o
    Ļe	~  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s"J |d d d j t”||ffks5J d S )Nr   é   )	r%   r   r1   r2   r4   r/   Ś
isinstanceZargumentZas_coeff_mul)Śexprr3   ŚmŚe© r=   śTD:\Projects\ConvertPro\env\Lib\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|| |s"J d S )Nr   ©ŚAddc                 S   s   g | ]
}|d  |d  qS )r   r8   r=   )Ś.0Śresr=   r=   r>   Ś
<listcomp>-   s    z2test_rewrite_single.<locals>.u.<locals>.<listcomp>)Śsympy.core.addrD   r%   Śreplacer   r   r-   )r:   r/   rD   Śrr<   r=   r=   r>   Śu*   s   
’ztest_rewrite_single.<locals>.ur   é’’’’é   é   )rB   r=   é@   éü’’’T)r/   r0   r   r   r%   r   r   r   r   r   ŚHalfr   r   )r6   rA   rK   r=   r=   r>   Śtest_rewrite_single   s$   $&*’’ž’rR   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 )NrN   r8   é   rB   r   T)r&   r/   r   r1   r2   r3   r4   r0   r=   r=   r=   r>   Śtest_rewrite1C   s   86’rT   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 )Né
   )r   r1   r2   r3   r4   Śrandcplxr   r'   r/   r-   ŚsubsŚdiff)Zfacr
   ŚgrW   Zintegralr=   r=   r>   r6   I   s   ’
&z0test_meijerint_indefinite_numerically.<locals>.trB   r8   rS   ś3/2rN   rM   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r"|du s$J d S )Nr   T)r*   r/   Śis_zeror   )Śvr2   r=   r=   r>   Śtest_meijerint_definiteY   s   r_   c                     s“   t t d tt d t tt tt tt d i  fdd} | t gtggtgtggtds0J | t tgtggtgtggtdsBJ | t gtggttgtggdtd  dsXJ d S )NrU   c                    sD   ddl m} t| ||}|t|| }t|  ”|  ”tdddS )Nr   )ŚMulg¹?g¹æ)r2   r4   )Zsympy.core.mulr`   r   r(   r-   rW   r/   )r1   r2   r
   Śnr`   Śm1Śm2©rW   r=   r>   r6   d   s   ztest_inflate.<locals>.trN   r8   )r1   rV   r2   r   r3   r4   r0   r/   r[   r=   rd   r>   Śtest_inflate`   s   ’"$0re   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s»J tttt| | | d  tdtfddtt	d dt
|| |   ksäJ 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   rB   rM   é   )Śsympy.core.symbolrg   r   r/   r    r   r$   Śexpandr   r   r   )rg   r1   r2   r3   rJ   r<   r=   r=   r>   Śtest_recursivep   s2   $
@’’’@H’’’,’,’rn   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sJ ttttttks§J |ddd
\}}ttt| td|d ||d  |d  ksČJ ttd d tt  tdtdksÜJ |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sJ tttd  tt tttdfksJ tttt tt tdksŖJ ttdt d d  tt tttd dfksĘJ tttdt d  tt tdksÜJ ttt| | d  d tdt |d   tt tdksžJ 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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sÕJ |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   )rm   rf   zs t muT©Śrealr8   rM   r5   rh   rB   rj   Fśa brN   )é   Tzsigma mu)r8   T)rB   Tc                 S   s(   ddt d    t | ” t d”d|   S ©NrB   r8   rL   )r/   rX   rW   )ra   r=   r=   r>   rF   ½   s   (ztest_meijerint.<locals>.resé   za b séž’’’©Ś
lowergammara   )ŚintegerŚalphar=   rL   rr   za s)!Śsympy.core.functionrm   rl   rg   r    r   r   Śis_Piecewiser/   r   r9   r   r'   r   r$   r*   r   r   r   r   r
   Śabsr   r   r   rQ   Śranger   r   r   Ś'sympy.functions.special.gamma_functionsrw   r   )rm   rg   r5   r6   Śmur1   r2   ŚsigmaŚir3   Ś_rF   ra   rw   ry   r=   r=   r>   Śtest_meijerint   sŅ   $’žž(
’&’
’ 
’ž’((.(&, 
’,$ 
’,.’
’&,(’(
’" ’
’’:8’’Bż
ż&	"
’$
’
’ &
’ ’’’
’*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sJ tt|dt tddt|dt ks¤J tt| dt tddt| dt ks¹J t|dttdd|dt ksĖJ t|dtd t tdd|dtd |dtd   d ksģJ 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sJ t|dtd t tdd|dtd  d ks“J d S )
Nr   ©ŚbesseliŚbesseljTŚnone©r   Ścondsr8   rB   rj   ru   )Śsympy.functions.special.besselr   r   r$   r    r1   r7   r2   r   r   r   r/   r0   r   rQ   r   r   r   r=   r=   r>   Śtest_besselķ   s^   "’.ž"’
’&’ž žż**$ ’*’’
’
’$
’ "’
’’r   c                  C   s"  ddl m}  ddlm} dd }|dtd d  tt|t ks$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 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>.invrB   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   sü   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   ©ŚSymbol)ŚInverseLaplaceTransformr1   Trh   ru   r2   ro   rL   rB   )rl   r   Śsympy.integrals.transformsr   r   r   r   r5   r+   r6   r{   rW   ŚargsZas_integral)r   r   r1   ŚFr   r2   Śf2ZILTr=   r=   r>   Ś!test_inversion_conditional_output.  s   $

2r   c                  C   sŠ   ddl m}  ddlm} | ddd}| ddd	}d
dt  }| d}tt|t ttj	r/J tt|t ttd u s=J tt|t ttd u sKJ tt|t tt}|j	sZJ t
|jd d |sfJ d S )Nr   r   )Ś
DiracDeltarJ   Tro   r3   F)Zextended_realrB   r8   r7   )rl   r   r   r   r   r+   r   r5   r6   r{   r9   r   )r   r   rJ   r3   r1   r7   r   r=   r=   r>   Ś%test_inversion_exp_real_nonreal_shiftC  s   
r   c                  C   s^  ddl m} m} ddlm} ddlm} i }t| | ” D ]\}}t	|t
dD ]\}}}	}
i }t|j|g D ]}t|drJ|jrJ|dd||< q8| d	d
||< q8t|ts[||}dd |D }tdd |D smJ |dd |D  }|j|d|j|d}}tt|t|}|dk rt||  ” dksJ q(t|| |  ” dks«J q(qd S )Nr   )ŚuniformŚ	randrangerC   )r7   )ŚkeyŚ
propertiesrB   rU   g      ų?g       @c                 S   s   g | ]\}}t |qS r=   r!   )rE   r   rY   r=   r=   r>   rG   f  ó    z%test_lookup_table.<locals>.<listcomp>c                 s   s"    | ]}|j p| t” V  qd S r?   )r{   Śhasr   )rE   r/   r=   r=   r>   Ś	<genexpr>g  s     z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| qS r=   r=   )rE   r   r/   r=   r=   r>   rG   j  r”   rd   g»½×Łß|Ū=)Śsympy.core.randomr   r   rH   rD   Śsympy.integrals.meijerintr7   r)   ŚitemsŚsortedr   ŚlistZfree_symbolsŚhasattrr    r9   Śallra   Śminr|   )r   r   rD   Zz_dummyŚtabler   ŚlZformulaZtermsZcondŚhintrW   ZaiŚexpandedr1   r2   rJ   r=   r=   r>   Śtest_lookup_tableR  s0   
ź’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   rv   )Ś	powdenestrN   Trj   ©Zpolarr8   rS   rt   )r~   rw   Śsympy.simplify.powsimpr±   r    r   r/   rX   r   r   r   r   )rw   r±   r=   r=   r>   Ś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   rB   Trj   )r   r   r    r   r/   r   r   r=   r=   r>   Śtest_linear_subs~  s   (0rµ   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sJ t	t
t|| t
t tftt tfdddks¼J t	t
t
 t|| t
t tftt tfddksÜJ t	tt
 t|| t
t tftt tfdd|ksüJ 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”rJ t|d d  ksØJ t	td t
 t|| t
t tftt tfdd|d |d  ksŃJ t	t
t
dtfdddksćJ t	t
t
 t
dtfddd ksłJ 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sJ t|t
t d |t
t d  |ks¢J |ddd
\}	}
t
|	d  dt
 |	 |
   t|	|
  t|	 t|
 }t	|t
dtfdddksÖJ t	t
| t
dtfddd}||d |d f|	|
d  d|
k fksśJ 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sJ tt	t
d | t
ddfdd||d  ||  || d  ks„J tt	t
t | t
ddfddt|| t|t  t| t|| t  ksŠJ | 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sJ |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sńJ 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sJ tt	t
| t
dtfddd||d  ks¶J tt	t
d | t
dtfddd|d |d  | |d   |d  ksÜJ |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sJ |ddd
\}	}
|
|	 t
|
d   |	|
d   dt
|
 |	|
   d  }tt	|t
dtfdksæJ tt	t
| t
dtfdd(t|	 |
 tt|
  ksÜJ 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sJ | d,dd-}| d.dd
}ttt
|  | d | }#t	|#t
t tfdddksøJ t	t
|# t
t tfdd|ksŹJ t	t
d |# t
t tfddd|d  |d  ksęJ | 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   rg   )Ś	gammasimp)Śpowsimpzmu1 mu2T)Znonzerozsigma1 sigma2rh   Ślambdac                 S   s6   dt dt |d   t| | d  d |d   S ©NrB   r8   )r   r   r   )r/   r   r   r=   r=   r>   Śnormal  s   6z test_probability.<locals>.normalc                 S   s   |t | |   S r?   )r   )r/   Śrater=   r=   r>   Śexponential  s   z%test_probability.<locals>.exponentialrj   rB   r8   rN   rL   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   Trj   )r    r/   r0   r   )r:   Zres1Zres2©r¶   r½   Zmu1r»   r¼   Zsigma1r=   r>   ŚEø  s   ’’ztest_probability.<locals>.Ez
alpha betaZseparater   rq   Śk)rx   ri   za b pr   zd1 d2rM   zlamda muéż’’’c                 S   s   t |  t”S r?   )r$   Śrewriter   r@   r=   r=   r>   Ś<lambda>  s    z"test_probability.<locals>.<lambda>rS   r3   rZ   )r   ra   )r   znu sigmar   ro   r2   )rz   r¶   rl   r   rg   Zsympy.simplify.gammasimpr·   r³   rø   r    r/   r   r0   r¢   r	   r$   r   r   r   r   r   r   r   r   r   r|   r   r   )$r   rg   r·   rø   Zmu2Zsigma2r   ræ   Śansry   ŚbetaZbetadistŚjr1   r2   rĄ   ŚchiZ
chisquaredŚpZdagumr
   Zd1Zd2r   Zlamdar   ŚdistZmysimpr3   Zdistnra   r   Śnur   ŚriceZlaplacer=   r¾   r>   Śtest_probability  s  & ’$’$’’’’’’’ ’
’$’

’$’

ž ’ ’
ž$
’ 

’.66.(’’.$’
’:"

’
’.
’:""
’*8"&

’&’
’8"*’
’.’
’.
’
’’"

’ "
’D"2:6’
’’
’"
’*
’D $
’*’’rĢ   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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sĖJ ttt t t|tfdd ” ||td
  ksęJ tttt tdtfdd|tksśJ 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sJ t|dttdd |” ” t|dt tt  ksØJ t|d
ttdd |” ” td
  |dt d
 ttt  d
  tt d
  ksÖJ 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s$J t|ttddt|t tt ks:J t||	|	dd ” |	||	 ||	 ksRJ t|ttt  tdtfddtd ksjJ t|dttt tdtfddtd
d
 ksJ dS )z% Test various exponential integrals. r   r   )Śsinh)ŚChiŚCiŚEiŚShiŚSiŚexpintrB   Tr   r   )Śfuncr8   rN   r6   rh   rj   rK   r²   rM   N)rl   r   Ś%sympy.functions.elementary.hyperbolicrĶ   Ś'sympy.functions.special.error_functionsrĪ   rĻ   rŠ   rŃ   rŅ   rÓ   r$   r   r    r   r7   r/   r0   r   rĀ   rm   r   r   r   r   Zas_independentr   r   )
r   rĶ   rĪ   rĻ   rŠ   rŃ   rŅ   rÓ   r6   rK   r=   r=   r>   Śtest_expintK  s    "’
žž’
ž ’
ž ’
ž. ’(* 
’$
’"
’"
’ 
’
6
ž’
’
ž,0,008r×   c                  C   sØ  ddl m} m} ddlm}m} ddlm} ddlm	}m
}m}m} ddlm}	m}
 |
|tttdd|t td	  t ddfksDJ |
|tttdd|tt t td	 d
kfks^J |
|tttddttd td
d
td	    d	t  t td	 d
kfksJ |
|ttttd
d  dttdkttdk@ fks£J |	|d
tt ttdd}|d jdd ” |d
 ftdtd
d	t  ktdd	t  k B fd	tdtd	  td	  d
  dftdkfkséJ t|t|dt tdtfddtd
td	 ksJ t|t|d
t tdtfddttjtd	d	  ks$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   Śacoth)r   Śatanr   )rĪ   ŚE1rŃ   rŅ   )Śfourier_transformŚlaplace_transformTr#   r8   rB   ru   rL   F)Znoconds)ŚdeeprP   rj   ) rÕ   r   rŲ   Ś(sympy.functions.elementary.trigonometricr   rŁ   r   r   rÖ   rĪ   rŚ   rŃ   rŅ   r   rŪ   rÜ   r/   r5   r   r   r   r1   r   Śfactorrm   r   r   r    r   rQ   r|   r   )r   rŲ   r   rŁ   r   rĪ   rŚ   rŃ   rŅ   rŪ   rÜ   rÄ   r=   r=   r>   Ś
test_messy  sD   ’
’4
’’$"’’’ 
’ 
’ 2’rą   c                   C   sJ   t tt td  tt tfddt tt ttt d  ks#J d S )Nr8   Trj   rM   )r    r   r   r/   r   r   r   r=   r=   r=   r>   Śtest_issue_6122Ø  s   "’rį   c                  C   s>   dt  ttt   tdd  } t| t dd}| t”rJ d S )NrB   rN   Trj   )r/   r1   r2   r   r    r¢   r   )r:   Zantir=   r=   r>   Śtest_issue_6252­  s   rā   c                   C   sD   t ttt dtd   tt tf ”  t”ttd ks J d S rs   )r    r   r   r/   r   r$   rĀ   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s2J d S )Nr   ©ŚfresnelcŚfresnelsr8   )	rÖ   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s'J |  ttjtj”tddks7J d S )Nr8   rN   rS   )	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s2J d S rŗ   )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s8J d S )Nr   ©ŚhŚwrB   r8   rN   )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s7J d S )	Nr   rf   zy LTrh   rB   r8   rN   )rl   rg   r    r   r/   )rg   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”sUJ d S )Nr   )ŚRR)ŚRrJ   r8   g      ą?Trj   gUUUUUUÕ?g      š?rN   g      ąærS   gź-q=)Zsympy.polys.domains.realfieldrņ   rī   ró   rJ   r    r   r   r   r   r   Zalmosteqra   )rņ   ró   rJ   r   rY   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   Trh   rB   r8   rL   )rl   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”s3J d S )Nr   r   r/   ra   Trj   r8   )rl   r   r    r   rW   Śequals)r   r/   ra   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s#J d S )NTrj   rB   )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 )NrB   r8   Trj   )r    r   r/   r   r   r   r	   r   r=   r=   r=   r>   Śtest_pr_23583ł  s   6’rł   N)hrz   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   rÕ   r   r   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   r   rŽ   r   r   r   r   rÖ   r   r   r~   r   r   Zsympy.functions.special.hyperr   r   Zsympy.integrals.integralsr   r    Zsympy.simplify.hyperexpandr"   Zsympy.simplify.simplifyr$   r„   r%   r&   r'   r(   r)   r*   r+   Zsympy.testing.pytestr,   r¤   r-   r.   rV   rī   r/   r0   r1   r2   r3   r4   r5   r6   r7   rR   rT   r\   r_   re   rn   r   r   r   r   r   r°   r“   rµ   rĢ   r×   rą   rį   rā   rć   rē   rč   ré   rź   rļ   rń   rō   rõ   r÷   rų   rł   r=   r=   r=   r>   Ś<module>   sp    $,)
j0
 
 G
6&
