a
    {žd	~  ć                   @   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 )Té    )Śexpand_func)ŚIŚRationalŚooŚpi)ŚS)Śdefault_sort_key)ŚAbsŚargŚreŚ
unpolarify)ŚexpŚ	exp_polarŚlog)ŚcoshŚacosh)Śsqrt)Ś	PiecewiseŚpiecewise_fold)ŚcosŚsinŚsincŚasin)ŚerfŚerfc)ŚgammaŚ	polygamma)ŚhyperŚmeijerg)ŚIntegralŚ	integrate©Śhyperexpand©Śsimplify)Ś_rewrite_singleŚ	_rewrite1Śmeijerint_indefiniteŚ
_inflate_gŚ_create_lookup_tableŚmeijerint_definiteŚmeijerint_inversion)Śslow)Śverify_numericallyŚrandom_complex_number)	ŚxŚyŚaŚbŚcŚdŚsŚtŚ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   é   )	r%   r   r1   r2   r4   r/   Ś
isinstanceŚargumentZas_coeff_mul)Śexprr3   ŚmŚe© r>   śm/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/integrals/tests/test_meijerint.pyr6      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   r1   r2   r3   r4   r/   ©r;   r>   r>   r?   Śtn!   s    ztest_rewrite_single.<locals>.tné   r8   c                 S   sH   ddl m} t| |}|dd |d D   tt”}t|| |sDJ d S )Nr   ©ŚAddc                 S   s   g | ]}|d  |d  qS )r   r8   r>   )Ś.0Śresr>   r>   r?   Ś
<listcomp>-   ó    z2test_rewrite_single.<locals>.u.<locals>.<listcomp>)Śsympy.core.addrE   r%   Śreplacer   r   r-   )r;   r/   rE   Śrr=   r>   r>   r?   Śu*   s    
’ztest_rewrite_single.<locals>.ur   é’’’’é   é   )rC   r>   é@   éü’’’T)r/   r0   r   r   r%   r   r   r   r   r   ŚHalfr   r   )r6   rB   rM   r>   r>   r?   Śtest_rewrite_single   s$    $&*’’ž’rT   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 )NrP   r8   é   rC   r   T)r&   r/   r   r1   r2   r3   r4   r0   r>   r>   r>   r?   Śtest_rewrite1C   s    86’rV   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 )Né
   )r   r1   r2   r3   r4   Śrandcplxr   r'   r/   r-   ŚsubsŚdiff)Zfacr
   ŚgrY   Zintegralr>   r>   r?   r6   I   s    ’
z0test_meijerint_indefinite_numerically.<locals>.trC   r8   rU   ś3/2rP   rO   z7/3)r/   r   ©r6   r>   r>   r?   Ś%test_meijerint_indefinite_numericallyH   s    

r^   c                  C   sL   t ttdd\} }| jr |du s$J t tttt\} }| jrD|du sHJ d S )Nr   T)r*   r/   Śis_zeror   )Śvr2   r>   r>   r?   Śtest_meijerint_definiteY   s    ra   c                     s“   t t d tt d t tt tt tt d i  fdd} | t gtggtgtggtds`J | t tgtggtgtggtdsJ | t gtggttgtggdtd  ds°J d S )NrW   c                    sD   ddl m} t| ||}|t|| }t|  ”|  ”tdddS )Nr   )ŚMulg¹?g¹æ)r2   r4   )Zsympy.core.mulrb   r   r(   r-   rY   r/   )r1   r2   r
   Śnrb   Śm1Śm2©rY   r>   r?   r6   d   s    ztest_inflate.<locals>.trP   r8   )r1   rX   r2   r   r3   r4   r0   r/   r]   r>   rf   r?   Śtest_inflate`   s    ’"$rg   c                  C   s$  ddl m}  | ddd\}}}tt| d  tt| d   }t|tdtfdd}t| ” tdtt	 t
td||  d d t|d  d ||  |d d    d	 ks¼J ttt| d  tt| d   t|t  tdtfdd}t|tdtt	 t
tdd| d|  |  d	 d  t|d  |d  d| d|  | d d
   d	 ksxJ tttt| | | d  tdtfddtt	d dt
|| |   ksĢJ tttt| | | d  tdtfddtt	d dt
|| |   ks J d S )Nr   ©Śsymbolsza b cT©Śpositiver8   ©r   rC   rO   é   )Śsympy.core.symbolri   r   r/   r    r   r$   Śexpandr   r   r   )ri   r1   r2   r3   rL   r=   r>   r>   r?   Śtest_recursivep   s2    $
@’’’@H’’’
,’
,’rp   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s¾J tt| tg g gdgg gt tdtfddt	|d ksüJ 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sJ ttd d tt  tdtdksĄJ |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sJ | ttttdtd ttd ksČJ | 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sJ tttdt d  tt tdksĄJ 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sņJ |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sJ tttd  tt tdtfddtttdtj d  ” ksŠJ 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s²J |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   )ro   rh   zs t muT©Śrealr8   rO   r5   rj   rC   rl   Fśa brP   )é   Tzsigma mu)r8   T)rC   Tc                 S   s(   ddt d    t | ” t d”d|   S ©NrC   r8   rN   )r/   rZ   rY   )rc   r>   r>   r?   rG   ½   s    ztest_meijerint.<locals>.resé   za b séž’’’©Ś
lowergammarc   )ŚintegerŚalphar>   rN   rt   za s)!Śsympy.core.functionro   rn   ri   r    r   r   Śis_Piecewiser/   r   r9   r   r'   r   r$   r*   r   r   r   r   r
   Śabsr   r   r   rS   Śranger   r   r   Ś'sympy.functions.special.gamma_functionsry   r   )ro   ri   r5   r6   Śmur1   r2   ŚsigmaŚir3   Ś_rG   rc   ry   r{   r>   r>   r?   Śtest_meijerint   sĪ    $’ž
(
’&’
’ 
’ž
’
*(.(&, ’
,$ ’
,.’’
&,(’(’
" ’
’’:8’’Bżż
	&"’
$’
’
 &
’ ’’’’
*4’r   c                  C   sv  ddl m} m} tt|tt|tt t tdtfddddt	t
td td    t
tt  tt   ksrJ tt|tt|tt t tdtfdddddt  ks°J ttt	tt td d ttj    tdtfdddd td t tt
 ttjt   |ttks J tt|dt tddt|dt ksLJ tt| dt tddt| dt ksxJ t|dttdd|dt ksJ t|dtd t tdd|dtd |dtd   d ksāJ t|dtd td  tddd	t |dtd  dt |dtd   d|dt |dt  |dtd t  ks^J t|dt|dt tdd|dtd  d ksJ ttd |dt |dt tddtd |dtd  d ksÜJ t|dt|dt t tddt|dtd  t|dtd   |dt|dt  ks<J t|dtd t tdd|dtd  d ksrJ d S )
Nr   ©ŚbesseliŚbesseljTŚnone©r   Ścondsr8   rC   rl   rw   )Śsympy.functions.special.besselr   r   r$   r    r1   r7   r2   r   r   r   r/   r0   r   rS   r   r   r   r>   r>   r?   Śtest_besselķ   s^    "’.ž"’
’&’ž žż
,,& ’
*’’’
’
$’
 "’’
’r   c                  C   s&  ddl m}  ddlm} dd }|dtd d  tt|t ksHJ |ttd d  tt|t kspJ |tt t |td ksJ |dt	dtd   | dt|t ksĄJ t
t	tt	dtd   ttd u sčJ |ttd d u sJ t
ttd  ttd u s"J d S )Nr   ©r   )Ś	Heavisidec                 S   s   t t| ttS r@   )r   r+   r5   r6   ©Śfr>   r>   r?   Śinv!  s    ztest_inversion.<locals>.invrC   r8   )r   r   Ś'sympy.functions.special.delta_functionsr   r5   r   r6   r   r   r   r+   )r   r   r   r>   r>   r?   Śtest_inversion  s    ((".(r   c                  C   sų   ddl m}  ddlm} | ddd}tt| tdt| tt  }t|tt	}|j
r^J | ddd	}| ||”}t|tt	}|j
sJ |jd d | ||”ksŖJ |jd
 d s¼J ||tt	d }|jd
 d |ksō|jd
 d |jksōJ d S )Nr   ©ŚSymbol)ŚInverseLaplaceTransformr1   Trj   rw   r2   rq   rN   rC   )rn   r   Śsympy.integrals.transformsr   r   r   r   r5   r+   r6   r}   rY   ŚargsZas_integral)r   r   r1   ŚFr   r2   Śf2ZILTr>   r>   r?   Ś!test_inversion_conditional_output.  s    $

r   c                  C   sŠ   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 sJ tt|t tt}|j	s“J t
|jd d |sĢJ d S )Nr   r   )Ś
DiracDeltarL   Trq   r3   F)Zextended_realrC   r8   r7   )rn   r   r   r   r   r+   r   r5   r6   r}   r9   r   )r   r   rL   r3   r1   r7   r   r>   r>   r?   Ś%test_inversion_exp_real_nonreal_shiftC  s    
r   c                  C   sf  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||< qt| d	d
||< qtt|tsŗ||}dd |D }tdd |D sŽJ |dd |D  }|j|d|j|d }}tt|t|}|dk rBt||  ” dks^J qRt|| |  ” dksRJ qRq<d S )Nr   )ŚuniformŚ	randrangerD   )r7   )ŚkeyŚ
propertiesrC   rW   g      ų?g       @c                 S   s   g | ]\}}t |qS r>   r!   )rF   r   r[   r>   r>   r?   rH   f  rI   z%test_lookup_table.<locals>.<listcomp>c                 s   s    | ]}|j p| t” V  qd S r@   )r}   Śhasr   )rF   r/   r>   r>   r?   Ś	<genexpr>g  rI   z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| qS r>   r>   )rF   r   r/   r>   r>   r?   rH   j  rI   rf   g»½×Łß|Ū=)Śsympy.core.randomr   r    rJ   rE   Śsympy.integrals.meijerintr7   r)   ŚitemsŚsortedr   ŚlistZfree_symbolsŚhasattrr¢   r9   Śallrc   Śminr~   )r   r    rE   Zz_dummyŚtabler   ŚlZformulaZtermsZcondŚhintrY   ZaiŚexpandedr1   r2   rL   r>   r>   r?   Śtest_lookup_tableR  s,    

r±   c                  C   s  ddl m}  ddlm} |tttd tdd t”dddttd  tt	dd d tt	d	d kspJ tttd tdddt ttd  tt	dd dtt	d	d  dtt	dd | t	ddtd
  dt
t tt	d	d   ksžJ d S )Nr   rx   )Ś	powdenestrP   Trl   ©Zpolarr8   rU   rv   )r   ry   Śsympy.simplify.powsimpr²   r    r   r/   rZ   r   r   r   r   )ry   r²   r>   r>   r?   Śtest_branch_bugs  s    ’.’2>’’rµ   c                  C   sd   ddl m}  tttd tddtdt  ks4J t| dtd tdd| ddt  ks`J d S )Nr   r   rC   Trl   )r   r   r    r   r/   r   r   r>   r>   r?   Śtest_linear_subs~  s    (r¶   c            $         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sJ t	t
t
 t
t tfddksĄJ t	t
d t
 t
t tfddd d  ksśJ 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s¾J 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sJ t	t
t d t
 t|| t
t tftt tfddd | ksīJ 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sŖJ t	t
t
dtfdddksĪJ t	t
t
 t
dtfddd ksśJ 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sJ d dd   }t|t
t d d |t
t d d  |ksčJ 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s“J t	t
| t
dtfddd}||d |d f|	|
d  d|
k fksüJ 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sŽJ 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sØJ | 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sJ d| d  t|d  t
|d d   tt
 d  }|t	|t
dtfdddksÜJ 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	sźJ 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
sŗJ |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sĄJ |d!dd
\}}t|d t t
td"d  t| t
| d  t
 d |d   }d#d$ }|t	|t
dtfdks:J |t	t
| t
dtf|ks\J |t	t
| d | t
dtf|d | ksJ |t	t
| d | t
dtfd|d%  |d  ksČJ | d&dd
}t	t|d t t| d t
|   t
| td'  t
|tfdks J |ddd
\}	}
|
|	 t
|
d   |	|
d   dt
|
 |	|
   d  }tt	|t
dtfdksJ tt	t
| t
dtfdd(t|	 |
 tt|
  ksĄJ tt	t
t | t
dtfdd(t|	t  t |
 ttt |
  ks
J | ddd
}| d)dd
}|| t
| |d   tt
| |   }tt	|t
dtfdksjJ tt	t
| | t
dtf|| td||   ks¤J dd*lm} |d+dd
\} }!t
|!d  tt
d | d   d |!d   |dt
|  |!d   }"t	|"t
dtfdddks"J | d,dd-}| d.dd
}ttt
|  | d | }#t	|#t
t tfdddksxJ t	t
|# t
t tfdd|ksJ t	t
d |# t
t tfddd|d  |d  ksŌJ | ddd
}| t	tt
t
|d   tt
  t| t
dtftd|ks*J d S )/Nr   )Ś
expand_mul)r   ri   )Ś	gammasimp)Śpowsimpzmu1 mu2T)Znonzerozsigma1 sigma2rj   Ślambdac                 S   s6   dt dt |d   t| | d  d |d   S ©NrC   r8   )r   r   r   )r/   r   r   r>   r>   r?   Śnormal  s    z test_probability.<locals>.normalc                 S   s   |t | |   S r@   )r   )r/   Śrater>   r>   r?   Śexponential  s    z%test_probability.<locals>.exponentialrl   rC   r8   rP   rN   c                    s   t | t t tdtftt tfdd}t | t t tt tftdtfdd} | |ks|J |S )Nr   Trl   )r    r/   r0   r   )r;   Zres1Zres2©r·   r¾   Zmu1r¼   r½   Zsigma1r>   r?   ŚEø  s    ’’ztest_probability.<locals>.Ez
alpha betaZseparater   rs   Śk)rz   rk   za b pr   zd1 d2rO   zlamda muéż’’’c                 S   s   t |  t”S r@   )r$   Śrewriter   rA   r>   r>   r?   Ś<lambda>  rI   z"test_probability.<locals>.<lambda>rU   r3   r\   )r   rc   )r   znu sigmar   rq   r2   )r|   r·   rn   r   ri   Zsympy.simplify.gammasimprø   r“   r¹   r    r/   r   r0   r£   r	   r$   r   r   r   r   r   r   r   r   r   r~   r   r   )$r   ri   rø   r¹   Zmu2Zsigma2r   rĄ   Śansr{   ŚbetaZbetadistŚjr1   r2   rĮ   ŚchiZ
chisquaredŚpZdagumr
   Śd1Zd2r   Zlamdar   ŚdistZmysimpr3   Zdistnrc   r   Śnur   ZriceZlaplacer>   ræ   r?   Śtest_probability  s   & ’$’$’
’’
’’
’’
 ’’
$’
’
$’
ž
 ’ ’ž
$’
 
’
.66.(’’.$’
’:"
’
’
.’
:""’
*8"&
’
&’’
8"*’’
.’’
.
’
’’"
’
 "’
D"2:6’’
’’
"’
*’
D $’
*’’rĶ   c            
      C   s  ddl m}  ddlm} ddlm}m}m}m}m	}m
} ttttt t tt  tdtfddd |”jdd	|ttksJ ttt t t tdtfddd |” ” |dtksĄJ ttt t td
  tdtfddd |” ” |d
t |” |”ksJ ttt t td  tdtfddd |” ” |dt |” |” ” ks`J | ddd}ttt t t|tfdd ” ||ksJ ttt t t|tfdd ” ||td
  ksŌJ tttt tdtfdd|tksžJ t|tt tdtfdd|tks(J ttt t tdd ”  |”tt |dt ksbJ ttt td
  tdd |” ” |dttt t  tt  ks®J | ddd}	tt|	|	 |	dd ”  |	”d ||	ksģJ tt|	|	 |	dd ”  |	”d ||	ksJ t|dttdd |” ” t|dt tt  ksZJ t|d
ttdd |” ” td
  |dt d
 ttt  d
  tt d
  ks¶J ttt|tttdd |”jdd	|td t ksöJ t|ttddt|t tt ks"J t||	|	dd ” |	||	 t|	 ksRJ t|ttddt|t tt ks~J t||	|	dd ” |	||	 ||	 ks®J t|ttt  tdtfddtd ksŽJ t|dttt tdtfddtd
d
 ksJ dS )z% Test various exponential integrals. r   r   )Śsinh)ŚChiŚCiŚEiŚShiŚSiŚexpintrC   Tr   r   )Śfuncr8   rP   r6   rj   rl   rM   r³   rO   N)rn   r   Ś%sympy.functions.elementary.hyperbolicrĪ   Ś'sympy.functions.special.error_functionsrĻ   rŠ   rŃ   rŅ   rÓ   rŌ   r$   r   r    r   r7   r/   r0   r   rĆ   ro   r   r   r   r   Zas_independentr   r   )
r   rĪ   rĻ   rŠ   rŃ   rŅ   rÓ   rŌ   r6   rM   r>   r>   r?   Śtest_expintK  s     "’žžž’’ž ’’ž
 ’’ž
0 ’
** ’
$’
"’
"’
’’
’6ž
’’’ž
,0,00rŲ   c                  C   s®  ddl m} m} ddlm}m} ddlm} ddlm	}m
}m}m} ddlm}	m}
 |
|tttdd|t td	  t ddfksJ |
|tttdd|tt t td	 d
kfks¼J |
|tttddttd td
d
td	    d	t  t td	 d
kfksJ |
|ttttd
d  dttdkttdk@ fksJJ |	|d
tt ttdd}|d jdd ” |d
 ftdtd
d	t  ktdd	t  k B fd	tdtd	  td	  d
  dftdkfksŲJ t|t|dt tdtfddtd
td	 ksJ t|t|d
t tdtfddttjtd	d	  ksNJ td
t td
td	   tddt| d
t  ttd d
kft|d
t  dfksŖJ d S )Nr   )r   Śacoth)r   Śatanr   )rĻ   ŚE1rŅ   rÓ   )Śfourier_transformŚlaplace_transformTr#   r8   rC   rw   rN   F)Znoconds)ŚdeeprR   rl   ) rÖ   r   rŁ   Ś(sympy.functions.elementary.trigonometricr   rŚ   r   r   r×   rĻ   rŪ   rŅ   rÓ   r   rÜ   rŻ   r/   r5   r   r   r   r1   r   Zfactorro   r   r   r    r   rS   r~   r   )r   rŁ   r   rŚ   r   rĻ   rŪ   rŅ   rÓ   rÜ   rŻ   rÅ   r>   r>   r?   Ś
test_messy  sD    ’’
4’’
$"’’’
 ’
 ’
 2’rą   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 )Nr8   Trl   rO   )r    r   r   r/   r   r   r   r>   r>   r>   r?   Śtest_issue_6122Ø  s    "’rį   c                  C   s>   dt  ttt   tdd  } t| t dd}| t”r:J d S )NrC   rP   Trl   )r/   r1   r2   r   r    r£   r   )r;   Zantir>   r>   r?   Śtest_issue_6252­  s    rā   c                   C   sD   t ttt dtd   tt tf ”  t”ttd ks@J d S ru   )r    r   r   r/   r   r$   rĆ   r   r>   r>   r>   r?   Śtest_issue_6348µ  s    .
’rć   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   ©ŚfresnelcŚfresnelsr8   )	r×   rå   rę   r   r    r   r   r/   r   rä   r>   r>   r?   Śtest_fresnelŗ  s    *rē   c                   C   s   t ttt  td u sJ d S r@   )r'   r/   r>   r>   r>   r?   Śtest_issue_6860Į  s    rč   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 )Nr8   rP   rU   )	r'   r/   r   ZtogetherZ_eval_intervalr   ZNegativeOneZOner   r   r>   r>   r?   Śtest_issue_7337Å  s    0ré   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   r/   r   r6   r>   r>   r>   r?   Śtest_issue_8368Ė  s    0’’
’rź   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   ©ŚhŚwrC   r8   rP   )Ś	sympy.abcrģ   rķ   r    r   r0   r/   rė   r>   r>   r?   Śtest_issue_10211Š  s    2&’rļ   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   rh   zy LTrj   rC   r8   rP   )rn   ri   r    r   r/   )ri   r0   ŚLr>   r>   r?   Śtest_issue_11806Ö  s
    ("’rń   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”sŖJ d S )Nr   )ŚRR)ŚRrL   r8   g      ą?Trl   gUUUUUUÕ?g      š?rP   g      ąærU   gź-q=)Zsympy.polys.domains.realfieldrņ   rī   ró   rL   r    r   r   r   r   r   Zalmosteqrc   )rņ   ró   rL   r   r[   r>   r>   r?   Śtest_issue_10681Ü  s    &*’rō   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   r1   Trj   rC   r8   rN   )rn   r   r    r/   r   )r   r1   r>   r>   r?   Śtest_issue_13536ä  s    rõ   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   r/   rc   Trl   r8   )rn   r   r    r   rY   Śequals)r   r/   rc   r>   r>   r?   Śtest_issue_6462ź  s    &’r÷   c                   C   sJ   t tt t  tddtdt   dtt  dt   td  ksFJ d S )NTrl   rC   )r    r2   r6   r1   r>   r>   r>   r?   Śtest_indefinite_1_bugō  s    (’rų   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   r8   Trl   )r    r   r/   r   r   r   r	   r   r>   r>   r>   r?   Śtest_pr_23583ł  s    6’rł   N)hr|   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   rÖ   r   r   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   r   rß   r   r   r   r   r×   r   r   r   r   r   Zsympy.functions.special.hyperr   r   Zsympy.integrals.integralsr   r    Zsympy.simplify.hyperexpandr"   Zsympy.simplify.simplifyr$   r¦   r%   r&   r'   r(   r)   r*   r+   Zsympy.testing.pytestr,   r„   r-   r.   rX   rī   r/   r0   r1   r2   r3   r4   r5   r6   r7   rT   rV   r^   ra   rg   rp   r   r   r   r   r   r±   rµ   r¶   rĶ   rŲ   rą   rį   rā   rć   rē   rč   ré   rź   rļ   rń   rō   rõ   r÷   rų   rł   r>   r>   r>   r?   Ś<module>   sn   $,)
j0
 
 G
6&
