o
    *ήc}                     @   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 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$m%Z%m&Z& d dl'm(Z(m)Z) d dl*m+Z+m,Z, d dl-m.Z. d dl/m0Z0 d dl1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8 d dl9m:Z: d dl;m<Z<m=Z> d dl?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZH dd ZIdd ZJdd ZKdd ZLdd ZMdd  ZNe:d!d" ZOd#d$ ZPd%d& ZQd'd( ZRd)d* ZSe:d+d, ZTd-d. ZUd/d0 ZVe:d1d2 ZWe:d3d4 ZXd5d6 ZYd7d8 ZZd9d: Z[d;d< Z\d=d> Z]d?d@ Z^dAdB Z_dCdD Z`dEdF ZadGdH ZbdIdJ ZcdKdL ZddMdN ZedOdP ZfdQdR ZgdSS )T    )expand_func)IRationaloopi)S)default_sort_key)Absargre
unpolarify)exp	exp_polarlog)coshacosh)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sJ d S )Nc                 S   sn   t ttgtg|gtg| t}|d usJ t|d d d ts"J |d d d jt||ffks5J d S )Nr      )	r$   r   r0   r1   r3   r.   
isinstanceargumentas_coeff_mul)exprr2   me r>   K/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/tests/test_meijerint.pyr5      s   *ztest_rewrite_single.<locals>.tc                 S   s*   t ttgtgtgtg| td u sJ d S N)r$   r   r0   r1   r2   r3   r.   r;   r>   r>   r?   tn!   s   *ztest_rewrite_single.<locals>.tn   r7   c                 S   sH   ddl m} t| |}|dd |d D  tt}t|| |s"J d S )Nr   Addc                 S   s   g | ]
}|d  |d  qS )r   r7   r>   ).0resr>   r>   r?   
<listcomp>-   s    z2test_rewrite_single.<locals>.u.<locals>.<listcomp>)sympy.core.addrE   r$   replacer   r   r,   )r;   r.   rE   rr=   r>   r>   r?   u*   s   
ztest_rewrite_single.<locals>.ur         )rC   r>   @   T)r.   r/   r   r   r$   r   r   r   r   r   Halfr   r   )r5   rB   rL   r>   r>   r?   test_rewrite_single   s$   $&*rS   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s;J d S )NrO   r7      rC   r   T)r%   r.   r   r0   r1   r2   r3   r/   r>   r>   r>   r?   test_rewrite1C   s   86rU   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s-J t	|
||t
|ts>J d S )N
   )r   r0   r1   r2   r3   randcplxr   r&   r.   r,   subsdiff)facr
   grX   integralr>   r>   r?   r5   I   s   
&z0test_meijerint_indefinite_numerically.<locals>.trC   r7   rT   3/2rO   rN   z7/3)r.   r   r5   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r"|du s$J d S )Nr   T)r)   r.   is_zeror   )vr1   r>   r>   r?   test_meijerint_definiteY   s   rb   c                     s   t t d tt d t tt tt tt d i  fdd} | t gtggtgtggtds0J | t tgtggtgtggtdsBJ | t gtggttgtggdtd  dsXJ d S )NrV   c                    sD   ddl m} t| ||}|t|| }t| | tdddS )Nr   )Mulg?g)r1   r3   )sympy.core.mulrc   r   r'   r,   rX   r.   )r0   r1   r
   nrc   m1m2rX   r>   r?   r5   d   s   ztest_inflate.<locals>.trO   r7   )r0   rW   r1   r   r2   r3   r/   r.   r^   r>   rh   r?   test_inflate`   s   "$0ri   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s^J 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sJ 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positiver7   r   rC   rN      )sympy.core.symbolrk   r   r.   r    r   r#   expandr   r   r   )rk   r0   r1   r2   rK   r=   r>   r>   r?   test_recursivep   s2   $
@@H,,rr   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s<J |d	dd
}tt| tg g gdgg gt tdtft	|d ks_J tt| tg g gdgg gt tdtfddt	|d ks~J t
tt| tg g gdgg gt tdtfddtsJ ttttttksJ |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sJ tt| t t|t  tdt\}}
t|d||  ks7J ttttt dtddfksJJ | ttttdtd ttd ks`J | ttt tdtd dttttt  tt  ksJ tttd  tt tttdfksJ tttt tt tdksJ 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sJ 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s'J dd }tdD ]}ttt tt t|  tdtfdd||ksMJ q/tttt tt|  tdtfddtdt|td   d ksuJ |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sJ ttt| tt|  tdtfddttt| tt|  tdtfks@J tttd  tt tdtfddtttdtj d  ksdJ ddlm} |ddd}tttt t|  tdd||d tksJ |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   )rq   rj   zs t muTrealr7   rN   r4   rl   rC   rn   Fa brO   )   Tzsigma mu)r7   T)rC   Tc                 S   s(   ddt d   t | t dd|   S NrC   r7   rM   )r.   rY   rX   )re   r>   r>   r?   rG      s   (ztest_meijerint.<locals>.res   za b s
lowergammare   )integeralphar>   rM   rv   za s)!sympy.core.functionrq   rp   rk   r    r   r   is_Piecewiser.   r   r8   r   r&   r   r#   r)   r   r   r   r   r
   absr   r   r   rR   ranger   r   r   'sympy.functions.special.gamma_functionsr{   r   )rq   rk   r4   r5   mur0   r1   sigmair2   _rG   re   r{   r}   r>   r>   r?   test_meijerint   s   $(
&
 
((.(&, 
,$ 
,.
&,((
" 
:8B
&	"
$

 &
 
*4r   c                  C   sl  ddl m} m} tt|tt|tt t tdtfddddt	t
td td    t
tt  tt   ks9J tt|tt|tt t tdtfdddddt  ksXJ ttt	tt td d ttj    tdtfdddd td t tt
 ttjt   |ttksJ tt|dt tddt|dt ksJ tt| dt tddt| dt ksJ t|dttdd|dt ksJ t|dtd t tdd|dtd |dtd   d ksJ t|dtd td  tddd	t |dtd  dt |dtd   d|dt |dt  |dtd t  ks*J t|dt|dt tdd|dtd  d ksFJ ttd |dt |dt tddtd |dtd  d ksiJ t|dt|dt t tddt|dtd  t|dtd   |dt|dt  ksJ t|dtd t tdd|dtd  d ksJ d S )
Nr   besselibesseljTnoner   condsr7   rC   rn   ry   )sympy.functions.special.besselr   r   r#   r    r0   r6   r1   r   r   r   r.   r/   r   rR   r   r   r   r>   r>   r?   test_bessel   s^   "."
& **$ *

$
 "
r   c                  C   s"  ddl m}  ddlm} dd }|dtd d  tt|t ks$J |ttd d  tt|t ks8J |tt t |td ksIJ |dt	dtd   | dt|t ks`J t
t	tt	dtd   ttd u stJ |ttd d u sJ t
ttd  ttd u sJ d S )Nr   r   )	Heavisidec                 S   s   t t| ttS r@   )r   r*   r4   r5   fr>   r>   r?   inv!  s   ztest_inversion.<locals>.invrC   r7   )r   r   'sympy.functions.special.delta_functionsr   r4   r   r5   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
sFJ |jd d |||ksUJ |jd
 d s^J ||tt	d }|jd
 d |ksz|jd
 d |jks|J d S d S )Nr   Symbol)InverseLaplaceTransformr0   Trl   ry   r1   rs   rM   rC   )rp   r   sympy.integrals.transformsr   r   r   r   r4   r*   r5   r   rX   argsas_integral)r   r   r0   Fr   r1   f2ILTr>   r>   r?   !test_inversion_conditional_output.  s   $

2r   c                  C   s   ddl m}  ddlm} | ddd}| ddd	}d
dt  }| d}tt|t ttj	r/J tt|t ttd u s=J tt|t ttd u sKJ tt|t tt}|j	sZJ t
|jd d |sfJ d S )Nr   r   )
DiracDeltarK   Trs   r2   F)extended_realrC   r7   r6   )rp   r   r   r   r   r*   r   r4   r5   r   r8   r   )r   r   rK   r2   r0   r6   r   r>   r>   r?   %test_inversion_exp_real_nonreal_shiftC  s   
r   c                  C   sb  ddl m} m} ddlm} ddlm} i }t| t|	 D ]\}}t|t
dD ]\}}}	}
i }t|j|g D ]}t|drL|jrL|dd||< q:| d	d
||< q:t|ts]||}dd |D }tdd |D soJ |dd |D  }|j|d|j|d}}tt|t|}|dk rt||  dksJ q*t|| |  dksJ q*q d S )Nr   )uniform	randrangerD   )r6   )key
propertiesrC   rV   g      ?g       @c                 S   s   g | ]\}}t |qS r>   r!   )rF   r   r[   r>   r>   r?   rH   f      z%test_lookup_table.<locals>.<listcomp>c                 s   s"    | ]}|j p|t V  qd S r@   )r   hasr   )rF   r.   r>   r>   r?   	<genexpr>g  s     z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| qS r>   r>   )rF   r   r.   r>   r>   r?   rH   j  r   rh   g|=)sympy.core.randomr   r   rI   rE   sympy.integrals.meijerintr6   r(   sorteditemsr   listfree_symbolshasattrr   r8   allre   minr   )r   r   rE   z_dummytabler   lformulatermscondhintrX   aiexpandedr0   r1   rK   r>   r>   r?   test_lookup_tableR  s0   
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s8J 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sJ d S )Nr   rz   )	powdenestrO   Trn   polarr7   rT   rx   )r   r{   sympy.simplify.powsimpr   r    r   r.   rY   r   r   r   r   )r{   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sJ t| dtd tdd| ddt  ks0J d S )Nr   r   rC   Trn   )r   r   r    r   r.   r   r   r>   r>   r?   test_linear_subs~  s   (0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sKJ t	t
t
 t
t tfddks`J t	t
d t
 t
t tfddd d  ks}J t	t
d t
 t
t tfddd d d   ksJ t	t
t|| t
t tftt tfdddksJ 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sJ t	t
t t
 t|| t
t tftt tfdd| ks!J t	t
t d t
 t|| t
t tftt tfddd | ksJJ t	t
t d t
 t|| t
t tftt tfddd | kssJ t	t
d t
 t|| t
t tftt tfdd}|trJ t|d d  ksJ 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s'J |t
t  ks4J |t
td  d  d   ksKJ d dd   }t|t
t d d |t
t d d  |kspJ t|t
t d d |t
t d d  |ksJ t|t
t d |t
t d  |ksJ |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sJ ||d |d d  |	|
 d |	 |
d  |
d d  ks5J |ddd
\}}t
|d  t
 d |d   t||  t|t|  }tt	|t
ddfdddkskJ tt	t
| t
ddfdd|||  ksJ tt	t
d | t
ddfdd||d  ||  || d  ksJ 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s(J tt	t
d | t
dtfdd|ks=J d| d  t|d  t
|d d   tt
 d  }|t	|t
dtfdddksjJ tt	t
| t
dtfdd|ks}J tt	t
d | t
dtfdd||d  ksJ |t	t
| td|  d | t
dtfdddtd t| ksJ |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s%J tt	t
| t
dtfddd||d  tdd|   t|d d|   || d t|  ksYJ |ddd
\}}t|t
 | ||  |t
 | ||   t
 t|d  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||d  ksJ 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sCJ |t	t
| d | t
dtfd|d%  |d  ks`J | d&dd
}t	t|d t t| d t
|   t
| td'  t
|tfdksJ |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s1J tt	t
| | t
dtf|| td||   ksNJ 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sJ | d,dd-}| d.dd
}ttt
|  | d | }#t	|#t
t tfdddksJ 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   rk   )	gammasimp)powsimpzmu1 mu2T)nonzerozsigma1 sigma2rl   lambdac                 S   s6   dt dt |d   t| | d  d |d   S NrC   r7   )r   r   r   )r.   r   r   r>   r>   r?   normal  s   6z test_probability.<locals>.normalc                 S   s   |t | |   S r@   )r   )r.   rater>   r>   r?   exponential  s   z%test_probability.<locals>.exponentialrn   rC   r7   rO   rM   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   Trn   )r    r.   r/   r   )r;   res1res2r   r   mu1r   r   sigma1r>   r?   E  s   ztest_probability.<locals>.Ez
alpha betaseparater   ru   k)r|   rm   za b pr   zd1 d2rN   zlamda muc                 S   s   t | tS r@   )r#   rewriter   rA   r>   r>   r?   <lambda>  s    z"test_probability.<locals>.<lambda>rT   r2   r]   )r   re   )r   znu sigmar   rs   r1   )r~   r   rp   r   rk   sympy.simplify.gammasimpr   r   r   r    r.   r   r/   r   r	   r#   r   r   r   r   r   r   r   r   r   r   r   r   )$r   rk   r   r   mu2sigma2r   r   ansr}   betabetadistjr0   r1   r   chi
chisquaredpdagumr
   d1d2r   lamdar   distmysimpr2   distnre   r   nur   ricelaplacer>   r   r?   test_probability  s  & $$ 
$

$

  
$
 

.66.(.$
:"


.
:""
*8"&

&
8"*
.
.

"

 "
D"2:6

"
*
D $
*r   c            
      C   s  ddl m}  ddlm} ddlm}m}m}m}m	}m
} ttttt t tt  tdtfddd|jdd	|ttksBJ ttt t t tdtfddd| |dtks`J ttt t td
  tdtfddd| |d
t||ksJ ttt t td  tdtfddd| |dt|| ksJ | ddd}ttt t t|tfdd ||ksJ ttt t t|tfdd ||td
  ksJ tttt tdtfdd|tksJ t|tt tdtfdd|tksJ ttt t tdd |tt |dt ks,J ttt td
  tdd| |dttt t  tt  ksRJ | ddd}	tt|	|	 |	dd |	d ||	ksqJ tt|	|	 |	dd |	d ||	ksJ t|dttdd| t|dt tt  ksJ t|d
ttdd| td
  |dt d
 ttt  d
  tt d
  ksJ ttt|tttdd|jdd	|td t ksJ t|ttddt|t tt ksJ t||	|	dd |	||	 t|	 ks$J t|ttddt|t tt ks:J t||	|	dd |	||	 ||	 ksRJ t|ttt  tdtfddtd ksjJ t|dttt tdtfddtd
d
 ksJ dS )z% Test various exponential integrals. r   r   )sinh)ChiCiEiShiSiexpintrC   Tr   r   )funcr7   rO   r5   rl   rn   rL   r   rN   N)rp   r   %sympy.functions.elementary.hyperbolicr   'sympy.functions.special.error_functionsr   r   r   r   r   r   r#   r   r    r   r6   r.   r/   r   r   rq   r   r   r   r   as_independentr   r   )
r   r   r   r   r   r   r   r   r5   rL   r>   r>   r?   test_expintK  s    "

 
 
. (* 
$
"
"
 

6


,0,008r   c                  C   s  ddl m} m} ddlm}m} ddlm} ddlm	}m
}m}m} ddlm}	m}
 |
|ttt|t td  t ddfksBJ |
|ttt|tt t td d	kfksZJ |
|tttttd
 td	d	td    dt  t td d	kfksJ |
|ttttd	d  dttd
kttdk@ fksJ |	|d	tt ttdd}t|d jdd |d	 gtdtd	dt  ktddt  k B fdtdtd  td  d	  dftdkfksJ t|t|dt tdtfddtd	td ksJ t|t|d	t tdtfddttjtdd  ks J td	t td	td   tddt| d	t  ttd
 d	kft |d	t  dfksNJ d S )Nr   )r   acoth)r   atanr   )r   E1r   r   )fourier_transformlaplace_transformr7   TrC   ry   rM   F)noconds)deeprQ   rn   )!r   r   r   (sympy.functions.elementary.trigonometricr   r   r   r   r   r   r   r   r   r   r   r   r.   r4   r   r   r   r0   r   tuplefactorrq   r   r   r    r   rR   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r>   r>   r?   
test_messy  s@   0
4
$" 
 
 2r  c                   C   sJ   t tt td  tt tfddt tt ttt d  ks#J d S )Nr7   Trn   rN   )r    r   r   r.   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 )NrC   rO   Trn   )r.   r0   r1   r   r    r   r   )r;   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 rw   )r    r   r   r.   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s2J d S )Nr   fresnelcfresnelsr7   )	r   r	  r
  r   r    r   r   r.   r   r  r>   r>   r?   test_fresnel  s   *.r  c                   C   s   t ttt  td u sJ d S r@   )r&   r.   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s'J | ttjtjtddks7J d S )Nr7   rO   rT   )	r&   r.   r   together_eval_intervalr   NegativeOneOner   r   r>   r>   r?   test_issue_7337  s   0$r  c                   C   sh   t tttt t  tt d tt t d tt   tt t  d td d  ks2J d S r   )r&   r   r.   r   r5   r>   r>   r>   r?   test_issue_8368  s   0
r  c                  C   st   ddl m} m} tdttt d | d  d  td|ftd|fdtd|d | d    |  d|   ks8J d S )Nr   hwrC   r7   rO   )	sympy.abcr  r  r    r   r/   r.   r  r>   r>   r?   test_issue_10211  s   2&r  c                  C   sr   ddl m}  | ddd\}}tdttd |d  d  t| |fd| |d t|d |d    ks7J d S )	Nr   rj   zy LTrl   rC   r7   rO   )rp   rk   r    r   r.   )rk   r/   Lr>   r>   r?   test_issue_11806  s
   ("r  c                  C   s   ddl m}  ddlm}m} t|d |d |d  d  |dd}d|d	  |d
  tdtd
dftddf|d tdt	 t
  |d   }| ||  d	dsUJ d S )Nr   )RR)RrK   r7   g      ?Trn   gUUUUUU?g      ?rO   g      rT   g-q=)sympy.polys.domains.realfieldr  r  r  rK   r    r   r   r   r   r   almosteqre   )r  r  rK   r   r[   r>   r>   r?   test_issue_10681  s   &*r  c                  C   s@   ddl m}  | ddd}tdtd  tt|fd| ksJ d S )	Nr   r   r0   Trl   rC   r7   rM   )rp   r   r    r.   r   )r   r0   r>   r>   r?   test_issue_13536  s   (r  c                  C   sj   ddl m}  | d}| d}tt|| ||  |dd|dtt|d |d  |dds3J d S )Nr   r   r.   re   Trn   r7   )rp   r   r    r   rX   equals)r   r.   re   r>   r>   r?   test_issue_6462  s   &r!  c                   C   sj   t tt t  tddt tt dtt  t  td   ttt dtt  t  td    ks3J d S )NTrn   rC   )r    r1   r5   r0   r>   r>   r>   r?   test_indefinite_1_bug  s
   $"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 )NrC   r7   Trn   )r    r   r.   r   r   r   r	   r   r>   r>   r>   r?   test_pr_23583  s   6r#  N)hr~   r   sympy.core.numbersr   r   r   r   sympy.core.singletonr   sympy.core.sortingr   $sympy.functions.elementary.complexesr	   r
   r   r   &sympy.functions.elementary.exponentialr   r   r   r   r   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   r   r   r   r   r   r   r   r   r   r   r   r   sympy.functions.special.hyperr   r   sympy.integrals.integralsr   r    sympy.simplify.hyperexpandr"   sympy.simplify.simplifyr#   r   r$   r%   r&   r'   r(   r)   r*   sympy.testing.pytestr+   r   r,   r-   rW   r  r.   r/   r0   r1   r2   r3   r4   r5   r6   rS   rU   r_   rb   ri   rr   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r  r  r  r  r!  r"  r#  r>   r>   r>   r?   <module>   sp    $,)
j0
 
 G
6%
