
    Rie                     *   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#m$Z$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$d          e#d                         Z4e#d             Z5e#d             Z6e#d             Z7e#e%d                         Z8e#e%d                         Z9e#e%d                         Z:e#e%d                         Z;e#d             Z<e#d             Z=e#d             Z>e#e%d                         Z?e#d             Z@e#d             ZAe#d             ZBe#d             ZCe#d              ZDe#e%d!                         ZEe#d"             ZFe#e%d#                         ZGe#e%d$                         ZHe#d%             ZIe%e#d&                         ZJe#d'             ZKe#e%d(                         ZLe#d)             ZMe#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             ZZd7S )8    )IRationaloopi)S)symbols)sign)explog)sechsinh)sqrt)	Piecewise)acosatancossintan)
DiracDelta)gamma)Integral	integrate)XFAILSKIPslowskipON_CI)xkcybhamzntzToo slow for @slowc                  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        Llib/python3.11/site-packages/sympy/integrals/tests/test_failing_integrals.pytest_issue_3880r1      s{     QAaCQqS1QTAqD[A1adQhQRlCSTVWXX\\]efffffffr/   c                      t          t          t                    t                                        t                    rJ d S N)r   r	   r   r-   r   r.   r/   r0   test_issue_4212r4      s2    a!$$((2222222r/   c                  Z   t          t          t                    dz  dt          t                    z
  z            t          t          t                    z
  dt          t                    z
  t          z   dt	          t
          j        t          z            dz  dz   z  t          z   fv sJ d S )Nr*   r,   )r   r   r   r   r   r   Halfr.   r/   r0   test_issue_4511r8   "   s    
 SVVQY!c!ff*-..1s1vv:q3q66zA~QVQJ"Q&'!+3- - - - - - -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,   )r   r   r   r!   r&   r   r   r7   r.   r/   r0   test_integrate_DiracDelta_failsr:   +   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$   r"   r    r-   r   r.   r/   r0   test_issue_4525r=   2   so     !Q$!a%!+q1Q3w1a4/?@1q!t8LqRSUViXX\\]efffffffr/   c            	         t           rt          d           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 )NToo slow for CI.r,   )r   r   r   r   r   r
   r-   r   r.   r/   r0   test_issue_4540r@   9   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 r3   )r   r   r   r!   r-   r   r.   r/   r0   test_issue_4891rB   D   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$   r-   r   r.   r/   r0   test_issue_1796arE   K   sQ     QqSUC1a4LL0!4488BBBBBBBr/   c                      t          t          dt          z  t          z            t          t           t          dz  z            z  t          t
           df                              t                    rJ d S Nr*   r   r   r
   r"   r   r$   r   r-   r   r.   r/   r0   test_issue_4895brI   Q   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 rD   rH   r.   r/   r0   test_issue_4895crK   V   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 rG   rH   r.   r/   r0   test_issue_4895drM   [   sU    QqSUC1a4LL01a*==AA(KKKKKKKr/   c            	          t           rt          d           t          t          dt	          t
          dz            dz  z             t
          ddf                              t                    rJ d S )Nr?   r,      r*   i   )r   r   r   r   r   r   r-   r   r.   r/   r0   test_issue_4941rQ   `   sf      !   a$qt**a-/001c2,??CCHMMMMMMMr/   c                     t          t          t                    t          t          dz
  z  z  t	          t                     z  t          t                    z  t          dt          f                              t                    rJ d S Nr,   r   )	r   r   r   r   r
   r   r   r-   r   r.   r/   r0   test_issue_4992rT   h   s`     Q!a!e*,sA2ww6qAAq":NNRRS[\\\\\\\r/   c            	          t          ddt          t          t                              z   z  t          t          dz  t          dz  f          } |                     t                    rJ d S )Nr,   r+      )r   r   r   r   r   r-   r   is    r0   test_issue_16396arY   n   sP    !QtCFF||^$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 r<   )r   r   r   r   r   r-   r   rW   s    r0   test_issue_16396br[   t   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/   r0   test_issue_16046r^   z   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/   r0   test_issue_15925ar`      sc    qQx!mSVVaK7881rc!eRT:JKKOOPXYYYYYYYr/   c            	         t           rt          d           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                              t                    rJ d S )Nr?   r*      r   rV   )
r   r   r   r   r   r   r   r   r-   r   r.   r/   r0   test_issue_15925brd      s      !   s3q6619}SVV3a7CFF3q66199Lq8PPQQQ1' ''*s8}}5 5 5 5 5r/   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 )Nrb   r*   rc   r   rV   Tmanual)r   r   r   r   r   r   r-   r   r.   r/   r0   test_issue_15925b_manualrh      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           rt          d           t          t          dt          z
            t          dt          z   dz            z  t          z  t          ddf          } |                     t                    rJ d S )Nr?   r,   r*   r   )r   r   r   r   r   r-   r   rW   s    r0   test_issue_15227rj      sn      !   #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   r7   r-   r   rW   s    r0   test_issue_14716rm      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 r<   )r   r   r   r#   r-   r   rW   s    r0   test_issue_14709aro      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 rD   )r   r
   r   r   r-   r   r.   r/   r0   test_issue_14398rq      sC     QT3q66)1--11(;;;;;;;r/   c                      t          t          t          t                              t          dt          dz  f          } |                     t                    rJ d S r]   )r   r   r   r   r   r-   r   rW   s    r0   test_issue_14074rs      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   rW   s    r0   test_issue_14078brv      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 rS   r   r   r   r-   r   rW   s    r0   test_issue_13792ry      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/   r0   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/   r0   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$   r   r   r-   r   r.   r/   r0   test_issue_11813r      sH    !a%(2q//1!3aAY??CCHMMMMMMMr/   c                      t          t          t                    dz  t          ddf                              t                    rJ d S )Nr*   r   r,   )r   r   r   r-   r   r.   r/   r0   test_issue_11254cr      s<    a!aAY//33H=======r/   c                      t          t          t          dz  dt          dz  z  z             t                                        t                    rJ d S )Nr*   r,   )r   r   r   r-   r   r.   r/   r0   test_issue_10584r      sD    adQq!tVm,,a0044X>>>>>>>r/   c            
          t          t          t          t          t          dz  t          dz  z   t
          dz  z             z             t
                                        t                    rJ d S rD   )r   r   r   r   r!   r&   r-   r   r.   r/   r0   test_issue_9101r      sV    QadQTkAqD&8!9!99::A>>BB8LLLLLLLr/   c                      t          t          t          t          t          dz  z  t          t          z  z   t
          z             dz  z  t                                        t                    rJ d S )Nr*   r+   )r   r   r   r$   r"   r    r-   r   r.   r/   r0   test_issue_7147r      sS    4!Q$1q 011144a88<<XFFFFFFFr/   c                      t          t          t          dz  t          dz  t          dz  z
  z            t                                        t
                    rJ d S rD   )r   r   r$   r   r-   r   r.   r/   r0   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   evalf)fs    r0   ,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/   r0   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    r0   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 )Nr,   rx   r.   r/   r0   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,   Trf   rx   r.   r/   r0   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.testing.pytestr   r   r   r   r   	sympy.abcr   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r1   r4   r8   r:   r=   r@   rB   rE   rI   rK   rM   rQ   rT   rY   r[   r^   r`   rd   rh   rj   rm   ro   rq   rs   rv   ry   r}   r   r   r   r   r   r   r   r   r   r   r   r   r.   r/   r0   <module>r      sx   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 ; ; ; ; ; ; ; ; @ ? ? ? ? ? ? ? ? ? ? ? ? ? 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 - - - 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 5 5  5 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/   