
    g                        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
 d dlmZmZ d dl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 d d
lmZ d dlmZ d dlm Z m!Z! d dl"m#Z# d dl$m%Z%m&Z&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3 e'e%d                         Z4d Z5e%d             Z6d Z7d Z8e%d             Z9e%e&d                         Z:e%e'd                         Z;e%e&d                         Z<e%e&d                         Z=e%d             Z>e%d             Z?e%d             Z@e%e&d                         ZAe%d             ZBe%d             ZCe%d              ZDe%d!             ZEe%d"             ZFd# ZGe%d$             ZHe%e'd%                         ZIe%e&d&                         ZJe%d'             ZKe&e%d(                         ZLe%d)             ZMe%e&d*                         ZNe%d+             ZOe%d,             ZPe%d-             ZQe%d.             ZRe%d/             ZSe%d0             ZTe%d1             ZUe%d2             ZVe%d3             ZWe%d4             ZXe%d5             ZYe%d6             ZZe%d7             Z[e%d8             Z\d9S ):    )IRationaloopi)S)symbols)sign)explog)sechsinh)sqrt)	Piecewise)acosatancossintan)
DiracDelta)gamma)Integral	integrate)fu)XFAILslowtooslow)xkcybhamzntc                  F   t          t          t                    t          dt          z            z  t	          dt          z            z  t          dz  t          dz  z   z  dt          dz  t          z   dz   z  z  t                                        t                    rJ d S )N         )r   r
   r   r   r   hasr        h/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/integrals/tests/test_failing_integrals.pytest_issue_3880r0      s{     QAaCQqS1QTAqD[A1adQhQRlCSTVWXX\\]efffffffr.   c                      t          dd          } t          |  | dk     f| df          }t          t          |           |           |k    sJ d S )NxrT)realr   )r   r   r   r	   )r2   negabsxs     r/   test_issue_4212_realr5      sX    	D	!	!	!B"b1fDz22GT"XXr""g------r.   c                      t          t          t                    t                                        t                    rJ d S N)r   r	   r   r,   r   r-   r.   r/   test_issue_4212r8   $   s4     a!$$((2222222r.   c                     t          t          t                    dz  dt          t                    z
  z  t                    } t	          |           t          t          t                    z
  dz
  k    sJ | t          t          t          dz            dz  z  t          z   dz
  t          t          dz            dz  dz   z                                  k    sJ d S Nr)   r+   )r   r   r   r   r   r   expandfs    r/   test_issue_4511r>   -   s    #a&&!)q3q66z*A..Aa55AAJN""""!C!HHaK-!#a'#ac((A+/:BBDDDDDDDDr.   c            
          t          t          t          t          t          t          z
  t          z
            t          dt
          f          t          ddfd          t          ddf          t          j        k    sJ d S )Nr   r+   F)meijergr   r   r   r    r%   r   r   Halfr-   r.   r/   $test_integrate_DiracDelta_no_meijergrC   4   s    Yy1q5191bz +  +-.1IuF F FHI1ayR RUVU[\ \ \ \ \ \r.   c            
          t          t          t          t          t          t          z
  t          z
            t          dt
          f          t          ddf          t          ddf          t          j        k    sJ d S )Nr   r+   rA   r-   r.   r/   test_integrate_DiracDelta_failsrE   9   s     Yy1q5191bz +  +-.1I7 79:Aq	C CFGfM M M M M Mr.   c                     t          t          t          z  dt          z
  t          z  z  t          t
          t          z  z   t          t          dz  z  z   z  dt          dz  z   z  t          ddf                              t                    rJ d S Nr+   r)   r   )	r   r   r$   r&   r#   r!   r   r,   r   r-   r.   r/   test_issue_4525rH   A   so     !Q$!a%!+q1Q3w1a4/?@1q!t8LqRSUViXX\\]efffffffr.   c            	         t          t          dt          z            t          t          t                    z  z
  t          dt          z             t          t          t                    z  z   t          z  t          t          dt          z            z  z   z  t                                        t
                    rJ d S Nr+   )r   r   r   r
   r,   r   r-   r.   r/   test_issue_4540rK   H   s     	QqSAc!ffH	qs88)aAh
	!Ac!A#hhJ	.	0124 447CMMB B B B Br.   c                      t          t          t                    t          z  t                                        t
                    rJ d S r7   )r   r   r   r    r,   r   r-   r.   r/   test_issue_4891rM   Q   s8     QA&&**84444444r.   c                      t          t          dt          z  t          z            t          t           t          dz  z            z  t                                        t                    rJ d S Nr)   )r   r
   r!   r   r#   r,   r   r-   r.   r/   test_issue_1796arP   X   sQ     QqSUC1a4LL0!4488BBBBBBBr.   c                      t          t          dt          z  t          z            t          t           t          dz  z            z  t          t
           df                              t                    rJ d S Nr)   r   r   r
   r!   r   r#   r   r,   r   r-   r.   r/   test_issue_4895brT   ^   sW    QqSUC1a4LL01rc1+>>BB8LLLLLLLr.   c                      t          t          dt          z  t          z            t          t           t          dz  z            z  t          t
           t
          f                              t                    rJ d S rO   rS   r-   r.   r/   test_issue_4895crV   c   sW    QqSUC1a4LL01rc2,??CCHMMMMMMMr.   c                      t          t          dt          z  t          z            t          t           t          dz  z            z  t          dt
          f                              t                    rJ d S rR   rS   r-   r.   r/   test_issue_4895drX   h   sU    QqSUC1a4LL01a*==AA(KKKKKKKr.   c            	          t          t          dt          t          dz            dz  z             t          ddf                              t
                    rJ d S )Nr+      r)   i   )r   r   r   r   r,   r   r-   r.   r/   test_issue_4941r\   m   sO     a$qt**a-/001c2,??CCHMMMMMMMr.   c                     t          t          t                    t          t          dz
  z  z  t	          t                     z  t          t                    z  t          dt          f                              t                    rJ d S Nr+   r   )	r   r   r   r   r
   r   r   r,   r   r-   r.   r/   test_issue_4992r_   s   s`     Q!a!e*,sA2ww6qAAq":NNRRS[\\\\\\\r.   c            	          t          ddt          t          t                              z   z  t          t          dz  t          dz  f          } |                     t                    rJ d S )Nr+   r*      )r   r   r   r   r   r,   r   is    r/   test_issue_16396ard   y   sP    !QtCFF||^$q"Q$1o66AuuXr.   c                      t          t          t          t                    z  dt          t                    dz  z   z  t          dt          f          } |                     t                    rJ d S rG   )r   r   r   r   r   r,   r   rb   s    r/   test_issue_16396brf      sP    !CFF(Ac!ffaiK(1a*55AuuXr.   c                      t          t          t          t          t          z                      t          ddt          z  g          dt          z  k    sJ d S Nr   r)   )r   r
   r   r   r   r-   r.   r/   test_issue_16046ri      sA    SQqS]]Q1R4L11QrT999999r.   c                     t          t          dt          t                    z   dz  t	          t                    dz  z             t          t
           dz  t
          dz  f                              t                    rJ d S )Nr+   r)   )r   r   r   r   r   r   r,   r   r-   r.   r/   test_issue_15925ark      sc    qQx!mSVVaK7881rc!eRT:JKKOOPXYYYYYYYr.   c                  R   t          dt          t                    dz  z  t          t                    z  dz  dt          t                    z  t          t                    dz  z  dz  z             } t	          | t          dt
          dz  f          t          dd          k    sJ d S )Nr)      r   ra   r*   )r   r   r   r   r   r   r   r<   s    r/   test_issue_15925bro      s    c#a&&!)mCFF"Q&3q66	#a&&!)(;a'??@@AQAr!t%%!Q777777r.   c            	      ^   t          t          dt          t                    dz  z  t	          t                    z  dz  dt          t                    z  t	          t                    dz  z  dz  z             t          dt
          dz  fd                              t                    rJ d S )Nrm   r)   rn   r   ra   Tmanual)r   r   r   r   r   r   r,   r   r-   r.   r/   test_issue_15925b_manualrs      s    s3q6619}SVV3a7CFF3q66199Lq8PPQQQ1d4 4 447CMMB B B B Br.   c                      t          t          dt          z
            t          dt          z   dz            z  t          z  t          ddf          } |                     t                    rJ d S rG   r   r   r   r,   r   rb   s    r/   test_issue_15227rv      sW     	#ac((3!ax==(*Q1I66AuuXr.   c                      t          t          t          dz             t          t          t          z            z  t          t
          j        df          } |                     t                    rJ d S )N   r+   )	r   r   r   r   r   r   rB   r,   r   rb   s    r/   test_issue_14716ry      sP     	#a!e**SAYY&161~66AuuXr.   c                      t          t          t          ddt          z  t          z  z
            z  t          dt          f          } |                     t
                    rJ d S rG   )r   r   r   r"   r,   r   rb   s    r/   test_issue_14709ar{      sJ    !DQqSUOO#aAY//AuuXr.   c                      t          t          t          dz            t          t                    z  t                                        t
                    rJ d S rO   )r   r
   r   r   r,   r   r-   r.   r/   test_issue_14398r}      sC     QT3q66)1--11(;;;;;;;r.   c                      t          t          t          t                              t          dt          dz  f          } |                     t                    rJ d S rh   )r   r   r   r   r   r,   r   rb   s    r/   test_issue_14074r      sC    #c!ff++1bd|,,AuuXr.   c                      t          t          dt          z            t          dt          z            z
  t          z  t          dt          f          } |                     t
                    rJ d S )N   r)   r   )r   r   r   r   r,   r   rb   s    r/   test_issue_14078br      sS     	4!99T!A#YY&)Aq":66AuuXr.   c                      t          t          dt          z            dt          z
  z  t          ddf          } |                     t                    rJ d S r^   ru   rb   s    r/   test_issue_13792r      sF    	3qs88q1u%1ay	1	1AuuXr.   c                      t          t          t          t          dz  z
            t          ddf                              t
                    rJ d S Nr*   r   r+   r   r
   r    r   r,   r   r-   r.   r/   test_issue_11845ar      s@    QAXAq	2266x@@@@@@@r.   c                      t          t          t           t          dz  z
            t          ddf                              t
                    rJ d S r   r   r-   r.   r/   test_issue_11845br      sB    aR!Q$Y!Q3377AAAAAAAr.   c                      t          t          t          z
  t          dd          z  t          z  t          dt          f                              t
                    rJ d S )Nr)   r   )r   r#   r   r   r,   r   r-   r.   r/   test_issue_11813r      sH    !a%(2q//1!3aAY??CCHMMMMMMMr.   c                      t          t          t                    dz  t          ddf                              t                    rJ d S )Nr)   r   r+   )r   r   r   r,   r   r-   r.   r/   test_issue_11254cr      s<    a!aAY//33H=======r.   c                      t          t          t          dz  dt          dz  z  z             t                                        t                    rJ d S r:   )r   r   r   r,   r   r-   r.   r/   test_issue_10584r      sD    adQq!tVm,,a0044X>>>>>>>r.   c            
          t          t          t          t          t          dz  t          dz  z   t
          dz  z             z             t
                                        t                    rJ d S rO   )r   r   r   r   r    r%   r,   r   r-   r.   r/   test_issue_9101r      sV    QadQTkAqD&8!9!99::A>>BB8LLLLLLLr.   c                      t          t          t          t          t          dz  z  t          t          z  z   t
          z             dz  z  t                                        t                    rJ d S )Nr)   r*   )r   r   r   r#   r!   r   r,   r   r-   r.   r/   test_issue_7147r      sS    4!Q$1q 011144a88<<XFFFFFFFr.   c                      t          t          t          dz  t          dz  t          dz  z
  z            t                                        t
                    rJ d S rO   )r   r   r#   r   r,   r   r-   r.   r/   test_issue_7109r      sI    adAqD1a4K01115599(CCCCCCCr.   c                  J   t          dt          dt          z  z
  dk     fdt          z  dt          z  dz   dz  z  t          dt          z  z
  dk    f          } t          t	          | t          dt
          f          dt          z  z
                                            dk    sJ d S )	Nr   g    @}@gW?j*@gVL?gףp=
?r)   g    @gHz>)r   r'   r   absr   r   evalfr<   s    r/   ,test_integrate_Piecewise_rational_over_realsr      s    	
Z]9Ja9OP	"	k!me3a7	7Z]9Ja9OP	R 	RA 	!aBZ((:b=8??AABBdJJJJJJr.   c                      t          t          t          dt          dz  z
            z  t                                        t                    rJ d S )N	   r)   )r   r   r   r,   r   r-   r.   r/   test_issue_4311_slowr     s@     3qAv;;**..x8888888r.   c                      t          dd          } t          d| t          t                    z  z   dz  t          ddt          z  f          dt          z  t          d| dz  z
            z  k    sJ d S )Nr#   T)positiver+   r   r   r)   )r   r   r   r   r   r   )r#   s    r/   test_issue_20370r     sl    d###Aa!c!ff*nr)Aq!b&>::q2vQQRTUQUX?VWWWWWWr.   c                      t          t          dt          z            t          dz   z  t                                        t                    rJ d S rJ   ru   r-   r.   r/   test_polylogr     sA     QqS1q5)1--11(;;;;;;;r.   c                      t          t          dt          z            t          dz   z  t          d                              t                    rJ d S )Nr+   Trq   ru   r-   r.   r/   test_polylog_manualr     sF     QqS1q5)1T:::>>xHHHHHHHr.   N)]sympy.core.numbersr   r   r   r   sympy.core.singletonr   sympy.core.symbolr   $sympy.functions.elementary.complexesr	   &sympy.functions.elementary.exponentialr
   r   %sympy.functions.elementary.hyperbolicr   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr   r   r   r   r   'sympy.functions.special.delta_functionsr   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   r   sympy.simplify.fur   sympy.testing.pytestr   r   r   	sympy.abcr   r   r   r    r!   r"   r#   r$   r%   r&   r'   r0   r5   r8   r>   rC   rE   rH   rK   rM   rP   rT   rV   rX   r\   r_   rd   rf   ri   rk   ro   rs   rv   ry   r{   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r-   r.   r/   <module>r      ss   5 4 4 4 4 4 4 4 4 4 4 4 " " " " " " % % % % % % 5 5 5 5 5 5 = = = = = = = = > > > > > > > > 9 9 9 9 9 9 : : : : : : P P P P P P P P P P P P P P > > > > > > 9 9 9 9 9 9 ; ; ; ; ; ; ; ;             6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 	g g  	g
. . . 3 3 3E E E\ \ \
 M M M g g  g
 B B 	 B 5 5  5
 C C  C M M M N N N L L L N N  N ] ] ]
   
   
 : : : Z Z Z8 8 8
 B B B
   	         < <  <           A A A B B B N N N > > > ? ? ? M M M G G G D D D K K K 9 9 9 X X X
 < < <
 I I I I Ir.   