o
    jgR                     @   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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   r2   r3   r5   r0   
isinstanceargumentas_coeff_mul)exprr4   me r@   \/var/www/html/zoom/venv/lib/python3.10/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@   rA   tn!   s   *ztest_rewrite_single.<locals>.tn   r9   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   r9   r@   ).0resr@   r@   rA   
<listcomp>-   s    z2test_rewrite_single.<locals>.u.<locals>.<listcomp>)sympy.core.addrG   r&   replacer   r   r.   )r=   r0   rG   rr?   r@   r@   rA   u*   s   
ztest_rewrite_single.<locals>.ur         )rE   r@   @   T)r0   r1   r   r   r&   r   r   r   r   r   Halfr   r   )r7   rD   rN   r@   r@   rA   test_rewrite_single   s$   $&*rU   c                   C   sz   t td ttgtgtgtgtd ttd    d tdtd ddttgtgtgtgtd td  fgdfks;J d S )NrQ   r9      rE   r   T)r'   r0   r   r2   r3   r4   r5   r1   r@   r@   r@   rA   test_rewrite1C   s   86rW   c                  C   s~   dd } | dt  | dt  | ddt   | dt d  | dt td  | t d t  | dt td  dt td	   d S )
Nc                 S   s   t tgtgtgtg||  }tt d tt d t tt tt i}t|t}|d us-J t	|
||t
|ts>J d S )N
   )r   r2   r3   r4   r5   randcplxr   r(   r0   r.   subsdiff)facr
   grZ   integralr@   r@   rA   r7   I   s   
&z0test_meijerint_indefinite_numerically.<locals>.trE   r9   rV   3/2rQ   rP   z7/3)r0   r   r7   r@   r@   rA   %test_meijerint_indefinite_numericallyH   s   

&ra   c                  C   sL   t ttdd\} }| jr|du sJ t tttt\} }| jr"|du s$J d S )Nr   T)r+   r0   is_zeror   )vr3   r@   r@   rA   test_meijerint_definiteY   s   rd   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 )NrX   c                    sD   ddl m} t| ||}|t|| }t| | tdddS )Nr   )Mulg?g)r3   r5   )sympy.core.mulre   r   r)   r.   rZ   r0   )r2   r3   r
   nre   m1m2rZ   r@   rA   r7   d   s   ztest_inflate.<locals>.trQ   r9   )r2   rY   r3   r   r4   r5   r1   r0   r`   r@   rj   rA   test_inflate`   s   "$0rk   c                  C   s   ddl m}  | ddd\}}}tt| d  tt| d   }t|tdtfdd}t| tdtt	 t
td||  d d t|d  d ||  |d d    d	 ks^J ttt| d  tt| d   t|t  tdtfdd}t|tdtt	 t
tdd| d|  |  d	 d  t|d  |d  d| d|  | d d
   d	 ksJ tttt| | | d  tdtfddtt	d dt
|| |   ksJ tttt| | | d  tdtfddtt	d dt
|| |   ksJ d S )Nr   symbolsza b cTpositiver9   r   rE   rP      )sympy.core.symbolrm   r   r0   r!   r   r%   expandr   r   r   )rm   r2   r3   r4   rM   r?   r@   r@   rA   test_recursivep   s2   $
@@H,,rt   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   )rs   rl   zs t muTrealr9   rP   r6   rn   rE   rp   Fa brQ   )   Tzsigma mu)r9   T)rE   Tc                 S   s(   ddt d   t | t dd|   S NrE   r9   rO   )r0   r[   rZ   )rg   r@   r@   rA   rI      s   (ztest_meijerint.<locals>.res   za b s
lowergammarg   )integeralphar@   rO   rx   za s)!sympy.core.functionrs   rr   rm   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_functionsr}   r   )rs   rm   r6   r7   mur2   r3   sigmair4   _rI   rg   r}   r   r@   r@   rA   test_meijerint   s   $(
&
 
((.(&, 
,$ 
,.
&,((
" 
:8B
&	"
$

 &
 
*4r   c                  C   sl  ddl m} m} tt|tt|tt t tdtfddddt	t
td td    t
tt  tt   ks9J tt|tt|tt t tdtfdddddt  ksXJ ttt	tt td d ttj    tdtfdddd td t tt
 ttjt   |ttksJ tt|dt tddt|dt ksJ tt| dt tddt| dt ksJ t|dttdd|dt ksJ t|dtd t tdd|dtd |dtd   d ksJ t|dtd td  tddd	t |dtd  dt |dtd   d|dt |dt  |dtd t  ks*J t|dt|dt tdd|dtd  d ksFJ ttd |dt |dt tddtd |dtd  d ksiJ t|dt|dt t tddt|dtd  t|dtd   |dt|dt  ksJ t|dtd t tdd|dtd  d ksJ d S )
Nr   besselibesseljTnoner   condsr9   rE   rp   r{   )sympy.functions.special.besselr   r   r%   r!   r2   r8   r3   r   r   r   r0   r1   r   rT   r   r   r   r@   r@   rA   test_bessel   s^   "."
& **$ *

$
 "
r   c                  C   s"  ddl m}  ddlm} dd }|dtd d  tt|t ks$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 rB   )r   r,   r6   r7   fr@   r@   rA   inv!  s   ztest_inversion.<locals>.invrE   r9   )r   r   'sympy.functions.special.delta_functionsr   r6   r   r7   r   r   r   r,   )r   r   r   r@   r@   rA   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)InverseLaplaceTransformr2   Trn   r{   r3   ru   rO   rE   )rr   r   sympy.integrals.transformsr   r   r   r   r6   r,   r7   r   rZ   argsas_integral)r   r   r2   Fr   r3   f2ILTr@   r@   rA   !test_inversion_conditional_output.  s   $

2r   c                  C   s   ddl m}  ddlm} | ddd}| ddd	}d
dt  }| d}tt|t ttj	r/J tt|t ttd u s=J tt|t ttd u sKJ tt|t tt}|j	sZJ t
|jd d |sfJ d S )Nr   r   )
DiracDeltarM   Tru   r4   F)extended_realrE   r9   r8   )rr   r   r   r   r   r,   r   r6   r7   r   r:   r   )r   r   rM   r4   r2   r8   r   r@   r@   rA   %test_inversion_exp_real_nonreal_shiftC  s   
r   c                  C   sZ  ddl m} m} ddlm} ddlm} i }t| | D ]}t	|t
dD ]\}}}}	i }
t|j|g D ]}t|drH|jrH|dd|
|< q6| d	d
|
|< q6t|tsY||
}dd |D }tdd |D skJ |dd |D  }|j|
d|j|
d}}tt|t|}|dk rt||  dksJ q&t|| |  dksJ q&qd S )Nr   )uniform	randrangerF   )r8   )key
propertiesrE   rX   g      ?g       @c                 S   s   g | ]\}}t |qS r@   r"   )rH   r   r]   r@   r@   rA   rJ   f      z%test_lookup_table.<locals>.<listcomp>c                 s   s"    | ]}|j p|t V  qd S rB   )r   hasr   )rH   r0   r@   r@   rA   	<genexpr>g  s     z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| qS r@   r@   )rH   r   r0   r@   r@   rA   rJ   j  r   rj   g|=)sympy.core.randomr   r   rK   rG   sympy.integrals.meijerintr8   r*   valuessortedr   listfree_symbolshasattrr   r:   allrg   minr   )r   r   rG   z_dummytablelformulatermscondhintrZ   aiexpandedr2   r3   rM   r@   r@   rA   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   r|   )	powdenestrQ   Trp   polarr9   rV   rz   )r   r}   sympy.simplify.powsimpr   r!   r   r0   r[   r   r   r   r   )r}   r   r@   r@   rA   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   rE   Trp   )r   r   r!   r   r0   r   r   r@   r@   rA   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   rm   )	gammasimp)powsimpzmu1 mu2Tnonzerozsigma1 sigma2rn   lambdac                 S   s6   dt dt |d   t| | d  d |d   S NrE   r9   )r   r   r   )r0   r   r   r@   r@   rA   normal  s   6z test_probability.<locals>.normalc                 S   s   |t | |   S rB   )r   )r0   rater@   r@   rA   exponential  s   z%test_probability.<locals>.exponentialrp   rE   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   Trp   )r!   r0   r1   r   )r=   res1res2r   r   mu1r   r   sigma1r@   rA   E  s   ztest_probability.<locals>.Ez
alpha betaseparater   rw   k)r~   ro   za b pr   zd1 d2rP   zlamda muc                 S   s   t | tS rB   )r%   rewriter   rC   r@   r@   rA   <lambda>  s    z"test_probability.<locals>.<lambda>rV   r4   r_   )r   rg   )r   znu sigmar   ru   r3   )r   r   rr   r   rm   sympy.simplify.gammasimpr   r   r   r!   r0   r   r1   r   r	   r%   r   r   r   r   r   r   r   r   r   r   r   r   )$r   rm   r   r   mu2sigma2r   r   ansr   betabetadistjr2   r3   r   chi
chisquaredpdagumr
   d1d2r   lamdar   distmysimpr4   distnrg   r   nur   ricelaplacer@   r   rA   test_probability  s  & $$ 
$

$

  
$
 

.66.(.$
:"


.
:""
*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   )r   )ChiCiEiShiSiexpintrE   Tr   r   )funcr9   rQ   r7   rn   rp   rN   r   rP   N)rr   r   %sympy.functions.elementary.hyperbolicr   'sympy.functions.special.error_functionsr   r   r   r   r   r   r%   r   r!   r   r8   r0   r1   r   r   rs   r   r   r   r   as_independentr   r   )
r   r   r   r   r   r   r   r   r7   rN   r@   r@   rA   test_expintK  s    "

 
 
. (* 
$
"
"
 

6


,0,008r   c                  C   s  ddl m} m} ddlm}m} ddlm} ddlm	}m
}m}m} ddlm}	m}
 |
|tttdd|t td	  t ddfksDJ |
|tttdd|tt t td	 d
kfks^J |
|tttddttd td
d
td	    d	t  t td	 d
kfksJ |
|ttttd
d  dttdkttdk@ fksJ |	|d
tt ttdd}|d jdd |d
 ftdtd
d	t  ktdd	t  k B fd	tdtd	  td	  d
  dftdkfksJ t|t|dt tdtfddtd
td	 ksJ t|t|d
t tdtfddttjtd	d	  ks$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sRJ d S )Nr   )r   acoth)r   atanr   )r   E1r   r   )fourier_transformlaplace_transformTr$   r9   rE   r{   rO   F)noconds)deeprS   rp   ) r   r   r   (sympy.functions.elementary.trigonometricr   r   r   r   r   r   r   r   r   r   r   r   r0   r6   r   r   r   r2   r   factorrs   r   r   r!   r   rT   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r@   r@   rA   
test_messy  sD   
4
$" 
 
 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 )Nr9   Trp   rP   )r!   r   r   r0   r   r   r   r@   r@   r@   rA   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 )NrE   rQ   Trp   )r0   r2   r3   r   r!   r   r   )r=   antir@   r@   rA   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 ry   )r!   r   r   r0   r   r%   r   r   r@   r@   r@   rA   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fresnelsr9   )	r   r
  r  r   r!   r   r   r0   r   r	  r@   r@   rA   test_fresnel  s   *.r  c                   C   s   t ttt  td u sJ d S rB   )r(   r0   r@   r@   r@   rA   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 )Nr9   rQ   rV   )	r(   r0   r   together_eval_intervalr   NegativeOneOner   r   r@   r@   rA   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   r0   r   r7   r@   r@   r@   rA   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wrE   r9   rQ   )	sympy.abcr  r  r!   r   r1   r0   r  r@   r@   rA   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   rl   zy LTrn   rE   r9   rQ   )rr   rm   r!   r   r0   )rm   r1   Lr@   r@   rA   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)RrM   r9   g      ?Trp   gUUUUUU?g      ?rQ   g      rV   g-q=)sympy.polys.domains.realfieldr  r  r  rM   r!   r   r   r   r   r   almosteqrg   )r  r  rM   r   r]   r@   r@   rA   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   Trn   rE   r9   rO   )rr   r   r!   r0   r   )r   r2   r@   r@   rA   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   r0   rg   Trp   r9   )rr   r   r!   r   rZ   equals)r   r0   rg   r@   r@   rA   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s%J d S )NTrp   rE   )r!   r3   r7   r2   r@   r@   r@   rA   test_indefinite_1_bug  s   N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 )NrE   r9   Trp   )r!   r   r0   r   r   r   r	   r   r@   r@   r@   rA   test_pr_23583  s   6r$  c                   C   s:   t ttd  tddfddttd td ksJ d S )Nr9   r   Trp   rV   )r!   r   r0   r   r   r   r@   r@   r@   rA   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s&J d S )Nr   rl   r1   Tr   rE   rO   g      пrp   g      ?)rr   rm   r!   r   r0   r   )rm   r1   r@   r@   rA   test_issue_25949  s   8r'  N)kr   r   sympy.core.numbersr   r   r   r   sympy.core.singletonr   sympy.core.sortingr   $sympy.functions.elementary.complexesr	   r
   r   r   &sympy.functions.elementary.exponentialr   r   r   r   r   r   r   (sympy.functions.elementary.miscellaneousr   $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/   rY   r  r0   r1   r2   r3   r4   r5   r6   r7   r8   rU   rW   ra   rd   rk   rt   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$  r&  r'  r@   r@   r@   rA   <module>   st    $,)
j0
 
 G
6&
