S n [         S-  S[         S-  -  -
  S[         S-  -  -
  S[         -  -   S-
  [         S-  S[         S-  -  -   S[         S-  -  -   S[         S-  -  -   -  nSS[         S-  -  -   S[         -  -   S	[         S	-  -  -   [         S
-  S[         S	-  -  -   S[         -  -   -  [        [         5      -   nU " [        [        U[         5      5      [         5      U:X  d   eg )Nc                     U R                   (       a:  [        U R                   Vs/ s H  o"R                  U5      (       d  M  UPM     sn6 $ U $ s  snf r<   )is_Addr   argshas)exprr5   args      r9   
drop_const"test_pmint_rat.<locals>.drop_const  s:    ;;B#ggaj#BCCK Cs   AArW      rL   rD      rI   rJ   rO   rH   )r5   r   r'   r*   )r   r0   gs      r9   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6r8   c                  .   [         [        [         5      -
  [        [         5      S-  -  [        [         5      -   n [         S-  * S-  [         [        [         5      -  -
  [        [        [         5      S-  S-   5      S-  -   n[        U [         5      U:X  d   eg )NrD   r2   )r5   r   r   r*   r0   r   s     r9   test_pmint_trigr     sp    	
SVs1vqy 3q6)A	
Aa!CF(SQQ/11AAq>Qr8   c                     S[         -   [         [        [         5      -  -   [         [        [         5      -   [        [         5      -   S-
  -  [         [        [         5      -   [        [         5      -   S-  -  [         -  n [        [         [        [         5      -   [        [         5      -   5      S[         [        [         5      -   [        [         5      -   -  -   n[        [	        U [         5      5      U:X  d   eg ri   )r5   r   r   r'   r*   r   s     r9   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'''r8   c                      [        [        S-  * 5      [        [        5      -  [        [        5      S-  [        [        5      S-  -
  [        [        5      -
  S-   -  n [        [        5      [        [        [        5      S-
  5      -  S-  [        [        5      [        [        [        5      S-   5      -  S-  -
  [        [        5      S[        [        5      -  S-
  -  -
  n[        [        U [        5      5      U:X  d   eg )NrD   rO   r2   r   rL   )r   r5   r#   r   r
   r   r'   r*   r   s     r9   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'''r8   c                      [        [        5      n [        [        [        5      -  [        -
  [        [        [        5      -  -   n[        U [        5      U:X  d   eg r<   )r   r5   r*   r   s     r9   test_pmint_LambertWr   "  s>    A	(1+AhqkM)AAq>Qr8   c                     [        [        S-   [        5      [        [        [        5      -  n [        [        [        5      -  [        [        [        [        5      5      -
  n[	        U [        5      U:X  d   e[        [        [        [        5      -  [        [        [        S-   [        5      -  -
  [        -  n [        [        [        5      n[	        U [        5      U:X  d   e[        [        S-   [        5      [        [        [        5      -  n [        [        [        5      -  [        [        [        [        5      5      -
  n[	        U [        5      U:X  d   eg )Nr2   )r   nur5   r   r*   r"   r   s     r9   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r8   c                      [         [        [        [         5      -  [        [        S[         -  5      -  n S[         -  [        [        [         5      -  [        [        S-
  S[         -  5      -  S-  [         [        [        S-
  [         5      -  [        [        S[         -  5      -  S-  -   n[	        U [         5      U:X  d   e[         [        [        [         5      -  [        [        S[         -  5      -  n S[         -  [        [        [         5      -  [        [        S-
  S[         -  5      -  S-  [         [        [        S-
  [         5      -  [        [        S[         -  5      -  S-  -
  n[	        U [         5      U:X  d   eg )NrD   rK   r2   rO   rH   )r5   r   r   r!   r*   r    r   s     r9   test_pmint_bessel_productsr   :  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r8   c                     S n SU " [         5      S[        U " [         5      5      [         U " [         5      -   -  -   -  -   SU " [         5      -   -  [         U " [         5      -   -  n[        [         [        [	        [         5      5      -   5      [        [        [	        [         5      5      5      -   n[        U[         5      U:X  d   eg )Nc                 *    [        [        U 5      5      $ r<   )r   r   )r5   s    r9   omega%test_pmint_WrightOmega.<locals>.omegaH  s    Ar8   r2   rD   )r5   r   r   r   r   r   r*   )r   r0   r   s      r9   test_pmint_WrightOmegar   G  s      
U1XSq]a%(l;;<	<q58|LaRWXYRZl[AAQ  !CQ(8$99AAq>Qr8   c                      [        [        SS[        S-  -  -   5      [        / S9S[        -  [        S[        S-  -  S-   5      -  S[        S[        -  5      -  -   :X  d   eg )Nr2   g      ?rD   rn         ?g      ?)r*   r   r5   r   r7   r8   r9   test_RRr   Q  s_     DT!Q$Y'"5Ad419q=!!Cc!e$445 5 5r8   c                     ^ [        S5      u  n m[        S5      " U 5      nU4S jn[        U" U5      U5      n[        U" U 5      U 5      nXCR                  X5      :X  d   eg )Nzt RrR   c                 2   > U [        TS-  U S-  -
  5      -  $ r_   r   )r5   Rs    r9   r0   test_issue_22527.<locals>.fe  s    adQTk"""r8   )r   r   r.   subs)trR   r0   UzUtr   s        @r9   test_issue_22527r   b  sW    6?DAqaA#	1Q4	B	1Q4	Br8   c                  b   [        SSS9n [        [        5      [        S[        -   S-  5      -  S-  n[        [        [        * U S-  -  S-  5      U SS45      U[        U-  -
  :X  d   e[        [        S-  * SS[        -
  S-  -  -  5      n[        U[        / S9b   e[        U S-  * SS[        -
  S-  -  -  5      n[        X/ S9b   e[        [        5      [        S[        -   S-  5      -  S-  n[        [        [        * [        S-  -  S-  5      [        SS45      U[        U-  -
  :X  d   eg )NrTrealr2   rD   r   rn   )	r   r   r
   r#   r   r.   r   r5   r*   )r   as     r9   %test_heurisch_complex_erf_issue_26338r   l  s    $ARa!eQY!AS!AqD^aAY/1qs7:::QTE1a!eaZ< !AAq#+++QTE1a!eaZ< !AA#+++Ra!eQY!AS!AqD^aAY/1qs7:::r8   c            	         [        S5      n [        SSSS9u  pp4[        [        U* U-  5      //5      n[	        SS5      nSSUSS	S
S/u  pxppnXzU-  S[        X8-
  * U-  5      -
  -  X-  S[        X8-
  * U-  5      -
  -  -   -  nXzU-  [        X8-
  * U-  5      -  [        X-
  U-  5      S-
  -  X-  [        X8-
  * U-  5      -  [        X-
  U-  5      S-
  -  -   -  n[        SX8:  4U[        X:*  X9:  5      4XU:*  45      n[        U " U5      U5      n[        X" U5      -  //5      nXUR                  X45      S-  -  UR                  UR                  UR                  5      R                  X45      -  n[        US   USU45      nUc   eg )NZ0zk01 k10 t sTr   rc   S   d   r   2   g333333?rD   x   r2   r   r@   )r   r   r&   r   r	   r   r%   r   r   lhsrhsr.   )r   k01k10r   sm_83r   bcder0   r   AIF_btfAIF_atfAIF_symaif_eqf_vec	integrandsolutions                        r9   test_issue_15498r   y  s   	$BMtDNCacT!VA
2s
C #sBQ<Q1q1a#hqj/)*QS!cAE(1*o2E-FFGG1S15!_$c15!)nq&8 
CaeHQJaeQY!!345 6GAE
Wc!&!%.@$AGRSVCTUG1wFSAYK=!E&&,""5::fjj&**#E#J#J1#PPI11ay1Hr8   c                  |   [         [        SS5      -  [        [         5      -  n S[         [        S5      S-  -  -  [        [         5      -  S-  S[         [        S5      S-  -  -  S-  -
  n[	        U [         5      U:X  d   e[        U [         5      U:X  d   e[        U [         SS45      [        S5      * S-  :X  d   eg )NrL   rO   rW   rq   rX   r   r2   )r5   r	   r   r/   r*   r.   )r   rT   s     r9   test_heurisch_issue_26930r     s    8Aq>!#a&(IQ1a[=Q!Aa!A$q&kM"$44DIq!T)))Y"d***YAq	*qteBh666r8   c            
         [        SSSS9u  pn[        SSS9nU* U-  [        U * US-  -  [        U5      U-  -
  5      -  nX2-  [        U * US-  -  [        U5      U-  -   5      -  n[        XB5      [        XR5      -   nU* [        U * US-  -  5      -  [        [        U5      U-  5      -  SU -  -  U[        U * US-  -  5      -  [        [        U5      * U-  5      -  SU -  -  -   [        [        5      U-  [        U5      -  [        USU -  -  5      -  [        [        U 5      U-  [        U5      S[        U 5      -  -  -
  5      -  SU [        S5      S-  -  -  -  -   [        [        5      U-  [        U5      -  [        USU -  -  5      -  [        [        U 5      U-  [        U5      S[        U 5      -  -  -   5      -  SU [        S5      S-  -  -  -  -   nUR                  S	S
9R                  5       U:X  d   eg )Nza, b, xTr   Cr   rD   rL   rO   F)r*   )	r   r   r   r$   r
   r#   r/   doitexpand)r   r   r5   r   i1i2iress           r9   test_heurisch_issue_26922r     s   idT:GA!$A
Ac1"QT'DGAI%&	&B	
S!AqD4719$%	%B(2/)A	
3r!Q$w<DGAI&!,
C1a4L.d1gXaZ
(!A#
.	/
r(1*T!W
SAaC\
)#d1gai$q'1T!W9:M.M*N
NPQRSVWXYVZ[\V\R]P]
^	_ r(1*T!W
SAaC\
)#d1gai$q'1T!W9:M.M*N
NPQRSVWXYVZ[\V\R]P]
^	_  6656!((*c111r8   N)gsympy.concrete.summationsr   sympy.core.addr   sympy.core.functionr   r   r   sympy.core.numbersr   r	   r
   sympy.core.relationalr   r   sympy.core.symbolr   r   &sympy.functions.elementary.exponentialr   r   r   %sympy.functions.elementary.hyperbolicr   r   r   r   (sympy.functions.elementary.miscellaneousr   $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.   sympyr/   r5   r6   rR   r   r0   r:   r>   rB   rF   rM   rP   rU   rZ   r]   r`   re   rg   rj   rl   rr   rt   rw   ry   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r7   r8   r9   <module>r      sR   )  < < 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"
; " 7 72r8   