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d Zčdd Zédd ZźeZdd Zėdd Zģdd Zķdd Zīdd Zļdd Zšdd Zńdd Zņd d! Zód"d# Zōd$d% Zõd&d' Zöd(d) Z÷d*d+ Zųd,d- Złd.d/ Zśd0d1 Zūd2d3 ZüeZd4d5 Zżd6d7 Zžd8d9 Z’d:d; Z d<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM Z	dNdO Z
dPdQ ZdRdS ZeZdTdU ZdVdW ZeZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo ZdpS (r  é    )KŚAbsŚacosŚacoshŚAddŚAndŚasinŚasinhŚatanŚCiŚcosŚsinhŚcoshŚtanhŚ
DerivativeŚdiffŚ
DiracDeltaŚEŚEiŚEqŚexpŚerfŚerfcŚerfiŚ
EulerGammaŚExprŚfactorŚFunctionŚgammaŚ	gammasimpŚIŚIdxŚimŚIndexedBaseŚ	integrateŚIntervalŚLambdaŚLambertWŚlogŚMatrixŚMaxŚmeijergŚMinŚnanŚNeŚOŚooŚpiŚ	PiecewiseŚ
polar_liftŚPolyŚ	polygammaŚRationalŚreŚSŚSiŚsignŚsimplifyŚsinŚsincŚSingularityFunctionŚsqrtŚsstrŚSumŚSymbolŚ	summationŚsymbolsŚsympifyŚtanŚtrigsimpŚTupleŚlerchphiŚ	exp_polarŚliŚhyperŚFloat)Ś	unchanged)Śperiodic_argument)Śfloor)ŚIntegral)ŚNonElementaryIntegral)Śunits)ŚraisesŚslowŚskipŚ	ON_TRAVISŚwarns_deprecated_sympy)Śverify_numericallyzx y a t x_1 x_2 z s bŚnT©ŚintegerŚfé   c                 K   s   t t| j|fi |¤ddS )NT)Z	full_prec)r?   rD   Śevalf)ŚerY   Śoptions© ra   śF/usr/lib/python3/dist-packages/sympy/integrals/tests/test_integrals.pyŚNS   s   rc   c                  C   s   t dt t} |  t”t td tddksJ t  t| t W d    n1 s*w   Y  t  t| tf W d    d S 1 sDw   Y  d S )Né   ZQQ)Śdomain)r3   Śxr#   rW   rP   ©Śpra   ra   rb   Śtest_poly_deprecated   s    ’"’ri   c                     s,  dt   t t t tf ” dksJ t tt tf ” ttdt   ks(J tt fdd tt fdd dt d d  tt t tf ”  ” t	d t
 d ksZJ ttfdd dt d d  } t| t t tf ” dkszJ t| t d	df ” td ksJ t t d d  }t|t t tf ” dks¢J t|t d	df ” dks°J t d t d d  }t|t t tf ” tu sÉJ t|t d	df ” td d
 ksÜJ dt d d dt d    }t|t t tf ” t
 d ksüJ t|t d	df ” td tdd  ksJ d S )Né   r   c                      s   t  t ” S ©N)rP   rf   Śprincipal_valuera   ©Śgra   rb   Ś<lambda>-   ó    z&test_principal_value.<locals>.<lambda>c                      s   t   ” S rk   )rP   rl   ra   rm   ra   rb   ro   .   ó    é   c                      s   t  tt df ” S ©Nrj   )rP   rf   r/   rl   ra   )Ślra   rb   ro   2   ó    rd   éž’’’é   )rf   rP   r/   rl   Śyr9   rS   Ś
ValueErrorŚtogetherr>   r0   r'   r	   )ŚdŚvŚsr\   ra   )rn   rt   rb   Śtest_principal_value(   s(   *0"&$4r~   c                 C   s<   | j }|D ]}|  |” ” |  ”  |”  ” dksJ q|S )zŗReturn the set of symbols, s, which were used in testing that
    i.diff(s) agrees with i.doit().diff(s). If there is an error then
    the assertion will fail, causing the test to fail.r   )Śfree_symbolsr   ŚdoitŚexpand)ŚiZsymsr}   ra   ra   rb   Ś	diff_testE   s   *r   c                   C   sd   t tttddfdksJ t td tdtfdksJ t ddtt  tdtftdks0J d S )Nr   rj   é’’’’rv   rd   )r#   r'   rf   r/   r   ra   ra   ra   rb   Śtest_improper_integralO   s   ,r   c                  C   s  t tt} | jttfksJ t ttf}|jttfksJ t tttdtf}|jttfks3J t ttt}|jttfksDJ t tttddf}|jttddfksZJ t ttdk}|jttdtfksmJ t ttdktdk @ }|jttddfksJ d S )Nrj   rd   é
   é   )	rP   rY   ŚlimitsrG   r@   rf   rx   r$   r/   )Śs1Śs2Zs3Zs4Zs5Zs6Zs7ra   ra   rb   Śtest_constructorU   s   
r   c                  C   sŠ  t dtdks	J t ttddfdksJ t tttksJ t tjttju s)J tt tttdks5J tt ttddftdksDJ tt ttttksPJ tt ttdtfttks_J td d } tt| tdtfttt | tdtft 	”  
”   krdt d  
” ksJ  J tt| tdtfttt | tdtft  kr¬dksÆJ  J tt| tdtfttt | tdtft  krĢdksĻJ  J tt| tttt | tt  krędkséJ  J t| tttf t”t | tttf t” 	”  
” ksJ t | tttf t” 	” dt d ksJ t| tttf t” 	” dt d   
” ks5J ttd ttdt f t”dtd  ksMJ t tt ” thksZJ t tttddf ” tjtjthkspJ tt ttdt fthksJ tt ttdt ftthksJ tttttfdks J tttt t fdksÆJ ttt tt ttt td d  tt ksĖJ t tjsÓJ tddd}t |t tjdu sęJ d S )	Nr   rj   rd   é   rr   rY   F©Zcommutative)rP   rf   r/   r7   ŚNaNr   rx   Śtr#   r   r   ŚaZatomsr\   ŚZeroŚOner   r   Śis_commutativerA   ©r_   rY   ra   ra   rb   Śtest_basicsk   sR   ’ž’’’’4
’,20,"$8r   c                  C   sz   G dd dt } |  }t|d ||d d | ksJ t|d |ddftddks-J ttdd  ttd	d  d S )
Nc                   @   s   e Zd ZdZdZdS )ztest_diff_wrt.<locals>.TestTN)Ś__name__Ś
__module__Ś__qualname__Z	_diff_wrtr   ra   ra   ra   rb   ŚTest   s    r   rj   rd   r   rr   c                   S   s   t td td S rs   ©r#   rf   ra   ra   ra   rb   ro   ¢   s    ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfS )Nrj   r   r   ra   ra   ra   rb   ro   £   s    )r   r#   r5   rS   ry   )r   r   ra   ra   rb   Śtest_diff_wrt   s   ""r   c                   C   s  t tttdt dt fttdt fthksJ t tttdt fttdt fthks/J t tttdt fttdt ftthksFJ t tttttthksTJ t ttt tttthksdJ t ttt ttdtfthksvJ t ttt tttftttftthksJ d S )Nrr   r   rd   rj   )r   rP   rf   rx   ra   ra   ra   rb   Śtest_basics_multiple¦   s   2,. $0r   c                  C   sō   t ddd\} }tddd}t| | |f}| ”  ” | ”  ” ks$J | ”  ” | ”  ” ks2J | ”  ” | ”  ” ks@J tddd}t| | |f}| ”  ” | ”  ” ks\J | ”  ” | ”  ” ksjJ | ”  ” | ”  ” ksxJ d S )NzA BFr   rf   T)Ścomplex©Śreal)rC   rA   rP   Zadjointr   Ś	conjugateZ	transpose)ŚAŚBrf   rh   ra   ra   rb   Śtest_conjugate_transpose°   s    r£   c                  C   s:  t dtdtfdksJ t dtdtfdt ksJ t ttdtftd d ks*J t dt tdtfdtd  d ks>J t dtd  tdtftd ksPJ t dt tdtfttks`J t dtd  tdtfdt d kstJ t td dt  d tdtftd d dtd  d  dt  ksJ t td ttd d ks§J t dt t d tdt d td  d ksĄJ td	} td
}t tt tdtfttd  d ksÜJ t ttd  tdtfttd  d ksņJ t ttd  | t  | tdtfttd  d | td  d  |t  ksJ d S )Nr   rr   rd   rj   r   r   é   é   ŚbŚcrw   )r#   r   rf   r'   rA   r   )r¦   r§   ra   ra   rb   Śtest_integrationĄ   s    ($ (H2(,VrØ   c                   C   s
  t td td  tddftddftdksJ t td td  tttddtd  td  ks3J t dtd  dt d  ttdt tdd tdt tdd  tddt  dtd     kshJ t ttt t tddftddftd d ksJ d S )	Nrd   r   rj   r   é	   rr   r¤   rw   )r#   rf   rx   r5   r'   r;   ra   ra   ra   rb   Śtest_multiple_integrationÓ   s   06F’:rŖ   c                   C   s"   t tt tdtfdksJ d S )Nr   rj   )r#   r   rf   r/   ra   ra   ra   rb   Śtest_issue_3532Ū   s   "r«   c                   C   sz   t ttd tdttd  d ksJ t tttdttd  d ks(J t dttd  tdtt ks;J d S )Nrr   rd   r   rj   rv   )r#   r>   rf   ra   ra   ra   rb   Śtest_issue_3560ß   s   *&*r¬   c                   C   s   t tdd  d S )Nc                   S   s   t ttfS rk   r   ra   ra   ra   rb   ro   ę   rq   z"test_issue_18038.<locals>.<lambda>)rS   ŚAttributeErrorra   ra   ra   rb   Śtest_issue_18038å   s   r®   c                  C   s4  t ttd t  td  tt} t  t| t}W d    n1 s#w   Y  t  t| t}W d    n1 s;w   Y  t|t du sIJ t|t du sRJ |jttfks[J |jttfksdJ | ” td d td t d  ttd   ks~J | ” tt td td  d  td d  ksJ d S )Nrd   rr   Trw   )r3   rf   rx   rW   r#   Ś
isinstanceŚgensŚas_expr)rh   ZqxZqyra   ra   rb   Śtest_integrate_polyé   s    ’’48r²   c                  C   s*  t ttd t  td  tt} t  t| tddf}W d    n1 s&w   Y  t  t| tdtf}W d    n1 sAw   Y  t|t du sOJ t|t du sXJ |jtfks`J |jtfkshJ | ” t	j
td  td  ksyJ | ” td d tt  td td  d  ksJ d S )Nrd   rr   r   rj   Trw   )r3   rf   rx   rW   r#   r0   rÆ   r°   r±   r7   ŚHalf)rh   ZQxZQyra   ra   rb   Śtest_integrate_poly_definedū   s    ’’"8r“   c                      sD   t d tttd d ksJ ttdd  tt fdd d S )Nrx   rd   c                   S   s   t dS ©Nrd   )r#   ra   ra   ra   rb   ro     s    z)test_integrate_omit_var.<locals>.<lambda>c                      s   t t  S rk   r   ra   ©rx   ra   rb   ro     rq   )rA   r#   rf   rS   ry   ra   ra   r¶   rb   Śtest_integrate_omit_var  s   r·   c                  C   sd   t d} ttt|  ttd t|  d ksJ ttd t|  ttd t|  d ks0J d S )Nrx   rd   ič  ié  )rA   r#   rf   r;   r¶   ra   ra   rb   Śtest_integrate_poly_accurately  s   *2rø   c                  C   sN   t d} ttd | td |  ksJ ttd | ddfdtd  ks%J d S )Nrx   rd   r   rj   )rA   r#   rf   r¶   ra   ra   rb   Śtest_issue_3635  s   (r¹   c                  C   s   t ddd} tt|  tddt| d  | d  ksJ tt| t d|   dt|   tddt|  t| t d|   dt|    dt|   ksMJ d S )Nrx   T©ŚpositiveŚnone©Zcondsrj   rd   )rA   r#   rf   r   r;   r¶   ra   ra   rb   Śtest_integrate_linearterm_pow'  s
   *(4’r¾   c                   C   s   t ttt tdt ttd  d ksJ t ttt tttd   tdt ttd  d dt ttd  d  ksBJ d S )Nrd   rr   r   )r#   r0   r>   rf   r   ra   ra   ra   rb   Śtest_issue_36180  s   . .’ræ   c                   C   s"  t ttd t tttttd  td  ttd dftdfks%J t ttd t tttttd  td  ttd dftdfksJJ t ttd t ttd t  tttttd  td  ttd dftdfttttd  td  ttd dftdf ksJ d S )Nrj   r   T)r#   r   rY   rf   r1   r;   r-   ra   ra   ra   rb   Śtest_issue_36236  s   *
’*
’$..’’rĄ   c                  C   s    t dddd} tdt t| t t d  tddgdtt|   t|   ks)J ttt| t t d  td	d tddgdtt|   t|   ksNJ d S )
NrY   T)r[   Śnonzerog      ąærd   rv   r   g       @r   )rA   r#   rf   r;   r0   r   r5   ©rY   ra   ra   rb   Śtest_issue_3664@  s   &’,’rĆ   c                   C   s4   t tdtd dt  d  tddfdksJ d S )Nrj   rd   r¤   é   rw   z1.10714871779409)rc   rP   rf   ra   ra   ra   rb   Śtest_issue_3679H  s   4rÅ   c                  C   sZ   ddl m} m} | tttd ttdtt |tdt tt  d ks+J d S )Nr   ©Śexpand_funcŚfresnelsrd   )ŚsympyrĒ   rČ   r#   r;   rf   r>   r0   rĘ   ra   ra   rb   Śtest_issue_3686M  s   *’rŹ   c                  C   s@   t j} t j}tt|  | td| d| fd|  | ksJ d S )Nrj   r   é   )rR   Śmr}   r#   rf   )rĢ   r}   ra   ra   rb   Śtest_integrate_unitsS  s   4rĶ   c                   C   s@   t tdt tt ttdt   ttdt   ksJ d S rµ   )r#   r&   rf   ra   ra   ra   rb   Śtest_transcendental_functionsY  s   $’rĪ   c                   C   sd   t tdt t tddftd  d ksJ t ttdt d  tddftd  d ks0J d S )Nrj   r   rd   r„   r   )r#   r'   rf   r0   ra   ra   ra   rb   Śtest_log_polylog^  s   .6rĻ   c                  C   s\   dt t dt td   } tt| tt}t|  td” ” | td” ”  dk s,J d S )Nrw   rd   é*   g»½×Łß|Ū=)r'   rf   r   r#   ŚabsŚsubsr^   )r\   Zfidra   ra   rb   Śtest_issue_3740c  s   0rÓ   c                   C   s&   t ddtd   tttksJ d S ©Nrj   rd   )r#   rf   r	   ra   ra   ra   rb   Śtest_issue_3788i  ó   &rÕ   c                      s6   t t t ttt ksJ tt fdd d S )Nc                      s   t  dt S rµ   r   ra   ©r\   ra   rb   ro   p  rp   z!test_issue_3952.<locals>.<lambda>)r;   rf   r#   r   rS   ry   ra   ra   r×   rb   Śtest_issue_3952m  s   rŲ   c                   C   s6   t dt dt  tdt td td  ksJ d S rµ   ©r#   rf   r'   ra   ra   ra   rb   Śtest_issue_4516s  ó   6rŚ   c                  C   sF   t tdt  t tdtf} t| tjkrt| t	ddks!J d S )Nrj   r   r   rd   )
r#   r   r   rf   r/   r6   r7   r³   r!   r5   )Zansra   ra   rb   Śtest_issue_7450w  s   (rÜ   c                	   C   sĄ   t dtdt  ddtdt    tdtft d tdt d  ks'J t dtdt  ddtdt    t d tdttdtt ttttd  t    d  ks^J d S )Nrj   rd   rr   r   r   ©r#   r   rf   r0   r>   r	   rE   rO   ra   ra   ra   rb   Śtest_issue_8623|  s   NF’’rŽ   c                   C   s   t ddtt  tdtfttd ksJ t ddtt  dtd ttdttd  tttd td  t    d ksDJ d S ©Nrj   rd   r   rr   rŻ   ra   ra   ra   rb   Śtest_issue_9569  s   ,`rą   c                  C   sĄ   t ddd} ttt d  d|  |   tdt |  |   }t|tttf}t|tdtftd|  ttd  d| d    dtt  tt	tdt d|    d  td  ks^J d S )Nr}   Trŗ   rd   r   )
rA   r   Śzrx   r>   r0   r#   rf   r/   r   )r}   ZpzZpzgxra   ra   rb   Śtest_issue_13733  s   2>’’rā   c                   C   s   t ddtt  tdtfttd ksJ t ddtt  dtd ttdttd  d tttd td  t    d ksFJ d S rß   rŻ   ra   ra   ra   rb   Śtest_issue_13749  s   ,drć   c                   C   s<   t ttdt d  tttttd d  tksJ d S rŌ   )r#   r   rf   rQ   ra   ra   ra   rb   Śtest_issue_18133  ó   <rä   c                  C   sä   t ddd} t ddd}t|t t|  t t t t  t|  t t t t  tt  t	dt t t| t t t t  dftt|  t t t t  df}t
dt t tt tt   d	  }t|t|kspJ d S )
Nz3999999.9999999995é5   )Z	precisionz2.5000000000000004e-7ē      š?r   Trv   gķµ ÷Ę >)rL   r1   r   r   r0   r   rx   rf   rį   r-   r   r#   )r   r¦   ŚrZfunra   ra   rb   Śtest_issue_21741  s   D(’ ž$ré   c                  C   sZ   t dddd } t| tt tt tdt  gtdt  tdt  ggks+J d S )Nrd   c                 S   s    | | d t | | d t  S rs   )r;   rf   )r   Śjra   ra   rb   ro   £  s     ztest_matrices.<locals>.<lambda>rr   )r(   r#   rf   r   )ŚMra   ra   rb   Śtest_matrices¢  s
   
žrģ   c                   C   s¬   t tttttttksJ t tttddfttttddfks&J t tttttt tttd d ks>J t tttttt ttttksTJ d S )Nr   rj   rd   )r#   r\   rf   rP   r   r'   ra   ra   ra   rb   Śtest_integrate_functions«  s    ,00rķ   c                   C   s   t tttttttksJ t tttttttttt ks%J t ttttd ttttttd tks?J d S rµ   )r#   r   r\   rf   rx   rP   ra   ra   ra   rb   Śtest_integrate_derivatives³  s
    *’rī   c                     sŽ  t td d tddf} t}dt d }|  ” |  ||” ” ks"J |  ||” ||”| ks0J dt d }t}|  ||” ||”| ksFJ t tdt tddf} |  tdt ”t tttd  tdtfksjJ |  tdt ” tdt ”| ks|J t ttd  tt tf} |  tdt ”t dtdtd   tt tfks„J t tt t| t ” ” t t| d  t ” ksæJ td}t ttd| f tdt ” ” t dtd  tt d| f ” ksēJ t ttd|f tdt ”t td td| tfksJ t tt tddftddf   ttdt  tf” ”   ttdt	  tf” ”   kr7dks:J  J t tt| t
f   tdt ”t dt t| d t
d fks[J tt fd	d
 tt fdd
 tt fdd
 tt fdd
 tt fdd
 t td tddf tt fdd
 tddd}tddd}t tt||f   tdt ”   tdt ”t dt t|d |d fksŠJ t tt| f   tdt ”t dt t| d fksķJ d S )Nrd   rj   r   rr   r   éü’’’éż’’’rw   c                      s      td”S rs   )Ś	transformrf   ra   ©r   ra   rb   ro   ×  rq   z test_transform.<locals>.<lambda>c                      s      ttt ”S rk   ©rń   rf   r}   r   ra   rņ   ra   rb   ro   Ų  ó    c                      s      tt ”S rk   ©rń   rf   r}   ra   rņ   ra   rb   ro   Ł  rp   c                      s      tttf”S rk   ró   ra   rņ   ra   rb   ro   Ś  rō   c                      s      dt dt ”S rµ   rõ   ra   rņ   ra   rb   ro   Ū  ó    c                      s      td t”S rµ   rõ   ra   rņ   ra   rb   ro   Ž  rō   r   T)Śnegativer¦   rŗ   )rP   rf   rx   r   rń   r;   r/   r   r7   rį   r¦   r}   rS   ry   rA   )r   ZfxZfyZ_3ŚamZbpra   rņ   rb   Śtest_transformŗ  sZ   0$6’  ’
’
’’220rł   c                  C   s^   t jtt ttdtd   d  } ttttt| ks J ttttt| ks-J d S rŌ   )	r7   r³   r   rf   r>   r#   r   r;   r   r×   ra   ra   rb   Śtest_issue_4052ź  s   &rś   c                  C   s  t tttddfddksJ tttd  tt tf} t | ddks&J t | d t ttdd  ddv s:J td	}d
t	d dd|d    }dt	d d| d  t	d|d  | d d  }d|d  d d|d  d|  d d  }t	dd|d  d|  d  d|d  d|  d d  }|||  | }t t||ddfdt dt	d dt  dt
t	d  d dksĘJ t tttdt dt td   tddfdt ddksęJ t tt
t	td d t	td d td d   tddfdt dtd  d dksJ t ttttt tt t  td d   tdtfdt ddks;J t ttttttt ttd td fdddt ddks^J t dttdttd  tt tf dddt ddks~J t dttdttd  tt tf dddt ddksJ t dttdttd  tt tf dddt ddks¾J t tdtd tddf  dd!dd"d#v sÕJ ttttd  tdtfjdd$}d%|  k rōd&k s÷J  J t ttttd  tdtfd'd(d)ksJ t tttt d t tt d*fd'd(d+ks(J t tttd,ks4J t ttttfd-ksBJ d S ).Nrd   r   r]   z10.5000000000000z1.77245385090552rj   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r   r¤   rr   é   rw   é   éł   é6   éA   r   é2   é1   é¢   rĖ   z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))é`   zlog(2)/2-1/4T©Śchopzpi/4*log(4*pi**3/gamma(1/4)**4)rÄ   é   é   zsqrt(1-x**2)é   )Śmaxnr  )z0.0Ś0)r	  g\Āõ(\ß?gRøėQą?Zosc)Zquadz0.504067061906928r   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rc   rP   rf   r   r/   r0   r   r5   rA   r>   r	   r'   r;   r   r^   rx   )Zgaussr   r   r¦   r§   r{   r\   ra   ra   rb   Śtest_evalf_integralsń  s¢   ’’’4,<,’0’4’’
’’
’’’
’4
’(’
’(’
’(’
’
’’
’$ ’
’’’
’ r  c                   C   s   t tdtd d  t td”dddv sJ t tdtd d  tddfdks+J t tdtd d  tddfdddksAJ d S )	Nrj   r   rw   Tr  )z-0.000976138910649103z0.965906660135753z1.93278945918216rd   z0.0144361088886740)rc   r#   rf   rŅ   rP   ra   ra   ra   rb   Śtest_evalf_issue_939%  s   $’(’’r  c                  C   s   t tttt  tddftddf} t| ddksJ | tdddtd d  ks,J t tttt  tddftddftju sCJ d S )	Nrj   rd   r   r]   z2.43790283299492rļ   rr   r¤   )	r#   r>   rf   rx   rc   r5   r;   r7   r   ©Śresra   ra   rb   Ś(test_double_previously_failing_integrals4  s   $"2r  c            	      C   s   t ttdt tdd } t ttdd t tdd }t| t|ks#J dt tdd dt tdd  }dt tdd	 dt tdd  }t|t|ksLJ d
td
  t dt tdd  d
t tdd  }d
td  t d d
t t tdd  dt tdd d  }td
 td
  dt t tdd  d
t tdd  }t|t|ks„J t|t|ks®J tt|tfs·J t|tt|tfksÄJ t|t ” |ksĻJ dt tdd d
t tdd  }dt tdd d d
t tdd  }t|tt tf|ksžJ tt tddtt tddksJ tt tddtt tfd	ks"J tdt tdd tt tfdks6J tt tddt	t tt tft	dksNJ d S )Nrr   r   r   rw   r   r   iś’’’rv   rj   rd   rļ   r   r¤   )
r=   rf   r   r#   rx   rM   rP   r   r/   r\   )	Zin_1Zout_1Zin_2Zout_2Zin_3Zout_3_1Zout_3_2Zin_4Zout_4ra   ra   rb   Ś"test_integrate_SingularityFunction?  s*     0<4 $$$(4r  c                  C   s  t tttt tt tftdksJ t ttd tt tftdks(J t t ddt  tt  dt  tt ttd  tddftddfdksPJ ttd td   t } t | ttdt   tt tftt tft | ttdt   tt tftt tf  krČt | tdt t  tt tftt tf  krČt | tdt t  tt tftt tf  krČdtdt  ksĖJ  J d S )Nr   rd   rw   rj   r   ée   )	r#   r   rf   r\   r/   rx   r   r0   r>   rg   ra   ra   rb   Śtest_integrate_DiracDelta\  s.   *&’
’’’’**’*ž*żür  c                   C   sā  t tt ttttd  td  ttdfttdfksJ t tt tttt tt tttdftdfks<J t ttt ttttt t ttdftdfksYJ t tttt  tttt d ttt  td  ttd dftd d dfksJ t ttt  ttttt d  tt d  ttt dfttdfks­J t ttt  ttttt  ttt  tttt dftdfksŅJ t ttt ttt	tt t ttdftdfksļJ t ttt d tttt d t	tt ttt  d  t ttdftdfksJ t tttt  tttt	tt  t ttt td   ttdftd d dfksMJ t t	tt ttttt  t ttdfdksjJ t t	tt d tttt d t	tt ttt  d  t ttdfdksJ t tt	tt  ttt ttt  t t	tt td   ttdfdksĮJ t ttt tdt
ftttt
 t dt  tt kttk @ ttd@ ft
dfksļJ d S )Nrj   r   Tr   rd   ©r   T)r#   rf   rx   r1   r-   r'   r   rY   r   r;   rį   r/   ra   ra   ra   rb   Ś test_integrate_returns_piecewisem  sN   &
’"
’
’:
’2
’.
’
’:’>’’6’4’8’r  c                  C   st  t ddd} tt| d| ddfdksJ tt| d | d | ddftdd	ks+J ttt| t|  d | ttd|  d | dkfd
td|  d  dfksUJ t ddd}tt|| t| d   | t tf}t|t| d   | t |f}t| t| d   | |tf}|||   krµtt	| t
| d tt	| d  t|d  d  ksøJ  J d S )Nrf   Tr   rd   r   rr   rw   r  rĖ   rj   rv   r§   )Zextended_real)rC   r#   r+   r)   r5   r   r1   r/   r>   r0   r   )rf   r§   Zint1Zint2Zint3ra   ra   rb   Śtest_integrate_max_min  s   ,,
’& &’’r  c                  C   s2  t tttddftddksJ t tttddftjks J t ttd tddftddks3J t ttd d tddfdksEJ t ttd dt  tdd	fd
ksYJ t tttddfdksgJ t tttt tt tfdkszJ t ttd td  tddftddksJ t	ddd\} }t t| | t
| d  d | dkf| d d dfks¶J t td|  d | t
| d  d|   | dkf| d d|   d dfksŻJ t t| |d  | ddfd|d  td|d  d|d   td|d d  d ksJ t tt|  | t
t| | dkfdt|   dfks+J t td|  d | t
|  | dk f| d dfksGJ t d|  t| d d  | t
| d | dk f| d  d | dk f| d dfksrJ t t| | |d ft
|d |d dkf| d |d dk fdksJ d S )Nrv   rj   r   rd   r   rr   rw   éń’’’r]   iÓ  r   rü   zt sTr   r„   é   r  )r#   r   rf   r5   r7   r³   r9   r;   r0   rC   r1   rŃ   r+   r   )r   r}   ra   ra   rb   Śtest_integrate_Abs_sign  s<   "&$(&."
’.
’:
’’’,’(’r  c                  C   sŽ   t ttt t} |  td”t ttd tksJ t ttt tddf} |  td”t ttd tddfks:J ttttd  }t |tt |t tt tf}| tdi”t tdtd  tt tfksmJ d S ©Nrr   r   rj   rd   rv   )rP   r   rf   rx   rŅ   r%   r/   ©r_   r\   Śconvra   ra   rb   Ś
test_subs1“  s   "("4r  c                  C   s  t ttt tt} |  td”t ttd ttksJ t ttt tddftddf} |  td”t ttd tddftddfksDJ ttttd  }t |tt |t tt tftddf}| tdi”t tdtd  tt tftddfksJ d S r  ©rP   r   rf   rx   r   rŅ   r%   r/   r  ra   ra   rb   Ś
test_subs2¾  s   $ 0*<r  c                  C   sŹ   t ttt tdtfttdf} |  td”t ttd tddftddfks(J ttttd  }t |tt |t tt tfttdf}| tdi”t tdtd  tt tftddfkscJ d S ©Nr   rj   rr   rd   rv   r  r  ra   ra   rb   Ś
test_subs3Č  s
    0*<r   c                  C   s¾   t tttdtfttdf} |  td”t tttddftddfks$J ttttd  }t |t|t tt tfttdf}| tdi”t tdtd  tt tftddfks]J d S r  r  r  ra   ra   rb   Ś
test_subs4Š  s
   ,&<r!  c                  C   sø  t ttd  tt tf} |  td”| ksJ t ttd  t t} |  td”t ttd  d tks8J t ttd  t ttf} |  td”t tttd  tdfks[J |  td”t ttd  d tksoJ t ttd  t tt tftt tf} |  td”| ksJ |  td”| ksJ t ttd  ttf} |  td”t ttd  tdfksøJ t ttt} |  td”|  td” t tttddf  ” jsŚJ d S )Nrd   r   rj   r   )rP   r   rf   r/   rŅ   rx   r   Śis_zero©r_   ra   ra   rb   Ś
test_subs5Ų  s    (*(*(*
’r$  c                  C   s  t d\} }ttt tttttf}| td”ttt ttdttfks*J | td”ttttttdfks>J ttt tttttftttttf}| td”ttt ttdttfttdttfksrJ | td”ttt tttttfttttdfksJ ttt tttt| ftttt| f}| | d”ttt ttttdfttttdfksÄJ d S )Nza brj   )rC   rP   rf   rx   r\   rŅ   )r   r¦   r_   ra   ra   rb   Ś
test_subs6ė  s   ,(,<<,@r%  c                  C   s¶   t ttdtftddf} |  tdtdi”| ksJ t tttt tttttftddf} |  ttd”| ks;J |  ttd”t tttt tdttftddfksYJ d S rŌ   )rP   rf   rx   rŅ   r;   r#  ra   ra   rb   Ś
test_subs7÷  s    ’*’r&  c                  C   s\   t ttttd  tdtf} |  ” t tttdtft ttd tdtf ks,J d S )Nrd   rj   )rP   r\   rf   rx   r   r#  ra   ra   rb   Śtest_expand   s    <r'  c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttd  dS ©Nrd   rr   )rP   r   rf   ra   ra   ra   rb   ro     rö   z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  dt tfS r(  )rP   r   rf   r/   ra   ra   ra   rb   ro     ó    )rS   ry   ra   ra   ra   rb   Śtest_integration_variable  s   r*  c                   C   sŹ   t ttd ttd d  tddf ” t ttd ttd  tddft ttd tddf ks6J t ttd ttd d  t ” t ttd ttd  tt ttd t kscJ d S )Nrd   rj   r   )rP   r   rf   r;   r   ra   ra   ra   rb   Śtest_expand_integral
  s   *"’’$’’r+  c                      sL  t ttd d tddf  jddddtd ksJ  jdddd	td
 dtd  ks2J  jddddtd d dtd d  dtd d  ksSJ  jd	dddtd d	td  d	td  dtd  kstJ t jd	dd ”   ”  dk sJ t ttd td  tddftddf tt fdd d S )Nrr   rj   rd   r   Śmidpoint©Śmethodr¤   éŁ   rw   r’   rĖ   é9   i	  é   iIĪ  iŚ  r   éV   r„   é   g      ą?r   c                      ó
      d”S )Nrw   ©Śas_sumra   r#  ra   rb   ro     ó   
 z'test_as_sum_midpoint1.<locals>.<lambda>)	rP   r>   rf   r6  rŃ   rY   rx   rS   ŚNotImplementedErrorra   ra   r#  rb   Śtest_as_sum_midpoint1  s$   *’
’
’
’

’&(r9  c                  C   s  t tt d tddf} tdddd}| jddd ” tdd	t td  ks)J | jddd ” td
dt td  ks?J | jddd ” tddt td  ksUJ | jd	dd ” tddt td  kskJ | j|dd ” td t tdd dd|d    ksJ d S )Nrd   r   rj   rY   T©r»   r[   r,  r-  rw   r   rū   rr   é#   él   é   é@   rĖ   )rP   rf   rx   rA   r6  r   r5   r   ra   ra   rb   Śtest_as_sum_midpoint2!  s   ,,,,$’r?  c                  C   s@  t tt d tddf} | jddd ” td ksJ | jddd ” tddtd  td  ks3J | jddd ” tdd	ttdd  td  ksNJ | jd
dd ” tddttdd
  td  ksiJ | jtdd ” td t tdd tt  ddt   ddtd    ksJ | jdddd t”sJ d S )Nrd   r   rj   Śleftr-  r¤   rr   r   r1  rw   r   é    r„   r   F)r.  Zevaluate)	rP   rf   rx   r6  r   r5   rY   Śhasr@   r#  ra   ra   rb   Śtest_as_sum_left,  s   0668’rC  c                  C   s8  t tt d tddf} | jddd ” ddt  td  ks!J | jddd ” tddttdd  td  ks<J | jddd ” td	d
ttdd  td  ksWJ | jddd ” tddttdd  td  ksrJ | jtdd ” td t tdd tt  ddt   ddtd    ksJ d S )Nrd   r   rj   Śrightr-  r   r¤   rr   r3  r1  rw   r]   rA  r„   )rP   rf   rx   r6  r   r5   rY   r#  ra   ra   rb   Śtest_as_sum_right7  s   *6668’rE  c                  C   s*  t tt d tddf} | jddd ” td t tj ks J | jddd ” td t tdd ks6J | jddd ” td t tdd	 ksLJ | jd
dd ” td t tdd ksbJ | jtdd ” td t tdd ddtd    ksJ t t	ttddf dd”tjksJ d S )Nrd   r   rj   Z	trapezoidr-  rr   r¤   é   rž   rw   rü   rA  r„   )
rP   rf   rx   r6  r   r7   r³   r5   rY   r9   r#  ra   ra   rb   Śtest_as_sum_trapezoidA  s   (,,,$’*rG  c                      sr   t tt d tddf tt fdd tt fdd ttdd  tt fdd tt fd	d d S )
Nrd   r   rj   c                      r4  )Nr   r5  ra   r#  ra   rb   ro   N  r7  z$test_as_sum_raises.<locals>.<lambda>c                      r4  ©Nr   r5  ra   r#  ra   rb   ro   O  r7  c                   S   s   t t d”S )Nrr   )rP   rf   r6  ra   ra   ra   rb   ro   P  rp   c                      s
      t”S rk   )r6  r/   ra   r#  ra   rb   ro   Q  r7  c                      s    j dddS )Nrr   Zxxxx2r-  r5  ra   r#  ra   rb   ro   R  rp   )rP   rf   rx   rS   ry   ra   ra   r#  rb   Śtest_as_sum_raisesL  s   rI  c                  C   s4   t t ttt} t ttt}|  ” | ” ksJ d S rk   )rP   rf   r   ©r_   r\   ra   ra   rb   Śtest_nested_doitU  s   rK  c                  C   s  t td td df} t td tdd f}|  ” tddksJ | ” tddks*J t tt td tf tt”t tt td tfksDJ t tt ttd f tt”t tt ttd fks^J ttd td dftddksoJ ttd tdd ftddksJ tddtddksJ d S )Nrd   rj   rr   r   zx**2)rf   Ś1N)rP   rf   r   r5   rx   rŅ   r   r#   rJ  ra   ra   rb   Śtest_issue_4665[  s   44""rM  c                  C   s*   t td tddf} | t | j ksJ d S )Nrd   r   rj   )rP   rf   Śargsr#  ra   ra   rb   Śtest_integral_reconstructh  s   rO  c                  C   s  t t dt tddf} |  ” tddksJ | jddtddks$J td}t |ttddf ” dks8J t dtdt |ttf ” dksKJ t ttdf ” dksXJ tdttftdff}t tg|¢R   ” tddkstJ t tgtt|¢R   ” dksJ d S )	Nrd   r   rj   rr   F)Zdeepr\   rw   )	rP   rf   r   r5   r   r   r   ŚlistŚreversed)r_   r\   r   ra   ra   rb   Śtest_doit_integralsm  s    &"(rR  c                   C   sš   t ttdt  tdtt td d  d dtt td  d  dtt d  ttd dkfdt tt  td d  d dt tt  td  d  dt tt  d  dfksdJ t tt dtt  tt ksvJ d S )Nrj   rd   r   r]   rw   T)r#   r>   rf   r1   r   r   r'   ra   ra   ra   rb   Śtest_issue_4884|  s   B’>’’ż’(rS  c                   C   s²   t tt tt tttt tt  tt td dt  d  ttt  tt td dt  d   ttt  td dt  d   ttdfttd d dfksWJ d S )Nrd   rj   r   T)r#   rf   rY   r'   r1   r-   ra   ra   ra   rb   Śtest_issue_18153  s   *&’’žż’rT  c               	   C   s  ddl m} m}m} ddlm}m} t| jdu sJ td| jdu s%J td| dfjdu s1J td| ddfjdu s>J td| d|fjdu sKJ td| |fjdu sWJ t| |jdu saJ t| |d| fjdu snJ t| |ddfjdu s{J t| | ddfjdu sJ t| |ddf}|jdu r| 	” dksJ t| |||f}|jdu r°| 	” dks²J td|||d f}|jdu rĒ| 	” dksÉJ t| | | ddf|ddfjdu sÜJ t| | | ddf|d|fjdu sļJ t| | dfjdu sūJ t| | dt||ddffjdu sJ tt
||ddf| ddfjdu s#J t|| d || d  d | jdu s:J tt| | ddfjdu sJJ d S )	Nr   ©rf   rx   rį   )r   r;   Frj   Trd   rr   )Ś	sympy.abcrf   rx   rį   rÉ   r   r;   rP   Z	is_numberrY   r@   r\   )rf   rx   rį   r   r;   r   ra   ra   rb   Śtest_is_number  s2   &&((.$rW  c                  C   s  ddl m} m}m} td| j| hksJ t| j| hksJ t| | d |fj|hks-J t| | |d fj|hks;J t| | d|fj|hksIJ t| | |dfj|hksWJ t| | | |fj| |hksfJ t| | |j| |hkssJ t| | ddfjt ksJ t| |ddfj| hksJ t| |||fj| |hksJ t| |ddf|d d fj| |hks±J t| |ddf| d|fj|hksĆJ td|ddf|d| f| ddfjt ksŁJ td|| df|d| f| ddfjt ksļJ td| ddf|| df|ddfj| hksJ d S )Nr   rU  rj   rd   )rV  rf   rx   rį   rP   r   ŚsetrU  ra   ra   rb   Śtest_symbols°  s&   &$,, ’rY  c                  C   s.  ddl m} m} td| d| fjsJ td| ddfjsJ td| ddftdfjdu s.J t| |dfjs8J t| | |dfjd u sFJ t||dt| f| df}|jd u sZJ t|| df|dt| fjdu slJ t| | ttfjswJ t| | t t fjsJ tt| | ddt	 fjd u sJ d S )Nr   )rf   rĢ   rj   rd   FT)
rV  rf   rĢ   rP   r"  rx   r   r/   r;   r0   )rf   rĢ   r   ra   ra   rb   Śtest_is_zeroĘ  s    $&rZ  c                     s\   ddl m}  tt| | | f}| | ” |j| dd ” t fddtdD  ks,J d S )Nr   ©rf   r¤   rĀ   c                    s   g | ]}t  qS ra   )Śnext)Ś.0rź   r#  ra   rb   Ś
<listcomp>Ż  rö   ztest_series.<locals>.<listcomp>rw   )	rV  rf   rP   r   ZlseriesZnseriesZremoveOr   Śrange)rf   r   ra   r#  rb   Śtest_seriesŁ  s   
4r`  c                  C   sV   t d} tdt|  |  | t| t|  ksJ tt| d |  |  t”s)J d S )Nrf   rj   rd   )rA   r#   r;   r'   r8   r   rB  r
   r[  ra   ra   rb   Ś!test_trig_nonelementary_integralsą  s   *$ra  c                  C   s$  t d} t d}t ddd}tt| d |d  | |d t| |  d | t| d |d   d  ks7J tt| d |d  | |d  t| |  d | t| d |d   d  ksaJ t ddd} t ddd}td| d |d  td	  | | |d t| d |d    ksJ d S )
Nrf   rx   rį   Trŗ   rd   r   rj   z3/2)rA   r#   r>   r   r   r7   rU  ra   ra   rb   Śtest_issue_4403č  s   2’4’ ’rb  c                   C   sT   t ttd  d tdtttdtd    ttdtd   d  ks(J d S )Nrd   rw   rv   rļ   )r#   r>   rf   r	   ra   ra   ra   rb   Śtest_issue_4403_2ł  s   2’rc  c                  C   sD   t ddd} tt| d td  td| ft| d  d ks J d S )NŚRTrŗ   rd   r   rw   )rA   r#   r>   rf   r0   )rd  ra   ra   rb   Śtest_issue_4100ž  s   8re  c                  C   sÄ  ddl m} m}m}m} td}tt||||t||||ks$J t||j||t|fks5J tt||j||t|t|fksKJ tt|||j||t|t|fksbJ tt||||j||t|t|fkszJ ttt|||||j||t|t|t|fksJ t	t||||t||||ks¬J t	t|||||t||| ksĮJ t	t||||t||| ||t||| fv sßJ t	td|||d ksķJ t	td||d| | ksżJ td||jtd||jksJ t|||||| 
” |d t|||| d ks+J t|||ddf| d|f|d|f 
” ||d  t|||ddf |d t|||ddf  ks`J d S )Nr   )Śwrf   rx   rį   r\   rd   rj   )rV  rf  rf   rx   rį   r   rP   rN  rG   r#   r   )rf  rf   rx   rį   r\   ra   ra   rb   Śtest_issue_5167  s(   (",.0’(*< ":&:’rg  c                  C   s  t ddd} ttttd  tttttdd tttt	j
  d ks*J ttttd tttttdd tttt	j
  d ksMJ tt|  ttd  ttttdd|    tt| tt ddt|     dt|   ksJ d S )Nrį   Trŗ   rd   rj   rw   r   )rA   r#   r   r'   rf   r>   r0   r5   r   r7   r³   r   ©rį   ra   ra   rb   Śtest_issue_4890  s   *’*’F’ri  c                   C   s,   t dttdtd    t t”rJ d S rŌ   )r#   rf   r>   rB  rP   ra   ra   ra   rb   Śtest_issue_4551$  s   ,rj  c               	   C   s   t dddd} tt| td|   d  tdtjf| d dd|   | d   | dd|     ddd|    | ddd|        dksFJ d S )NrY   T©r[   r»   rj   r   rd   )rA   r:   r#   rf   r7   r³   rĀ   ra   ra   rb   Śtest_issue_4376(  s   "N’’rl  c                   C   sX   t tttd  ttdd  tdttdd  d dttdd  d  ks*J d S )Nrr   rj   r„   r   rü   )r#   r>   rf   r5   ra   ra   ra   rb   Śtest_issue_4517.  s   "*’rm  c               
   C   sś  t ddd\} }tt| t t|t  tdtf ” tdt| dt|dB ft d t| | t| dt|d@ B ftd t| |t| dt|d@ B fdksSJ tt| t t|t  tftdtt| dt|dft t|t d  d tt	|t d  d  t|t t	|t  d|   t| | ftt|t d  d tt	|t d  d  t|t t	|t  d|   t| |f|t| t  t	|t  | d |d   | t|t  t	| t  | d |d    dfksūJ d S )Nzk mTrZ   r   rd   r  )
rC   r#   r;   rf   r0   r:   r1   r   r   r   )ŚkrĢ   ra   ra   rb   Śtest_issue_45273  s$   &($ż’ \X**’’üro  c                  C   sp   t ddd} ttt d t |  t t tt tfddttt d t |  t t tt tfks6J d S )Nrx   Trŗ   rd   r¼   r½   )rA   r#   r   r   r0   rf   r/   rP   )Zyposra   ra   rb   Śtest_issue_4199H  s   .*’rp  c                  C   s“  t dddd\} }}}tttd  t| t  ttt t|d  d  tt| d t  d ks7J tt| td  |t  | tttt| t|d  d|    tt| t |dt|     dt|   kssJ ddl	m
} ddlm} |tttd  tt| t  tt tfttt|d  d  ks¦J t d	dd
\} }|tt|  td  d| t  tt tfttt|d |   t|  ksŲJ d S )Nza:dT)r»   Zfiniterd   rw   r   )Ś
expand_mul)rn  za drŗ   )rC   r#   r   rf   r   r>   r0   r   r   rÉ   rq  rV  rn  r/   )r   r¦   r§   r{   rq  rn  ra   ra   rb   Śtest_issue_3940O  s    2’ P’.’.’rr  c                   C   sV   t t td td   tttt t t  d tttt t  d  ks)J d S rµ   )r#   r   rf   r   r'   ra   ra   ra   rb   Śtest_issue_5413_  s   Vrs  c               
   C   sø  t d\} }tddd}|  t|  }|  |t  ttd ttd   }ttd  ttd  }ttd  ttd  d }t|||  t||  |  t	|t  | | t t|    ||  |  t	|t  | | t t|    || | t	|t  | | t t|    || | t	|t  | | t t|    | | t | |  t	t t|  t|  | | t | |  t	t t|  t|  fv sŚJ d S )NzA zr§   T)rĮ   rd   rj   )
rC   rA   r   r   r;   rf   r   rx   r#   r'   )r”   rį   r§   ZP1ZP2Zh1Zh2ra   ra   rb   Śtest_issue_4892ae  s   &00,,..śrt  c                  C   s\   t ttd  dtt td   d td d  } ttt| t t”|  dks,J d S )Nrr   rd   rĖ   r   )r;   rx   rf   r   rF   r   r#   r   )Śexprra   ra   rb   Śtest_issue_4892bz  s   4	(rv  c                   C   sX   t ttttt tdtftdtftdtfdtttttdtftdtf ks*J d S ©Nr   rd   )r#   r;   rf   r\   rx   rį   r0   rP   ra   ra   ra   rb   Śtest_issue_5178  s   , ’rx  c                  C   sŖ   t t tdd”} td d td d  td d  td d	  td d
  ttd  }t| t|ks6J tt| tt| ksBJ tttd tttd ksSJ d S )Nr   r   rd   rw   é   r„   iŠ  r¤   i  i _7 rü   r   )r;   rf   Zseriesr.   r#   r   ©r\   rn   ra   ra   rb   Śtest_integrate_series  s
   H&r{  c                  C   s<   ddl m}  ddlm} || g g dgg ttd u sJ d S )Nr   ©r*   ©Śheurischrj   )rÉ   r*   Zsympy.integrals.heurischr~  rf   )r*   r~  ra   ra   rb   Śtest_atom_bug  s   $r  c                  C   sh   t ddd} tttt |  tdtftdtf ” t| ttd |   t	 dtt  |  ks2J d S )Nrį   F)Zzeror   rd   )
rA   r#   r;   rf   rx   r0   rz   r'   r
   r   rh  ra   ra   rb   Śtest_limit_bug  s   &*’r  c                  C   s,   t d} ttt| t t t”sJ d S )Nrn   )r   r#   r   rf   rB  rP   rm   ra   ra   rb   Śtest_issue_4703¢  ó   $r  c                  C   s.   t d} t| t t”d t t”sJ d S )Nr\   rd   )r   r#   rf   r   rB  rP   r×   ra   ra   rb   Śtest_issue_1888§  s   &r  c                  C   sR   ddl m}  tttt tt d td ftdtfd| td d  ks'J d S )Nr   ©r8   rd   )rÉ   r8   r#   r   rf   rx   r0   r  ra   ra   rb   Śtest_issue_3558®  s   Fr  c                   C   s6   t dtddtd    tttd d ksJ d S )Nrj   rū   rw   rd   )r#   r>   rf   r   ra   ra   ra   rb   Śtest_issue_4422³  rŪ   r  c                  C   sZ   ddl m}  | tttddt   ttdt d dtd  t d  d ks+J d S )Nr   ©r:   rj   rd   r„   r]   )rÉ   r:   r#   rf   r>   r  ra   ra   rb   Śtest_issue_4493·  s   &’r  c                   C   sh   t ttt tt tftksJ t ttt tdtftd ks#J t ttt tttks2J d S rw  )r#   r;   rf   r/   r0   r8   ra   ra   ra   rb   Śtest_issue_4737½  s   "$"r  c                  C   st   ddl m} m}m}m} tddd}| |ttt t	t t|  tdt
f||d| d || ks8J d S )Nr   )r:   rĒ   r4   r   r   Trŗ   rj   )rÉ   r:   rĒ   r4   r   rA   r#   r   rf   r'   r/   )r:   rĒ   r4   r   r   ra   ra   rb   Śtest_issue_4992Ć  s
   ,’r  c                  C   sB   ddl m} m} |ttt tt  t| td tksJ d S )Nr   ©Ś
lowergammar:   rj   )rÉ   r  r:   r#   r   rf   rx   r  ra   ra   rb   Śtest_issue_4487Ė  s   2r  c                  C   s,   t d} td| d  | ddftu sJ d S )Nrf   rj   rd   r   )rA   r#   r/   r[  ra   ra   rb   Śtest_issue_4215Š  r  r  c                  C   s    t dddd} tt|  tt t| t t|   tt | d d|   d  tt|   tt | d d|   d   tt|   | d d|   d   ksNJ d S )NrY   Trk  rd   rj   )rA   r#   rf   r'   rĀ   ra   ra   rb   Śtest_issue_4400Õ  s   R’’r  c                   C   sZ   t tdt tdt  d t tddttt d ttd  d t tks+J d S )Nrj   rd   Tr|  )r#   r>   rf   rP   ra   ra   ra   rb   Śtest_issue_6253Ü  s   (&’r  c                   C   sč   t ddt t t  tddftddftddfdtd dtd d  dtd d  dtd  d	td
  dtd dtd
  dtd d  dtd dtd d  dtd dtd d  dtd d  fv srJ d S )Nrj   r   iō’’’rr   r„   rd   r¤   r   r   rw   r1  r  é/   ©r#   rf   rx   rį   r'   ra   ra   ra   rb   Śtest_issue_4153ć  s
   .B@*żr  c                  C   sf   t d\} }}t|t|  |  | t| d td   t| | | f}| t”r*J | t”r1J d S )NzR b hrd   )rC   r#   rf   r>   rB  r,   rP   )rd  r¦   Śhr_   ra   ra   rb   Śtest_issue_4326ź  s   8r  c                   C   s>   t dt dt  tdt td dt td  ksJ d S r(  rŁ   ra   ra   ra   rb   Śtest_powersō  s   >r  c                   C   s<   t tdd  ttdt t tddfdd t”sJ d S )Nc                   S   ó   t dt tdddS )Nrj   T)Śmanualr*   r   ra   ra   ra   rb   ro   ł  rö   z$test_manual_option.<locals>.<lambda>rj   r   T)r  )rS   ry   r#   r'   rf   rB  rP   ra   ra   ra   rb   Śtest_manual_optionų  s   .r  c                   C   s6   t tdd  ttttddttttksJ d S )Nc                   S   r  )Nrj   T)r*   Śrischr   ra   ra   ra   rb   ro   ’  rö   z%test_meijerg_option.<locals>.<lambda>Tr|  )rS   ry   r#   rE   rf   rP   ra   ra   ra   rb   Śtest_meijerg_optionž  s   (r  c                   C   sŖ   t tdd  tttd  tddtttd  tksJ ttdt t ttddtd ttdt  d td   ksAJ ttttddt	tttksSJ d S )Nc                   S   s   t dtt tdtfddS )Nrj   r   T©r  )r#   r'   rf   r/   ra   ra   ra   rb   ro     r)  z#test_risch_option.<locals>.<lambda>rd   Tr  rj   )
rS   ry   r#   r   rf   rQ   r'   rx   r   rP   ra   ra   ra   rb   Śtest_risch_option  s   0D(r  c                   C   s,  t tdd  tttd tddtttt d ksJ tttt tddtttt tks4J tt	tt
t	t ttdd  tddd	ttd
d  tt	t d dttd
d  t
t	t d  dttd
d  tt	t d dttd
d  t
t	t d  t	t  ksJ d S )Nc                   S   r  )Nrj   T)r  r~  r   ra   ra   ra   rb   ro     rö   z&test_heurisch_option.<locals>.<lambda>rd   Tr}  rr   rw   Fi’’’rj   i!  éš   rū   rÄ   )rS   ry   r#   r   rf   r>   r0   r   rP   r'   r   r5   r;   ra   ra   ra   rb   Śtest_heurisch_option  s   .,*BJ’’r  c                  C   s:   ddt d  d  } t| t  t ”}t| |ddsJ d S )Nrj   gHįz®Gń?rd   g333333@gź-q=)Ztol)rf   r#   r   rX   rz  ra   ra   rb   Śtest_issue_6828  s   r   c                  C   sX   t d} ttt t| t  tt  tttt|  tt  tt t ks*J d S )NŚx_max)rA   r#   rx   r0   r   rf   r   r   )r”  ra   ra   rb   Śtest_issue_4803   s   ""’r¢  c                   C   s@   t dtdttd   tttdttd   ksJ d S rŌ   )r#   r>   rE   rf   ra   ra   ra   rb   Śtest_issue_4234&  s   @r£  c                   C   s  t ttd tdtd   tttdtd  dtd   dt  dttd d  ttdt d    dttd d   dttd d k fdtd  dtd   dt  dttd  d  ttdt d   dttd  d   d	fksJ d S )
Nrd   r   r]   rr   é   r¤   rj   rv   T)	r:   r#   rf   r>   r1   r   r   r   r   ra   ra   ra   rb   Śtest_issue_4492*  s   "J’’H’’żr„  c                  C   s  dt t tt  } t| tddf}t| tddf ” |ks J t| tt tddf|td td ks8J td|  tt tddfd| td td ksTJ ttdt t	 t t
 t  t
 tdtfttdt t	 t tdt t	 td  t
  tdtfksJ d S )Nrj   rd   rr   g333333ó?r   g333333óæ)r   rį   r'   rQ   rP   r   r#   r   rY   r}   r   rf   )r\   Z
integral_fra   ra   rb   Śtest_issue_27082  s   0’,0’’r¦  c                  C   sD   dt  dt  d tdt   } t| t ddf}t|dks J d S )NgŗõJ  @gģD @g      $@g¹?gÉ?z%1.86831064982608*y + 2.16387491480008)rf   rx   r   r#   Śstr)r\   r_   ra   ra   rb   Śtest_issue_2884@  s    rØ  c                   C   sü  t tt t tt tdtftttt ttd  d   ttd dk fdtt ddtd     ttd dk ft	t
jfdfdt
jfdfttd df tttttd ttk tttttd td tttd  d dkttd dfttt t tt tdtfdfksJ t tt t tt tdtftdtd  d dt d  d  ttdt dtttttd k tttttd kttttttt d dkfttt t tt tdtfdfksüJ d S )	Nr   rd   rj   rv   )r   r   )r   Tr   )r#   r   r}   rf   r   r/   r1   r0   r   r*   r7   r³   r2   r   rN   r   r>   r-   rP   r   ra   ra   ra   rb   Śtest_issue_8368F  sV    ’’

żüū4żõ žļ’   ü’ ’ł’r©  c                   C   s   t tdt dtdt  ksJ t tdt dt dttdt d   ks,J t ttttttd  ks>J d S )Nrē   rj   )r#   r   rf   r   r   r'   ra   ra   ra   rb   Śtest_issue_8901h  s   $4(rŖ  c                   C   s¶   t ttd t tddftd d dtd d  ksJ t ttd t tdtftd ks3J t ttd td  ttdt  tdt dt   ddt   ksYJ d S )Nrr   r   rj   rw   rd   )r#   r;   rf   r8   r/   r0   r   ra   ra   ra   rb   Śtest_issue_8945n  s   >(Pr«  c                  C   sd   t rtd td\} }}}tt|  t | d ||t    t”}tt|td|fj	vs0J d S )NzToo slow for travis.zi L a brd   r   )
rV   rU   rC   r   r0   rf   Zrewriter   r#   r   )r   ŚLr   r¦   Ś	integrandra   ra   rb   Śtest_issue_7130u  s
   *r®  c                  C   sx   t d\} }}}t| | ||g}t||t|| ” ksJ t||t| |d  d g|| g|| ggks:J d S )Nza b c trd   )rC   r(   r#   rP   r   )r   r¦   r§   r   Zvtra   ra   rb   Śtest_issue_10567~  s   :rÆ  c                  C   s2   t d} ttt|  | tt|  t ksJ d S )Nr   )rC   r#   r<   r0   r8   )r   ra   ra   rb   Śtest_issue_11856  s   *r°  c                   C   s0   t ttdt tddfttd ksJ d S ©Nrj   r   rd   )r#   r>   r'   rf   r0   ra   ra   ra   rb   Śtest_issue_11876  s   0r²  c                   C   sV   t dtt dtdt   tdt  tdtdt  dtdt   ks)J d S )NiÄ’’’g3333333@rw   g333333Ąr¤   g      (@r   )r#   r   rf   ra   ra   ra   rb   Śtest_issue_4950  s   ,’r³  c                   C   sP   t tttd ttttd  d dt tttd  d  ks&J d S )Nrd   r   )r#   r;   r'   rf   r   ra   ra   ra   rb   Śtest_issue_4968  s   Pr“  c                   C   s²   t dtd  tt tftu sJ t dtd  tddftu s!J t dtd d  tddftu s3J t dtd  tddft u sDJ t dtd d  tddft u sWJ d S )Nrj   rd   r   rv   )r#   rf   r/   ra   ra   ra   rb   Śtest_singularities  s
   " $"*rµ  c                  C   sø   t ddd\} }tt| |  |  ||  | tt||   tt||  f|tt ttftt| d |d  | t|d  t  t|d  t f|tt ttfksZJ d S )Nzx yTr   rr   rd   )rC   r#   r;   r>   r0   rP   )rf   rx   ra   ra   rb   Śtest_issue_12645”  s   "ž&žżr¶  c                   C   s6   t ttttd  tdtd ftddksJ d S )Nrr   r   r„   rj   )r#   r;   rf   r   r0   r5   ra   ra   ra   rb   Śtest_issue_12677«  rŪ   r·  c                   C   s6   t tdt tt t tdtftd ksJ d S )Nrr   r   )r#   r   rf   r/   r'   ra   ra   ra   rb   Śtest_issue_14078Æ  rŪ   rø  c                   C   s(   t dtt tdtftd ksJ d S r±  )r#   r   rf   r/   r0   ra   ra   ra   rb   Śtest_issue_14064³  s   (r¹  c                	   C   sp   t ddtttj dtt    ttttjtttttjdttj    ttjt   ks6J d S rs   )r#   r   rf   r7   r³   r'   r   ra   ra   ra   rb   Śtest_issue_14027·  s   &>’rŗ  c                   C   s&   t tttdtd ftju sJ d S rw  )r#   rE   rf   r0   r7   ZInfinityra   ra   ra   rb   Śtest_issue_8170¼  rÖ   r»  c                   C   sD   t dt tddftju sJ t dtd  tddftju s J d S )Nrj   r   rv   rr   )r#   rf   r7   r   ra   ra   ra   rb   Śtest_issue_8440_14040Ą  s   &r¼  c                   C   s   t dtt d  tddfdtd  dt  ksJ t ddt t t d  tddftddftddfdtd dtd  dtd	  ksHJ d S )
Nrj   rd   r   r   rļ   rw   r„   r©   rr   r  ra   ra   ra   rb   Śtest_issue_14096Å  s   42"’r½  c                   C   sh   t tdtdtd   tddf ” d dk sJ t ttdtd  tddf ” d dk s2J d S )Nrj   rr   r   gQ£dVoö?gķµ ÷Ę°>g)Ś ģź?)r   r#   r>   rf   rY   ra   ra   ra   rb   Śtest_issue_14144Ė  s   44r¾  c                   C   s(   t ttt tt t t”sJ d S rk   )r#   r   r   rf   r'   rB  r   ra   ra   ra   rb   Śtest_issue_14375Š  s   (ræ  c                  C   sX   t dttt} t| tddftddftddft| tddftddftddfks*J d S )Nr\   r   rj   rd   rr   )r   rf   rx   rį   r#   rP   r×   ra   ra   rb   Śtest_issue_14437Ö  s   ’rĄ  c                   C   sZ   t dtttd  ttddtttd   tddtttd    ks+J d S )Nrj   r   )r#   r>   r   rf   r'   ra   ra   ra   rb   Śtest_issue_14470Ü  s   6’rĮ  c                  C   sØ   t dt td t  dtd   dtd  t  dt td t  d  } t| tt dtd  tt td   d  tt dtd   t dtd    ksRJ d S ©Nrj   rd   rr   )r   rf   r#   r×   ra   ra   rb   Śtest_issue_14877į  s   LH’rĆ  c                  C   sB   t td  d td  t  } t| tddgt d ksJ d S )Nrd   rj   r   r¤   )r>   rf   r#   r0   r×   ra   ra   rb   Śtest_issue_14782ē  s    "rÄ  c                  C   sJ   t td  d td  t  } t| tddgtjd td  ks#J d S )Nrd   rj   r   rr   rū   )r>   rf   r#   r7   r   r0   r×   ra   ra   rb   Śtest_issue_14782_slowģ  s    *rÅ  c                  C   s4   t tdd tt   } t| t dtgtu sJ d S )Nrš   rd   r   )rf   r5   r   r#   r/   r×   ra   ra   rb   Śtest_issue_12081ņ  s   rĘ  c                  C   sD   dt  d } d|  td|   t d  }t|t ddgdks J d S )Nrj   rw   rv   rd   r   )rf   r   r#   )rx   r\   ra   ra   rb   Śtest_issue_15285÷  s   rĒ  c                   C   s   t tt tt  tt tdtf ” tttd t	dt ttd t  t
td dkfttt tt  tt tdtfdfksHJ d S )Nr   rj   T)r#   rf   rY   r   r'   r/   r   r1   r   r4   r6   rP   ra   ra   ra   rb   Śtest_issue_15432ż  s   *4(žrČ  c                  C   s   t d} tdtd\}}tttt | | | |   tddt ttt | |   ttt | |   | | | |   ks@J d S )NŚomegazm p)Śclsr¼   r½   )r"   rC   r    r#   r   rf   r   )rÉ  rĢ   rh   ra   ra   rb   Śtest_issue_15124  s
   $<’rĖ  c                   C   sx  t   tttt W d    n1 sw   Y  t   ttttttttttttks3J W d    n1 s=w   Y  t   ttttt ” ttd d tt ks]J W d    n1 sgw   Y  t   ttt t”ttd d tt ksJ W d    n1 sw   Y  tttttddfttjtks§J ttt tddf”ttjtksŗJ d S )Nrd   r   rj   )	rW   rP   r   rf   rx   r   r#   r7   r³   ra   ra   ra   rb   Śtest_issue_15218
  s   ’,’0’,’&*rĢ  c                  C   s   t ttd  tdt  ttd tdt   tdtf} t| ts&J t	| t
td tt   ttd ”dks>J d S )Nrd   r   r„   )r#   r   rf   r   r   r;   r/   rÆ   r1   r   r>   r0   rŅ   r  ra   ra   rb   Śtest_issue_15292  s   >4rĶ  c                   C   s.   t tdt tt tdtt ksJ d S rµ   )r#   r;   rf   ra   ra   ra   rb   Śtest_issue_4514  s   .rĪ  c                  C   sč   t ddd\} }}ttt| d | ||f}ttt| d | }| |d|di”ddt  ks3J | | d”| | d” ddt  ksGJ | |d|d	i”td td
 ks[J | | d	”| | d” td td
 ksrJ d S )Nzx a bTr   rd   rj   rr   rv   rš   r   r   )rC   r#   r   r   rŅ   r   )rf   r   r¦   ZdefiniteZ
indefinitera   ra   rb   Śtest_issue_15457#  s   "((2rĻ  c                   C   sN   t ttt tt tttt tt tt tt tt ks%J d S rk   )r#   rf   r   r'   r   ra   ra   ra   rb   Śtest_issue_15431-  s   *’rŠ  c                  C   sü   t tt  } tdtt  }t| t |kr| t ”| ksJ t d tt d  } t d  tt  dtdtt    }t| t |krI| t ”| ksKJ ttt t d  } tt tttt  d ttt t   }t| t |krz| t ”| ks|J d S )Nrd   rr   rw   )rf   r'   r   r#   r   r>   r0   r   )r\   ŚFra   ra   rb   Ś"test_issue_15640_log_substitutions2  s    & .$rŅ  c                  C   sØ   ddl m}  | d}|j}ttt| t |ttfddt	t
tt t  t t
tt t t  tt kttk @ ttd@ ft tt ttt  dfksRJ d S )Nr   )Ś
CoordSys3DŚNTr}  )Zsympy.vectorrÓ  rf   r#   r   r   r¦   Śx_1Śx_2r1   r;   r/   r-   )rÓ  rŌ  rf   ra   ra   rb   Śtest_issue_15509>  s    Džr×  c                  C   s¢   t ddd} t| td| d   | t| d d d| d  d  | dkf| d  d d| d  d  tdd | d	kf| d d d| d  d  dfksOJ d S )
Nrf   Tr   r©   rd   rw   rš   éQ   rr   )rC   r#   rŃ   r1   r5   r[  ra   ra   rb   Śtest_issue_4311_fastG  s   ".żrŁ  c               	   C   są  t dddd} t ddd}t ddd}t ddd}ttt |  |d  ||  |tttt tt |d  d	|    td
t |  | | dt|  tt    dt|   ks_J tddt|d    |t tt t|ttt    d tt t|ttt    d   ksJ ttt |d  |ttttt|  dtt  ksµJ tdtt| d  || d tttt| d  d  ks×J tdtt| d  |ddt ft ksīJ d S )NŚKT©r   r»   rf   r   rĢ   r   rd   rw   rv   rj   r   )	rA   r#   r   r   r>   r0   r   r'   r   )rŚ  rf   rĢ   r   ra   ra   rb   Ś%test_integrate_with_complex_constantsO  s"   >’,’

’>"’@D2rÜ  c                  C   sx   t d} t dddd}t|| |d   | d  | |d | |  t| ttt  d| t| t|d  ks:J d S )Nrf   rY   Tr:  rj   rd   )rA   r#   rH   rI   r   r0   r   ©rf   rY   ra   ra   rb   Śtest_issue_14241^  s
   :’rŽ  c                   C   s<   t ttd ddtt   tddt gtd ksJ d S )Nrd   r   rw   r   )r#   r;   r   r   r0   ra   ra   ra   rb   Śtest_issue_13112e  rå   rß  c                  C   sP   t ddd} tttddt |    td| f}|d| d  t d ks&J d S )	Nr  Trŗ   rj   rd   r   r   rū   )rA   r#   rf   r   r0   )r  r   ra   ra   rb   Śtest_issue_14709bi  s   $ rą  c                  C   sl   t d} t d}tt|| |t | ft| ksJ tt|  td|   |  | dtftdks4J d S )Nrf   r   rv   r   rd   )rA   r#   r   r/   r   r'   )rf   r   ra   ra   rb   Śtest_issue_8614p  s   &6rį  c                  C   sō   t dddd} t| d dtd|    t|  t|  }t|| }|tjks)J t| | d”d dks7J t| d dttd	d
 |    t|  t|  }t|| dtd|  d
  d dtd|  d  d  td|  d  ksxJ d S )Nr}   TrŪ  rd   gł?rj   gĻRt?,eĄg:0āyE>r¤   r   iö’’’é   rr   )rC   r   r#   r7   r   rŃ   rŅ   )r}   r­  Zsolutionra   ra   rb   Śtest_issue_15494w  s   ,
4Rrć  c               	   C   s~   t d} tt| td  t ” ttttd |   ttdttd |   d  ttd |    t	| dfdks=J d S )Nrx   rd   rr   r   r  )
rA   rP   rJ   rf   r   r1   r   r'   r>   r-   r¶   ra   ra   rb   Śtest_li_integral  s   ,.’žžrä  c               	   C   sĘ   t d} t d}tt| | | | | |  ttdd dd|    ttdd dd|   ftdd tdd dd|   f| d|   d  d| ttdd dd|     ksaJ d S )Nrf   rY   rj   rd   rr   rw   )rA   r#   r;   r   r7   rK   rŻ  ra   ra   rb   Śtest_issue_17473  s   @"ž"ž’rå  c                   C   s¤   t ttttd  tdtgt ksJ t ttttd  tdtgtd d td  ks2J t ttttd  tdtgdtd d td  ksPJ d S )Nrd   rj   rr   r   rv   r©   )r#   r'   rf   r/   r   ra   ra   ra   rb   Śtest_issue_17671  s   *:@rę  c                  C   s~   t d} t d}t d}td|d | tdd   ||  d | d f| |tdd  td| d d|     ks=J d S )Nrf  ŚCrx   rj   rd   rr   rw   )rA   r#   r7   r>   )rf  rē  rx   ra   ra   rb   Śtest_issue_2975  s   frč  c                     sŌ  t d\ } tddd}tt   d|fd |d d |d   ks*J ttt   d|ftd t  d  d|fksKJ ttt   d|fttt     t dfd	 d|fkssJ tttt   d|ftttt    d  t df   df d|f t	 k t	k @ t d@ fd	ks¶J tt d| f| d  d ksĖJ t
t fd
d t
t fdd t
tfdd d S )Nzx n MrŌ  TrZ   rj   rd   rw   r   r  c                      s   t tt ftS rk   ©r#   r@   rx   ra   ©rY   rf   ra   rb   ro   °  ru   z!test_issue_7827.<locals>.<lambda>c                      s   t td f S rs   )r#   r@   ra   rź  ra   rb   ro   ±  ru   c                      s   t t  dtf S rs   ré  ra   r[  ra   rb   ro   ²  ru   )rC   rA   r#   rB   r;   r@   r1   r   r-   r/   rS   ry   )rė   rŌ  ra   rź  rb   Śtest_issue_7827¤  s,   :’,’"2’’’’*rė  c               	   C   s   ddt   tt tt  ddt     t d  t t tt tt    tt tt    } t| t dtt tt   dtt tt tt     ksKJ d S rĀ  )rf   r>   r'   r#   r×   ra   ra   rb   Śtest_issue_4231µ  s   XBrģ  c                  C   s@   t dtd t t  t} t| tdtd t t  ksJ d S rŌ   )r   rf   r   r#   r×   ra   ra   rb   Śtest_issue_17841ŗ  s   &rķ  c                  C   sJ  t dddd} | | d  tdd  | t| ttd   d  }| ttd | | dd|      }t|| | d  dtdd   | d	 t| ttd   d| d	  d	  d	|  t| ttd   d	t| ttd   ksxJ t|| t| d	 tdd  d	 d	td
 ttd t	d	td
 |    ks£J d S )Nrf   T©r   rĮ   rw   r   rj   rĖ   r„   rd   rr   )
rA   r   r   r'   r   r   r#   r7   r>   r	   )rf   Śf1Śf2ra   ra   rb   Śtest_issue_21034æ  s   6$x’F’rń  c                   C   sd   t tttt  ttt tt tt  ksJ t tttt  tdtft ks0J d S rH  )r#   r'   rf   r   r   r/   r   ra   ra   ra   rb   Śtest_issue_4187Ė  s   8,rņ  c                  C   s\  t dddd} t| td|   td|  td  }| t| d  | ddtd    d|  d|  td  t|   | tdd	  td|  td   tdtd|  td  d	  }|t|| kshJ | td | d  }t| td|   }|t|| ksJ | d td
 |  }| d d td
t|   }|t|| ks¦J | d|  td  }| d td|  td td d  }|t|| ksĶJ | td|   }| d d t| td  }|t|| ksģJ t| td
|   }| t| td
|    |  dttd
d t| ttdd   }|t|| ks"J | d
 | t  }| d
 d
 t| d  d  | d td d  | d td d  | td  td
t| t   }|t|| ksfJ d|  | td
  }d|  dt| td
  td
  }|t|| ksJ | d d|  td  }| d d | td d  td|  td tdd  d  }|t|| ksĀJ | d  | t  }| d  d t|   tdt| t   }|t|| ksźJ d|  d td
 |  }d|  td
 dtd
 t|   }|t|| ksJ | d t	d|   }| d d d|   t| t	d  }|t|| ks8J | td| d   }| d d tdd| d    }|t|| ks\J d|  td	 |  }d|  td	t|   }|t|| ks|J | d | td
 d  |  }| d d | d tddtd
   d|  td  dtd t| td
   td| td
   }|t|| ksĒJ | | td| d    |  }| d d | d d  tdt|   }|t|| ksóJ | | d
|  td   }| d d | d
  td
|  td td d  }|t|| ks#J | td d| d  d|    }tdt|  d tddtdd  t| d   }|t|| ksXJ t| dtd  }| t| dtd   |  dt| dtd   td  }|t|| ksJ |  dtdtd|   d  t
d |   }| d  td d dt|  t
d  d| d  td
 t
d td d|  td t
d tdd   dtd t
d tdd   d| d    td }|t|| ksžJ d| d  td d	|   }d| d  d d	td t|   td }|t|| ks,J d S )Nrf   Trī  rw   rr   rd   rj   rv   r„   r   éū’’’r¤   r   r]   r  r¤  iL’’’éZ   r  rļ   )rA   r'   r   r#   r   r   r5   r	   r   r   r;   )rf   r\   rŃ  ZF_truera   ra   rb   Śtest_issue_21024Š  s   (B"’’(Dd$@*$$ f(4 6<.n’
’’,rõ  c                  C   sD   t d} ttd|  ddt|    | ddt ftd ks J d S )NŚthetarr   r   rw   r   rd   rĖ   )rC   r#   r   r0   )rö  ra   ra   rb   Śtest_issue_21831)  s   <r÷  N)r]   (  rÉ   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   Zsympy.core.exprrM   Z$sympy.functions.elementary.complexesrN   Z#sympy.functions.elementary.integersrO   Zsympy.integrals.integralsrP   Zsympy.integrals.rischrQ   Zsympy.physicsrR   Zsympy.testing.pytestrS   rT   rU   rV   rW   Zsympy.testing.randtestrX   rf   rx   r   r   rÕ  rÖ  rį   r}   r¦   rY   r\   rc   ri   r~   r   r   r   r   r   r   r£   rØ   rŖ   r«   r¬   r®   r²   r“   r·   rø   r¹   r¾   ræ   rĄ   rĆ   rÅ   rŹ   rĶ   rĪ   rĻ   rÓ   rÕ   rŲ   rŚ   rÜ   rŽ   rą   rā   rć   rä   ré   rģ   rķ   rī   rł   rś   r  r  r  r  r  r  r  r  r  r  r   r!  r$  r%  r&  r'  r*  r+  r9  r?  rC  rE  rG  rI  rK  rM  rO  rR  rS  rT  rW  rY  rZ  r`  ra  rb  rc  re  rg  ri  rj  rl  rm  ro  rp  rr  rs  rt  rv  rx  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¦  rØ  r©  rŖ  r«  r®  rÆ  r°  r²  r³  r“  rµ  r¶  r·  rø  r¹  rŗ  r»  r¼  r½  r¾  ræ  rĄ  rĮ  rĆ  rÄ  rÅ  rĘ  rĒ  rČ  rĖ  rĢ  rĶ  rĪ  rĻ  rŠ  rŅ  r×  rŁ  rÜ  rŽ  rß  rą  rį  rć  rä  rå  rę  rč  rė  rģ  rķ  rń  rņ  rõ  r÷  ra   ra   ra   rb   Ś<module>   s  ž 6 
	

.
			

	0
3

		
		
!


	
"	

		Y