U
    L?hR                     @   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td S )Nc                 S   sn   t ttgtg|gtg| t}|d k	s*tt|d d d tsDt|d d d j	t||ffksjtd S )Nr      )
r&   r   r2   r3   r5   r0   AssertionError
isinstanceargumentZas_coeff_mul)exprr4   me r@   V/var/www/html/venv/lib/python3.8/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 ks&td S N)r&   r   r2   r3   r4   r5   r0   r:   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|| |sDt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:   )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   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svtd S )NrQ   r9      rE   r   T)	r'   r0   r   r2   r3   r4   r5   r1   r:   r@   r@   r@   rA   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 k	sZt	t
|||t|ts|t	d S )N
   )r   r2   r3   r4   r5   randcplxr   r(   r0   r:   r.   subsdiff)Zfacr
   grZ   Z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    

r_   c                  C   sL   t ttdd\} }| jr |dks$tt tttt\} }| jrD|dksHtd S )Nr   T)r+   r0   is_zeror:   r   )vr3   r@   r@   rA   test_meijerint_definiteY   s    rb   c                     s   t t d tt d t tt tt tt d i  fdd} | t gtggtgtggtds`t| t tgtggtgtggtdst| t gtggttgtggdtd  dstd S )NrX   c                    sD   ddl m} t| ||}|t|| }t| | tdddS )Nr   )Mulg?g)r3   r5   )Zsympy.core.mulrc   r   r)   r.   rZ   r0   )r2   r3   r
   nrc   m1m2rZ   r@   rA   r7   d   s    ztest_inflate.<locals>.trQ   r9   )	r2   rY   r3   r   r4   r5   r1   r0   r:   r^   r@   rg   rA   test_inflate`   s       "$rh   c                  C   s$  ddl m}  | ddd\}}}tt| d  tt| d   }t|tdtfdd}t| tdtt	 t
td||  d d t|d  d ||  |d d    d	 kstttt| d  tt| d   t|t  tdtfdd}t|tdtt	 t
tdd| d|  |  d	 d  t|d  |d  d| d|  | d d
   d	 ksxttttt| | | d  tdtfddtt	d dt
|| |   ksttttt| | | d  tdtfddtt	d dt
|| |   ks td S )Nr   symbolsza b cTpositiver9   r   rE   rP      )sympy.core.symbolrj   r   r0   r!   r   r%   expandr   r   r   r:   )rj   r2   r3   r4   rM   r?   r@   r@   rA   test_recursivep   s2    $
@@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sxt|d	dd
}tt	| tg g gdgg gt	 t	dtft
|d ksttt	| tg g gdgg gt	 t	dtfddt
|d kstttt	| tg g gdgg gt	 t	dtfddts6tttt	t	tt	ksRt|ddd
\}}ttt	| t	d|d ||d  |d  ksttt	d d tt	  t	dtdkst|ddd
\}}ttt	| d|  d  t	dt\}}	t|tt| dt|d|    ks&t|	dks4ttt| t	 t|t	  t	dt\}}
t|d||  ksvtttt	t	t dtddfkst| ttt	t	dtd ttd kst| ttt	 t	dt	d dttttt	  tt	  kstttt	d  t	t tttdfks8ttttt	 t	t tdks\tttdt	 d d  t	t tttd dfksttttdt	 d  t	t tdkstttt	| | d  d tdt |d   t	t tdkstttt	d t	t ttdfks*tttt	 tt	 t	dttjdfksVtdd }tdD ]>}ttt	 tt	 t	|  t	dtfdd||ksftqftttt	 tt	|  t	dtfddtdt|td   d kst|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s6tttt	| tt	|  t	dtfddttt	| tt	|  t	dtfkstttt	d  tt	 t	dtfddtttdtj d  kstddlm } |ddd}tttt	 t	|  t	dd||d t	kst|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st|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*td S )!Nr   )rp   ri   zs t muTrealr9   rP   r6   rk   rE   rm   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   )rd   r@   r@   rA   rI      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_Piecewiser:   r0   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   _rI   rd   rz   r|   r@   r@   rA   test_meijerint   s    $
(
&
  

*(.(&, 
,$ 
,.  
&,((
" 
  :8B
	&"
$

 &
 

*4r   c                  C   sv  ddl m} m} tt|tt|tt t tdtfddddt	t
td td    t
tt  tt   ksrttt|tt|tt t tdtfdddddt  kstttt	tt td d ttj    tdtfdddd td t tt
 ttjt   |ttks ttt|dt tddt|dt ksLttt| dt tddt| dt ksxtt|dttdd|dt kstt|dtd t tdd|dtd |dtd   d kstt|dtd td  tddd	t |dtd  dt |dtd   d|dt |dt  |dtd t  ks^tt|dt|dt tdd|dtd  d kstttd |dt |dt tddtd |dtd  d kstt|dt|dt t tddt|dtd  t|dtd   |dt|dt  ks<tt|dtd t tdd|dtd  d ksrtd S )
Nr   besselibesseljTnoner   condsr9   rE   rm   rx   )sympy.functions.special.besselr   r   r%   r!   r2   r8   r3   r   r   r   r:   r0   r1   r   rT   r   r   r   r@   r@   rA   test_bessel   sf    " ." 
&   
,,& 
*

$
 "
r   c                  C   s&  ddl m}  ddlm} dd }|dtd d  tt|t ksHt|ttd d  tt|t kspt|t	t t |td kst|dt
dtd   | dt|t ksttt
tt
dtd   ttd kst|t	td d ksttt	td  ttd ks"t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@   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^t| ddd	}|||}t|tt	}|j
st|jd d |||kst|jd
 d st||tt	d }|jd
 d |ks|jd
 d |jkstd S )Nr   Symbol)InverseLaplaceTransformr2   Trk   rx   r3   rr   rO   rE   )ro   r   sympy.integrals.transformsr   r   r   r   r6   r,   r7   r~   r:   rZ   argsZas_integral)r   r   r2   Fr   r3   f2ZILTr@   r@   rA   !test_inversion_conditional_output.  s    $

r   c                  C   s   ddl m}  ddlm} | ddd}| ddd	}d
dt  }| d}tt|t ttj	r^t
tt|t ttd kszt
tt|t ttd kst
tt|t tt}|j	st
t|jd d |st
d S )Nr   r   )
DiracDeltarM   Trr   r4   F)Zextended_realrE   r9   r8   )ro   r   r   r   r   r,   r   r6   r7   r~   r:   r;   r   )r   r   rM   r4   r2   r8   r   r@   r@   rA   %test_inversion_exp_real_nonreal_shiftC  s    
r   c                  C   sb  ddl m} m} ddlm} ddlm} i }t| | D ]}t	|t
dD ]
\}}}}	i }
t|j|g D ]2}t|dr|jr|dd|
|< qp| d	d
|
|< qpt|ts||
}dd |D }tdd |D st|dd |D  }|j|
d|j|
d }}tt|t|}|dk r>t||  dksZtqNt|| |  dksNtqNq<d S )Nr   )uniform	randrangerF   )r8   )key
propertiesrE   rX   g      ?g       @c                 S   s   g | ]\}}t |qS r@   r"   )rH   r   r\   r@   r@   rA   rJ   f  s     z%test_lookup_table.<locals>.<listcomp>c                 s   s    | ]}|j p|t V  qd S rB   )r~   hasr   )rH   r0   r@   r@   rA   	<genexpr>g  s     z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| qS r@   r@   )rH   r   r0   r@   r@   rA   rJ   j  s     rg   g|=)sympy.core.randomr   r   rK   rG   sympy.integrals.meijerintr8   r*   valuessortedr   listZfree_symbolshasattrr   r;   allr:   rd   minr   )r   r   rG   Zz_dummytablelZformulaZtermsZcondhintrZ   Zaiexpandedr2   r3   rM   r@   r@   rA   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spt
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st
d S )Nr   ry   )	powdenestrQ   Trm   Zpolarr9   rV   rw   )r   rz   sympy.simplify.powsimpr   r!   r   r0   r[   r   r   r:   r   r   )rz   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s4tt| dtd tdd| ddt  ks`td S )Nr   r   rE   Trm   )r   r   r!   r   r0   r   r:   r   r@   r@   rA   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stt	t
t
 t
t tfddkstt	t
d t
 t
t tfddd d  kstt	t
d t
 t
t tfddd d d   ks>tt	t
t|| t
t tftt tfdddks|tt	t
t
 t|| t
t tftt tfddkstt	tt
 t|| t
t tftt tfdd|ks tt	t
t t
 t|| t
t tftt tfdd| ksJtt	t
t d t
 t|| t
t tftt tfddd | kstt	t
t d t
 t|| t
t tftt tfddd | kstt	t
d t
 t|| t
t tftt tfdd}|tr:tt|d d  ksXtt	td t
 t|| t
t tftt tfdd|d |d  kstt	t
t
dtfdddkstt	t
t
 t
dtfddd kstt	t
d t
 t
dtfdddd  ks.t fdd}|ddksVt|t
t  kspt|t
td  d  d   kstd dd   }t|t
t d d |t
t d d  |kstt|t
t d d |t
t d d  |kstt|t
t d |t
t d  |ksLt|ddd
\}	}
t
|	d  dt
 |	 |
   t|	|
  t|	 t|
 }t	|t
dtfdddkstt	t
| t
dtfddd}||d |d f|	|
d  d|
k fkstt	t
d | t
dtfddd}|d |
dkks0t||d |d d  |	|
 d |	 |
d  |
d d  ksrt|ddd
\}}t
|d  t
 d |d   t||  t|t|  }tt	|t
ddfdddksttt	t
| t
ddfdd|||  ksttt	t
d | t
ddfdd||d  ||  || d  ksRttt	t
t | t
ddfddt|| t|t  t| t|| t  kst| 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ttt	t
| t
dtfddtdt|d d  t|d  ksXttt	t
d | t
dtfdd|kstd| d  t|d  t
|d d   tt
 d  }|t	|t
dtfdddksttt	t
| t
dtfdd|k	sttt	t
d | t
dtfdd||d  k	s4t|t	t
| td|  d | t
dtfdddtd t| k	s~t|ddd
\}}}|| t
 t
| ||   dt
| ||   |d   }tt	|t
dtfdddk	stt
| }tt	|t
dtfddd|| tdd|   t|d d|   || d t|  k
sRttt	t
| t
dtfddd||d  tdd|   t|d d|   || d t|  k
st|ddd
\}}t|t
 | ||  |t
 | ||   t
 t|d  t|d  t|| d  }tt	|t
dtfdddksDttt	t
| t
dtfddd||d  kstttt	t
d | t
dtfddd|d |d  | |d   |d  kst|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:t|t	t
| t
dtf|ks\t|t	t
| d | t
dtf|d | kst|t	t
| d | t
dtfd|d%  |d  kst| d&dd
}t	t|d t t| d t
|   t
| td'  t
|tfdks t|ddd
\}	}
|
|	 t
|
d   |	|
d   dt
|
 |	|
   d  }tt	|t
dtfdksttt	t
| t
dtfdd(t|	 |
 tt|
  ksttt	t
t | t
dtfdd(t|	t  t |
 ttt |
  ks
t| ddd
}| d)dd
}|| t
| |d   tt
| |   }tt	|t
dtfdksjttt	t
| | t
dtf|| td||   kst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"t| d,dd-}| d.dd
}ttt
|  | d | }#t	|#t
t tfdddksxtt	t
|# t
t tfdd|kstt	t
d |# t
t tfddd|d  |d  kst| ddd
}| t	tt
t
|d   tt
  t| t
dtftd|ks*t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 NrE   r9   )r   r   r   )r0   r   r   r@   r@   rA   normal  s    z test_probability.<locals>.normalc                 S   s   |t | |   S rB   )r   )r0   rater@   r@   rA   exponential  s    z%test_probability.<locals>.exponentialrm   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|t|S )Nr   Trm   )r!   r0   r1   r   r:   )r=   Zres1Zres2r   r   Zmu1r   r   Zsigma1r@   rA   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 rB   )r%   rewriter   rC   r@   r@   rA   <lambda>      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   r:   r1   r   r	   r%   r   r   r   r   r   r   r   r   r   r   r   r   )$r   rj   r   r   Zmu2Zsigma2r   r   ansr|   betaZbetadistjr2   r3   r   chiZ
chisquaredpZdagumr
   Zd1Zd2r   Zlamdar   distZmysimpr4   Zdistnrd   r   nur   riceZlaplacer@   r   rA   test_probability  s   & $$

 
 

 
 

 
 
 
 
 
$
 
 

$
 
 

 
 
  
 
 
$
 

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

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

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

 "
D"2:6

"
*
D $
*r   c            
      C   s  ddl m}  ddlm} ddlm}m}m}m}m	}m
} ttttt t tt  tdtfddd|jdd	|ttkstttt t t tdtfddd| |dtkstttt t td
  tdtfddd| |d
t||kstttt t td  tdtfddd| |dt|| ks`t| ddd}ttt t t|tfdd ||kstttt t t|tfdd ||td
  ksttttt tdtfdd|tkstt|tt tdtfdd|tks(tttt t tdd |tt |dt ksbtttt td
  tdd| |dttt t  tt  kst| ddd}	tt|	|	 |	dd |	d ||	ksttt|	|	 |	dd |	d ||	kstt|dttdd| t|dt tt  ksZtt|d
ttdd| td
  |dt d
 ttt  d
  tt d
  kstttt|tttdd|jdd	|td t kstt|ttddt|t tt ks"tt||	|	dd |	||	 t|	 ksRtt|ttddt|t tt ks~tt||	|	dd |	||	 ||	 kstt|ttt  tdtfddtd kstt|dttt tdtfddtd
d
 kstdS )z% Test various exponential integrals. r   r   )r   )ChiCiEiShiSiexpintrE   Tr   r   )funcr9   rQ   r7   rk   rm   rN   r   rP   N)ro   r   %sympy.functions.elementary.hyperbolicr   'sympy.functions.special.error_functionsr   r   r   r   r   r   r%   r   r!   r   r8   r0   r1   r   r   rp   r:   r   r   r   r   Zas_independentr   r   )
r   r   r   r   r   r   r   r   r7   rN   r@   r@   rA   test_expintK  s     "  
 
0 
** 
$
"
"

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st|
|tttdd|tt t td	 d
kfkst|
|tttddttd td
d
td	    d	t  t td	 d
kfkst|
|ttttd
d  dttdkttdk@ fksJt|	|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stt|t|dt tdtfddtd
td	 kstt|t|d
t tdtfddttjtd	d	  ksNt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std S )Nr   )r   acoth)r   atanr   )r   E1r   r   )fourier_transformlaplace_transformTr$   r9   rE   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   r   r2   r   factorrp   r   r   r!   r   rT   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r@   r@   rA   
test_messy  sL    
  

&  

$"
 
 
 2r   c                   C   sJ   t tt td  tt tfddt tt ttt d  ksFtd S )Nr9   Trm   rP   )r!   r   r   r0   r   r   r   r:   r@   r@   r@   rA   test_issue_6122  s    "r   c                  C   s>   dt  ttt   tdd  } t| t dd}|tr:td S )NrE   rQ   Trm   )r0   r2   r3   r   r!   r   r   r:   )r=   Zantir@   r@   rA   test_issue_6252  s    r   c                   C   sD   t ttt dtd   tt tf tttd ks@td S rv   )	r!   r   r   r0   r   r%   r   r   r:   r@   r@   r@   rA   test_issue_6348  s    .
r   c                  C   sh   ddl m} m} tttttd  d t|tks:tttt	ttd  d t| tksdtd S )Nr   fresnelcfresnelsr9   )
r   r   r   r   r!   r   r   r0   r:   r   r   r@   r@   rA   test_fresnel  s    *r   c                   C   s   t ttt  td kstd S rB   )r(   r0   r:   r@   r@   r@   rA   test_issue_6860  s    r   c                  C   sr   t ttdt d  t } | tdt d dtd  t d  d ksNt| ttjtjt	ddksntd S )Nr9   rQ   rV   )
r(   r0   r   Ztogetherr:   Z_eval_intervalr   ZNegativeOneZOner   r   r@   r@   rA   test_issue_7337  s    0r   c                   C   sh   t tttt t  tt d tt t d tt   tt t  d td d  ksdtd S r   )r(   r   r0   r   r7   r:   r@   r@   r@   rA   test_issue_8368  s    $ 
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sptd S )Nr   hwrE   r9   rQ   )	sympy.abcr   r   r!   r   r1   r0   r:   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sntd S )	Nr   ri   zy LTrk   rE   r9   rQ   )ro   rj   r!   r   r0   r:   )rj   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st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   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<td S )	Nr   r   r2   Trk   rE   r9   rO   )ro   r   r!   r0   r   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sftd S )Nr   r   r0   rd   Trm   r9   )ro   r   r!   r   rZ   equalsr:   )r   r0   rd   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sJtd S )NTrm   rE   )r!   r3   r7   r2   r:   r@   r@   r@   rA   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\td S )NrE   r9   Trm   )	r!   r   r0   r   r   r   r	   r   r:   r@   r@   r@   rA   test_pr_23583  s    6r   c                   C   s:   t ttd  tddfddttd td ks6td S )Nr9   r   Trm   rV   )r!   r   r0   r   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sLtd S )Nr   ri   r1   Tr   rE   rO   g      пrm   g      ?)ro   rj   r!   r   r0   r   r:   )rj   r1   r@   r@   rA   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@   rA   <module>   sr   $,)
j0
 
 G
6&
