a
    khR                     @   s  d dl 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 d dlmZmZmZ d dlmZmZ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! d dl"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- d dl.m/Z/ d dl0m1Z1 d dl2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9 d dl:m;Z; d dl<m=Z=m>Z? d dl@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZI dd ZJdd ZKdd ZLdd ZMdd ZNdd  ZOe;d!d" ZPd#d$ ZQd%d& ZRd'd( ZSd)d* ZTe;d+d, ZUd-d. ZVd/d0 ZWe;d1d2 ZXe;d3d4 ZYd5d6 ZZd7d8 Z[d9d: Z\d;d< Z]d=d> Z^d?d@ Z_dAdB Z`dCdD ZadEdF ZbdGdH ZcdIdJ ZddKdL ZedMdN ZfdOdP ZgdQdR ZhdSdT ZidUdV ZjdWS )X    )expand_func)IRationaloopi)S)default_sort_key)Absargre
unpolarify)exp	exp_polarlog)coshacoshsinh)sqrt)	Piecewisepiecewise_fold)cossinsincasin)erferfc)gamma	polygamma)hypermeijerg)Integral	integratehyperexpandsimplify)_rewrite_single	_rewrite1meijerint_indefinite
_inflate_g_create_lookup_tablemeijerint_definitemeijerint_inversion)slow)verify_numericallyrandom_complex_number)	xyabcdstzc                  C   s"  dd } dd }| t dt  | t d dt d  | t d tt d   td t d  |t d t   |t t  dd }|tt  tt  t  ttt tt  t td dtt  d	ttd
dd	tddt	j
tddfdfdtd
dd	ffdtdt t  t d  fgdfksJ d S )Nc                 S   sn   t ttgtg|gtg| t}|d us*J t|d d d tsDJ |d d d jt||ffksjJ d S )Nr      )	r&   r   r2   r3   r5   r0   
isinstanceargumentZas_coeff_mul)exprr4   me r?   R/var/www/auris/lib/python3.9/site-packages/sympy/integrals/tests/test_meijerint.pyr7      s    ztest_rewrite_single.<locals>.tc                 S   s*   t ttgtgtgtg| td u s&J d S N)r&   r   r2   r3   r4   r5   r0   r<   r?   r?   r@   tn!   s    ztest_rewrite_single.<locals>.tn   r9   c                 S   sH   ddl m} t| |}|dd |d D  tt}t|| |sDJ d S )Nr   Addc                 S   s   g | ]}|d  |d  qS )r   r9   r?   ).0resr?   r?   r@   
<listcomp>-       z2test_rewrite_single.<locals>.u.<locals>.<listcomp>)sympy.core.addrF   r&   replacer   r   r.   )r<   r0   rF   rr>   r?   r?   r@   u*   s    
ztest_rewrite_single.<locals>.ur         )rD   r?   @   T)r0   r1   r   r   r&   r   r   r   r   r   Halfr   r   )r7   rC   rN   r?   r?   r@   test_rewrite_single   s$    $&*rU   c                   C   sz   t td ttgtgtgtgtd ttd    d tdtd ddttgtgtgtgtd td  fgdfksvJ d S )NrQ   r9      rD   r   T)r'   r0   r   r2   r3   r4   r5   r1   r?   r?   r?   r@   test_rewrite1C   s    86rW   c                  C   s~   dd } | dt  | dt  | ddt   | dt d  | dt td  | t d t  | dt td  dt td	   d S )
Nc                 S   s   t tgtgtgtg||  }tt d tt d t tt tt i}t|t}|d usZJ t	|
||t
|ts|J d S )N
   )r   r2   r3   r4   r5   randcplxr   r(   r0   r.   subsdiff)Zfacr
   grZ   Zintegralr?   r?   r@   r7   I   s    
z0test_meijerint_indefinite_numerically.<locals>.trD   r9   rV   3/2rQ   rP   z7/3)r0   r   r7   r?   r?   r@   %test_meijerint_indefinite_numericallyH   s    

r_   c                  C   sL   t ttdd\} }| jr |du s$J t tttt\} }| jrD|du sHJ d S )Nr   T)r+   r0   is_zeror   )vr3   r?   r?   r@   test_meijerint_definiteY   s    rb   c                     s   t t d tt d t tt tt tt d i  fdd} | t gtggtgtggtds`J | t tgtggtgtggtdsJ | t gtggttgtggdtd  dsJ d S )NrX   c                    sD   ddl m} t| ||}|t|| }t| | tdddS )Nr   )Mulg?g)r3   r5   )Zsympy.core.mulrc   r   r)   r.   rZ   r0   )r2   r3   r
   nrc   m1m2rZ   r?   r@   r7   d   s    ztest_inflate.<locals>.trQ   r9   )r2   rY   r3   r   r4   r5   r1   r0   r^   r?   rg   r@   test_inflate`   s    "$rh   c                  C   s$  ddl m}  | ddd\}}}tt| d  tt| d   }t|tdtfdd}t| tdtt	 t
td||  d d t|d  d ||  |d d    d	 ksJ ttt| d  tt| d   t|t  tdtfdd}t|tdtt	 t
tdd| d|  |  d	 d  t|d  |d  d| d|  | d d
   d	 ksxJ tttt| | | d  tdtfddtt	d dt
|| |   ksJ tttt| | | d  tdtfddtt	d dt
|| |   ks J d S )Nr   symbolsza b cTpositiver9   r   rD   rP      )sympy.core.symbolrj   r   r0   r!   r   r%   expandr   r   r   )rj   r2   r3   r4   rM   r>   r?   r?   r@   test_recursivep   s2    $
@@H
,
,rq   c               	   C   s.  ddl m}  ddlm} |ddd\}}}ttg g dgg || tg g |d g| d g|d d  |dtfjsxJ |d	dd
}tt| tg g gdgg gt tdtft	|d ksJ tt| tg g gdgg gt tdtfddt	|d ksJ t
tt| tg g gdgg gt tdtfddts6J ttttttksRJ |ddd
\}}ttt| td|d ||d  |d  ksJ ttd d tt  tdtdksJ |ddd
\}}ttt| d|  d  tdt\}}	t|tt| dt|d|    ks&J |	dks4J tt| t t|t  tdt\}}
t|d||  ksvJ ttttt dtddfksJ | ttttdtd ttd ksJ | ttt tdtd dttttt  tt  ksJ tttd  tt tttdfks8J tttt tt tdks\J ttdt d d  tt tttd dfksJ tttdt d  tt tdksJ ttt| | d  d tdt |d   tt tdksJ tttd tt ttdfks*J ttt tt tdttjdfksVJ dd }tdD ]>}ttt tt t|  tdtfdd||ksfJ qftttt tt|  tdtfddtdt|td   d ksJ |d\}}}ttg g |d g| d gtd tg g |d g| d gtd  t|d   tdtddd| d   t	d| d  t	|d |d  |  t	| d |d  | d t	|d |d  | d  t	|d |d  | d   t|dk t|tdd k @ t|d t|d  t| dk@ fks6J ttt| tt|  tdtfddttt| tt|  tdtfksJ tttd  tt tdtfddtttdtj d  ksJ ddlm} |ddd}tttt t|  tdd||d tksJ |ddd
}tdt | t|t  tddtt| t	|d  td|d tj |d d ffddtjft ddff|d d  d dfksJ |d dd
\}}ttt| t| td   tt tf|| d tj  d| d  t	|d tj  d ks*J d S )!Nr   )rp   ri   zs t muTrealr9   rP   r6   rk   rD   rm   Fa brQ   )   Tzsigma mu)r9   T)rD   Tc                 S   s(   ddt d   t | t dd|   S NrD   r9   rO   )r0   r[   rZ   )rd   r?   r?   r@   rH      s    ztest_meijerint.<locals>.res   za b s
lowergammard   )integeralphar?   rO   ru   za s)!sympy.core.functionrp   ro   rj   r!   r   r   is_Piecewiser0   r   r:   r    r(   r   r%   r+   r   r   r   r   r
   absr   r   r   rT   ranger   r   r   'sympy.functions.special.gamma_functionsrz   r   )rp   rj   r6   r7   mur2   r3   sigmair4   _rH   rd   rz   r|   r?   r?   r@   test_meijerint   s    $
(
&
 


*(.(&, 
,$ 
,.
&,((
" 
:8B
	&"
$

 &
 
*4r   c                  C   sv  ddl m} m} tt|tt|tt t tdtfddddt	t
td td    t
tt  tt   ksrJ tt|tt|tt t tdtfdddddt  ksJ ttt	tt td d ttj    tdtfdddd td t tt
 ttjt   |ttks J tt|dt tddt|dt ksLJ tt| dt tddt| dt ksxJ t|dttdd|dt ksJ t|dtd t tdd|dtd |dtd   d ksJ t|dtd td  tddd	t |dtd  dt |dtd   d|dt |dt  |dtd t  ks^J t|dt|dt tdd|dtd  d ksJ ttd |dt |dt tddtd |dtd  d ksJ t|dt|dt t tddt|dtd  t|dtd   |dt|dt  ks<J t|dtd t tdd|dtd  d ksrJ d S )
Nr   besselibesseljTnoner   condsr9   rD   rm   rx   )sympy.functions.special.besselr   r   r%   r!   r2   r8   r3   r   r   r   r0   r1   r   rT   r   r   r   r?   r?   r@   test_bessel   s^    "."
& 
,,& 
*

$
 "
r   c                  C   s&  ddl m}  ddlm} dd }|dtd d  tt|t ksHJ |ttd d  tt|t kspJ |tt t |td ksJ |dt	dtd   | dt|t ksJ t
t	tt	dtd   ttd u sJ |ttd d u sJ t
ttd  ttd u s"J d S )Nr   r   )	Heavisidec                 S   s   t t| ttS rA   )r   r,   r6   r7   fr?   r?   r@   inv!  s    ztest_inversion.<locals>.invrD   r9   )r   r   'sympy.functions.special.delta_functionsr   r6   r   r7   r   r   r   r,   )r   r   r   r?   r?   r@   test_inversion  s    ((".(r   c                  C   s   ddl m}  ddlm} | ddd}tt| tdt| tt  }t|tt	}|j
r^J | ddd	}|||}t|tt	}|j
sJ |jd d |||ksJ |jd
 d sJ ||tt	d }|jd
 d |ks|jd
 d |jksJ d S )Nr   Symbol)InverseLaplaceTransformr2   Trk   rx   r3   rr   rO   rD   )ro   r   sympy.integrals.transformsr   r   r   r   r6   r,   r7   r~   rZ   argsZas_integral)r   r   r2   Fr   r3   f2ZILTr?   r?   r@   !test_inversion_conditional_output.  s    $

r   c                  C   s   ddl m}  ddlm} | ddd}| ddd	}d
dt  }| d}tt|t ttj	r^J tt|t ttd u szJ tt|t ttd u sJ tt|t tt}|j	sJ t
|jd d |sJ d S )Nr   r   )
DiracDeltarM   Trr   r4   F)Zextended_realrD   r9   r8   )ro   r   r   r   r   r,   r   r6   r7   r~   r:   r   )r   r   rM   r4   r2   r8   r   r?   r?   r@   %test_inversion_exp_real_nonreal_shiftC  s    
r   c                  C   sb  ddl m} m} ddlm} ddlm} i }t| | D ]}t	|t
dD ]
\}}}}	i }
t|j|g D ]2}t|dr|jr|dd|
|< qp| d	d
|
|< qpt|ts||
}dd |D }tdd |D sJ |dd |D  }|j|
d|j|
d }}tt|t|}|dk r>t||  dksZJ qNt|| |  dksNJ qNq<d S )Nr   )uniform	randrangerE   )r8   )key
propertiesrD   rX   g      ?g       @c                 S   s   g | ]\}}t |qS r?   r"   )rG   r   r\   r?   r?   r@   rI   f  rJ   z%test_lookup_table.<locals>.<listcomp>c                 s   s    | ]}|j p|t V  qd S rA   )r~   hasr   )rG   r0   r?   r?   r@   	<genexpr>g  rJ   z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| qS r?   r?   )rG   r   r0   r?   r?   r@   rI   j  rJ   rg   g|=)sympy.core.randomr   r   rK   rF   sympy.integrals.meijerintr8   r*   valuessortedr   listZfree_symbolshasattrr   r:   allrd   minr   )r   r   rF   Zz_dummytablelZformulaZtermsZcondhintrZ   Zaiexpandedr2   r3   rM   r?   r?   r@   test_lookup_tableR  s,    

r   c                  C   s  ddl m}  ddlm} |tttd tddtdddttd  tt	dd d tt	d	d kspJ tttd tdddt ttd  tt	dd dtt	d	d  dtt	dd | t	ddtd
  dt
t tt	d	d   ksJ d S )Nr   ry   )	powdenestrQ   Trm   Zpolarr9   rV   rw   )r   rz   sympy.simplify.powsimpr   r!   r   r0   r[   r   r   r   r   )rz   r   r?   r?   r@   test_branch_bugs  s    .2>r   c                  C   sd   ddl m}  tttd tddtdt  ks4J t| dtd tdd| ddt  ks`J d S )Nr   r   rD   Trm   )r   r   r!   r   r0   r   r   r?   r?   r@   test_linear_subs~  s    (r   c            $         s.  ddl m  ddlm} m} ddlm} ddlm} |ddd\}|d	dd
\}| ddd
dd dd t	t
t
t tfdddksJ t	t
t
 t
t tfddksJ t	t
d t
 t
t tfddd d  ksJ t	t
d t
 t
t tfddd d d   ks>J t	t
t|| t
t tftt tfdddks|J t	t
t
 t|| t
t tftt tfddksJ t	tt
 t|| t
t tftt tfdd|ks J t	t
t t
 t|| t
t tftt tfdd| ksJJ t	t
t d t
 t|| t
t tftt tfddd | ksJ t	t
t d t
 t|| t
t tftt tfddd | ksJ t	t
d t
 t|| t
t tftt tfdd}|tr:J t|d d  ksXJ t	td t
 t|| t
t tftt tfdd|d |d  ksJ t	t
t
dtfdddksJ t	t
t
 t
dtfddd ksJ t	t
d t
 t
dtfdddd  ks.J  fdd}|ddksVJ |t
t  kspJ |t
td  d  d   ksJ d dd   }t|t
t d d |t
t d d  |ksJ t|t
t d d |t
t d d  |ksJ t|t
t d |t
t d  |ksLJ |ddd
\}	}
t
|	d  dt
 |	 |
   t|	|
  t|	 t|
 }t	|t
dtfdddksJ t	t
| t
dtfddd}||d |d f|	|
d  d|
k fksJ t	t
d | t
dtfddd}|d |
dkks0J ||d |d d  |	|
 d |	 |
d  |
d d  ksrJ |ddd
\}}t
|d  t
 d |d   t||  t|t|  }tt	|t
ddfdddksJ tt	t
| t
ddfdd|||  ksJ tt	t
d | t
ddfdd||d  ||  || d  ksRJ tt	t
t | t
ddfddt|| t|t  t| t|| t  ksJ | dddd}dd|d   t
|d   tt
d  d  t|d  }|t	|t
dtfdddksJ tt	t
| t
dtfddtdt|d d  t|d  ksXJ tt	t
d | t
dtfdd|ksJ d| d  t|d  t
|d d   tt
 d  }|t	|t
dtfdddksJ tt	t
| t
dtfdd|k	sJ tt	t
d | t
dtfdd||d  k	s4J |t	t
| td|  d | t
dtfdddtd t| k	s~J |ddd
\}}}|| t
 t
| ||   dt
| ||   |d   }tt	|t
dtfdddk	sJ t
| }tt	|t
dtfddd|| tdd|   t|d d|   || d t|  k
sRJ tt	t
| t
dtfddd||d  tdd|   t|d d|   || d t|  k
sJ |ddd
\}}t|t
 | ||  |t
 | ||   t
 t|d  t|d  t|| d  }tt	|t
dtfdddksDJ tt	t
| t
dtfddd||d  kstJ tt	t
d | t
dtfddd|d |d  | |d   |d  ksJ |d!dd
\}}t|d t t
td"d  t| t
| d  t
 d |d   }d#d$ }|t	|t
dtfdks:J |t	t
| t
dtf|ks\J |t	t
| d | t
dtf|d | ksJ |t	t
| d | t
dtfd|d%  |d  ksJ | d&dd
}t	t|d t t| d t
|   t
| td'  t
|tfdks J |ddd
\}	}
|
|	 t
|
d   |	|
d   dt
|
 |	|
   d  }tt	|t
dtfdksJ tt	t
| t
dtfdd(t|	 |
 tt|
  ksJ tt	t
t | t
dtfdd(t|	t  t |
 ttt |
  ks
J | ddd
}| d)dd
}|| t
| |d   tt
| |   }tt	|t
dtfdksjJ tt	t
| | t
dtf|| td||   ksJ dd*lm} |d+dd
\} }!t
|!d  tt
d | d   d |!d   |dt
|  |!d   }"t	|"t
dtfdddks"J | d,dd-}| d.dd
}ttt
|  | d | }#t	|#t
t tfdddksxJ t	t
|# t
t tfdd|ksJ t	t
d |# t
t tfddd|d  |d  ksJ | ddd
}| t	tt
t
|d   tt
  t| t
dtftd|ks*J d S )/Nr   )
expand_mul)r   rj   )	gammasimp)powsimpzmu1 mu2TZnonzerozsigma1 sigma2rk   lambdac                 S   s6   dt dt |d   t| | d  d |d   S NrD   r9   )r   r   r   )r0   r   r   r?   r?   r@   normal  s    z test_probability.<locals>.normalc                 S   s   |t | |   S rA   )r   )r0   rater?   r?   r@   exponential  s    z%test_probability.<locals>.exponentialrm   rD   r9   rQ   rO   c                    s   t | t t tdtftt tfdd}t | t t tt tftdtfdd} | |ks|J |S )Nr   Trm   )r!   r0   r1   r   )r<   Zres1Zres2r   r   Zmu1r   r   Zsigma1r?   r@   E  s    ztest_probability.<locals>.Ez
alpha betaZseparater   rt   k)r{   rl   za b pr   zd1 d2rP   zlamda muc                 S   s   t | tS rA   )r%   rewriter   rB   r?   r?   r@   <lambda>  rJ   z"test_probability.<locals>.<lambda>rV   r4   r]   )r   rd   )r   znu sigmar   rr   r3   )r}   r   ro   r   rj   Zsympy.simplify.gammasimpr   r   r   r!   r0   r   r1   r   r	   r%   r   r   r   r   r   r   r   r   r   r   r   r   )$r   rj   r   r   Zmu2Zsigma2r   r   ansr|   betaZbetadistjr2   r3   r   chiZ
chisquaredpZdagumr
   d1Zd2r   Zlamdar   distZmysimpr4   Zdistnrd   r   nur   ZriceZlaplacer?   r   r@   test_probability  s   & $$



 
$

$

  
$
 

.66.(.$
:"


.
:""
*8"&

&
8"*
.
.

"

 "
D"2:6

"
*
D $
*r   c            
      C   s  ddl m}  ddlm} ddlm}m}m}m}m	}m
} ttttt t tt  tdtfddd|jdd	|ttksJ ttt t t tdtfddd| |dtksJ ttt t td
  tdtfddd| |d
t||ksJ ttt t td  tdtfddd| |dt|| ks`J | ddd}ttt t t|tfdd ||ksJ ttt t t|tfdd ||td
  ksJ tttt tdtfdd|tksJ t|tt tdtfdd|tks(J ttt t tdd |tt |dt ksbJ ttt td
  tdd| |dttt t  tt  ksJ | ddd}	tt|	|	 |	dd |	d ||	ksJ tt|	|	 |	dd |	d ||	ksJ t|dttdd| t|dt tt  ksZJ t|d
ttdd| td
  |dt d
 ttt  d
  tt d
  ksJ ttt|tttdd|jdd	|td t ksJ t|ttddt|t tt ks"J t||	|	dd |	||	 t|	 ksRJ t|ttddt|t tt ks~J t||	|	dd |	||	 ||	 ksJ t|ttt  tdtfddtd ksJ t|dttt tdtfddtd
d
 ksJ dS )z% Test various exponential integrals. r   r   )r   )ChiCiEiShiSiexpintrD   Tr   r   )funcr9   rQ   r7   rk   rm   rN   r   rP   N)ro   r   %sympy.functions.elementary.hyperbolicr   'sympy.functions.special.error_functionsr   r   r   r   r   r   r%   r   r!   r   r8   r0   r1   r   r   rp   r   r   r   r   Zas_independentr   r   )
r   r   r   r   r   r   r   r   r7   rN   r?   r?   r@   test_expintK  s     " 
 
0 
** 
$
"
"

6

,0,00r   c                  C   s  ddl m} m} ddlm}m} ddlm} ddlm	}m
}m}m} ddlm}	m}
 |
|tttdd|t td	  t ddfksJ |
|tttdd|tt t td	 d
kfksJ |
|tttddttd td
d
td	    d	t  t td	 d
kfksJ |
|ttttd
d  dttdkttdk@ fksJJ |	|d
tt ttdd}|d jdd |d
 ftdtd
d	t  ktdd	t  k B fd	tdtd	  td	  d
  dftdkfksJ t|t|dt tdtfddtd
td	 ksJ t|t|d
t tdtfddttjtd	d	  ksNJ td
t td
td	   tddt| d
t  ttd d
kft|d
t  dfksJ d S )Nr   )r   acoth)r   atanr   )r   E1r   r   )fourier_transformlaplace_transformTr$   r9   rD   rx   rO   F)Znoconds)deeprS   rm   ) r   r   r   (sympy.functions.elementary.trigonometricr   r   r   r   r   r   r   r   r   r   r   r   r0   r6   r   r   r   r2   r   Zfactorrp   r   r   r!   r   rT   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r?   r?   r@   
test_messy  sD    
4
$"
 
 
 2r   c                   C   sJ   t tt td  tt tfddt tt ttt d  ksFJ d S )Nr9   Trm   rP   )r!   r   r   r0   r   r   r   r?   r?   r?   r@   test_issue_6122  s    "r   c                  C   s>   dt  ttt   tdd  } t| t dd}|tr:J d S )NrD   rQ   Trm   )r0   r2   r3   r   r!   r   r   )r<   Zantir?   r?   r@   test_issue_6252  s    r   c                   C   sD   t ttt dtd   tt tf tttd ks@J d S rv   )r!   r   r   r0   r   r%   r   r   r?   r?   r?   r@   test_issue_6348  s    .
r   c                  C   sh   ddl m} m} tttttd  d t|tks:J tttttd  d t| tksdJ d S )Nr   fresnelcfresnelsr9   )	r   r   r   r   r!   r   r   r0   r   r   r?   r?   r@   test_fresnel  s    *r   c                   C   s   t ttt  td u sJ d S rA   )r(   r0   r?   r?   r?   r@   test_issue_6860  s    r   c                  C   sr   t ttdt d  t } | tdt d dtd  t d  d ksNJ | ttjtjtddksnJ d S )Nr9   rQ   rV   )	r(   r0   r   ZtogetherZ_eval_intervalr   ZNegativeOneZOner   r   r?   r?   r@   test_issue_7337  s    0r   c                   C   sh   t tttt t  tt d tt t d tt   tt t  d td d  ksdJ d S r   )r(   r   r0   r   r7   r?   r?   r?   r@   test_issue_8368  s    0
r   c                  C   st   ddl m} m} tdttt d | d  d  td|ftd|fdtd|d | d    |  d|   kspJ d S )Nr   hwrD   r9   rQ   )	sympy.abcr   r   r!   r   r1   r0   r   r?   r?   r@   test_issue_10211  s    2&r   c                  C   sr   ddl m}  | ddd\}}tdttd |d  d  t| |fd| |d t|d |d    ksnJ d S )	Nr   ri   zy LTrk   rD   r9   rQ   )ro   rj   r!   r   r0   )rj   r1   Lr?   r?   r@   test_issue_11806  s
    ("r   c                  C   s   ddl m}  ddlm}m} t|d |d |d  d  |dd}d|d	  |d
  tdtd
dftddf|d tdt	 t
  |d   }| ||  d	dsJ d S )Nr   )RR)RrM   r9   g      ?Trm   gUUUUUU?g      ?rQ   g      rV   g-q=)Zsympy.polys.domains.realfieldr   r   r   rM   r!   r   r   r   r   r   Zalmosteqrd   )r   r   rM   r   r\   r?   r?   r@   test_issue_10681  s    &*r   c                  C   s@   ddl m}  | ddd}tdtd  tt|fd| ks<J d S )	Nr   r   r2   Trk   rD   r9   rO   )ro   r   r!   r0   r   )r   r2   r?   r?   r@   test_issue_13536  s    r   c                  C   sj   ddl m}  | d}| d}tt|| ||  |dd|dtt|d |d  |ddsfJ d S )Nr   r   r0   rd   Trm   r9   )ro   r   r!   r   rZ   equals)r   r0   rd   r?   r?   r@   test_issue_6462  s    &r   c                   C   sN   t tt t  tddt dtt  dt   ttt  tt   ksJJ d S )NTrm   rD   )r!   r3   r7   r2   r?   r?   r?   r@   test_indefinite_1_bug  s    r   c                   C   s`   t dttt d d  ddtttt ttt d dkft ttt  dfks\J d S )NrD   r9   Trm   )r!   r   r0   r   r   r   r	   r   r?   r?   r?   r@   test_pr_23583  s    6r   c                   C   s:   t ttd  tddfddttd td ks6J d S )Nr9   r   Trm   rV   )r!   r   r0   r   r   r   r?   r?   r?   r@   0test_integrate_function_of_square_over_negatives  s    r   c                  C   sP   ddl m}  | ddd}tt|td  tddfdd	td
| | ksLJ d S )Nr   ri   r1   Tr   rD   rO   g      пrm   g      ?)ro   rj   r!   r   r0   r   )rj   r1   r?   r?   r@   test_issue_25949  s    r   N)kr}   r   Zsympy.core.numbersr   r   r   r   Zsympy.core.singletonr   Zsympy.core.sortingr   Z$sympy.functions.elementary.complexesr	   r
   r   r   Z&sympy.functions.elementary.exponentialr   r   r   r   r   r   r   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.functions.special.hyperr   r   Zsympy.integrals.integralsr    r!   Zsympy.simplify.hyperexpandr#   Zsympy.simplify.simplifyr%   r   r&   r'   r(   r)   r*   r+   r,   Zsympy.testing.pytestr-   r   r.   r/   rY   r   r0   r1   r2   r3   r4   r5   r6   r7   r8   rU   rW   r_   rb   rh   rq   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r?   r?   r?   r@   <module>   sr   $,)
j0
 
 G
6&
