o
    GZh                     @   s  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$m%Z%m&Z&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3 e'e%dd Z4dd Z5e%dd Z6dd Z7dd Z8e%dd Z9e%e&dd Z:e%e'dd Z;e%e&d d! Z<e%e&d"d# Z=e%d$d% Z>e%d&d' Z?e%d(d) Z@e%e&d*d+ ZAe%d,d- ZBe%d.d/ ZCe%d0d1 ZDe%d2d3 ZEe%d4d5 ZFd6d7 ZGe%d8d9 ZHe%e'd:d; ZIe%e&d<d= ZJe%d>d? ZKe&e%d@dA ZLe%dBdC ZMe%e&dDdE ZNe%dFdG ZOe%dHdI ZPe%dJdK ZQe%dLdM ZRe%dNdO ZSe%dPdQ ZTe%dRdS ZUe%dTdU ZVe%dVdW ZWe%dXdY ZXe%dZd[ ZYe%d\d] ZZe%d^d_ Z[e%d`da Z\dbS )c    )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                   C   sX   t tttdt  tdt  td td   dtd t d   ttr*J d S )N         )r   r	   r   r   r   hasr    r+   r+   [/var/www/auris/lib/python3.10/site-packages/sympy/integrals/tests/test_failing_integrals.pytest_issue_3880   s   Xr-   c                  C   s>   t ddd} t|  | dk f| df}tt| | |ksJ d S )NxrT)realr   )r   r   r   r   )r.   Znegabsxr+   r+   r,   test_issue_4212_real   s   r0   c                   C   s   t ttttrJ d S N)r   r   r   r*   r   r+   r+   r+   r,   test_issue_4212$   s   r2   c                  C   sz   t ttd dtt  t} t| ttt d ksJ | tttd d  t d ttd d d   ks;J d S Nr'   r)   )r   r   r   r   r   r   expandfr+   r+   r,   test_issue_4511-   s   @r7   c                   C   sF   t t t ttt t tdtftddfddtddftjks!J d S )Nr   r)   F)Zmeijergr   r   r   r   r$   r   r   Halfr+   r+   r+   r,   $test_integrate_DiracDelta_no_meijerg4   s   
r:   c                   C   sB   t t t ttt t tdtftddftddftjksJ d S )Nr   r)   r8   r+   r+   r+   r,   test_integrate_DiracDelta_fails9   s   r;   c                   C   sR   t tt dt t  ttt  ttd    dtd   tddftr'J d S Nr)   r'   r   )	r   r   r#   r%   r"   r    r   r*   r   r+   r+   r+   r,   test_issue_4525A   s   Rr=   c                   C   sZ   t tdt ttt  tdt  ttt  t ttdt    ttr+J d S Nr)   )r   r   r   r	   r*   r   r+   r+   r+   r,   test_issue_4540H   s   ,
r?   c                   C   s    t ttt ttrJ d S r1   )r   r   r   r   r*   r   r+   r+   r+   r,   test_issue_4891Q   s    r@   c                   C   s6   t tdt t tt td   ttrJ d S Nr'   )r   r	   r    r   r"   r*   r   r+   r+   r+   r,   test_issue_1796aX   s   6rB   c                   C   s>   t tdt t tt td   tt dftrJ d S Nr'   r   r   r	   r    r   r"   r   r*   r   r+   r+   r+   r,   test_issue_4895b^      >rE   c                   C   s>   t tdt t tt td   tt tftrJ d S rA   rD   r+   r+   r+   r,   test_issue_4895cc   rF   rG   c                   C   s<   t tdt t tt td   tdtftrJ d S rC   rD   r+   r+   r+   r,   test_issue_4895dh   s   <rH   c                   C   s2   t tdttd d  tddftrJ d S )Nr)      r'   i   )r   r   r   r   r*   r   r+   r+   r+   r,   test_issue_4941m   s   2rK   c                   C   s@   t ttttd   tt  tt tdtftrJ d S Nr)   r   )	r   r
   r   r   r	   r   r   r*   r   r+   r+   r+   r,   test_issue_4992s   s   @rM   c                  C   s:   t ddttt  ttd td f} | trJ d S )Nr)   r(      )r   r   r   r   r   r*   r   ir+   r+   r,   test_issue_16396ay      (rQ   c                  C   s:   t ttt dttd   tdtf} | trJ d S r<   )r   r   r   r   r   r*   r   rO   r+   r+   r,   test_issue_16396b   rR   rS   c                   C   s0   t tttt tddt gdt ksJ d S Nr   r'   )r   r	   r   r   r   r+   r+   r+   r,   test_issue_16046      0rU   c                   C   sD   t tdtt d ttd  tt d td ftr J d S )Nr)   r'   )r   r   r   r   r   r   r*   r   r+   r+   r+   r,   test_issue_15925a   s   DrW   c                  C   sb   t dttd  tt d dtt ttd  d  } t| tdtd ftddks/J d S )Nr'      r   rN   r(   )r   r   r   r   r   r   r   r5   r+   r+   r,   test_issue_15925b   s   <&rZ   c                   C   s^   t tdttd  tt d dtt ttd  d  tdtd fddtr-J d S )NrX   r'   rY   r   rN   TZmanual)r   r   r   r   r   r   r*   r   r+   r+   r+   r,   test_issue_15925b_manual   s
   <
r\   c                  C   s>   t tdt tdt d  t tddf} | trJ d S r<   r   r
   r   r*   r   rO   r+   r+   r,   test_issue_15227   s   ,r^   c                  C   s8   t ttd ttt  ttjdf} | trJ d S )N   r)   )	r   r
   r   r   r   r   r9   r*   r   rO   r+   r+   r,   test_issue_14716   s   &r`   c                  C   s6   t ttddt t   tdtf} | trJ d S r<   )r   r   r   r!   r*   r   rO   r+   r+   r,   test_issue_14709a   s   $ra   c                   C   s(   t ttd tt ttrJ d S rA   )r   r	   r   r   r*   r   r+   r+   r+   r,   test_issue_14398      (rb   c                  C   s.   t ttttdtd f} | trJ d S rT   )r   r
   r   r   r   r*   r   rO   r+   r+   r,   test_issue_14074   s   rd   c                  C   s:   t tdt tdt  t tdtf} | trJ d S )N   r'   r   )r   r   r   r   r*   r   rO   r+   r+   r,   test_issue_14078b   s   (rf   c                  C   s2   t tdt dt  tddf} | trJ d S rL   r]   rO   r+   r+   r,   test_issue_13792   s    rg   c                   C   s*   t tttd  tddftrJ d S Nr(   r   r)   r   r	   r   r   r*   r   r+   r+   r+   r,   test_issue_11845a   s   *rj   c                   C   s,   t tt td  tddftrJ d S rh   ri   r+   r+   r+   r,   test_issue_11845b      ,rk   c                   C   s0   t tt tdd t tdtftrJ d S )Nr'   r   )r   r"   r   r   r*   r   r+   r+   r+   r,   test_issue_11813   rV   rn   c                   C   s&   t ttd tddftrJ d S )Nr'   r   r)   )r   r   r   r*   r   r+   r+   r+   r,   test_issue_11254c   s   &ro   c                   C   s,   t ttd dtd   ttrJ d S r3   )r   r   r   r*   r   r+   r+   r+   r,   test_issue_10584   rl   rp   c                   C   s8   t ttttd td  td   ttrJ d S rA   )r   r
   r   r   r   r$   r*   r   r+   r+   r+   r,   test_issue_9101      8rq   c                   C   s8   t ttttd  tt  t d  ttrJ d S )Nr'   r(   )r   r   r   r"   r    r   r*   r   r+   r+   r+   r,   test_issue_7147   rr   rs   c                   C   s0   t ttd td td   ttrJ d S rA   )r   r   r"   r   r*   r   r+   r+   r+   r,   test_issue_7109   rV   rt   c                  C   sj   t dtdt  dk fdt dt d d  tdt  dkf} tt| tdtfdt   dks3J d S )	Nr   g    @}@gW?j*@gVL?gףp=
?r'   g    @gHz>)r   r&   r   absr   r   Zevalfr5   r+   r+   r,   ,test_integrate_Piecewise_rational_over_reals   s
   &,rv   c                   C   s(   t ttdtd   ttrJ d S )N	   r'   )r   r   ru   r*   r   r+   r+   r+   r,   test_issue_4311_slow  rc   rx   c                  C   sP   t ddd} td| tt  d tddt fdt td| d   ks&J d S )Nr"   T)Zpositiver)   rm   r   r'   )r   r   r   r   r   r   )r"   r+   r+   r,   test_issue_20370  s   Dry   c                   C   s(   t tdt td  ttrJ d S r>   r]   r+   r+   r+   r,   test_polylog  rc   rz   c                   C   s,   t tdt td  tddtrJ d S )Nr)   Tr[   r]   r+   r+   r+   r,   test_polylog_manual  s   ,r{   N)]Zsympy.core.numbersr   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   Z$sympy.functions.elementary.complexesr   Z&sympy.functions.elementary.exponentialr	   r
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