o
    GZŽh(= ã                   @   s  d dl Z d dlmZmZ d dlmZ d dlmZ d dlm	Z	 d dl
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d„ Z dd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zedd„ ƒZdd„ Zdd„ Z	dd„ Z
d d!„ Zd"d#„ Zd$d%„ Zd&d'„ Zd(d)„ Zed*d+„ ƒZed,d-„ ƒZd.d/„ Zd0d1„ Zd2d3„ Zed4d5„ ƒZd6d7„ Zd8d9„ Zd:d;„ Zd<d=„ Zd>d?„ Zd@dA„ ZdBdC„ ZdDdE„ ZdFdG„ ZdHdI„ ZdJdK„ Z dLdM„ Z!dNdO„ Z"dPdQ„ Z#dRdS„ Z$dTdU„ Z%dVdW„ Z&edXdY„ ƒ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„ Z0dldm„ Z1dndo„ Z2dpdq„ Z3drds„ Z4dtdu„ Z5dvdw„ Z6dxdy„ Z7dzd{„ Z8ed|d}„ ƒZ9d~d„ Z:d€d„ Z;d‚dƒ„ Z<d„d…„ Z=d†d‡„ Z>dˆd‰„ Z?dŠd‹„ Z@dŒd„ ZAdŽd„ ZBdd‘„ ZCd’d“„ ZDd”d•„ ZEd–d—„ ZFd˜d™„ ZGedšd›„ ƒZHedœd„ ƒZIdždŸ„ ZJd d¡„ ZKd¢d£„ ZLd¤d¥„ ZMd¦d§„ ZNd¨d©„ ZOdªd«„ ZPd¬d­„ ZQd®d¯„ ZRd°d±„ ZSd²d³„ ZTd´dµ„ ZUd¶d·„ ZVd¸d¹„ ZWdºd»„ ZXd¼d½„ ZYd¾d¿„ ZZdÀdÁ„ Z[edÂdÃ„ ƒZ\dÄdÅ„ Z]dÆdÇ„ Z^dÈdÉ„ Z_dÊdË„ Z`dÌdÍ„ ZadÎdÏ„ ZbdS (Ñ  é    N)ÚSumÚ	summation)ÚAdd)ÚTuple)ÚExpr)Ú
DerivativeÚFunctionÚLambdaÚdiff)Ú
EulerGamma)ÚEÚIÚRationalÚnanÚooÚpiÚzooÚ	all_close)ÚEqÚNe)ÚS)ÚSymbolÚsymbols)Úsympify)ÚAbsÚimÚ
polar_liftÚreÚsign)ÚLambertWÚexpÚ	exp_polarÚlog)ÚacoshÚasinhÚcoshÚcothÚcschÚsinhÚtanhÚsech)ÚMaxÚMinÚsqrt)Ú	Piecewise)ÚacosÚasinÚatanÚcosÚsinÚsincÚtanÚsec)Ú
DiracDeltaÚ	Heaviside)ÚCiÚEiÚSiÚerfÚerfcÚerfiÚfresnelcÚli)ÚgammaÚ	polygamma)ÚhyperÚmeijerg)ÚSingularityFunction)Úlerchphi©Ú	integrate)ÚAnd)ÚMatrix)ÚPolyÚfactor)Ússtr)ÚO)ÚInterval)Ú	gammasimp)Úsimplify)Útrigsimp)ÚIdxÚIndexedBase)Ú	unchanged)Úfloor)ÚIntegral)ÚNonElementaryIntegral)Úunits)ÚraisesÚslowÚwarns_deprecated_sympyÚwarns)ÚSymPyDeprecationWarning)Úverify_numericallyzx y z a b c d e s t x_1 x_2ÚnT©ÚintegerÚfé   c                 K   s   t t| ƒj|fi |¤ŽddS )NT)Z	full_prec)rM   r   Úevalf)Úer`   Úoptions© rh   úS/var/www/auris/lib/python3.10/site-packages/sympy/integrals/tests/test_integrals.pyÚNS3   s   rj   c                  C   s¢   t dt tƒ} |  t¡t td tddksJ ‚ttdd t| tƒ W d   ƒ n1 s-w   Y  ttdd t| tfƒ W d   ƒ d S 1 sJw   Y  d S )Né   ZQQ)ÚdomainF©Ztest_stacklevel)rK   ÚxrH   r]   r^   rW   ©Úprh   rh   ri   Útest_poly_deprecated7   s    ÿ"ÿrq   c                     s,  dt  ‰ tˆ t t tfƒ ¡ dksJ ‚tˆ tt tfƒ ¡ ttdt  ƒ ks(J ‚tt‡ fdd„ƒ tt‡ fdd„ƒ dt d d  ‰tˆt t tfƒ ¡  ¡ t	dƒ t
 d ksZJ ‚tt‡fdd„ƒ dt d d  } t| t t tfƒ ¡ dkszJ ‚t| t d	dfƒ ¡ tdƒ ks‹J ‚t t d d  }t|t t tfƒ ¡ dks¢J ‚t|t d	dfƒ ¡ dks°J ‚t d t d d  }t|t t tfƒ ¡ tu sÉJ ‚t|t d	dfƒ ¡ tdƒ d
 ksÜJ ‚dt d d dt d    }t|t t tfƒ ¡ t
 d ksüJ ‚t|t d	dfƒ ¡ tdƒ tdƒd  ksJ ‚d S )Né   r   c                      s   t ˆ tƒ ¡ S ©N)rW   rn   Úprincipal_valuerh   ©Úgrh   ri   Ú<lambda>F   ó    z&test_principal_value.<locals>.<lambda>c                      s   t ˆ ƒ ¡ S rs   )rW   rt   rh   ru   rh   ri   rw   G   ó    é   c                      s   t ˆ tt dfƒ ¡ S ©Nrr   )rW   rn   r   rt   rh   )Úlrh   ri   rw   K   ó    rk   éþÿÿÿé   )rn   rW   r   rt   Úyr   rZ   Ú
ValueErrorÚtogetherr-   r   r"   r1   )ÚdÚvÚsrc   rh   )rv   r|   ri   Útest_principal_valueA   s(   *0"&$4r†   c                 C   s<   | j }|D ]}|  |¡ ¡ |  ¡  |¡  ¡ dksJ ‚q|S )zºReturn 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   )Úfree_symbolsr
   ÚdoitÚexpand)ÚiZsymsr…   rh   rh   ri   Ú	diff_test^   s   *r‹   c                   C   sd   t ttƒtddfƒdksJ ‚t td tdtfƒdksJ ‚t ddttƒ  tdtfƒtdƒks0J ‚d S )Nr   rr   éÿÿÿÿr~   rk   )rH   r"   rn   r   r    rh   rh   rh   ri   Útest_improper_integralh   s   ,r   c                  C   s  t ttƒ} | jttƒfksJ ‚t ttfƒ}|jttƒfksJ ‚t tttdtfƒƒ}|jttƒfks3J ‚t tttƒƒ}|jttƒfksDJ ‚t tttddƒfƒ}|jttddƒfksZJ ‚t ttdkƒ}|jttdtƒfksmJ ‚t ttdktdk @ ƒ}|jttddƒfks„J ‚d S )Nrr   rk   é
   é   )	rW   r`   Úlimitsr   r   rn   r€   rO   r   )Ús1Ús2Zs3Zs4Zs5Zs6Zs7rh   rh   ri   Útest_constructorn   s   
r“   c                  C   sÐ  t dtƒdks	J ‚t ttddfƒdksJ ‚t ttƒtksJ ‚t tjtƒtju s)J ‚tt ttƒtƒdks5J ‚tt ttddfƒtƒdksDJ ‚tt ttƒtƒtksPJ ‚tt ttdtfƒtƒtks_J ‚td d } tt| tdtfƒtƒtt | tdtfƒtƒ 	¡  
¡   krŒdt d  
¡ ksJ ‚ J ‚tt| tdtfƒtƒtt | tdtfƒtƒ  kr¬dks¯J ‚ J ‚tt| tdtfƒtƒtt | tdtfƒtƒ  krÌdksÏJ ‚ J ‚tt| tƒtƒtt | tƒtƒ  krædkséJ ‚ J ‚t| tttfƒ t¡t | tttfƒ t¡ 	¡  
¡ ksJ ‚t | tttfƒ t¡ 	¡ dt d ksJ ‚t| tttfƒ t¡ 	¡ dt d   
¡ ks5J ‚ttd ttdt fƒ t¡dtd  ksMJ ‚t ttƒ ¡ thksZJ ‚t ttƒtddfƒ ¡ tjtjthkspJ ‚tt ttdt fƒƒthksJ ‚tt ttdt fƒƒtthks“J ‚tttttfƒdks J ‚tttt t fƒdks¯J ‚ttt ttƒ tƒtt td d  ttƒ ksËJ ‚t tƒjsÓJ ‚tddd}t |t tƒjdu sæJ ‚d S )	Nr   rr   rk   é   rz   r`   F©Zcommutative)rW   rn   r   r   ÚNaNr
   r€   ÚtrH   rˆ   r‰   ÚaZatomsrc   ÚZeroÚOner‹   r    Úis_commutativer   ©rf   r`   rh   rh   ri   Útest_basics„   sR   ÿþÿÿÿÿ4
ÿ,20,"$8r   c                  C   sz   G dd„ dt ƒ} | ƒ }t|d |ƒ|d d | ksJ ‚t|d |ddfƒtddƒks-J ‚ttdd„ ƒ ttd	d„ ƒ d S )
Nc                   @   s   e Zd ZdZdZdS )ztest_diff_wrt.<locals>.TestTN)Ú__name__Ú
__module__Ú__qualname__Z	_diff_wrtr›   rh   rh   rh   ri   ÚTest³   s    r¡   rr   rk   r   rz   c                   S   s   t td td ƒS r{   ©rH   rn   rh   rh   rh   ri   rw   »   s    ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfƒS )Nrr   r   r¢   rh   rh   rh   ri   rw   ¼   ó    )r   rH   r   rZ   r   )r¡   r—   rh   rh   ri   Útest_diff_wrt²   s   ""r¤   c                   C   s  t tttdt dt fttdt fƒƒthksJ ‚t tttdt fttdt fƒƒthks/J ‚t tttdt fttdt fƒƒtthksFJ ‚t ttttƒƒtthksTJ ‚t ttt ttƒƒtthksdJ ‚t ttt ttdtfƒƒthksvJ ‚t ttt tttftttfƒƒtthksŒJ ‚d S )Nrz   r   rk   rr   )r‹   rW   rn   r€   rh   rh   rh   ri   Útest_basics_multiple¿   s   2,. $0r¥   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks$J ‚| ¡  ¡ | ¡  ¡ ks2J ‚| ¡  ¡ | ¡  ¡ ks@J ‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks\J ‚| ¡  ¡ | ¡  ¡ ksjJ ‚| ¡  ¡ | ¡  ¡ ksxJ ‚d S )NzA BFr•   rn   T)Úcomplex©Úreal)r   r   rW   Zadjointrˆ   Ú	conjugateZ	transpose)ÚAÚBrn   rp   rh   rh   ri   Útest_conjugate_transposeÉ   s    r¬   c                  C   s:  t dtdtfƒdksJ ‚t dtdtfƒdt ksJ ‚t ttdtfƒtd d ks*J ‚t dt tdtfƒdtd  d ks>J ‚t dtd  tdtfƒtd ksPJ ‚t dt tdtfƒttƒks`J ‚t dtd  tdtfƒdt d kstJ ‚t td dt  d tdtfƒtd d dtd  d  dt  ks˜J ‚t td tƒtd d ks§J ‚t dt t d tƒdt d td  d ksÀJ ‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÜJ ‚t ttd  tdtfƒttd  d ksòJ ‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ksJ ‚d S )Nr   rz   rk   rr   rŒ   r   é   é   ÚbÚcr   )rH   r—   rn   r"   r   r˜   )r¯   r°   rh   rh   ri   Útest_integrationÙ   s    ($ (H2(,Vr±   c                   C   s
  t td td  tddftddfƒtdƒksJ ‚t td td  ttƒtddƒtd  td  ks3J ‚t dtd  dt d  tƒtdt ƒtddƒ tdt ƒtddƒ  tddt  dtd     kshJ ‚t ttt ƒt tddftddfƒtdƒ d ksƒJ ‚d S )	Nrk   r   rr   rŒ   é	   rz   r­   r   )rH   rn   r€   r   r"   r3   rh   rh   rh   ri   Útest_multiple_integrationì   s   06Fÿ:r³   c                   C   s"   t tt ƒtdtfƒdksJ ‚d S ©Nr   rr   )rH   r    rn   r   rh   rh   rh   ri   Útest_issue_3532ô   s   "rµ   c                   C   sz   t ttƒd tƒdttƒd  d ksJ ‚t ttƒtƒdttƒd  d ks(J ‚t dttƒd  tƒdttƒ ks;J ‚d S )Nrz   rk   r   rr   r~   )rH   r-   rn   rh   rh   rh   ri   Útest_issue_3560ø   s   *&*r¶   c                   C   s   t tdd„ ƒ d S )Nc                   S   s   t ttfƒS rs   r¢   rh   rh   rh   ri   rw   ÿ   ry   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorrh   rh   rh   ri   Útest_issue_18038þ   s   r¸   c                  C   sp  t ttd t  td  ttƒ} tƒ  t| tƒ}W d   ƒ n1 s#w   Y  ttdd t| tƒ}W d   ƒ n1 s>w   Y  ttdd t| tƒ}W d   ƒ n1 sYw   Y  t|t ƒdu sgJ ‚t|t ƒdu spJ ‚|j	ttfksyJ ‚|j	ttfks‚J ‚| 
¡ td d td t d  ttd   ksœJ ‚| 
¡ tt td td  d  td d  ks¶J ‚d S )Nrk   rz   Frm   Tr   )rK   rn   r€   r\   rW   r]   r^   rH   Ú
isinstanceÚgensÚas_expr)rp   ZqxZqyrh   rh   ri   Útest_integrate_poly  s     ÿÿÿ48r¼   c                  C   sl  t ttd t  td  ttƒ} tƒ  t| tddfƒ}W d   ƒ n1 s&w   Y  ttdd t| tddfƒ}W d   ƒ n1 sDw   Y  ttdd t| tdtfƒ}W d   ƒ n1 sbw   Y  t	|t ƒdu spJ ‚t	|t ƒdu syJ ‚|j
tfksJ ‚|j
tfks‰J ‚| ¡ tjtd  td  ksšJ ‚| ¡ td d tt  td td  d  ks´J ‚d S )	Nrk   rz   r   rr   Frm   Tr   )rK   rn   r€   r\   rW   r]   r^   rH   r   r¹   rº   r»   r   ÚHalf)rp   ZQxZQyrh   rh   ri   Útest_integrate_poly_definite  s     ÿÿÿ"8r¾   c                      sD   t dƒ‰ ttƒtd d ksJ ‚ttdd„ ƒ tt‡ fdd„ƒ d S )Nr€   rk   c                   S   s   t dƒS ©Nrk   rG   rh   rh   rh   ri   rw   0  s    z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS rs   r¢   rh   ©r€   rh   ri   rw   1  ry   )r   rH   rn   rZ   r   rh   rh   rÀ   ri   Útest_integrate_omit_var+  s   rÁ   c                  C   sd   t dƒ} ttt| ƒ tƒtd t| ƒ d ksJ ‚ttd t| ƒ tƒtd t| ƒ d ks0J ‚d S )Nr€   rk   iè  ié  )r   rH   rn   r3   rÀ   rh   rh   ri   Útest_integrate_poly_accurately4  s   *2rÂ   c                  C   sN   t dƒ} ttd | ƒtd |  ksJ ‚ttd | ddfƒdtd  ks%J ‚d S )Nr€   rk   rŒ   rr   )r   rH   rn   rÀ   rh   rh   ri   Útest_issue_3635=  s   (rÃ   c                  C   sž   t ddd} tt|  tddt| d  | d  ksJ ‚tt| ƒt d|   dt| ƒ  tddt|  ƒt| ƒt d|   dt| ƒ   dt| ƒ  ksMJ ‚d S )Nr€   T©ÚpositiveÚnone©Zcondsrr   rk   )r   rH   rn   r    r3   rÀ   rh   rh   ri   Útest_integrate_linearterm_powE  s
   *(4ÿrÈ   c                   C   sˆ   t tttƒ tƒdt ttƒd  d ksJ ‚t tttƒ tttƒd   tƒdt ttƒd  d dt ttƒd  d  ksBJ ‚d S )Nrk   rz   r   )rH   r   r-   rn   r   rh   rh   rh   ri   Útest_issue_3618N  s   . .ÿrÉ   c                   C   s"  t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒks%J ‚t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒksJJ ‚t ttd t ƒttd t ƒ tƒttttd  ƒtd  ttd dƒftdfƒttttd  ƒtd  ttd dƒftdfƒ ksJ ‚d S )Nrr   r   T)rH   r2   r`   rn   r.   r3   r   rh   rh   rh   ri   Útest_issue_3623T  s   *
ÿ*
ÿ$..ÿÿrÊ   c                  C   s    t dddd} tdt t| t t d ƒ tddgƒdtt|  ƒ t|   ks)J ‚ttt| t t d ƒ td	dƒ tddgƒdtt|  ƒ t|   ksNJ ‚d S )
Nr`   T)rb   Únonzerog      à¿rk   r~   r   ç       @rŒ   )r   rH   rn   r3   r   r2   r   ©r`   rh   rh   ri   Útest_issue_3664^  s   &ÿ,ÿrÎ   c                   C   s4   t tdtd dt  d  tddfƒƒdksJ ‚d S )Nrr   rk   r­   é   r   z1.10714871779409)rj   rW   rn   rh   rh   rh   ri   Útest_issue_3679f  s   4rÐ   c                  C   sb   ddl m}  ddlm} | tttd ƒtƒƒtdƒttƒ |tdƒt ttƒ ƒ d ks/J ‚d S )Nr   ©Úexpand_func)Úfresnelsrk   )	Úsympy.core.functionrÒ   Ú'sympy.functions.special.error_functionsrÓ   rH   r3   rn   r-   r   )rÒ   rÓ   rh   rh   ri   Útest_issue_3686k  s
   *ÿrÖ   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ksJ ‚d S )Nrr   r   é   )rY   Úmr…   rH   rn   )rØ   r…   rh   rh   ri   Útest_integrate_unitsr  s   4rÙ   c                   C   s@   t tdt ƒtƒt ttdt ƒ  ttdt ƒ  ksJ ‚d S r¿   )rH   r   rn   rh   rh   rh   ri   Útest_transcendental_functionsx  s   $ÿrÚ   c                   C   sd   t tdt ƒt tddfƒtd  d ksJ ‚t ttƒdt d  tddfƒtd  d ks0J ‚d S )Nrr   r   rk   r®   rŒ   )rH   r"   rn   r   rh   rh   rh   ri   Útest_log_polylog}  s   .6rÛ   c                  C   s\   dt tƒ dt tƒd   } tt| tƒtƒ}t|  td¡ ¡ | td¡ ¡  ƒdk s,J ‚d S )Nr   rk   é*   g»½×Ùß|Û=)r"   rn   r
   rH   ÚabsÚsubsre   )rc   Zfidrh   rh   ri   Útest_issue_3740‚  s   0rß   c                   C   s&   t ddtd   tƒttƒksJ ‚d S ©Nrr   rk   )rH   rn   r1   rh   rh   rh   ri   Útest_issue_3788ˆ  ó   &rá   c                      s6   t tƒ‰ tˆ tƒttƒ ksJ ‚tt‡ fdd„ƒ d S )Nc                      s   t ˆ dt ƒS r¿   r¢   rh   ©rc   rh   ri   rw     rx   z!test_issue_3952.<locals>.<lambda>)r3   rn   rH   r2   rZ   r   rh   rh   rã   ri   Útest_issue_3952Œ  s   rä   c                   C   s6   t dt dt  tƒdt tdƒ td  ksJ ‚d S r¿   ©rH   rn   r"   rh   rh   rh   ri   Útest_issue_4516’  ó   6ræ   c                  C   sF   t tdt  t ƒtdtfƒ} t| ƒtjkrt| ƒt	ddƒks!J ‚d S )Nrr   r   rŒ   rk   )
rH   r    r   rn   r   r   r   r½   r   r   )Úansrh   rh   ri   Útest_issue_7450–  s   (ré   c                	   C   sÀ   t dtdt ƒ ddtdt ƒ   tdtfƒt d tdƒt d  ks'J ‚t dtdt ƒ ddtdt ƒ   ƒt d tdƒttdƒttƒ ƒttttd  t ƒ   d  ks^J ‚d S )Nrr   rk   rz   r   r   ©rH   r2   rn   r   r-   r1   r5   rV   rh   rh   rh   ri   Útest_issue_8623›  s   NFÿÿrë   c                   C   sŒ   t ddttƒ  tdtfƒttdƒ ksJ ‚t ddttƒ  ƒdtdƒ ttdƒttd ƒ ƒtttd td  t ƒ   d ksDJ ‚d S ©Nrr   rk   r   rz   rê   rh   rh   rh   ri   Útest_issue_9569¡  s   ,`rí   c                  C   sÀ   t ddd} ttt d  d|  |   ƒtdt |  |  ƒ }t|tttfƒ}t|tdtfƒtdƒ|  ttd  d| d   ƒ dttƒ  tt	tdƒt d|   ƒ d  td  ks^J ‚d S )Nr…   TrÄ   rk   r   )
r   r    Úzr€   r-   r   rH   rn   r   r<   )r…   ZpzZpzgxrh   rh   ri   Útest_issue_13733¦  s   2>ÿÿrï   c                   C   s   t ddttƒ  tdtfƒttdƒ ksJ ‚t ddttƒ  ƒdtdƒ ttdƒttd ƒ d ƒtttd td  t ƒ   d ksFJ ‚d S rì   rê   rh   rh   rh   ri   Útest_issue_13749®  s   ,drð   c                   C   s<   t ttƒdt d  tƒtttƒtd d  tƒksJ ‚d S rà   )rH   r    rn   rX   rh   rh   rh   ri   Útest_issue_18133³  ó   <rñ   c                  C   s¶   d} d}t |t t|  t t t t ƒ t|  t t t t ƒ tt  ttdƒftt|  t t t t ƒ dfƒ}t	dt t tt tt   d  }t
t|tƒ|ƒsYJ ‚d S )Ng    €„NAgíµ ÷Æ>r   Tr~   gŽíµ ÷Æ >)r.   r   r    r   r—   r€   rn   rî   r   r   r   rH   )r˜   r¯   ÚrZfunrh   rh   ri   Útest_issue_21741·  s   N ÿ$rô   c                  C   sZ   t dddd„ ƒ} t| tƒt ttƒ tdt ƒ gtdt ƒ tdt ƒ ggƒks+J ‚d S )Nrk   c                 S   s    | | d t | | d t ƒ S r{   )r3   rn   )rŠ   Újrh   rh   ri   rw   Á  s     ztest_matrices.<locals>.<lambda>rz   )rJ   rH   rn   r2   )ÚMrh   rh   ri   Útest_matricesÀ  s
   
þr÷   c                   C   s¬   t ttƒtƒtttƒtƒksJ ‚t ttƒtddfƒtttƒtddfƒks&J ‚t ttƒtttƒtƒ tƒttƒd d ks>J ‚t tttƒtƒttƒ tƒtttƒƒksTJ ‚d S ©Nr   rr   rk   )rH   rc   rn   rW   r
   r"   rh   rh   rh   ri   Útest_integrate_functionsÉ  s    ,00rù   c                   C   s‚   t tttƒtƒtƒttƒksJ ‚t tttƒtƒtƒttttƒtƒ ks%J ‚t tttƒtƒd tƒttttƒtƒd tƒks?J ‚d S r¿   )rH   r   rc   rn   r€   rW   rh   rh   rh   ri   Útest_integrate_derivativesÑ  s
    *ÿrú   c                     sÞ  t td d tddfƒ} t}dt d }|  ¡ |  ||¡ ¡ ks"J ‚|  ||¡ ||¡| ks0J ‚dt d }t}|  ||¡ ||¡| ksFJ ‚t tdt ƒtddfƒ} |  tdt ¡t ttƒtd  tdtfƒksjJ ‚|  tdt ¡ tdt ¡| ks|J ‚t ttd  ƒtt tfƒ} |  tdt ¡t dtdtd  ƒ tt tfƒks¥J ‚t ttƒ t| t ¡ ¡ t t| d  tƒ ¡ ks¿J ‚tdƒ}t ttd| fƒ tdt ¡ ¡ t dtd  tt d| fƒ ¡ ksçJ ‚t ttd|fƒ tdt ¡t td td| tfƒksJ ‚t tt tddftddfƒ‰ ˆ  ttdt  tf¡ ¡ ˆ  ttdt	  tf¡ ¡   kr7dks:J ‚ J ‚t tt| t
fƒ‰ ˆ  tdt ¡t dt t| d t
d fƒks[J ‚tt‡ fd	d
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ t td tddfƒ‰ tt‡ fdd
„ƒ tddd}tddd}t tt||fƒ‰ ˆ  tdt ¡ ˆ  tdt ¡t dt t|d |d fƒksÐJ ‚t tt| fƒ‰ ˆ  tdt ¡t dt t| d fƒksíJ ‚d S )Nrk   rr   rŒ   rz   r   éüÿÿÿéýÿÿÿr   c                      s   ˆ   td¡S r{   )Ú	transformrn   rh   ©rŠ   rh   ri   rw   õ  ry   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S rs   ©rý   rn   r…   r—   rh   rþ   rh   ri   rw   ö  ó    c                      s   ˆ   tt ¡S rs   ©rý   rn   r…   rh   rþ   rh   ri   rw   ÷  rx   c                      s   ˆ   tttf¡S rs   rÿ   rh   rþ   rh   ri   rw   ø  r   c                      s   ˆ   dt dt ¡S r¿   r  rh   rþ   rh   ri   rw   ù  ó    c                      s   ˆ   td t¡S r¿   r  rh   rþ   rh   ri   rw   ü  r   r˜   T)Únegativer¯   rÄ   )rW   rn   r€   rˆ   rý   r3   r   r    r   rî   r¯   r…   rZ   r   r   )r˜   ZfxÚfyZ_3ÚamÚbprh   rþ   ri   Útest_transformØ  sZ   0$6ÿ  ÿ
ÿ
ÿÿ220r  c                  C   s^   t jttƒ ttdtd  ƒ d  } ttttƒƒtƒ| ks J ‚ttttƒƒtƒ| ks-J ‚d S rà   )	r   r½   r0   rn   r-   rH   r2   r3   r/   rã   rh   rh   ri   Útest_issue_4052  s   &r  c                  C   sˆ  t tttddfƒdƒdksJ ‚tttd  ƒtt tfƒ} t | dƒdks&J ‚t | d t ttddƒ  dƒdv s:J ‚td	ƒ}d
t	dƒ dd|d    }dt	dƒ d| d  t	d|d  | d ƒd  }d|d  d d|d  d|  d d  }t	dƒd|d  d|  d  d|d  d|  d d  }|||  | }t t||ddfƒdƒt dt	dƒ dt  dt
t	dƒƒ  d dƒksÆJ ‚t tttdt ƒƒdt td   tddfƒdƒt ddƒksæJ ‚t tt
t	td d ƒƒt	td d ƒtd d   tddfƒdƒt dtd  d dƒksJ ‚t ttttt ƒtt t ƒ td d   tdtfƒdƒt ddƒks;J ‚t tttttƒttƒ ƒƒttd td fƒdddt ddƒks^J ‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks~J ‚t dttdttd ƒ ƒtt tfƒ dddt ddƒksžJ ‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks¾J ‚t tdtd tddfƒ  dd!dd"d#v sÕJ ‚tttƒtd  tdtfƒjdd$}d%|  k rôd&k s÷J ‚ J ‚t tttƒtd  tdtfƒd'd(d)ksJ ‚t tttt d ƒt tt d*fƒd'd(d+ks(J ‚t tttƒƒd,ks4J ‚t ttttfƒƒd-ksBJ ‚d S ).Nrk   r   rd   z10.5000000000000z1.77245385090552rr   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r—   r­   rz   é   r   é   éù   é6   éA   r   é2   é1   é¢   r×   z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))é`   zlog(2)/2-1/4T©Úchopzpi/4*log(4*pi**3/gamma(1/4)**4)rÏ   é   é   zsqrt(1-x**2)é   )Úmaxnr  )z0.0Ú0)r  g\Âõ(\ß?gR¸…ëQà?Úosc)Úquadz0.504067061906928rŒ   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rj   rW   rn   r    r   r   r   r   r   r-   r1   r"   r3   r2   re   r€   )Úgaussr—   r˜   r¯   r°   rƒ   rc   rh   rh   ri   Útest_evalf_integrals  s¢   ÿÿÿ4,<,ÿ0ÿ4ÿÿ
ÿÿ
ÿÿÿ
ÿ4
ÿ(ÿ
ÿ(ÿ
ÿ(ÿ
ÿ
ÿÿ
ÿ$ ÿ
ÿÿÿ
ÿ r  c                   C   s†   t tdtd d  tƒ td¡dddv sJ ‚t tdtd d  tddfƒƒdks+J ‚t tdtd d  tddfƒdddksAJ ‚d S )	Nrr   r   r   Tr  )z-0.000976138910649103z0.965906660135753z1.93278945918216rk   z0.0144361088886740)rj   rH   rn   rÞ   rW   rh   rh   rh   ri   Útest_evalf_issue_939C  s   $ÿ(ÿÿr  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdksJ ‚| tddƒdtdƒ d  ks,J ‚t tttt  ƒtddftddfƒtju sCJ ‚d S )	Nrr   rk   rŒ   rd   z2.43790283299492rû   rz   r­   )	rH   r-   rn   r€   rj   r   r3   r   r™   ©Úresrh   rh   ri   Ú(test_double_previously_failing_integralsR  s   $"2r   c            	      C   s   t ttdƒt tddƒ } t ttdƒd t tddƒ }t| tƒ|ks#J ‚dt tddƒ dt tddƒ  }dt tdd	ƒ dt tddƒ  }t|tƒ|ksLJ ‚d
td
  t dt tddƒ  d
t tddƒ  }d
td  t d d
t t tddƒ  dt tddƒ d  }td
 td
  dt t tddƒ  d
t tddƒ  }t|tƒ|ks¥J ‚t|tƒ|ks®J ‚tt|tfƒs·J ‚t|tƒt|tfƒksÄJ ‚t|tƒ ¡ |ksÏJ ‚dt tddƒ d
t tddƒ  }dt tddƒ d d
t tddƒ  }t|tt tfƒ|ksþJ ‚tt tddƒtƒt tddƒksJ ‚tt tddƒtt tfƒd	ks"J ‚tdt tddƒ tt tfƒdks6J ‚tt tddƒt	tƒ tt tfƒt	dƒksNJ ‚d S )Nrz   r   rŒ   r   r   rŽ   iúÿÿÿr~   rr   rk   rû   r”   r­   )
rE   rn   r˜   rH   r€   rU   rW   rˆ   r   rc   )	Zin_1Zout_1Zin_2Zout_2Zin_3Zout_3_1Zout_3_2Zin_4Zout_4rh   rh   ri   Ú"test_integrate_SingularityFunction]  s*     0<4 $$$(4r!  c                  C   sš  t ttƒttƒ tt tfƒtdƒksJ ‚t ttƒd tt tfƒtdƒks(J ‚t t ddt  tt  dt  ttƒ ttd ƒ tddfƒtddfƒdksPJ ‚ttd td   ƒt } t | ttdt  ƒ tt tftt tfƒt | ttdt  ƒ tt tftt tfƒ  krÈt | tdt t ƒ tt tftt tfƒ  krÈt | tdt t ƒ tt tftt tfƒ  krÈdtdt ƒ ksËJ ‚ J ‚d S )Nr   rk   r   rr   rŽ   ée   )	rH   r7   rn   rc   r   r€   r    r   r-   ro   rh   rh   ri   Útest_integrate_DiracDeltaz  s.   *&ÿ
ÿÿÿÿ**ÿ*þ*ýür#  c                	   C   sb  t tt tƒtttd  td  ttdƒfttƒdfƒksJ ‚t tt tƒttt ttƒ tttƒdƒftdfƒks<J ‚t ttt ƒtƒtttt ƒt ttdƒftdfƒksYJ ‚t tttt ƒ tƒttt d ttt ƒ td  ttd dƒftd d dfƒks†J ‚t ttt  tƒtttt d  tt d  ttt dƒfttƒdfƒks­J ‚t ttt  tƒtttt  tttƒ  ttttƒ dƒftdfƒksÒJ ‚t ttt ƒtƒtt	tt ƒt ttdƒftdfƒksïJ ‚t ttt ƒd tƒttt d t	tt ƒttt ƒ d  t ttdƒftdfƒksJ ‚t tttt ƒ tƒttt	tt ƒ t ttt ƒtd   ttdƒftd d dfƒksMJ ‚t t	tt ƒtƒtttt ƒ t ttdƒfdƒksjJ ‚t t	tt ƒd tƒttt d t	tt ƒttt ƒ d  t ttdƒfdƒks–J ‚t tt	tt ƒ tƒtt ttt ƒ t t	tt ƒtd   ttdƒfdƒksÁJ ‚t ttt ƒtdt
fƒtttt
 ƒt dt  tt kttk @ ttdƒ@ ft
dfƒksïJ ‚t ttƒtt ttt ƒ ƒ tƒtttƒ ttt ƒttttt ƒ ƒ ttttt ƒ ƒ  tttd ƒftdfƒks/J ‚d S )Nrr   rŒ   Tr   rk   ©r   T)rH   rn   r€   r.   r   r"   r    r`   r2   r3   rî   r   r—   r-   rh   rh   rh   ri   Ú test_integrate_returns_piecewise‹  sZ   &
ÿ"
ÿ
ÿ:
ÿ2
ÿ.
ÿ
ÿ:ÿ>ÿÿ6ÿ4ÿ8ÿ$<ÿþr%  c                  C   st  t ddd} tt| dƒ| ddfƒdksJ ‚tt| d | d ƒ| ddfƒtdd	ƒks+J ‚ttt| ƒt|  ƒƒd | ƒttd|  ƒd | dkfd
td|  ƒd  dfƒksUJ ‚t ddd}tt|| ƒt| d  ƒ | t tfƒ}t|t| d  ƒ | t |fƒ}t| t| d  ƒ | |tfƒ}|||   krµtt	ƒ| t
|ƒ d tt	ƒ| d  t|d  ƒd  ks¸J ‚ J ‚d S )Nrn   Tr§   rk   r   rz   r   r  r×   rr   r~   r°   )Zextended_real)r   rH   r,   r+   r   r    r.   r   r-   r   r<   )rn   r°   Zint1Zint2Zint3rh   rh   ri   Útest_integrate_max_min¬  s   ,,
ÿ& &ÿÿr&  c                  C   s2  t ttƒtddfƒtddƒksJ ‚t ttƒtddfƒtjks J ‚t ttd ƒtddfƒtddƒks3J ‚t ttd d ƒtddfƒdksEJ ‚t ttd dt  ƒtdd	fƒd
ksYJ ‚t ttƒtddfƒdksgJ ‚t ttƒttƒ tt tfƒdkszJ ‚t ttd ƒtd  tddfƒtddƒks‘J ‚t	ddd\} }t t| ƒ| ƒt
| d  d | dkf| d d dfƒks¶J ‚t td|  d ƒ| ƒt
| d  d|   | dkf| d d|   d dfƒksÝJ ‚t t| |d  ƒ| ddfƒd|d  td|d ƒ d|d   td|d ƒd  d ksJ ‚t tt| ƒ ƒ| ƒt
t| ƒ| dkfdt|  ƒ dfƒks+J ‚t td|  d ƒ| ƒt
|  | dk f| d dfƒksGJ ‚t d|  t| d d ƒ | ƒt
| d | dk f| d  d | dk f| d dfƒksrJ ‚t t| ƒ| |d fƒt
|d |d dkf| d |d dk fdƒks—J ‚d S )Nr~   rr   r   rk   r   rz   r   éñÿÿÿrd   iÓ  rŒ   r
  zt sTr§   r®   é   r$  )rH   r   rn   r   r   r½   r   r3   r   r   r.   rÝ   r,   r    )r—   r…   rh   rh   ri   Útest_integrate_Abs_sign»  s<   "&$(&."
ÿ.
ÿ:
ÿÿÿ,ÿ(ÿr)  c                  C   sÞ   t ttt ƒtƒ} |  td¡t ttd ƒtƒksJ ‚t ttt ƒtddfƒ} |  td¡t ttd ƒtddfƒks:J ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfƒ}| tdi¡t tdtd  ƒtt tfƒksmJ ‚d S ©Nrz   r   rr   rk   r~   )rW   r    rn   r€   rÞ   r	   r   ©rf   rc   Úconvrh   rh   ri   Ú
test_subs1Ö  s   "("4r-  c                  C   s  t ttt ƒttƒ} |  td¡t ttd ƒttƒksJ ‚t ttt ƒtddftddfƒ} |  td¡t ttd ƒtddftddfƒksDJ ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tftddfƒ}| tdi¡t tdtd  ƒtt tftddfƒksJ ‚d S r*  ©rW   r    rn   r€   r—   rÞ   r	   r   r+  rh   rh   ri   Ú
test_subs2à  s   $ 0*<r/  c                  C   sÊ   t ttt ƒtdtfttdfƒ} |  td¡t ttd ƒtddftddfƒks(J ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒkscJ ‚d S ©Nr   rr   rz   rk   r~   r.  r+  rh   rh   ri   Ú
test_subs3ê  s
    0*<r1  c                  C   s¾   t ttƒtdtfttdfƒ} |  td¡t ttƒtddftddfƒks$J ‚ttttd  ƒƒ}t |tƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒks]J ‚d S r0  r.  r+  rh   rh   ri   Ú
test_subs4ò  s
   ,&<r2  c                  C   s¸  t ttd  ƒtt tfƒ} |  td¡| ksJ ‚t ttd  t ƒtƒ} |  td¡t ttd  d ƒtƒks8J ‚t ttd  t ƒttfƒ} |  td¡t tttd  ƒtdfƒks[J ‚|  td¡t ttd  d ƒtƒksoJ ‚t ttd  t ƒtt tftt tfƒ} |  td¡| ksŽJ ‚|  td¡| ks˜J ‚t ttd  ƒttfƒ} |  td¡t ttd  ƒtdfƒks¸J ‚t ttƒtƒ} |  td¡|  td¡ t ttƒtddfƒ  ¡ jsÚJ ‚d S )Nrk   r   rr   r   )rW   r    rn   r   rÞ   r€   rˆ   Úis_zero©rf   rh   rh   ri   Ú
test_subs5ú  s    (*(*(*
ÿr5  c                  C   sŒ  t dƒ\} }ttt tttƒttƒfƒ}| td¡ttt ttdƒttƒfƒks*J ‚| td¡tttttƒtdƒfƒks>J ‚ttt tttƒttƒftttƒttƒfƒ}| td¡ttt ttdƒttƒfttdƒttƒfƒksrJ ‚| td¡ttt tttƒttƒftttƒtdƒfƒksJ ‚ttt tttƒt| ƒftttƒt| ƒfƒ}| | d¡ttt tttƒtdƒftttƒtdƒfƒksÄJ ‚d S )Nza brr   )r   rW   rn   r€   rc   rÞ   )r˜   r¯   rf   rh   rh   ri   Ú
test_subs6  s   ,(,<<,@r6  c                  C   s¶   t ttdtftddfƒ} |  tdtdi¡| ksJ ‚t ttƒttƒ tttƒttƒftddfƒ} |  ttƒd¡| ks;J ‚|  ttƒd¡t ttƒttƒ tdttƒftddfƒksYJ ‚d S rà   )rW   rn   r€   rÞ   r3   r4  rh   rh   ri   Ú
test_subs7  s    ÿ*ÿr7  c                  C   sÈ   t ttƒttd ƒ tdtfƒ} |  ¡ t ttƒtdtfƒt ttd ƒtdtfƒ ks,J ‚t ttƒttd ƒ tdtfƒ} |  ¡ | ksDJ ‚| jddt ttƒtdtfƒt ttd ƒtdtfƒ ksbJ ‚d S )Nrk   rr   T)Úforce)rW   rc   rn   r€   r‰   r   r4  rh   rh   ri   Útest_expand"  s    8 ÿr9  c                   C   s    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t ttd  ƒdƒS ©Nrk   rz   )rW   r    rn   rh   rh   rh   ri   rw   ,  r  z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  ƒdt tfƒS r:  )rW   r    rn   r   rh   rh   rh   ri   rw   -  ó    )rZ   r   rh   rh   rh   ri   Útest_integration_variable+  s   r<  c                   C   sÊ   t ttd ƒttd ƒd  tddfƒ ¡ t ttd ƒttd ƒ tddfƒt ttd ƒtddfƒ ks6J ‚t ttd ƒttd ƒd  tƒ ¡ t ttd ƒttd ƒ tƒt ttd ƒtƒ kscJ ‚d S )Nrk   rr   r   )rW   r2   rn   r3   r‰   rh   rh   rh   ri   Útest_expand_integral0  s   *"ÿÿ$ÿÿr=  c                      sL  t ttd d ƒtddfƒ‰ ˆ jddddtdƒ ksJ ‚ˆ jdddd	td
ƒ dtdƒ  ks2J ‚ˆ jddddtdƒ d dtdƒ d  dtdƒ d  ksSJ ‚ˆ jd	dddtdƒ d	tdƒ  d	tdƒ  dtdƒ  kstJ ‚tˆ jd	dd ¡ ˆ  ¡  ƒdk s‡J ‚t ttd td  ƒtddftddfƒ‰ tt‡ fdd„ƒ d S )Nrz   rr   rk   rŽ   Úmidpoint©Úmethodr­   éÙ   r   r  r×   é9   i	  é   iIÎ  iÚ  r”   éV   r®   é   g      à?r   c                      ó
   ˆ   d¡S )Nr   ©Úas_sumrh   r4  rh   ri   rw   D  ó   
 z'test_as_sum_midpoint1.<locals>.<lambda>)	rW   r-   rn   rH  rÝ   r`   r€   rZ   ÚNotImplementedErrorrh   rh   r4  ri   Útest_as_sum_midpoint19  s$   *ÿ
ÿ
ÿ
ÿ

ÿ&(rK  c                  C   s  t tt d tddfƒ} tdddd}| jddd ¡ tdd	ƒt td  ks)J ‚| jddd ¡ td
dƒt td  ks?J ‚| jddd ¡ tddƒt td  ksUJ ‚| jd	dd ¡ tddƒt td  kskJ ‚| j|dd ¡ td t tddƒ dd|d    ks‰J ‚d S )Nrk   r   rr   r`   T©rÅ   rb   r>  r?  r   r   r	  rz   é#   él   é   é@   r×   )rW   rn   r€   r   rH  r‰   r   rœ   rh   rh   ri   Útest_as_sum_midpoint2G  s   ,,,,$ÿrQ  c                  C   s@  t tt d tddfƒ} | jddd ¡ td ksJ ‚| jddd ¡ tddƒtd  td  ks3J ‚| jddd ¡ tdd	ƒttddƒ  td  ksNJ ‚| jd
dd ¡ tddƒttdd
ƒ  td  ksiJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks‘J ‚| jdddd t¡sžJ ‚d S )Nrk   r   rr   Úleftr?  r­   rz   r   rC  r   r”   é    r®   rŽ   F)r@  Úevaluate)	rW   rn   r€   rH  r‰   r   r`   Úhasr   r4  rh   rh   ri   Útest_as_sum_leftR  s   0668ÿrV  c                  C   s8  t tt d tddfƒ} | jddd ¡ ddt  td  ks!J ‚| jddd ¡ tddƒttddƒ  td  ks<J ‚| jddd ¡ td	d
ƒttddƒ  td  ksWJ ‚| jddd ¡ tddƒttddƒ  td  ksrJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ksšJ ‚d S )Nrk   r   rr   Úrightr?  r   r­   rz   rE  rC  r   rd   rS  r®   )rW   rn   r€   rH  r‰   r   r`   r4  rh   rh   ri   Útest_as_sum_right]  s   *6668ÿrX  c                  C   s*  t tt d tddfƒ} | jddd ¡ td t tj ks J ‚| jddd ¡ td t tddƒ ks6J ‚| jddd ¡ td t tdd	ƒ ksLJ ‚| jd
dd ¡ td t tddƒ ksbJ ‚| jtdd ¡ td t tddƒ ddtd    ks€J ‚t t	tƒtddfƒ dd¡tjks“J ‚d S )Nrk   r   rr   Z	trapezoidr?  rz   r­   é   r  r   r
  rS  r®   )
rW   rn   r€   rH  r‰   r   r½   r   r`   r   r4  rh   rh   ri   Útest_as_sum_trapezoidg  s   (,,,$ÿ*rZ  c                      sr   t tt d tddfƒ‰ tt‡ fdd„ƒ tt‡ fdd„ƒ ttdd„ ƒ tt‡ fdd„ƒ tt‡ fd	d„ƒ d S )
Nrk   r   rr   c                      rF  )NrŒ   rG  rh   r4  rh   ri   rw   t  rI  z$test_as_sum_raises.<locals>.<lambda>c                      rF  ©Nr   rG  rh   r4  rh   ri   rw   u  rI  c                   S   s   t tƒ d¡S )Nrz   )rW   rn   rH  rh   rh   rh   ri   rw   v  rx   c                      s
   ˆ   t¡S rs   )rH  r   rh   r4  rh   ri   rw   w  rI  c                      s   ˆ j dddS )Nrz   Zxxxx2r?  rG  rh   r4  rh   ri   rw   x  rx   )rW   rn   r€   rZ   r   rh   rh   r4  ri   Útest_as_sum_raisesr  s   r\  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ksJ ‚d S rs   )rW   rn   rˆ   ©rf   rc   rh   rh   ri   Útest_nested_doit{  s   r^  c                  C   s  t td td dfƒ} t td tdd fƒ}|  ¡ tddƒksJ ‚| ¡ tddƒks*J ‚t tt td tfƒ tt¡t tt td tfƒksDJ ‚t tt ttd fƒ tt¡t tt ttd fƒks^J ‚ttd td dfƒtddƒksoJ ‚ttd tdd fƒtddƒks€J ‚tddƒtddƒksŒJ ‚d S )Nrk   rr   rz   rŒ   zx**2)rn   Ú1N)rW   rn   rˆ   r   r€   rÞ   r—   rH   r]  rh   rh   ri   Útest_issue_4665  s   44""r`  c                  C   s*   t td tddfƒ} | t | jŽ ksJ ‚d S )Nrk   rŒ   rr   )rW   rn   Úargsr4  rh   rh   ri   Útest_integral_reconstructŽ  s   rb  c                  C   s  t t dt ƒtddfƒ} |  ¡ tddƒksJ ‚| jddtddƒks$J ‚tdƒ}t |tƒtddfƒ ¡ dks8J ‚t dtdt |tƒtƒfƒ ¡ dksKJ ‚t ttdfƒ ¡ dksXJ ‚tdttƒftdff}t tg|¢R Ž  ¡ tddƒkstJ ‚t tgtt|ƒƒ¢R Ž  ¡ dks†J ‚d S )	Nrk   r   rr   rz   F©Údeeprc   r   )	rW   rn   rˆ   r   r   r˜   r    ÚlistÚreversed)rf   rc   r   rh   rh   ri   Útest_doit_integrals“  s    &"(rg  c                   C   sð   t ttƒdt  ƒtdttƒ td d  d dttƒ td  d  dttƒ d  ttd ƒdkfdt tt ƒ td d  d dt tt ƒ td  d  dt tt ƒ d  dfƒksdJ ‚t tt dttƒ  ƒtt ksvJ ‚d S )Nrr   rk   r   rd   r   T)rH   r-   rn   r.   r   r   r"   rh   rh   rh   ri   Útest_issue_4884¢  s   Bÿ>ÿÿýÿ(rh  c                   C   s²   t tt ttƒ tƒttt tt  ttƒ td dt  d  ttt  ttƒ td dt  d   ttt  td dt  d   ttdƒfttƒd d dfƒksWJ ‚d S )Nrk   rr   rŒ   T)rH   rn   r`   r"   r.   r   rh   rh   rh   ri   Útest_issue_18153«  s   *&ÿÿþýÿri  c               	   C   sˆ  ddl m} m}m} t| ƒjdu sJ ‚td| ƒjdu sJ ‚td| dfƒjdu s)J ‚td| ddfƒjdu s6J ‚td| d|fƒjdu sCJ ‚td| |fƒjdu sOJ ‚t| |ƒjdu sYJ ‚t| |d| fƒjdu sfJ ‚t| |ddfƒjdu ssJ ‚t| | ddfƒjdu s€J ‚t| |ddfƒ}|jdu r“| ¡ dks•J ‚t| |||fƒ}|jdu r¨| ¡ dksªJ ‚td|||d fƒ}|jdu r¿| ¡ dksÁJ ‚t| | | ddf|ddfƒjdu sÔJ ‚t| | | ddf|d|fƒjdu sçJ ‚t| | dfƒjdu sóJ ‚t| | dt||ddfƒfƒjdu sJ ‚tt||ddfƒ| ddfƒjdu sJ ‚tt| ƒd t	| ƒd  d | ƒjdu s2J ‚tt
| ƒ| ddfƒjdu sBJ ‚d S )	Nr   ©rn   r€   rî   Frr   Trk   rÌ   rz   )Ú	sympy.abcrn   r€   rî   rW   Z	is_numberr`   r   r3   r2   rc   )rn   r€   rî   rŠ   rh   rh   ri   Útest_is_number´  s0   &&((.$rl  c                  C   s\  ddl m} m}m} td| ƒj| hksJ ‚t| ƒj| hksJ ‚t| | d |fƒj|hks-J ‚t| | |d fƒj|hks;J ‚t| | d|fƒj|hksIJ ‚t| | |dfƒj|hksWJ ‚t| | | |fƒj| |hksfJ ‚t| | |ƒj| |hkssJ ‚t| | ddfƒjtƒ ksJ ‚t| |ddfƒj| hksJ ‚t| |||fƒj| |hksžJ ‚t| |ddf|d d fƒj| |hks±J ‚t| |ddf| d|fƒj|hksÃJ ‚td|ddf|d| f| ddfƒjtƒ ksÙJ ‚td|| df|d| f| ddfƒjtƒ ksïJ ‚td| ddf|| df|ddfƒj| hksJ ‚tt| ƒt| ƒd|fƒj|hksJ ‚tt| ƒt| ƒd| fƒj| hks,J ‚d S )Nr   rj  rr   rk   )rk  rn   r€   rî   rW   r‡   Úsetrc   rj  rh   rh   ri   Útest_free_symbolsÔ  s:   ÿÿÿÿ
ÿ&*rn  c                  C   s.  ddl m} m} td| d| fƒjsJ ‚td| ddfƒjsJ ‚td| ddftdfƒjdu s.J ‚t| |dfƒjs8J ‚t| | |dfƒjd u sFJ ‚t||dt| ƒf| dfƒ}|jd u sZJ ‚t|| df|dt| ƒfƒjdu slJ ‚t| | ttfƒjswJ ‚t| | t t fƒjs„J ‚tt| ƒ| ddt	 fƒjd u s•J ‚d S )Nr   )rn   rØ   rr   rk   FT)
rk  rn   rØ   rW   r3  r€   r    r   r3   r   )rn   rØ   rŠ   rh   rh   ri   Útest_is_zeroð  s    $&ro  c                     s\   ddl m}  tt| ƒ| | fƒ}| | ¡‰ |j| dd ¡ t‡ fdd„tdƒD ƒŽ ks,J ‚d S )Nr   ©rn   r­   rÍ   c                    s   g | ]}t ˆ ƒ‘qS rh   )Únext)Ú.0rõ   r4  rh   ri   Ú
<listcomp>  r  ztest_series.<locals>.<listcomp>r   )	rk  rn   rW   r2   ZlseriesZnseriesZremoveOr   Úrange)rn   rŠ   rh   r4  ri   Útest_series  s   
4ru  c                  C   sV   t dƒ} tdt| ƒ |  | ƒt| ƒt| ƒ ksJ ‚tt| ƒd |  | ƒ t¡s)J ‚d S )Nrn   rr   rk   )r   rH   r3   r"   r;   r2   rU  r9   rp  rh   rh   ri   Ú!test_trig_nonelementary_integrals
  s   *$rv  c               	   C   s2  t dƒ} t dƒ}t ddd}tt| d |d  ƒ| ƒ|d t| | ƒ d | t| d |d  ƒ d  ks7J ‚tt| d |d  ƒ| ƒ| t| d |d  ƒ d |d t| t| d |d  ƒ ƒ d  kshJ ‚t ddd} t ddd}td| d |d  td	ƒ  | ƒ| |d t| d |d  ƒ  ks—J ‚d S )
Nrn   r€   rî   TrÄ   rk   r§   rr   z3/2)r   rH   r-   r$   r"   r   rj  rh   rh   ri   Útest_issue_4403  s   2ÿBÿ ÿrw  c                   C   sT   t ttd  d ƒtƒdtttdtd  ƒ ƒ ttdtd  ƒ d  ks(J ‚d S )Nrk   r   r~   rû   )rH   r-   rn   r1   rh   rh   rh   ri   Útest_issue_4403_2#  s   2ÿrx  c                  C   sD   t ddd} tt| d td  ƒtd| fƒt| d  d ks J ‚d S )NÚRTrÄ   rk   r   r   )r   rH   r-   rn   r   )ry  rh   rh   ri   Útest_issue_4100(  s   8rz  c                  C   sÄ  ddl m} m}m}m} tdƒ}tt||ƒ|ƒ|ƒt||ƒ||ƒks$J ‚t||ƒƒj||ƒt|ƒfks5J ‚tt||ƒƒƒj||ƒt|ƒt|ƒfksKJ ‚tt||ƒƒ|ƒj||ƒt|ƒt|ƒfksbJ ‚tt||ƒ|ƒ|ƒj||ƒt|ƒt|ƒfkszJ ‚ttt||ƒ|ƒ|ƒ|ƒj||ƒt|ƒt|ƒt|ƒfks˜J ‚t	t||ƒ|ƒ|ƒt||ƒ||ƒks¬J ‚t	t||ƒ|ƒ|ƒ|t||ƒ|ƒ ksÁJ ‚t	t||ƒ|ƒ|ƒt|||ƒ |ƒ|t||ƒ|ƒ fv sßJ ‚t	td|ƒ|ƒ|d ksíJ ‚t	td|ƒ|ƒd| | ksýJ ‚td||ƒjtd||ƒjksJ ‚t||ƒ||||ƒ 
¡ |d t||ƒ||ƒ d ks+J ‚t||ƒ|ddf| d|f|d|fƒ 
¡ ||d  t||ƒ|ddfƒ |d t||ƒ|ddfƒ  ks`J ‚d S )Nr   )Úwrn   r€   rî   rc   rk   rr   )rk  r{  rn   r€   rî   r   rW   ra  r   rH   rˆ   )r{  rn   r€   rî   rc   rh   rh   ri   Útest_issue_5167-  s(   (",.0ÿ(*< ":&:ÿr|  c                  C   s  t ddd} ttttƒd  ƒtƒttƒttddƒƒ tttƒt	j
 ƒ d ks*J ‚ttttƒd ƒtƒttƒttddƒƒ tttƒt	j
 ƒ d ksMJ ‚tt|  ttƒd  ƒtƒttƒtdd|   ƒ tt| ƒttƒ ddt| ƒ   ƒ dt| ƒ  ksJ ‚d S )Nrî   TrÄ   rk   rr   r   rŒ   )r   rH   r    r"   rn   r-   r   r   r<   r   r½   r>   ©rî   rh   rh   ri   Útest_issue_4890D  s   *ÿ*ÿFÿr~  c                   C   s,   t dttdtd  ƒ  tƒ t¡rJ ‚d S rà   )rH   rn   r-   rU  rW   rh   rh   rh   ri   Útest_issue_4551N  s   ,r  c               	   C   s   t dddd} tt| td|   d  tdtjfƒ| d dd|   | d   | dd|     ddd|    | ddd|        ƒdksFJ ‚d S )Nr`   T©rb   rÅ   rr   r   rk   )r   rQ   rH   rn   r   r½   rÍ   rh   rh   ri   Útest_issue_4376R  s   "Nÿÿr  c                   C   sX   t ttƒtd  ttddƒ  tƒdttddƒ  d dttddƒ  d  ks*J ‚d S )Nrz   rr   r®   r”   r
  )rH   r-   rn   r   rh   rh   rh   ri   Útest_issue_4517X  s   "*ÿr‚  c               
   C   sú  t ddd\} }tt| t ƒt|t ƒ tdtfƒ ¡ tdt| dƒt|dƒB ft d t| | ƒt| dƒt|dƒ@ B ftd t| |ƒt| dƒt|dƒ@ B fdƒksSJ ‚tt| t ƒt|t ƒ tfƒtdtt| dƒt|dƒƒft t|t ƒd  d tt	|t ƒd  d  t|t ƒt	|t ƒ d|   t| | ƒftt|t ƒd  d tt	|t ƒd  d  t|t ƒt	|t ƒ d|   t| |ƒf|t| t ƒ t	|t ƒ | d |d   | t|t ƒ t	| t ƒ | d |d    dfƒksûJ ‚d S )Nzk mTra   r   rk   r$  )
r   rH   r3   rn   r   rQ   r.   r   rI   r2   )ÚkrØ   rh   rh   ri   Útest_issue_4527]  s$   &($ýÿ \X**ÿÿür„  c                  C   sp   t ddd} ttt d t |  t ƒt tt tfddttt d t |  t ƒt tt tfƒks6J ‚d S )Nr€   TrÄ   rk   rÆ   rÇ   )r   rH   r    r   r   rn   r   rW   )Zyposrh   rh   ri   Útest_issue_4199r  s   .*ÿr…  c                  C   s®  t ddd\} }}}tttd  t| t  ƒtƒttƒ t|d  d ƒ tt| d t ƒ d ks6J ‚tt| td  |t  | ƒtƒ ttƒt||d d|    ƒ t	d|  t | dt| ƒ  ƒ dt| ƒ  ¡spJ ‚ddl
m} ddlm} |tttd  ƒtt| t ƒ tt tfƒƒttƒt|d  d ƒ ks£J ‚t d	dd\} }|tt|  td  d| t  ƒtt tfƒƒttƒt|d |  ƒ t| ƒ ksÕJ ‚d S )
Nza:dTrÄ   rk   r   r   )Ú
expand_mul)rƒ  za d)r   rH   r    rn   r   r-   r   r<   Úequalsr>   rÔ   r†  rk  rƒ  r   )r˜   r¯   r°   rƒ   r†  rƒ  rh   rh   ri   Útest_issue_3940y  s    2ÿ"Jÿ.ÿ.ÿrˆ  c                   C   sV   t t td td   tƒttt t t ƒ d tttt t ƒ d  ks)J ‚d S r¿   )rH   r˜   rn   r   r"   rh   rh   rh   ri   Útest_issue_5413‰  s   Vr‰  c               
   C   s¸  t dƒ\} }tddd}|  t| ƒ }|  |t  ttƒd ttƒd   }ttƒd  ttƒd  }ttƒd  ttƒd  d }t|||  tƒ||  |  t	|t ƒ | | t t| ƒ   ||  |  t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   | | t | |  t	tƒ t|ƒ  t| ƒ | | t | |  t	tƒ t|ƒ  t| ƒ fv sÚJ ‚d S )NzA zr°   T)rË   rk   rr   )
r   r   r    r—   r3   rn   r2   r€   rH   r"   )rª   rî   r°   ZP1ZP2Zh1Zh2rh   rh   ri   Útest_issue_4892a  s   &00,,..úrŠ  c                  C   s\   t tƒtd  dttƒ td   d td d  } ttt| tƒ t¡|  ƒƒdks,J ‚d S )Nrz   rk   r×   r   )r3   r€   rn   r2   rR   rL   rH   r
   )Úexprrh   rh   ri   Útest_issue_4892b¤  s   4	(rŒ  c                   C   sX   t ttƒtttƒ tdtftdtftdtfƒdttttƒtdtftdtfƒ ks*J ‚d S ©Nr   rk   )rH   r3   rn   rc   r€   rî   r   rW   rh   rh   rh   ri   Útest_issue_5178±  s   , ÿrŽ  c                  C   sª   t tƒ tdd¡} td d td d  td d  td d	  td d
  ttd ƒ }t| tƒ|ks6J ‚tt| tƒtƒ| ksBJ ‚tttd ƒtƒttd ƒksSJ ‚d S )Nr   rŽ   rk   r   é   r®   iÐ  r­   i€  i _7 r
  r   )r3   rn   ÚseriesrN   rH   r
   ©rc   rv   rh   rh   ri   Útest_integrate_series¶  s
   H&r’  c                  C   s0   ddl m}  | tg g dgg tƒtƒd u sJ ‚d S )Nr   ©Úheurischrr   )Zsympy.integrals.heurischr”  rD   rn   r“  rh   rh   ri   Útest_atom_bugÀ  s   $r•  c                  C   sh   t ddd} tttt |  ƒtdtftdtfƒ ¡ t| ƒttd |  ƒ t	 dttƒ  |  ks2J ‚d S )Nrî   F©Úzeror   rk   )
r   rH   r3   rn   r€   r   r‚   r"   r9   r   r}  rh   rh   ri   Útest_limit_bugÅ  s   &*ÿr˜  c                  C   s,   t dƒ} tttƒ| tƒ tƒ t¡sJ ‚d S )Nrv   )r   rH   r    rn   rU  rW   ru   rh   rh   ri   Útest_issue_4703Ë  ó   $r™  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡sJ ‚d S )Nrc   rk   )r   rH   rn   r
   rU  rW   rã   rh   rh   ri   Útest_issue_1888Ð  s   &r›  c                   C   sF   t ttt ƒtt d td ftdtfƒdttd d ƒ ks!J ‚d S )Nrk   r   )rH   r2   rn   r€   r   r;   rh   rh   rh   ri   Útest_issue_3558×  s   Frœ  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ksJ ‚d S )Nrr   r	  r   rk   )rH   r-   rn   r$   rh   rh   rh   ri   Útest_issue_4422Û  rç   r  c                   C   sN   t tttddt  ƒ tƒƒtdt d ƒdtd  t d  d ks%J ‚d S )Nrr   rk   r®   rd   )rQ   rH   rn   r-   rh   rh   rh   ri   Útest_issue_4493ß  s   &ÿrž  c                   C   sh   t ttƒt tt tfƒtksJ ‚t ttƒt tdtfƒtd ks#J ‚t ttƒt tƒttƒks2J ‚d S r  )rH   r3   rn   r   r   r;   rh   rh   rh   ri   Útest_issue_4737ä  s   "$"rŸ  c                  C   sh   ddl m}  tddd}t| ttt ƒttƒ t|  tdtfƒƒƒ|t	d|ƒ d t
|ƒ ks2J ‚d S )Nr   rÑ   r˜   TrÄ   rr   )rÔ   rÒ   r   rQ   rH   r    rn   r"   r   rB   rA   )rÒ   r˜   rh   rh   ri   Útest_issue_4992ê  s
   ,ÿr   c                  C   s>   ddl m}  tttt ƒtt  tƒƒ| td tƒksJ ‚d S )Nr   ©Ú
lowergammarr   )Ú'sympy.functions.special.gamma_functionsr¢  rQ   rH   r    rn   r€   r¡  rh   rh   ri   Útest_issue_4487ò  s   2r¤  c                  C   s,   t dƒ} td| d  | ddfƒtu sJ ‚d S )Nrn   rr   rk   rŒ   )r   rH   r   rp  rh   rh   ri   Útest_issue_4215÷  rš  r¥  c                  C   s    t dddd} tt|  ttƒ tƒ| t t|   ttƒ | d d|   d  tt|   ttƒ | d d|   d   tt|   | d d|   d   ksNJ ‚d S )Nr`   Tr€  rk   rr   )r   rH   rn   r"   rÍ   rh   rh   ri   Útest_issue_4400ü  s   Rÿÿr¦  c                   C   sZ   t tdt ƒtdt ƒ d t tddttt d ƒttd ƒ d t tƒks+J ‚d S )Nrr   rk   T©rD   )rH   r-   rn   rW   rh   rh   rh   ri   Útest_issue_6253  s   (&ÿr¨  c                   C   sè   t ddt t t  tddftddftddfƒdtdƒ dtdƒ d  dtdƒ d  dtdƒ  d	td
ƒ  dtdƒ dtd
ƒ  dtdƒ d  dtdƒ dtdƒ d  dtdƒ dtdƒ d  dtdƒ d  fv srJ ‚d S )Nrr   r   iôÿÿÿrz   r®   rk   r­   r   r”   r   rC  r  é/   ©rH   rn   r€   rî   r"   rh   rh   rh   ri   Útest_issue_4153
  s
   .B@*ýr«  c                  C   sf   t dƒ\} }}t|t|  |  | t| d td  ƒ t| | | fƒ}| t¡r*J ‚| t¡r1J ‚d S )NzR b hrk   )r   rH   rn   r-   rU  r   rW   )ry  r¯   Úhrf   rh   rh   ri   Útest_issue_4326  s   8r­  c                   C   s>   t dt dt  tƒdt tdƒ dt tdƒ  ksJ ‚d S r:  rå   rh   rh   rh   ri   Útest_powers  s   >r®  c                   C   s<   t tdd„ ƒ ttdt ƒt tddfdd t¡sJ ‚d S )Nc                   S   ó   t dt tdddS )Nrr   T)ÚmanualrD   r¢   rh   rh   rh   ri   rw      r  z$test_manual_option.<locals>.<lambda>rr   r   T©r°  )rZ   r   rH   r"   rn   rU  rW   rh   rh   rh   ri   Útest_manual_option  s   .r²  c                   C   s6   t tdd„ ƒ tttƒtddtttƒtƒksJ ‚d S )Nc                   S   r¯  )Nrr   T)rD   Úrischr¢   rh   rh   rh   ri   rw   &  r  z%test_meijerg_option.<locals>.<lambda>Tr§  )rZ   r   rH   r5   rn   rW   rh   rh   rh   ri   Útest_meijerg_option%  s   (r´  c                   C   sª   t tdd„ ƒ tttd  ƒtddtttd  ƒtƒksJ ‚ttdt ƒt ttddtd ttdt ƒ d td   ksAJ ‚tttƒtddt	ttƒtƒksSJ ‚d S )Nc                   S   s   t dttƒ tdtfddS )Nrr   r   T©r³  )rH   r"   rn   r   rh   rh   rh   ri   rw   -  r;  z#test_risch_option.<locals>.<lambda>rk   Trµ  rr   )
rZ   r   rH   r    rn   rX   r"   r€   r<   rW   rh   rh   rh   ri   Útest_risch_option+  s   0D(r¶  c                   C   s,  t tdd„ ƒ tttd ƒtddttƒttƒ d ksJ ‚tttƒt tddtttƒt tƒks4J ‚tt	tƒt
t	tƒƒ ttddƒ  tddd	ttd
dƒ  tt	tƒƒ d dttd
dƒ  t
t	tƒƒ d  dttd
dƒ  tt	tƒƒ d dttd
dƒ  t
t	tƒƒ d  t	tƒ  ks”J ‚d S )Nc                   S   r¯  )Nrr   T)r³  r”  r¢   rh   rh   rh   ri   rw   6  r  z&test_heurisch_option.<locals>.<lambda>rk   Tr“  rz   r   Fi€ÿÿÿrr   i!  éð   r	  rÏ   )rZ   r   rH   r    rn   r-   r   r>   rW   r"   r2   r   r3   rh   rh   rh   ri   Útest_heurisch_option4  s   .,*BJÿÿr¸  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |ddsJ ‚d S )Nrr   gHáz®Gñ?rk   g333333@gê-™—q=)Ztol)rn   rH   r
   r_   r‘  rh   rh   ri   Útest_issue_6828A  s   r¹  c                  C   sX   t dƒ} ttt t| t  ttƒ ƒ tƒttt|  ttƒ ƒ ttƒ t ks*J ‚d S )NÚx_max)r   rH   r€   r   r    rn   r2   r˜   )rº  rh   rh   ri   Útest_issue_4803G  s   ""ÿr»  c                   C   s@   t dtdttƒd  ƒ ƒttƒtdttƒd  ƒ ksJ ‚d S rà   )rH   r-   r5   rn   rh   rh   rh   ri   Útest_issue_4234M  s   @r¼  c                	   C   s  t ttd tdtd  ƒ tƒƒjddttdtd  dtd   dt  dttd d ƒ ttdƒt d ƒ   dttd d ƒ  ttdƒkttdƒ k B fdtd  dtd   dt  dtdtd  ƒ ttdƒt d ƒ  d	ttd  d ƒ  dfƒks†J ‚d S )
Nrk   r   Trc  rd   rz   é   r­   iøÿÿÿ)	rQ   rH   rn   r-   rL   r.   r   r#   r0   rh   rh   rh   ri   Útest_issue_4492Q  s    "ÿJÿÿFÿÿýÿr¾  c                  C   s  dt t ttƒ  } t| tddfƒ}t| tddfƒ ¡ |ks J ‚t| ttƒ tddfƒ|tdƒ tdƒ ks8J ‚td|  ttƒ tddfƒd| tdƒ tdƒ ksTJ ‚ttdt t	 t t
 t  t
 ƒtdtfƒttdt t	 t ƒtdt t	 td  t
 ƒ tdtfƒks‹J ‚d S )Nrr   rk   rz   g333333ó?r   g333333ó¿)r˜   rî   r"   rX   rW   rˆ   rH   r    r`   r…   r—   rn   )rc   Z
integral_frh   rh   ri   Útest_issue_2708Z  s   0ÿ,0ÿÿr¿  c                  C   sD   dt  dt  d tdt  ƒ } t| t ddfƒ}t|ƒdks J ‚d S )NgºõJ‡  @gìD” @g      $@gš™™™™™¹?gš™™™™™É?z%1.86831064982608*y + 2.16387491480008)rn   r€   r    rH   Ústr)rc   rf   rh   rh   ri   Útest_issue_2884h  s    rÁ  c                  C   s”  ddl m} m} ttt t ƒttƒ tdtfƒt	t
t	t t
td  d   |td ƒdk fdt
t ddtd     |td ƒdk fttjfdfdtjfdfttƒd ƒdfƒ td dkfttt t ƒttƒ tdtfƒdfƒksvJ ‚ttt t ƒttƒ tdtfƒt	d	td  d dt d  d  t|tƒdk|| tƒƒt
d k || tƒƒt
d kƒfttt t ƒttƒ tdtfƒdfƒksÈJ ‚d S )
Nr   ©Úargr   rk   rr   r~   )r   r   )r   TrŒ   )Ú$sympy.functions.elementary.complexesrÃ  r   rH   r    r…   rn   r%   r   r.   r   rD   r   r½   r   rW   r(   rI   rÂ  rh   rh   ri   Útest_issue_8368in  sN    ÿÿ

ýüû
õ þòÿ  
ýÿ ÿùÿrÅ  c                   C   s€   t tdt ƒƒdtdt ƒ ksJ ‚t tdt ƒƒdt dttdt ƒd ƒ  ks,J ‚t ttƒƒttttƒd ƒ ks>J ‚d S )Nç      ð?rr   )rH   r(   rn   r%   r)   r"   rh   rh   rh   ri   Útest_issue_8901Ž  s   $4(rÇ  c                   C   s¶   t ttƒd t tddfƒtdƒ d dtdƒ d  ksJ ‚t ttƒd t tdtfƒtd ks3J ‚t ttƒd td  tƒtdt ƒ tdt ƒdt   ddt   ksYJ ‚d S )Nrz   r   rr   r   rk   )rH   r3   rn   r;   r   r   r2   rh   rh   rh   ri   Útest_issue_8945”  s   >(PrÈ  c                  C   sX   t dƒ\} }}}tt|  t | ƒd ||t    t¡}tt|td|fƒjvs*J ‚d S )Nzi L a brk   r   )r   r2   r   rn   Zrewriter    rH   r‡   )rŠ   ÚLr˜   r¯   Ú	integrandrh   rh   ri   Útest_issue_7130›  s   *rË  c                  C   sx   t dƒ\} }}}t| | ||gƒ}t||ƒt||ƒ ¡ ksJ ‚t||ƒt| |d  d g|| g|| ggƒks:J ‚d S )Nza b c trk   )r   rJ   rH   rW   rˆ   )r˜   r¯   r°   r—   Úvtrh   rh   ri   Útest_issue_10567¢  s   :rÍ  c                   C   s6   t ttd  dt  d ƒtddfƒdt ksJ ‚d S )Nrk   r­   é0   r   r×   r	  )rH   r-   rn   r   rh   rh   rh   ri   Útest_issue_11742©  rç   rÏ  c                  C   s2   t dƒ} ttt|  ƒ| ƒtt|  ƒt ksJ ‚d S )Nr—   )r   rH   r4   r   r;   )r—   rh   rh   ri   Útest_issue_11856­  s   *rÐ  c                   C   s0   t ttdt ƒƒtddfƒttƒd ksJ ‚d S ©Nrr   r   rk   )rH   r-   r"   rn   r   rh   rh   rh   ri   Útest_issue_11876²  s   0rÒ  c                   C   sV   t dttƒ dtdt ƒ  tdt ƒ tƒdtdt ƒ dtdt ƒ  ks)J ‚d S )NiÄÿÿÿg3333333@r   g333333Àr­   g      (@r   )rH   r    rn   rh   rh   rh   ri   Útest_issue_4950·  s   ,ÿrÓ  c                   C   sP   t tttd ƒƒƒttttd ƒƒ d dt tttd ƒƒ d  ks&J ‚d S )Nrk   r   )rH   r3   r"   rn   r2   rh   rh   rh   ri   Útest_issue_4968¼  s   PrÔ  c                   C   s²   t dtd  tt tfƒtu sJ ‚t dtd  tddfƒtu s!J ‚t dtd d  tddfƒtu s3J ‚t dtd  tddfƒt u sDJ ‚t dtd d  tddfƒt u sWJ ‚d S )Nrr   rk   rŒ   r~   )rH   rn   r   rh   rh   rh   ri   Útest_singularitiesÀ  s
   " $"*rÕ  c                  C   s¸   t ddd\} }tt| |  |  ||  ƒ| tt||  ƒ tt||  ƒf|ttƒ ttƒfƒtt| d |d  ƒ| t|d  t ƒ t|d  t ƒf|ttƒ ttƒfƒksZJ ‚d S )Nzx yTr§   rz   rk   )r   rH   r3   r-   r   rW   )rn   r€   rh   rh   ri   Útest_issue_12645É  s   "þ&þýrÖ  c                   C   s6   t ttƒttƒd  tdtd fƒtddƒksJ ‚d S )Nrz   r   r®   rr   )rH   r3   rn   r2   r   r   rh   rh   rh   ri   Útest_issue_12677Ó  rç   r×  c                   C   s6   t tdt ƒttƒ t tdtfƒtdƒ ksJ ‚d S )Nrz   r   )rH   r2   rn   r   r"   rh   rh   rh   ri   Útest_issue_14078×  rç   rØ  c                   C   s(   t dttƒ tdtfƒtd ksJ ‚d S rÑ  )rH   r%   rn   r   r   rh   rh   rh   ri   Útest_issue_14064Û  s   (rÙ  c                	   C   sp   t ddtttj ƒdttƒ    tƒtttjƒtttƒttjƒdttjƒ   ƒ ttjƒt   ks6J ‚d S r{   )rH   r    rn   r   r½   r"   r   rh   rh   rh   ri   Útest_issue_14027ß  s   &>ÿrÚ  c                   C   s&   t ttƒtdtd fƒtju sJ ‚d S r  )rH   r5   rn   r   r   ÚInfinityrh   rh   rh   ri   Útest_issue_8170ä  râ   rÜ  c                   C   sD   t dt tddfƒtju sJ ‚t dtd  tddfƒtju s J ‚d S )Nrr   rŒ   r~   rz   )rH   rn   r   r–   rh   rh   rh   ri   Útest_issue_8440_14040è  s   &rÝ  c                   C   s”   t dtt d  tddfƒ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ƒdtdƒ dtdƒ  dtd	ƒ  ksHJ ‚d S )
Nrr   rk   r   rŒ   rû   r   r®   r²   rz   rª  rh   rh   rh   ri   Útest_issue_14096í  s   42"ÿrÞ  c                   C   sh   t tdtdtd  ƒ tddfƒ ¡ d ƒdk sJ ‚t ttdtd  ƒtddfƒ ¡ d ƒdk s2J ‚d S )Nrr   rz   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rn   r`   rh   rh   rh   ri   Útest_issue_14144ó  s   44rß  c                   C   s(   t ttt ƒttƒ tƒ t¡sJ ‚d S rs   )rH   r    r   rn   r"   rU  r:   rh   rh   rh   ri   Útest_issue_14375ø  s   (rà  c                  C   sX   t dƒtttƒ} t| tddftddftddfƒt| tddftddftddfƒks*J ‚d S )Nrc   r   rr   rk   rz   )r   rn   r€   rî   rH   rW   rã   rh   rh   ri   Útest_issue_14437þ  s   ÿrá  c                   C   sR   t dtttƒd ƒ tƒttttƒd ƒd ƒttttƒd ƒd ƒ ks'J ‚d S r{   ©rH   r-   r    rn   r"   rh   rh   rh   ri   Útest_issue_14470  s   Rrã  c                  C   s¨   t dt td ƒt  dtd   ƒdtd  t  dt td ƒt  d  } t| tƒt dtd  tt td ƒ  d ƒ tt dtd  ƒ t dtd  ƒ  ksRJ ‚d S ©Nrr   rk   rz   )r    rn   rH   rã   rh   rh   ri   Útest_issue_14877  s   LHÿrå  c                  C   sB   t td  d ƒtd  t  } t| tddgƒt d ksJ ‚d S )Nrk   rr   rŒ   r­   )r-   rn   rH   r   rã   rh   rh   ri   Útest_issue_14782  s    "ræ  c                  C   sJ   t td  d ƒtd  t  } t| tddgƒtjd td  ks#J ‚d S )Nrk   rr   r   rz   r	  )r-   rn   rH   r   rš   r   rã   rh   rh   ri   Útest_issue_14782_slow  s    *rç  c                  C   s4   t tddƒ tt  ƒ } t| t dtgƒtu sJ ‚d S )Nrü   rk   r   )rn   r   r    rH   r   rã   rh   rh   ri   Útest_issue_12081  s   rè  c                  C   sD   dt  d } d|  td|  ƒ t d  }t|t ddgƒdks J ‚d S )Nrr   r   r~   rk   r   )rn   r    rH   )r€   rc   rh   rh   ri   Útest_issue_15285  s   ré  c                   C   s”   t tt tt ƒ ttƒ tdtfƒ ¡ tttd ƒt	dtƒ ttd ƒt  t
tƒd dkfttt tt ƒ ttƒ tdtfƒdfƒksHJ ‚d S )Nr   rr   T)rH   rn   r`   r    r"   r   rP   r.   rA   rB   r   rW   rh   rh   rh   ri   Útest_issue_15432$  s   *4(þrê  c                  C   s„   t dƒ} tdtd\}}tttt | | | |   ƒtddt ttt | |  ƒ ttt | |  ƒ | | | |   ks@J ‚d S )NÚomegazm p)ÚclsrÆ   rÇ   )rT   r   rS   rH   r    rn   r   )rë  rØ   rp   rh   rh   ri   Útest_issue_15124*  s
   $<ÿrí  c                   C   s~  t ƒ  ttttƒƒ W d   ƒ n1 sw   Y  t ƒ  ttttƒtƒttttƒtttƒƒks3J ‚W d   ƒ n1 s=w   Y  t ƒ  ttttƒtƒ ¡ ttd d tt ƒks]J ‚W d   ƒ n1 sgw   Y  ttdd tttƒ t¡ttd d tt ƒksˆJ ‚W d   ƒ n1 s’w   Y  ttttƒtddfƒtt	j
tƒksªJ ‚tttƒ tddf¡tt	j
tƒks½J ‚d S )Nrk   Frm   r   rr   )r\   rW   r   rn   r€   rˆ   r]   r^   rH   r   r½   rh   rh   rh   ri   Útest_issue_152181  s   ÿ,ÿ0ÿ,ý&*rî  c                  C   s€   t ttd  tdt ƒ ƒttd tdt ƒ ƒ tdtfƒ} t| tƒs&J ‚t	| t
tƒd ttƒ   ttd ¡ƒdks>J ‚d S )Nrk   r   r®   )rH   r    rn   r2   r—   r3   r   r¹   r.   rP   r-   r   rÞ   r  rh   rh   ri   Útest_issue_15292B  s   >4rï  c                   C   s.   t tdt ƒttƒ tƒdttƒ ksJ ‚d S r¿   )rH   r3   rn   rh   rh   rh   ri   Útest_issue_4514H  ó   .rð  c                  C   sè   t ddd\} }}ttt| d ƒƒ| ||fƒ}ttt| d ƒƒ| ƒ}| |d|di¡ddt  ks3J ‚| | d¡| | d¡ ddt  ksGJ ‚| |d|d	i¡tdƒ td
ƒ ks[J ‚| | d	¡| | d¡ tdƒ td
ƒ ksrJ ‚d S )Nzx a bTr§   rk   rr   rz   r~   rü   rŒ   r   )r   rH   r    r   rÞ   r   )rn   r˜   r¯   ZdefiniteZ
indefiniterh   rh   ri   Útest_issue_15457L  s   "((2rò  c                   C   sN   t tttƒ ttƒ tƒtttƒ ttƒ ttƒ ttƒ ttƒ ks%J ‚d S rs   )rH   rn   r    r"   r:   rh   rh   rh   ri   Útest_issue_15431V  s   *ÿró  c                  C   sü   t tt ƒ } tdtt ƒ ƒ}t| t ƒ|kr| t ¡| ksJ ‚t d tt ƒd  } t d  tt ƒ dtdtt ƒ ƒ  }t| t ƒ|krI| t ¡| ksKJ ‚ttt ƒƒt d  } ttƒ tttt ƒƒƒ d ttt ƒƒt   }t| t ƒ|krz| t ¡| ks|J ‚d S )Nrk   rz   r   )rn   r"   r:   rH   r
   r-   r   r=   )rc   ÚFrh   rh   ri   Ú"test_issue_15640_log_substitutions[  s    & .$rõ  c                  C   s¨   ddl m}  | dƒ}|j}ttt| t ƒ|ttfddt	t
tt t ƒ t t
tt t ƒt  tt kttk @ ttdƒ@ ft ttƒ tttƒ  dfƒksRJ ‚d S )Nr   )Ú
CoordSys3DÚNTr“  )Zsympy.vectorrö  rn   rH   r2   r˜   r¯   Úx_1Úx_2r.   r3   r   r   )rö  r÷  rn   rh   rh   ri   Útest_issue_15509g  s    Dþrú  c                  C   s¢   t ddd} t| td| d  ƒ | ƒt| d d d| d  d  | dkf| d  d d| d  d  tddƒ | d	kf| d d d| d  d  dfƒksOJ ‚d S )
Nrn   Tr§   r²   rk   r   rü   éQ   rz   )r   rH   rÝ   r.   r   rp  rh   rh   ri   Útest_issue_4311_fastp  s   ".ýrü  c               	   C   sà  t ddd} t ddd}t ddd}t ddd}ttt |  |d  ||  ƒ|ƒttƒtt |d  d	|   ƒ td
t |  | | dt| ƒ tt ƒ  ƒ dt| ƒ tt ƒ  ks_J ‚tddt|d    |ƒt tt ƒt|ttt ƒ  ƒ d tt ƒt|ttt ƒ  ƒ d   ks•J ‚ttt |d  ƒ|ƒttƒtttƒ| ƒ dttƒ  ksµJ ‚tdtt| ƒd  |ƒ| d tttt| ƒd ƒ d  ks×J ‚tdtt| ƒd  |ddt fƒt ksîJ ‚d S )NÚKTrÄ   rn   r§   rØ   r—   rk   r   r~   rr   r   )	r   rH   r    r   r-   r   r>   r"   r<   )rý  rn   rØ   r—   rh   rh   ri   Ú%test_integrate_with_complex_constantsx  s"   6ÿ,ÿ
ÿ>"ÿ@D2rþ  c                  C   sx   t dƒ} t dddd}t|| |d   | d  | ƒ|d | |  t| ttt ƒ d|ƒ t|ƒ t|d ƒ ks:J ‚d S )Nrn   r`   TrL  rr   rk   )r   rH   rF   r!   r   r   rA   )rn   r`   rh   rh   ri   Útest_issue_14241‡  s
   :ÿrÿ  c                   C   s<   t ttƒd ddttƒ   tddt gƒtd ksJ ‚d S )Nrk   r   r   r   )rH   r3   r—   r2   r   rh   rh   rh   ri   Útest_issue_13112Ž  rò   r   c                  C   sP   t ddd} tttddt |   ƒ td| fƒ}|d| d  t d ks&J ‚d S )	Nr¬  TrÄ   rr   rk   r   r   r	  )r   rH   rn   r/   r   )r¬  rŠ   rh   rh   ri   Útest_issue_14709b’  s   $ r  c                  C   sl   t dƒ} t dƒ}tt|ƒ| |t | fƒt| ƒksJ ‚tt|  ƒtd|  ƒ |  | dtfƒtdƒks4J ‚d S )Nrn   r—   r~   r   rk   )r   rH   r    r   r:   r"   )rn   r—   rh   rh   ri   Útest_issue_8614˜  s   &6r  c                  C   sò   t ddd} t| d ƒdtd|  ƒ  t| ƒ t| ƒ }t|| ƒ}|tjks(J ‚t| | d¡d ƒdks6J ‚t| d ƒdttd	ƒd
 |  ƒ  t| ƒ t| ƒ }t|| ƒdtd|  d
 ƒ d dtd|  d ƒ d  td|  ƒd  kswJ ‚d S )Nr…   TrÄ   rk   gš™™™™™ù?rr   gÏRt?,eÀç:Œ0âŽyE>r­   r   iöÿÿÿé   rz   )r   r    rH   r   r–   rÝ   rÞ   )r…   rÊ  Zsolutionrh   rh   ri   Útest_issue_15494Ÿ  s   ,
4Rr  c               	   C   s~   t dƒ} tt| td  ƒtƒ ¡ ttttd |  ƒ ttdttd |  ƒ d ƒ ttd |  ƒ  t	| dƒfdƒks=J ‚d S )Nr€   rk   rz   r   r$  )
r   rW   r@   rn   rˆ   r.   r:   r"   r-   r   rÀ   rh   rh   ri   Útest_li_integral¯  s   ,.ÿþþr  c                  C   sà   t dƒ} t dƒ}tj}| |d  t|||  ƒ t|||  fd| d| ||  f| d|   d ƒ d| td| ||  ƒ  }tt| | ƒ| ƒ}||ksRJ ‚t ddd}| |i}tt|| ƒ|ƒ| |¡ ¡ ksnJ ‚d S )	Nrn   r`   rr   rz   rk   r   Fr–  )	r   r   r½   rA   rC   rH   r3   Zxreplacer‰   )rn   r`   r¬  rè   ÚgotZ_xZrepsrh   rh   ri   Útest_issue_17473¶  s   (&ÿÿ(r  c                   C   s¢   t tttƒƒtd  tdtgƒt ksJ ‚t tttƒƒtd  tdtgƒtdƒ d td  ks2J ‚t tttƒƒtd  tdtgƒtdƒ d td  ksOJ ‚d S )Nrk   rr   rz   rŽ   r²   )rH   r"   rn   r   r   rh   rh   rh   ri   Útest_issue_17671Ã  s   *:>r	  c                  C   s~   t dƒ} t dƒ}t dƒ}td|d | tdƒd   ||  d | d fƒ| |tdƒd  td| d d|   ƒ  ks=J ‚d S )Nr{  ÚCr€   rr   rk   rz   r   )r   rH   r   r-   )r{  r
  r€   rh   rh   ri   Útest_issue_2975É  s   fr  c                     sÔ  t dƒ\‰‰ } tddd}ttˆˆ  ˆ d|fƒˆƒˆd |d d |d   ks*J ‚ttˆtˆ ƒ ˆ d|fƒˆƒtˆd tˆ ƒ d ˆ d|fƒksKJ ‚tttˆ ˆ ƒˆ d|fƒˆƒtttˆ ˆ ƒ ˆ  tˆ dƒfd	ƒˆ d|fƒkssJ ‚ttttˆ ˆ ƒˆ d|fƒˆƒˆƒttttˆ ˆ ƒ ˆ d  tˆ dƒfˆ ˆ  dfƒˆ d|fƒˆ t	 kˆ t	k @ tˆ dƒ@ fd	ƒks¶J ‚ttˆˆ d| fƒˆƒ| ˆd  d ksËJ ‚t
t‡ ‡fd
d„ƒ t
t‡ ‡fdd„ƒ t
t‡fdd„ƒ d S )Nzx n Mr÷  Tra   rr   rk   r   r   r$  c                      s   t tˆˆtˆ fƒtƒS rs   ©rH   r   r€   rh   ©r`   rn   rh   ri   rw   Ü  r}   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS r{   )rH   r   rh   r  rh   ri   rw   Ý  r}   c                      s   t tˆ ˆ dtfƒˆ ƒS r{   r  rh   rp  rh   ri   rw   Þ  r}   )r   r   rH   r   r3   r   r.   r2   r   r   rZ   r   )rö   r÷  rh   r  ri   Útest_issue_7827Ð  s,   :ÿ,ÿ"2ÿÿÿÿ*r  c               	   C   sš   ddt   tt tt ƒ ƒddt     t d  t t tt tt ƒ ƒ  tt tt ƒ ƒ  } t| t ƒdtt tt ƒ ƒ dtt tt tt ƒ ƒ ƒ  ksKJ ‚d S rä  )rn   r-   r"   rH   rã   rh   rh   ri   Útest_issue_4231á  s   XBr  c                  C   s@   t dtd t t  tƒ} t| tƒdtd t t  ksJ ‚d S rà   )r
   rn   r   rH   rã   rh   rh   ri   Útest_issue_17841æ  s   &r  c                  C   sJ  t dddd} | | d  tdƒd  | t| ttdƒƒ ƒ  d  }| ttdƒƒ | | dd|      }t|| ƒ| d  dtdƒd   | d	 t| ttdƒƒ ƒ  d| d	  d	  d	|  t| ttdƒƒ ƒ  d	t| ttdƒƒ ƒ  ksxJ ‚t|| ƒt| d	 tdƒd  ƒd	 d	td
ƒ ttdƒƒ t	d	td
ƒ |  ƒ  ks£J ‚d S )Nrn   T©r¨   rË   r   r   rr   r×   r®   rk   rz   )
r   r0   r(   r"   r%   r2   rH   r   r-   r1   )rn   Úf1Úf2rh   rh   ri   Útest_issue_21034ë  s   6$xÿFÿr  c                   C   sd   t ttƒtt ƒ tƒtt ƒtt ƒttƒ  ksJ ‚t ttƒtt ƒ tdtfƒt ks0J ‚d S r[  )rH   r"   rn   r    r:   r   r   rh   rh   rh   ri   Útest_issue_4187÷  s   8,r  c               	   C   s0  t dƒ} t dƒ}t dƒ}t dƒ}t|d t|ƒd  ||  d | d fƒ|d  |  d t| d ƒt| d ƒ d   |d | d t| d ƒt| d ƒ d    ksUJ ‚t|d t|| ƒd  ||  d | d fƒt|d  |  | d t| | d ƒt| | d ƒ d   | |d | | d t| | d ƒt| | d ƒ d   |  |t k|tk @ t|dƒ@ f| |d  dfƒksÃJ ‚dt | |  }tdƒt| ƒ |d  t	tdƒt| ƒ ƒ t
tjd ƒ d	t
td
ƒd ƒ  | |d  d  }t|d t|| ƒd  ||  d | d fƒ|ksJ ‚d S )NrÉ  rî   Úr0ÚR0rk   r   r   Tr	  r   )r   rH   r2   r3   r.   r   r   r   r-   r?   rA   r   rš   )rÉ  rî   r  r  r{  Zsolrh   rh   ri   Útest_issue_5547ü  s(   8ÿ*
ÿ.>:ÿÿ
ý^<r  c                   C   s6   t dddt d  d  tdtfƒtddƒksJ ‚d S )Nrr   rk   rz   r   )rH   rn   r   r   rh   rh   rh   ri   Útest_issue_15810  rç   r  c                  C   sZ  t dddd} t| ƒtd|  ƒ td|  tdƒ ƒ }| t| ƒd  | td|  tdƒ ƒ  | ddtdƒ    d|  d|  tdƒ  t| ƒ  tdƒtd|  tdƒ ƒ d  }|t|| ƒksbJ ‚| tdƒ | d  }t| ƒtdƒ|   }|t|| ƒksJ ‚| d td	ƒ |  }| d d td	ƒt| ƒ  }|t|| ƒks J ‚| d|  tdƒ  }| d td|  tdƒ ƒtdƒ d  }|t|| ƒksÇJ ‚| tdƒ|   }| d d t| ƒtdƒ  }|t|| ƒksæJ ‚t| td	ƒ|   ƒ}| t| td	ƒ|   ƒ |  dttd	dƒƒ t| ttd
dƒƒ ƒ  }|t|| ƒksJ ‚| d	 | t  }| d	 d	 t| d  d  | d tdƒ d  | d tdƒ d  | tdƒ  td	ƒt| t ƒ  }|t|| ƒks`J ‚d|  | td	ƒ  }d|  dt| td	ƒ ƒ td	ƒ  }|t|| ƒks†J ‚| d d|  tdƒ  }| d d | tdƒ d  td|  tdƒ ƒtdƒd  d  }|t|| ƒks¼J ‚| d  | t  }| d  d t|   tdƒt| t ƒ  }|t|| ƒksäJ ‚d|  d td	ƒ |  }d|  td	ƒ dtd	ƒ t| ƒ  }|t|| ƒksJ ‚| d t	dƒ|   }| d d d|   t| ƒt	dƒ  }|t|| ƒks2J ‚| tdƒ| d   }| d d tdƒd| d    }|t|| ƒksVJ ‚d|  tdƒ |  }d|  tdƒt| ƒ  }|t|| ƒksvJ ‚| d | td	ƒ d  |  }| d d | d tddƒtd	ƒ   d|  tdƒ  dtdƒ t| td	ƒ ƒ  tdƒ| td	ƒ   }|t|| ƒksÁJ ‚| | tdƒ| d    |  }| d d | d d  tdƒt| ƒ  }|t|| ƒksíJ ‚| | d	|  tdƒ   }| d d | d	  td	|  tdƒ ƒtdƒ d  }|t|| ƒksJ ‚| tdƒ d| d  d|    }tdƒt| ƒ d tdƒt| d ƒ d  t| d ƒd  }|t|| ƒ 
¡ ksWJ ‚t| dtdƒ  ƒ}| t| dtdƒ  ƒ |  dt| dtdƒ  ƒ tdƒ  }|t|| ƒks‰J ‚|  dtd
ƒtdƒ|   d  tdƒ |   }| d  tdƒ d dt| ƒ tdƒ  d| d  td	ƒ tdƒ tdƒ d|  tdƒ tdƒ tdƒd   dtdƒ tdƒ tdƒd   d| d    tdƒ }|t|| ƒksýJ ‚d| d  tdƒ d|   }d| d  d dtdƒ t| ƒ  tdƒ }|t|| ƒks+J ‚d S )Nrn   Tr  r   rz   rk   rr   r~   r   éûÿÿÿr­   r®   rŽ   rd   r  r½  iLÿÿÿéZ   r'  rû   )r   r"   r    rH   r)   r(   r   r1   r   r%   r‰   r3   )rn   rc   rô  ZF_truerh   rh   ri   Útest_issue_21024  s”   (:ÿÿ(Dd$@*$$ f(4 <<.nÿ
ÿÿ,r  c                  C   s`   t dƒ} tdtdt|  d    tt tfƒ ¡ tt| ƒd dƒ tt| ƒd dƒ ks.J ‚d S )Nr˜   rr   rk   r   )r   rH   r   rn   r   r‰   r8   r   ©r˜   rh   rh   ri   Útest_issue_21721n  s   ($ÿr  c                  C   s€   t dƒ} ttd|  ƒddt| ƒ   | ddt fƒtd ks J ‚td|  ƒddt| ƒ   }t|| ddt fƒtd ks>J ‚d S )	NÚthetarz   r   r   r   rk   r×   r®   )r   rH   r2   r   )r  rÊ  rh   rh   ri   Útest_issue_21831t  s   8$r   c                   C   sB   t td tddƒ d tdtd  ƒ tddfƒtd ksJ ‚d S )Nrk   rr   r   rŒ   rS  )rH   rn   r   r-   r   rh   rh   rh   ri   Útest_issue_22033_integral{  s   Br!  c                	   C   sº   t dttd td  dtd  td  fttdtd  ƒ tdtd  ƒftddfƒtks/J ‚t ddtd  tdƒd   d dtdtd  ƒ ddtd     tddfƒtks[J ‚d S )Nrr   rk   rŒ   rû   rz   )rH   rî   rn   r€   r-   r   r   rh   rh   rh   ri   Útest_issue_21671€  s   ^\r"  c                  C   sr   t ddd} ttƒdttƒd   }t| t| ¡| dd | t¡}t|tdd|  kr4t|tƒks7J ‚ J ‚d S )NÚxrTr§   r   rk   r±  )r   r2   rn   r3   rH   rÞ   rW   )r#  r‹  Zres_realrh   rh   ri   Útest_issue_18527†  s   0r$  c               	   C   sÀ  dt ttƒ tttƒ   } tt t  ttd ƒ ttd t d  ƒt   ƒ ttd t d  ƒ tt t  ttd ƒ ttd t d  ƒt   ƒttd t d  ƒ  }tt	tttd ƒd ƒ tttd ƒd ƒ  t
tdƒt
t dƒ@ ftttd ƒƒt t
t dƒft t t  ttƒ t ttƒ   t
tt t  ƒfttt  ttƒ t ttƒ   t
ttt  ƒf|dfƒ}t| tƒ|ksÁJ ‚tddd\}}t|t |i}t|  |¡tƒ| |¡ksÞJ ‚d S )Nrr   rk   r   Tza, brÄ   )r¯   r2   rn   r˜   r3   r"   r5   r-   r.   r   r   r   rH   r   rÞ   )rc   ZFposrô  Zapr  Úreprh   rh   ri   Útest_issue_23718  s   FDÿ@2,ø
"r&  c                  C   sR   t dttd d ƒ tddfƒ} | tdtdƒ ƒ ksJ ‚t |  ¡ d¡s'J ‚d S )Nrr   rk   r~   rŒ   rz   gC˜qBõ?)rH   r-   rn   r"   ÚmathÚiscloser`   rþ   rh   rh   ri   Útest_issue_23566¤  s    r)  c                   C   s\   t dttt d d ƒ ƒtttt ƒttt d ƒdkft ttt ƒ dfƒks,J ‚d S )Nrr   rk   T)rH   r-   rn   r   r.   r#   r   r0   rh   rh   rh   ri   Útest_pr_23583ª  s   \r*  c                   C   sX   t ttƒtdtdt ƒ ƒ ƒttdt ƒd ƒttƒ d tttƒƒd  ks*J ‚d S rà   )rH   r    rn   r-   r$   rh   rh   rh   ri   Útest_issue_7264¯  s   Xr+  c                   C   s.   t ttƒtddfƒdtttjƒƒ ksJ ‚d S rø   )rH   r*   rn   r1   r)   r   r½   rh   rh   rh   ri   Útest_issue_11254a³  rñ  r,  c                   C   sB   t ttƒtƒtttd ƒƒksJ ‚t ttƒtddfƒtksJ ‚d S )Nrk   r   rr   )rH   r'   rn   r"   r)   r   rh   rh   rh   ri   Útest_issue_11254b·  s   " r-  c                   C   s|   t dtttt d  ddd  tƒdtdt ƒd  ksJ ‚t ttƒd tƒdttd ƒ ttd ƒd d  ks<J ‚d S )NrŒ   rk   F©rT  r~   rr   )rH   r(   rn   r   r   r    r%   r)   rh   rh   rh   ri   Útest_issue_11254d¼  s   >>r/  c                  C   s   t dtd  td  dt  d ttd dt  d ƒ tddfƒ} | dtdƒ d dtddtdƒ  ƒ d	  ks<J ‚t |  ¡ d
¡sFJ ‚d S )Nrz   rk   r   r   rr   i›ÿÿÿr­   é‡   r	  g€2É{¢ÙÀ)rH   rn   r-   r"   r'  r(  r`   rþ   rh   rh   ri   Útest_issue_22863Â  s   D4r1  c                   C   s,  t ttttƒ ƒƒdtttƒt ƒ ttƒd td  tdƒd   tdttƒ dtttƒt ƒ  d ƒd  ks<J ‚t tdt d tdt d ƒ ƒd ƒtdt tdt d ƒ d ƒdt d	 d
dt d tdƒd   d  tdt d ƒd  dt d d d	  td
ƒd	   d ks”J ‚d S )Nrk   r×   rz   rr   r­   r   r   r²   rŽ   r
  é(   ©rH   r-   rn   r   r"   rh   rh   rh   ri   Útest_issue_9723È  s   ^ÿ&^ÿÿÿr4  c                   C   sl   t ttƒtd  ttd  tt  t  tddtttƒttd  ttd   ttd    tƒks4J ‚d S )Nrk   Trµ  rz   r   )rH   r"   rn   r°   r¯   r˜   rX   rh   rh   rh   ri   Útest_issue_23704Ð  s   00ÿr5  c                   C   sd   t dtdtdt ƒ ƒ ƒttdtdt ƒ ƒd ƒd ttdtdt ƒ ƒd ƒd  ks0J ‚d S rà   râ  rh   rh   rh   ri   Útest_exp_substitutionØ  s   dr6  c                   C   sx   t ttƒƒttttƒd ƒ tttƒƒ ksJ ‚t ttƒƒdtttd ƒƒ ks*J ‚t ttƒƒtttd ƒƒks:J ‚d S rà   )rH   r&   rn   r"   r)   r*   r1   r'   rh   rh   rh   ri   Útest_hyperbolicÜ  s   0$$r7  c                   C   sÌ   t ttd ƒƒtttd ƒ d ksJ ‚t tttdƒd  ƒƒdt tttdƒd  ƒ d ks2J ‚t dttd ƒ ƒtttƒ ttd ƒ ksJJ ‚t tttd ƒ ƒtd ttd ƒ ttƒ ksdJ ‚d S )Nrk   r   rz   r®   r
  rr   rû   r3  rh   rh   rh   ri   Útest_nested_powâ  s   (<08r8  c                   C   sä  t dtdtd  dt  d ƒ ƒtdƒtdtdƒ ttdƒd   d ƒ d ks,J ‚t dtdtd  dt  d ƒ ƒtdƒtdtdƒ ttdƒd   d ƒ d ksXJ ‚t dtdtd  dt  d ƒ ƒtdƒtd	t dtdƒ tdtd  dt  d ƒ  d ƒ d ksŽJ ‚t dtdtd  dt  d ƒ ƒttj tttj ƒ dtttj d ƒ  ks¹J ‚t dttt	t  t
td   ƒ tƒttt	dtt
ƒ ttt	t  t
td   ƒ  dt
 t  ƒtt
ƒ tt
d
ƒttt	d dt
   d
ƒ@ ft	dt
  t tt	dt
  t ƒ tt
t	dt
  t d  ƒ tt
d
ƒfdttt	t  ƒ t	 tt	d
ƒftttƒ dfƒks@J ‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ tdtdƒ ttdƒd   d ƒ d  ks…J ‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ tdtdƒ ttdƒd   d ƒ d  ksÊJ ‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ td	t dtdƒ tdtd  dt  d ƒ  d ƒ d  ksJ ‚t ttt  ttt	t  t
td   ƒ tƒtt	 t dt
  t ttt	dtt
ƒ ttt	t  t
td   ƒ  dt
 t  ƒtt
ƒ ttt	d dt
   d
ƒft	dt
  t tt	dt
  t ƒ tt
t	dt
  t d  ƒ dfƒ tttt	t  t
td   ƒ t
  tt
d
ƒfdt ttt	t  ƒ dt t ttt	t  ƒ tt	t  tdƒd  d   t	  t	 tt	d
ƒftt ttd  d  ttƒ dfƒksëJ ‚t dtd  td  dt  d ttd dt  d ƒ ƒttd dt  d ƒtd dt d  tdƒd   dtdt dttd dt  d ƒ  d ƒ d  ksBJ ‚t tdtd  dt  d ƒƒtd tdƒd  tdtd  dt  d ƒ dtdƒ tdt d tdƒd  ƒ d  ksƒJ ‚t ttt	t  t
td   ƒtƒttd t	d dt
   ttt	dtt
ƒ ttt	t  t
td   ƒ  dt
 t  ƒtt
ƒ ttt	d dt
   d
ƒft	dt
  t tt	dt
  t ƒ tt
t	dt
  t d  ƒ dfƒ t	dt
  td  ttt	t  t
td   ƒ  tt
d
ƒfdtt	t  tdƒd   dt	  tt	d
ƒfttƒt dfƒks1J ‚t tttd dt  d ƒ ƒtd d td	  tdƒd	  ttd dt  d ƒ dttdƒtd  d ƒ d  kspJ ‚d S )Nrr   rz   rk   r   r   r
  rü   rY  r®   r   Tr”   r²   iùÿÿÿrS  r  r"  r­   r0  r	  iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rn   r$   r   r0   r"   r½   r˜   r¯   r°   r.   r   rƒ   rf   rh   rh   rh   ri   Útest_sqrt_quadraticé  st   XXlV$hH.þ
ÿ*V
ÿ*V
ÿ*j
ÿ,^Bÿÿ"ýýb"û
ÿ:j
ÿ.*ÿ
ÿ ^Bÿÿ.ýý,û
ÿVÿr9  c                   C   sî   t tttƒ ttƒ ƒtttƒ tttƒttƒ ƒ ksJ ‚t tttƒd  tƒtttƒ tttƒƒ ks7J ‚t td tttƒtdfƒ ƒtd tttƒtdfƒ dtd  tttƒtdfƒ  dt tttƒtƒ  dttƒ  ksuJ ‚d S )Nrk   rz   r   r®   )rH   rn   r6   r5   r"   r2   r   rc   rh   rh   rh   ri   Útest_mul_pow_derivative  s
   <2Xÿr:  c                  C   s´   t dtdk fdƒ} t dtdk fdƒ }| | }ttdƒ df}t| |ƒdks(J ‚t||ƒdks1J ‚t|  |ƒdks;J ‚t| |ƒdksEJ ‚t||ƒdksNJ ‚t| |ƒdksXJ ‚d S )	Nr   g        )rr   TrÆ  ÚInfrr   rŒ   g      ð¿)r.   rn   ÚfloatrH   )Zfun1Zfun2Zfun_sumrÉ  rh   rh   ri   Útest_issue_20782  s   r=  c               	      s˜   dd„ ‰ ‡ fdd„} t tdƒ t f}t| dƒ|ƒ}|dt  tdt ƒ tt tdddd	ƒ ks0J ‚t| d
ƒt tdƒ t fƒdt  dtd
t ƒ  ksJJ ‚d S )Nc                 S   s   t dt| k fdt| kfƒS r´   )r.   rn   r  rh   rh   ri   rw   )  s    z"test_issue_20781.<locals>.<lambda>c                    s   ˆ t | ƒƒˆ t| ƒƒ S rs   )Úintr<  r  ©ÚPrh   ri   rw   *  r£   r;  rr   rk   rÆ  Fr.  r   )rn   r<  rH   r,   r+   )rc   rÉ  r  rh   r?  ri   Útest_issue_20781(  s   .ÿrA  c                  C   sâ   t dƒ} t| d td| d  ƒ | ddfƒtd ksJ ‚td| d  td| d  ƒ | ddfƒt d ks7J ‚tdtd| d  ƒ | ddfƒtd ksMJ ‚t| d d| d   d td| d  ƒ | ddfƒdt d ksoJ ‚d S )	Nrn   r   rr   rk   rŒ   r	  r~   r   )r   rH   r-   r   rp  rh   rh   ri   Útest_issue_194274  s
   06,HrB  c                  C   s(  t dttdt d  dt d  ƒ tdtfƒ} | jtdddt dttd dtd   dt  d ƒ tdtfƒttd tdfƒ ksEJ ‚t dttdt d  dt d  ƒ tdtfƒ}|jtdddt dtdtd  dtd   d	td   d
t  d ƒ tdtfƒttd tdfƒ ks’J ‚d S )Nrr   rz   rk   r   rÍ   r   r   rS  éÁ   iö  i  )rW   r-   r˜   rn   rî   r  rN   )ÚI1ÚI2rh   rh   ri   Útest_issue_23942B  s   0Z0nrF  c                  C   sv   dt  tdt  ƒ } ddt t d dt   tdt t ƒ dtdt ƒ  }t| t tdfƒ}| |tj¡s9J ‚d S )Nrr   y        >ÚÃT¶üí?rÆ  gÇÅzðñ¿g	
šT8ò?gÇÅzðñ?g>ÚÃT¶üí?)rn   r    r   r€   rH   Zis_samer'  r(  )rc   ZF_exprô  rh   rh   ri   Útest_issue_25886I  s   ÿþþýrG  c                  C   sÄ   t tttd ƒƒt ƒ} | tttd ƒƒd ksJ ‚t dtd td  tddƒ  tƒ}|ttd ttd td  d ƒ  ksBJ ‚t dttƒd  tddt fƒ}|dtdƒ t d ks`J ‚d S )Nrk   rr   rz   r   )	rH   r2   r"   rn   r3   r€   r   r-   r   )rD  rE  ZI3rh   rh   ri   Útest_old_issuesT  s   $,  rH  c                  C   s‚   t ddd} t dddd}t|| t  ƒd }t|| t t d fƒ}td }d}| ||¡ ¡ }| ¡ }t|| ƒd	ks?J ‚d S )
Nrn   Tr§   r˜   )r¨   rÅ   rk   r   rr   r   )r   r3   r   rH   rÞ   re   rQ   )rn   r˜   Úintegral_exprZsymbolic_resultZcorrect_resultZa_valueZnumeric_symbolic_resultZnumeric_correct_resultrh   rh   ri   Útest_integral_issue_26566`  s   rJ  c                  C   sp   t ddd} tdd| d d   ƒ}t|| ddfƒ}| ¡ }td	ƒd
 dt d  }t|| ¡  ƒdk s6J ‚d S )Nrn   Tr§   rr   g      â?gOUUUUUÕ?rk   rŒ   rz   r®   r   r²   r  )r   r-   rH   re   r   rÝ   )rn   rI  Zresult_symbolicZresult_numericÚexpected_resultrh   rh   ri   Ú.test_definite_integral_with_floats_issue_27231u  s   rL  c                  C   s´   t td td  ƒ} tt|  t dƒ ƒ|  }t|ttƒ tt tt tt  ƒfg¡}dt dƒ t td  ttd  td  d ƒ dt t	ƒ  }t
t|tt tfƒƒ|ksXJ ‚d S )Nrk   r~   rz   )r-   rn   rî   r<   r˜   r
   rÞ   r¯   r    r   rQ   rH   )ró   ÚuZEcrK  rh   rh   ri   Útest_issue_27374…  s
   (>"rN  )rd   (c  r'  Zsympy.concrete.summationsr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.exprr   rÔ   r   r   r	   r
   Z
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