a
    kº”h(= 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   úR/var/www/auris/lib/python3.9/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 sZ0    Y  ttdd t| tfƒ W d   ƒ n1 s’0    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     (rq   c                     s8  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sPJ ‚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s´J ‚tt‡fdd„ƒ dt d d  } t| t t tfƒ ¡ dksôJ ‚t| t d	dfƒ ¡ tdƒ ksJ ‚t t d d  }t|t t tfƒ ¡ dksHJ ‚t|t d	dfƒ ¡ dksfJ ‚t d t d d  }t|t t tfƒ ¡ tu sšJ ‚t|t d	dfƒ ¡ tdƒ d
 ksÂJ ‚dt d d dt d    }t|t t tfƒ ¡ t
 d ksJ ‚t|t d	dfƒ ¡ tdƒ tdƒd  ks4J ‚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   rx   é   c                      s   t ˆ tt dfƒ ¡ S ©Nrr   )rW   rn   r   rt   rh   )Úlrh   ri   rw   K   rx   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$  (&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symsrƒ   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s8J ‚t ddttƒ  tdtfƒtdƒks`J ‚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sfJ ‚t tttƒƒ}|jttƒfksˆJ ‚t tttddƒfƒ}|jttddƒfks´J ‚t ttdkƒ}|jttdtƒfksÚJ ‚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   sØ  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 sRJ ‚tt ttƒtƒdksjJ ‚tt ttddfƒtƒdksˆJ ‚tt ttƒtƒtks J ‚tt ttdtfƒtƒtks¾J ‚td d } tt| tdtfƒtƒtt | tdtfƒtƒ 	¡  
¡   krdt d  
¡ ks n J ‚tt| tdtfƒtƒtt | tdtfƒtƒ  kr\dksbn J ‚tt| tdtfƒtƒtt | tdtfƒtƒ  krždks¤n J ‚tt| tƒtƒtt | tƒtƒ  krÔdksÚn 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srJ ‚ttd ttdt fƒ t¡dtd  ks¢J ‚t ttƒ ¡ thks¼J ‚t ttƒtddfƒ ¡ tjtjthksèJ ‚tt ttdt fƒƒthks
J ‚tt ttdt fƒƒtthks.J ‚tttttfƒdksHJ ‚tttt t fƒdksfJ ‚ttt ttƒ tƒtt td d  ttƒ ksžJ ‚t tƒjs®J ‚tddd}t |t tƒjdu sÔJ ‚d S )	Nr   rr   rk   é   ry   r`   F©Zcommutative)rW   rn   r   r   ÚNaNr
   r~   ÚtrH   r†   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
ÿ6ÿ
,20,"$8r›   c                  C   sz   G dd„ dt ƒ} | ƒ }t|d |ƒ|d d | ks8J ‚t|d |ddfƒtddƒksZJ ‚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   rŸ   rr   rk   r   ry   c                   S   s   t td td ƒS rz   ©rH   rn   rh   rh   rh   ri   rw   »   rx   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   rx   )r   rH   r   rZ   r   )rŸ   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s2J ‚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sŒJ ‚t ttttƒƒtthks¨J ‚t ttt ttƒƒtthksÈJ ‚t ttt ttdtfƒƒthksìJ ‚t ttt tttftttfƒƒtthksJ ‚d S )Nry   r   rk   rr   )r‰   rW   rn   r~   rh   rh   rh   ri   Útest_basics_multiple¿   s    2,. $r¢   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ksHJ ‚| ¡  ¡ | ¡  ¡ ksdJ ‚| ¡  ¡ | ¡  ¡ ks€J ‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks¸J ‚| ¡  ¡ | ¡  ¡ ksÔJ ‚| ¡  ¡ | ¡  ¡ ksðJ ‚d S )NzA BFr“   rn   T)Úcomplex©Úreal)r   r   rW   Zadjointr†   Ú	conjugateZ	transpose)ÚAÚBrn   rp   rh   rh   ri   Útest_conjugate_transposeÉ   s    r©   c                  C   sD  t dtdtfƒdksJ ‚t dtdtfƒdt ks4J ‚t ttdtfƒtd d ksTJ ‚t dt tdtfƒdtd  d ks|J ‚t dtd  tdtfƒtd ks J ‚t dt tdtfƒttƒksÀJ ‚t dtd  tdtfƒdt d ksèJ ‚t td dt  d tdtfƒtd d dtd  d  dt  ks2J ‚t td tƒtd d ksRJ ‚t dt t d tƒdt d td  d ks†J ‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÀJ ‚t ttd  tdtfƒttd  d ksîJ ‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ks@J ‚d S )Nr   ry   rk   rr   rŠ   r   é   é   ÚbÚcr}   )rH   r•   rn   r"   r   r–   )r¬   r­   rh   rh   ri   Útest_integrationÙ   s     ($ (J 4*.r®   c                   C   s  t td td  tddftddfƒtdƒks0J ‚t td td  ttƒtddƒtd  td  ksfJ ‚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sÐJ ‚t ttt ƒt tddftddfƒtdƒ d ksJ ‚d S )	Nrk   r   rr   rŠ   é	   ry   rª   r}   )rH   rn   r~   r   r"   r3   rh   rh   rh   ri   Útest_multiple_integrationì   s    06Fÿr°   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    r²   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sPJ ‚t dttƒd  tƒdttƒ ksvJ ‚d S )Nry   rk   r   rr   r|   )rH   r-   rn   rh   rh   rh   ri   Útest_issue_3560ø   s    *&r³   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   rx   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorrh   rh   rh   ri   Útest_issue_18038þ   s    rµ   c                  C   sv  t ttd t  td  ttƒ} tƒ  t| tƒ}W d   ƒ n1 sF0    Y  ttdd t| tƒ}W d   ƒ n1 s|0    Y  ttdd t| tƒ}W d   ƒ n1 s²0    Y  t|t ƒdu sÎJ ‚t|t ƒdu sàJ ‚|j	ttfksòJ ‚|j	ttfksJ ‚| 
¡ td d td t d  ttd   ks<J ‚| 
¡ tt td td  d  td d  ksrJ ‚d S )Nrk   ry   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     (((6r¹   c                  C   st  t ttd t  td  ttƒ} tƒ   t| tddfƒ}W d   ƒ n1 sL0    Y  ttdd  t| tddfƒ}W d   ƒ n1 sˆ0    Y  ttdd  t| tdtfƒ}W d   ƒ n1 sÄ0    Y  t	|t ƒdu sàJ ‚t	|t ƒdu sòJ ‚|j
tfksJ ‚|j
tfksJ ‚| ¡ tjtd  td  ks:J ‚| ¡ td d tt  td td  d  kspJ ‚d S )	Nrk   ry   r   rr   Frm   Tr}   )rK   rn   r~   r\   rW   r]   r^   rH   r   r¶   r·   r¸   r   ÚHalf)rp   ZQxZQyrh   rh   ri   Útest_integrate_poly_definite  s     ...$r»   c                      sD   t dƒ‰ ttƒtd d ks J ‚ttdd„ ƒ tt‡ fdd„ƒ d S )Nr~   rk   c                   S   s   t dƒS ©Nrk   rG   rh   rh   rh   ri   rw   0  rx   z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS rs   r    rh   ©r~   rh   ri   rw   1  rx   )r   rH   rn   rZ   r   rh   rh   r½   ri   Útest_integrate_omit_var+  s    r¾   c                  C   sd   t dƒ} ttt| ƒ tƒtd t| ƒ d ks2J ‚ttd t| ƒ tƒtd t| ƒ d ks`J ‚d S )Nr~   rk   iè  ié  )r   rH   rn   r3   r½   rh   rh   ri   Útest_integrate_poly_accurately4  s    *r¿   c                  C   sN   t dƒ} ttd | ƒtd |  ks&J ‚ttd | ddfƒdtd  ksJJ ‚d S )Nr~   rk   rŠ   rr   )r   rH   rn   r½   rh   rh   ri   Útest_issue_3635=  s    rÀ   c                  C   sž   t ddd} tt|  tddt| d  | d  ks6J ‚tt| ƒt d|   dt| ƒ  tddt|  ƒt| ƒt d|   dt| ƒ   dt| ƒ  ksšJ ‚d S )Nr~   T©ÚpositiveÚnone©Zcondsrr   rk   )r   rH   rn   r    r3   r½   rh   rh   ri   Útest_integrate_linearterm_powE  s
    *(4ÿrÅ   c                   C   sˆ   t tttƒ tƒdt ttƒd  d ks.J ‚t tttƒ tttƒd   tƒdt ttƒd  d dt ttƒd  d  ks„J ‚d S )Nrk   ry   r   )rH   r   r-   rn   r   rh   rh   rh   ri   Útest_issue_3618N  s    . .ÿrÆ   c                   C   s$  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sJJ ‚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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s J ‚d S )Nrr   r   T)rH   r2   r`   rn   r.   r3   r   rh   rh   rh   ri   Útest_issue_3623T  s    *ÿ
*ÿ
$..ÿÿrÇ   c                  C   s    t dddd} tdt t| t t d ƒ tddgƒdtt|  ƒ t|   ksRJ ‚ttt| t t d ƒ td	dƒ tddgƒdtt|  ƒ t|   ksœJ ‚d S )
Nr`   T)rb   Únonzerog      à¿rk   r|   r   ç       @rŠ   )r   rH   rn   r3   r   r2   r   ©r`   rh   rh   ri   Útest_issue_3664^  s    &ÿ,ÿrË   c                   C   s4   t tdtd dt  d  tddfƒƒdks0J ‚d S )Nrr   rk   rª   é   r}   z1.10714871779409)rj   rW   rn   rh   rh   rh   ri   Útest_issue_3679f  s    rÍ   c                  C   sb   ddl m}  ddlm} | tttd ƒtƒƒtdƒttƒ |tdƒt ttƒ ƒ d ks^J ‚d S )Nr   ©Úexpand_func)Úfresnelsrk   )	Úsympy.core.functionrÏ   Ú'sympy.functions.special.error_functionsrÐ   rH   r3   rn   r-   r   )rÏ   rÐ   rh   rh   ri   Útest_issue_3686k  s
    *ÿrÓ   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ks<J ‚d S )Nrr   r   é   )rY   Úmrƒ   rH   rn   )rÕ   rƒ   rh   rh   ri   Útest_integrate_unitsr  s    rÖ   c                   C   s@   t tdt ƒtƒt ttdt ƒ  ttdt ƒ  ks<J ‚d S r¼   )rH   r   rn   rh   rh   rh   ri   Útest_transcendental_functionsx  s    $ÿr×   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s`J ‚d S )Nrr   r   rk   r«   rŠ   )rH   r"   rn   r   rh   rh   rh   ri   Útest_log_polylog}  s    .rØ   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 sXJ ‚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    rÜ   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  s    rÞ   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 r¼   r    rh   ©rc   rh   ri   rw     rx   z!test_issue_3952.<locals>.<lambda>)r3   rn   rH   r2   rZ   r   rh   rh   rß   ri   Útest_issue_3952Œ  s    rà   c                   C   s6   t dt dt  tƒdt tdƒ td  ks2J ‚d S r¼   ©rH   rn   r"   rh   rh   rh   ri   Útest_issue_4516’  s    râ   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sBJ ‚d S )Nrr   r   rŠ   rk   )
rH   r    r   rn   r   r   r   rº   r   r   )Úansrh   rh   ri   Útest_issue_7450–  s    rä   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sNJ ‚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s¼J ‚d S )Nrr   rk   ry   r   r   ©rH   r2   rn   r   r-   r1   r5   rV   rh   rh   rh   ri   Útest_issue_8623›  s    NFÿÿræ   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sˆJ ‚d S ©Nrr   rk   r   ry   rå   rh   rh   rh   ri   Útest_issue_9569¡  s    ,rè   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s¼J ‚d S )Nrƒ   TrÁ   rk   r   )
r   r    Úzr~   r-   r   rH   rn   r   r<   )rƒ   ZpzZpzgxrh   rh   ri   Útest_issue_13733¦  s    2>ÿÿrê   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sŒJ ‚d S rç   rå   rh   rh   rh   ri   Útest_issue_13749®  s    ,rë   c                   C   s<   t ttƒdt d  tƒtttƒtd d  tƒks8J ‚d S rÝ   )rH   r    rn   rX   rh   rh   rh   ri   Útest_issue_18133³  s    rì   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s²J ‚d S )Ng    €„NAgíµ ÷Æ>r   Tr|   gŽíµ ÷Æ >)r.   r   r    r   r•   r~   rn   ré   r   r   r   rH   )r–   r¬   ÚrZfunrh   rh   ri   Útest_issue_21741·  s    N ÿ$rî   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sVJ ‚d S )Nrk   c                 S   s    | | d t | | d t ƒ S rz   )r3   rn   )rˆ   Újrh   rh   ri   rw   Á  rx   ztest_matrices.<locals>.<lambda>ry   )rJ   rH   rn   r2   )ÚMrh   rh   ri   Útest_matricesÀ  s
    
þrñ   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sLJ ‚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s¨J ‚d S ©Nr   rr   rk   )rH   rc   rn   rW   r
   r"   rh   rh   rh   ri   Útest_integrate_functionsÉ  s     ,0ró   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sJJ ‚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 r¼   )rH   r   rc   rn   r~   rW   rh   rh   rh   ri   Útest_integrate_derivativesÑ  s
     *ÿrô   c                     sâ  t td d tddfƒ} t}dt d }|  ¡ |  ||¡ ¡ ksDJ ‚|  ||¡ ||¡| ks`J ‚dt d }t}|  ||¡ ||¡| ksŒJ ‚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sÔJ ‚|  tdt ¡ tdt ¡| ksøJ ‚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sLJ ‚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sÔJ ‚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rrdksxn J ‚t tt| t
fƒ‰ ˆ  tdt ¡t dt t| d t
d fƒksºJ ‚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s¤J ‚t tt| fƒ‰ ˆ  tdt ¡t dt t| d fƒksÞJ ‚d S )Nrk   rr   rŠ   ry   r   éüÿÿÿéýÿÿÿr}   c                      s   ˆ   td¡S rz   )Ú	transformrn   rh   ©rˆ   rh   ri   rw   õ  rx   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S rs   ©r÷   rn   rƒ   r•   rh   rø   rh   ri   rw   ö  rx   c                      s   ˆ   tt ¡S rs   ©r÷   rn   rƒ   rh   rø   rh   ri   rw   ÷  rx   c                      s   ˆ   tttf¡S rs   rù   rh   rø   rh   ri   rw   ø  rx   c                      s   ˆ   dt dt ¡S r¼   rú   rh   rø   rh   ri   rw   ù  rx   c                      s   ˆ   td t¡S r¼   rú   rh   rø   rh   ri   rw   ü  rx   r–   T)Únegativer¬   rÁ   )rW   rn   r~   r†   r÷   r3   r   r    r   ré   r¬   rƒ   rZ   r   r   )r–   ZfxZfyZ_3ÚamÚbprh   rø   ri   Útest_transformØ  sZ    0$8ÿ
  ÿ
ÿ
ÿ
ÿ22rþ   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sZJ ‚d S rÝ   )	r   rº   r0   rn   r-   rH   r2   r3   r/   rß   rh   rh   ri   Útest_issue_4052  s    &rÿ   c                  C   sŠ  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sLJ ‚t | d t ttddƒ  dƒdv stJ ‚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sŽJ ‚t tttdt ƒƒdt td   tddfƒdƒt ddƒksÐJ ‚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szJ ‚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sÀJ ‚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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 tdtd tddfƒ  dd!dd"d#v s®J ‚tttƒtd  tdtfƒjdd$}d%|  k rêd&k sðn J ‚t tttƒtd  tdtfƒd'd(d)ksJ ‚t tttt d ƒt tt d*fƒd'd(d+ksRJ ‚t tttƒƒd,ksjJ ‚t ttttfƒƒd-ks†J ‚d S ).Nrk   r   rd   z10.5000000000000z1.77245385090552rr   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r•   rª   ry   é   r}   é   éù   é6   éA   r   é2   é1   é¢   rÔ   z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))é`   zlog(2)/2-1/4T©Úchopzpi/4*log(4*pi**3/gamma(1/4)**4)rÌ   é   é   zsqrt(1-x**2)é   )Úmaxnr
  )z0.0Ú0)r  g\Âõ(\ß?gR¸…ëQà?Zosc)Zquadz0.504067061906928rŠ   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rj   rW   rn   r    r   r   r   r   r   r-   r1   r"   r3   r2   re   r~   )Úgaussr•   r–   r¬   r­   r   rc   rh   rh   ri   Útest_evalf_integrals  s¢    ÿÿÿ4,<,ÿ
0ÿ
4ÿÿÿ
ÿ
ÿÿÿÿ
4ÿ
(ÿÿ
(ÿÿ
(ÿÿ

ÿÿÿ
$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sVJ ‚t tdtd d  tddfƒdddks‚J ‚d S )	Nrr   r   r}   Tr	  )z-0.000976138910649103z0.965906660135753z1.93278945918216rk   z0.0144361088886740)rj   rH   rn   rÛ   rW   rh   rh   rh   ri   Útest_evalf_issue_939C  s    $ÿ(ÿÿr  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdks6J ‚| tddƒdtdƒ d  ksXJ ‚t tttt  ƒtddftddfƒtju s†J ‚d S )	Nrr   rk   rŠ   rd   z2.43790283299492rõ   ry   rª   )	rH   r-   rn   r~   rj   r   r3   r   r—   ©Úresrh   rh   ri   Ú(test_double_previously_failing_integralsR  s    $"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sFJ ‚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s˜J ‚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sLJ ‚t|tƒ|ks`J ‚tt|tfƒstJ ‚t|tƒt|tfƒksJ ‚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 d
t tddƒ  }t|tt tfƒ|ksJ ‚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sPJ ‚tdt tddƒ tt tfƒdksxJ ‚tt tddƒt	tƒ tt tfƒt	dƒks¨J ‚d S )Nry   r   rŠ   r}   r   rŒ   iúÿÿÿr|   rr   rk   rõ   r’   rª   )
rE   rn   r–   rH   r~   rU   rW   r†   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 $$$(r  c                  C   s   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sPJ ‚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s J ‚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r–t | tdt t ƒ tt tftt tfƒ  kr–t | tdt t ƒ tt tftt tfƒ  kr–dtdt ƒ ksœn J ‚d S )Nr   rk   r}   rr   rŒ   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   sj  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sxJ ‚t ttt ƒtƒtttt ƒt ttdƒftdfƒks²J ‚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s^J ‚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sªJ ‚t ttt ƒtƒtt	tt ƒt ttdƒftdfƒksæJ ‚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sBJ ‚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s¢J ‚t t	tt ƒtƒtttt ƒ t ttdƒfdƒksÜJ ‚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s4J ‚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sŠJ ‚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sæJ ‚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sfJ ‚d S )Nrr   rŠ   Tr   rk   ©r   T)rH   rn   r~   r.   r   r"   r    r`   r2   r3   ré   r   r•   r-   rh   rh   rh   ri   Ú test_integrate_returns_piecewise‹  sZ    &ÿ
"ÿ
ÿ
:ÿ2ÿ.ÿÿ:ÿ>ÿÿ6ÿ4ÿ8ÿ$<ÿþr  c                  C   sv  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sVJ ‚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sªJ ‚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rltt	ƒ| t
|ƒ d tt	ƒ| d  t|d  ƒd  ksrn J ‚d S )Nrn   Tr¤   rk   r   ry   r}   r  rÔ   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   s8  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sfJ ‚t ttd d ƒtddfƒdksŠJ ‚t ttd dt  ƒtdd	fƒd
ks²J ‚t ttƒtddfƒdksÎJ ‚t ttƒttƒ tt tfƒdksôJ ‚t ttd ƒtd  tddfƒtddƒks$J ‚t	ddd\} }t t| ƒ| ƒt
| d  d | dkf| d d dfƒkspJ ‚t td|  d ƒ| ƒt
| d  d|   | dkf| d d|   d dfƒksÀJ ‚t t| |d  ƒ| ddfƒd|d  td|d ƒ d|d   td|d ƒd  d ksJ ‚t tt| ƒ ƒ| ƒt
t| ƒ| dkfdt|  ƒ dfƒks\J ‚t td|  d ƒ| ƒt
|  | dk f| d dfƒks”J ‚t d|  t| d d ƒ | ƒt
| d | dk f| d  d | dk f| d dfƒksêJ ‚t t| ƒ| |d fƒt
|d |d dkf| d |d dk fdƒks4J ‚d S )Nr|   rr   r   rk   r   ry   r}   éñÿÿÿrd   iÓ  rŠ   r  zt sTr¤   r«   é   r  )rH   r   rn   r   r   rº   r   r3   r   r   r.   rÚ   r,   r    )r•   rƒ   rh   rh   ri   Útest_integrate_Abs_sign»  s<    "&$(&0"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s4J ‚t ttt ƒtddfƒ} |  td¡t ttd ƒtddfƒkstJ ‚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sÚJ ‚d S ©Nry   r   rr   rk   r|   )rW   r    rn   r~   rÛ   r	   r   ©rf   rc   Úconvrh   rh   ri   Ú
test_subs1Ö  s    "("r"  c                  C   s  t ttt ƒttƒ} |  td¡t ttd ƒttƒks8J ‚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sˆJ ‚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sþJ ‚d S r  ©rW   r    rn   r~   r•   rÛ   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sPJ ‚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sÆJ ‚d S ©Nr   rr   ry   rk   r|   r#  r   rh   rh   ri   Ú
test_subs3ê  s
     0*r&  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sHJ ‚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sºJ ‚d S r%  r#  r   rh   rh   ri   Ú
test_subs4ò  s
    ,&r'  c                  C   sÀ  t ttd  ƒtt tfƒ} |  td¡| ks0J ‚t ttd  t ƒtƒ} |  td¡t ttd  d ƒtƒkspJ ‚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sÞJ ‚t ttd  t ƒtt tftt tfƒ} |  td¡| ksJ ‚|  td¡| ks4J ‚t ttd  ƒttfƒ} |  td¡t ttd  ƒtdfƒksvJ ‚t ttƒtƒ} |  td¡|  td¡ t ttƒtddfƒ  ¡ js¼J ‚d S )Nrk   r   rr   r   )rW   r    rn   r   rÛ   r~   r†   Úis_zero©rf   rh   rh   ri   Ú
test_subs5ú  s    (*(**r*  c                  C   s  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sTJ ‚| 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säJ ‚| td¡ttt tttƒttƒftttƒtdƒfƒks"J ‚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sŒJ ‚d S )Nza brr   )r   rW   rn   r~   rc   rÛ   )r–   r¬   rf   rh   rh   ri   Ú
test_subs6  s    ,(,<>,r+  c                  C   s¶   t ttdtftddfƒ} |  tdtdi¡| ks2J ‚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svJ ‚|  ttƒd¡t ttƒttƒ tdttƒftddfƒks²J ‚d S rÝ   )rW   rn   r~   rÛ   r3   r)  rh   rh   ri   Ú
test_subs7  s     ÿ*ÿr,  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sXJ ‚t ttƒttd ƒ tdtfƒ} |  ¡ | ksˆJ ‚| jddt ttƒtdtfƒt ttd ƒtdtfƒ ksÄJ ‚d S )Nrk   rr   T)Úforce)rW   rc   rn   r~   r‡   r   r)  rh   rh   ri   Útest_expand"  s     8 ÿr.  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   ry   )rW   r    rn   rh   rh   rh   ri   rw   ,  rx   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   -  rx   )rZ   r   rh   rh   rh   ri   Útest_integration_variable+  s    r0  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slJ ‚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sÆJ ‚d S )Nrk   rr   r   )rW   r2   rn   r3   r‡   rh   rh   rh   ri   Útest_expand_integral0  s    *"ÿÿ$ÿÿr1  c                      sN  t ttd d ƒtddfƒ‰ ˆ jddddtdƒ ks:J ‚ˆ jdddd	td
ƒ dtdƒ  ksdJ ‚ˆ jddddtdƒ d dtdƒ d  dtdƒ d  ks¦J ‚ˆ jd	dddtdƒ d	tdƒ  d	tdƒ  dtdƒ  ksèJ ‚tˆ jd	dd ¡ ˆ  ¡  ƒdk sJ ‚t ttd td  ƒtddftddfƒ‰ tt‡ fdd„ƒ d S )Nry   rr   rk   rŒ   Úmidpoint©Úmethodrª   éÙ   r}   r  rÔ   é9   i	  é   iIÎ  iÚ  r’   éV   r«   é   g      à?r   c                      s
   ˆ   d¡S )Nr}   ©Úas_sumrh   r)  rh   ri   rw   D  rx   z'test_as_sum_midpoint1.<locals>.<lambda>)	rW   r-   rn   r;  rÚ   r`   r~   rZ   ÚNotImplementedErrorrh   rh   r)  ri   Útest_as_sum_midpoint19  s$    *ÿÿ

ÿ
ÿ
ÿ
((r=  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sRJ ‚| 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sªJ ‚| jd	dd ¡ tddƒt td  ksÖJ ‚| j|dd ¡ td t tddƒ dd|d    ksJ ‚d S )Nrk   r   rr   r`   T©rÂ   rb   r2  r3  r}   r   r   ry   é#   él   é   é@   rÔ   )rW   rn   r~   r   r;  r‡   r   rš   rh   rh   ri   Útest_as_sum_midpoint2G  s    ,,,,$ÿrC  c                  C   sD  t tt d tddfƒ} | jddd ¡ td ks6J ‚| jddd ¡ tddƒtd  td  ksfJ ‚| jddd ¡ tdd	ƒttddƒ  td  ksœJ ‚| jd
dd ¡ tddƒttdd
ƒ  td  ksÒJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks$J ‚| jdddd t¡s@J ‚d S )Nrk   r   rr   Úleftr3  rª   ry   r   r7  r}   r’   é    r«   rŒ   F)r4  Úevaluate)	rW   rn   r~   r;  r‡   r   r`   Úhasr   r)  rh   rh   ri   Útest_as_sum_leftR  s    0668ÿ
rH  c                  C   s:  t tt d tddfƒ} | jddd ¡ ddt  td  ksBJ ‚| jddd ¡ tddƒttddƒ  td  ksxJ ‚| 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säJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks6J ‚d S )Nrk   r   rr   Úrightr3  r   rª   ry   r9  r7  r}   rd   rE  r«   )rW   rn   r~   r;  r‡   r   r`   r)  rh   rh   ri   Útest_as_sum_right]  s    *6668ÿrJ  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slJ ‚| jddd ¡ td t tdd	ƒ ks˜J ‚| jd
dd ¡ td t tddƒ ksÄJ ‚| 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	trapezoidr3  ry   rª   é   r  r}   r  rE  r«   )
rW   rn   r~   r;  r‡   r   rº   r   r`   r   r)  rh   rh   ri   Útest_as_sum_trapezoidg  s    (,,,$ÿ
rL  c                      sr   t tt d tddfƒ‰ tt‡ fdd„ƒ tt‡ fdd„ƒ ttdd„ ƒ tt‡ fdd„ƒ tt‡ fd	d„ƒ d S )
Nrk   r   rr   c                      s
   ˆ   d¡S )NrŠ   r:  rh   r)  rh   ri   rw   t  rx   z$test_as_sum_raises.<locals>.<lambda>c                      s
   ˆ   d¡S ©Nr   r:  rh   r)  rh   ri   rw   u  rx   c                   S   s   t tƒ d¡S )Nry   )rW   rn   r;  rh   rh   rh   ri   rw   v  rx   c                      s
   ˆ   t¡S rs   )r;  r   rh   r)  rh   ri   rw   w  rx   c                      s   ˆ j dddS )Nry   Zxxxx2r3  r:  rh   r)  rh   ri   rw   x  rx   )rW   rn   r~   rZ   r   rh   rh   r)  ri   Útest_as_sum_raisesr  s    rN  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ks0J ‚d S rs   )rW   rn   r†   ©rf   rc   rh   rh   ri   Útest_nested_doit{  s    rP  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sTJ ‚t tt td tfƒ tt¡t tt td tfƒksˆJ ‚t tt ttd fƒ tt¡t tt ttd fƒks¼J ‚ttd td dfƒtddƒksÞJ ‚ttd tdd fƒtddƒksJ ‚tddƒtddƒksJ ‚d S )Nrk   rr   ry   rŠ   zx**2)rn   Ú1N)rW   rn   r†   r   r~   rÛ   r•   rH   rO  rh   rh   ri   Útest_issue_4665  s    44"$rR  c                  C   s*   t td tddfƒ} | t | jŽ ks&J ‚d S )Nrk   rŠ   rr   )rW   rn   Úargsr)  rh   rh   ri   Útest_integral_reconstructŽ  s    rT  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sHJ ‚tdƒ}t |tƒtddfƒ ¡ dkspJ ‚t dtdt |tƒtƒfƒ ¡ dks–J ‚t ttdfƒ ¡ dks°J ‚tdttƒftdff}t tg|¢R Ž  ¡ tddƒksèJ ‚t tgtt|ƒƒ¢R Ž  ¡ dksJ ‚d S )	Nrk   r   rr   ry   F©Údeeprc   r}   )	rW   rn   r†   r   r   r–   r    ÚlistÚreversed)rf   rc   rŽ   rh   rh   ri   Útest_doit_integrals“  s     &"rY  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sÈJ ‚t tt dttƒ  ƒtt ksìJ ‚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rZ  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s®J ‚d S )Nrk   rr   rŠ   T)rH   rn   r`   r"   r.   r   rh   rh   rh   ri   Útest_issue_18153«  s    *&ÿÿþýÿr[  c               	   C   sœ  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 sRJ ‚td| ddfƒjdu slJ ‚td| d|fƒjdu s†J ‚td| |fƒjdu sžJ ‚t| |ƒjdu s²J ‚t| |d| fƒjdu sÌJ ‚t| |ddfƒjdu sæJ ‚t| | ddfƒjdu sJ ‚t| |ddfƒ}|jdu r,| ¡ dks0J ‚t| |||fƒ}|jdu rZ| ¡ dks^J ‚td|||d fƒ}|jdu rŒ| ¡ dksJ ‚t| | | ddf|ddfƒjdu s¸J ‚t| | | ddf|d|fƒjdu sàJ ‚t| | dfƒjdu súJ ‚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 sJJ ‚tt| ƒd t	| ƒd  d | ƒjdu sxJ ‚tt
| ƒ| ddfƒjdu s˜J ‚d S )	Nr   ©rn   r~   ré   Frr   Trk   rÉ   ry   )Ú	sympy.abcrn   r~   ré   rW   Z	is_numberr`   r   r3   r2   rc   )rn   r~   ré   rˆ   rh   rh   ri   Útest_is_number´  s0    ((((.r^  c                  C   sj  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sZJ ‚t| | |d fƒj|hksvJ ‚t| | d|fƒj|hks’J ‚t| | |dfƒj|hks®J ‚t| | | |fƒj| |hksÌJ ‚t| | |ƒj| |hksæJ ‚t| | ddfƒjtƒ ksJ ‚t| |ddfƒj| hks"J ‚t| |||fƒj| |hksBJ ‚t| |ddf|d d fƒj| |hksjJ ‚t| |ddf| d|fƒj|hksJ ‚td|ddf|d| f| ddfƒjtƒ ks¾J ‚td|| df|d| f| ddfƒjtƒ ksìJ ‚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sfJ ‚d S )Nr   r\  rr   rk   )r]  rn   r~   ré   rW   r…   Úsetrc   r\  rh   rh   ri   Útest_free_symbolsÔ  s:     ÿ
ÿ
 ÿ
 ÿ
 ÿ
&r`  c                  C   s2  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spJ ‚t| | |dfƒjd u sŒJ ‚t||dt| ƒf| dfƒ}|jd u s´J ‚t|| df|dt| ƒfƒjdu sØJ ‚t| | ttfƒjsîJ ‚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   rÕ   rr   rk   FT)
r]  rn   rÕ   rW   r(  r~   r    r   r3   r   )rn   rÕ   rˆ   rh   rh   ri   Útest_is_zeroð  s     $ra  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sXJ ‚d S )Nr   ©rn   rª   rÊ   c                    s   g | ]}t ˆ ƒ‘qS rh   )Únext)Ú.0rï   r)  rh   ri   Ú
<listcomp>  rx   ztest_series.<locals>.<listcomp>r}   )	r]  rn   rW   r2   ZlseriesZnseriesZremoveOr   Úrange)rn   rˆ   rh   r)  ri   Útest_series  s    
rg  c                  C   sV   t dƒ} tdt| ƒ |  | ƒt| ƒt| ƒ ks2J ‚tt| ƒd |  | ƒ t¡sRJ ‚d S )Nrn   rr   rk   )r   rH   r3   r"   r;   r2   rG  r9   rb  rh   rh   ri   Ú!test_trig_nonelementary_integrals
  s    *rh  c               	   C   s4  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snJ ‚tt| d |d  ƒ| ƒ| t| d |d  ƒ d |d t| t| d |d  ƒ ƒ d  ksÐJ ‚t ddd} t ddd}td| d |d  td	ƒ  | ƒ| |d t| d |d  ƒ  ks0J ‚d S )
Nrn   r~   ré   TrÁ   rk   r¤   rr   z3/2)r   rH   r-   r$   r"   r   r\  rh   rh   ri   Útest_issue_4403  s    2ÿBÿ ÿri  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sPJ ‚d S )Nrk   r}   r|   rõ   )rH   r-   rn   r1   rh   rh   rh   ri   Útest_issue_4403_2#  s    2ÿrj  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RTrÁ   rk   r   r}   )r   rH   r-   rn   r   )rk  rh   rh   ri   Útest_issue_4100(  s    rl  c                  C   sÐ  ddl m} m}m}m} tdƒ}tt||ƒ|ƒ|ƒt||ƒ||ƒksHJ ‚t||ƒƒj||ƒt|ƒfksjJ ‚tt||ƒƒƒj||ƒt|ƒt|ƒfks–J ‚tt||ƒƒ|ƒj||ƒt|ƒt|ƒfksÄJ ‚tt||ƒ|ƒ|ƒj||ƒt|ƒt|ƒfksôJ ‚ttt||ƒ|ƒ|ƒ|ƒj||ƒt|ƒt|ƒt|ƒfks2J ‚t	t||ƒ|ƒ|ƒt||ƒ||ƒks\J ‚t	t||ƒ|ƒ|ƒ|t||ƒ|ƒ ksˆJ ‚t	t||ƒ|ƒ|ƒt|||ƒ |ƒ|t||ƒ|ƒ fv sÆJ ‚t	td|ƒ|ƒ|d ksäJ ‚t	td|ƒ|ƒd| | ksJ ‚td||ƒjtd||ƒjks(J ‚t||ƒ||||ƒ 
¡ |d t||ƒ||ƒ d ksbJ ‚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sÌJ ‚d S )Nr   )Úwrn   r~   ré   rc   rk   rr   )r]  rm  rn   r~   ré   r   rW   rS  r   rH   r†   )rm  rn   r~   ré   rc   rh   rh   ri   Útest_issue_5167-  s(    (",.0ÿ
*,>"":&:ÿrn  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sTJ ‚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sšJ ‚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sJ ‚d S )Nré   TrÁ   rk   rr   r}   rŠ   )r   rH   r    r"   rn   r-   r   r   r<   r   rº   r>   ©ré   rh   rh   ri   Útest_issue_4890D  s    *ÿ*ÿFÿrp  c                   C   s,   t dttdtd  ƒ  tƒ t¡r(J ‚d S rÝ   )rH   rn   r-   rG  rW   rh   rh   rh   ri   Útest_issue_4551N  s    rq  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sŒJ ‚d S )Nr`   T©rb   rÂ   rr   r   rk   )r   rQ   rH   rn   r   rº   rÊ   rh   rh   ri   Útest_issue_4376R  s    "Nÿÿrs  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sTJ ‚d S )Nry   rr   r«   r’   r  )rH   r-   rn   r   rh   rh   rh   ri   Útest_issue_4517X  s    "*ÿrt  c               
   C   sü  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s¦J ‚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søJ ‚d S )Nzk mTra   r   rk   r  )
r   rH   r3   rn   r   rQ   r.   r   rI   r2   )ÚkrÕ   rh   rh   ri   Útest_issue_4527]  s$    &($ýÿ \X**ÿÿürv  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slJ ‚d S )Nr~   TrÁ   rk   rÃ   rÄ   )r   rH   r    r   r   rn   r   rW   )Zyposrh   rh   ri   Útest_issue_4199r  s    .*ÿrw  c                  C   s²  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slJ ‚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  ¡sàJ ‚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sHJ ‚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s®J ‚d S )
Nza:dTrÁ   rk   r}   r   )Ú
expand_mul)ru  za d)r   rH   r    rn   r   r-   r   r<   Úequalsr>   rÑ   rx  r]  ru  r   )r–   r¬   r­   r   rx  ru  rh   rh   ri   Útest_issue_3940y  s     2ÿ"Jÿ.ÿ
.ÿrz  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sRJ ‚d S r¼   )rH   r–   rn   r   r"   rh   rh   rh   ri   Útest_issue_5413‰  s    r{  c               
   C   sº  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 s¶J ‚d S )NzA zr­   T)rÈ   rk   rr   )
r   r   r    r•   r3   rn   r2   r~   rH   r"   )r§   ré   r­   ZP1ZP2Úh1Úh2rh   rh   ri   Útest_issue_4892a  s    &00,,..úr~  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sXJ ‚d S )Nry   rk   rÔ   r   )r3   r~   rn   r2   rR   rL   rH   r
   )Úexprrh   rh   ri   Útest_issue_4892b¤  s    	4r€  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sTJ ‚d S ©Nr   rk   )rH   r3   rn   rc   r~   ré   r   rW   rh   rh   rh   ri   Útest_issue_5178±  s    , ÿr‚  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slJ ‚tt| tƒtƒ| ks„J ‚tttd ƒtƒttd ƒks¦J ‚d S )Nr   rŒ   rk   r}   é   r«   iÐ  rª   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.heurischrˆ  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sdJ ‚d S )Nré   F©Zzeror   rk   )
r   rH   r3   rn   r~   r   r€   r"   r9   r   ro  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   rG  rW   ru   rh   rh   ri   Útest_issue_4703Ë  s    rŒ  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡s*J ‚d S )Nrc   rk   )r   rH   rn   r
   rG  rW   rß   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sBJ ‚d S )Nrk   r   )rH   r2   rn   r~   r   r;   rh   rh   rh   ri   Útest_issue_3558×  s    rŽ  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ks2J ‚d S )Nrr   r   r}   rk   )rH   r-   rn   r$   rh   rh   rh   ri   Útest_issue_4422Û  s    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sJJ ‚d S )Nrr   rk   r«   rd   )rQ   rH   rn   r-   rh   rh   rh   ri   Útest_issue_4493ß  s    &ÿr  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sFJ ‚t ttƒt tƒttƒksdJ ‚d S r  )rH   r3   rn   r   r   r;   rh   rh   rh   ri   Útest_issue_4737ä  s    "$r‘  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sdJ ‚d S )Nr   rÎ   r–   TrÁ   rr   )rÑ   rÏ   r   rQ   rH   r    rn   r"   r   rB   rA   )rÏ   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    r–  c                  C   s,   t dƒ} td| d  | ddfƒtu s(J ‚d S )Nrn   rr   rk   rŠ   )r   rH   r   rb  rh   rh   ri   Útest_issue_4215÷  s    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sœJ ‚d S )Nr`   Trr  rk   rr   )r   rH   rn   r"   rÊ   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sVJ ‚d S )Nrr   rk   T©rD   )rH   r-   rn   rW   rh   rh   rh   ri   Útest_issue_6253  s    (&ÿrš  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 säJ ‚d S )Nrr   r   iôÿÿÿry   r«   rk   rª   r   r’   r}   r7  r  é/   ©rH   rn   r~   ré   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¡rTJ ‚| t¡rbJ ‚d S )NzR b hrk   )r   rH   rn   r-   rG  r   rW   )rk  r¬   Úhrf   rh   rh   ri   Útest_issue_4326  s    8rŸ  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/  rá   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¡s8J ‚d S )Nc                   S   s   t dt tdddS )Nrr   T)ÚmanualrD   r    rh   rh   rh   ri   rw      rx   z$test_manual_option.<locals>.<lambda>rr   r   T©r¡  )rZ   r   rH   r"   rn   rG  rW   rh   rh   rh   ri   Útest_manual_option  s    r£  c                   C   s6   t tdd„ ƒ tttƒtddtttƒtƒks2J ‚d S )Nc                   S   s   t dt tdddS )Nrr   T)rD   Úrischr    rh   rh   rh   ri   rw   &  rx   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s‚J ‚tttƒtddt	ttƒtƒks¦J ‚d S )Nc                   S   s   t dttƒ tdtfddS )Nrr   r   T©r¤  )rH   r"   rn   r   rh   rh   rh   ri   rw   -  rx   z#test_risch_option.<locals>.<lambda>rk   Tr¦  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shJ ‚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   s   t dt tdddS )Nrr   T)r¤  rˆ  r    rh   rh   rh   ri   rw   6  rx   z&test_heurisch_option.<locals>.<lambda>rk   Tr‡  ry   r}   Fi€ÿÿÿrr   i!  éð   r   rÌ   )rZ   r   rH   r    rn   r-   r   r>   rW   r"   r2   r   r3   rh   rh   rh   ri   Útest_heurisch_option4  s    .,*BJÿÿr©  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |dds6J ‚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    rª  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sTJ ‚d S )NÚx_max)r   rH   r~   r   r    rn   r2   r–   )r«  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 rÝ   )rH   r-   r5   rn   rh   rh   rh   ri   Útest_issue_4234M  s    r­  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   TrU  rd   ry   é   rª   iøÿÿÿ)	rQ   rH   rn   r-   rL   r.   r   r#   r0   rh   rh   rh   ri   Útest_issue_4492Q  s     "ÿJÿÿFÿÿýÿr¯  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spJ ‚td|  ttƒ tddfƒd| tdƒ tdƒ ks¨J ‚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   ry   g333333ó?r   g333333ó¿)r–   ré   r"   rX   rW   r†   rH   r    r`   rƒ   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      $@gš™™™™™¹?gš™™™™™É?z%1.86831064982608*y + 2.16387491480008)rn   r~   r    rH   Ústr)rc   rf   rh   rh   ri   Útest_issue_2884h  s     r²  c                  C   s–  ddl m} m} ttt t ƒttƒ tdtfƒt	t
t	t t
td  d   |td ƒdk fdt
t ddtd     |td ƒdk fttjfdfdtjfdfttƒd ƒdfƒ td dkfttt t ƒttƒ tdtfƒdfƒksìJ ‚ttt t ƒttƒ tdtfƒt	d	td  d dt d  d  t|tƒdk|| tƒƒt
d k || tƒƒt
d kƒfttt t ƒttƒ tdtfƒdfƒks’J ‚d S )
Nr   ©Úargr   rk   rr   r|   )r   r   )r   TrŠ   )Ú$sympy.functions.elementary.complexesr´  r   rH   r    rƒ   rn   r%   r   r.   r   rD   r   rº   r   rW   r(   rI   r³  rh   rh   ri   Útest_issue_8368in  sN     ÿÿ

ýüû
õ þòÿ  
ýÿ ÿùÿr¶  c                   C   s€   t tdt ƒƒdtdt ƒ ks$J ‚t tdt ƒƒdt dttdt ƒd ƒ  ksXJ ‚t ttƒƒttttƒd ƒ ks|J ‚d S )Nç      ð?rr   )rH   r(   rn   r%   r)   r"   rh   rh   rh   ri   Útest_issue_8901Ž  s    $4r¸  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sfJ ‚t ttƒd td  tƒtdt ƒ tdt ƒdt   ddt   ks²J ‚d S )Nry   r   rr   r}   rk   )rH   r3   rn   r;   r   r   r2   rh   rh   rh   ri   Útest_issue_8945”  s    >(r¹  c                  C   sX   t dƒ\} }}}tt|  t | ƒd ||t    t¡}tt|td|fƒjvsTJ ‚d S )Nzi L a brk   r   )r   r2   r   rn   Zrewriter    rH   r…   )rˆ   ÚLr–   r¬   Ú	integrandrh   rh   ri   Útest_issue_7130›  s    *r¼  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stJ ‚d S )Nza b c trk   )r   rJ   rH   rW   r†   )r–   r¬   r­   r•   Zvtrh   rh   ri   Útest_issue_10567¢  s    r½  c                   C   s6   t ttd  dt  d ƒtddfƒdt ks2J ‚d S )Nrk   rª   é0   r}   rÔ   r   )rH   r-   rn   r   rh   rh   rh   ri   Útest_issue_11742©  s    r¿  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    rÀ  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    rÂ  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sRJ ‚d S )NiÄÿÿÿg3333333@r}   g333333Àrª   g      (@r   )rH   r    rn   rh   rh   rh   ri   Útest_issue_4950·  s    ,ÿrÃ  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sLJ ‚d S )Nrk   r   )rH   r3   r"   rn   r2   rh   rh   rh   ri   Útest_issue_4968¼  s    rÄ  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 sBJ ‚t dtd d  tddfƒtu sfJ ‚t dtd  tddfƒt u sˆJ ‚t dtd d  tddfƒt u s®J ‚d S )Nrr   rk   rŠ   r|   )rH   rn   r   rh   rh   rh   ri   Útest_singularitiesÀ  s
    " $"rÅ  c                  C   s¸   t ddd\} }tt| |  |  ||  ƒ| tt||  ƒ tt||  ƒf|ttƒ ttƒfƒtt| d |d  ƒ| t|d  t ƒ t|d  t ƒf|ttƒ ttƒfƒks´J ‚d S )Nzx yTr¤   ry   rk   )r   rH   r3   r-   r   rW   )rn   r~   rh   rh   ri   Útest_issue_12645É  s    "þ&þýrÆ  c                   C   s6   t ttƒttƒd  tdtd fƒtddƒks2J ‚d S )Nry   r   r«   rr   )rH   r3   rn   r2   r   r   rh   rh   rh   ri   Útest_issue_12677Ó  s    rÇ  c                   C   s6   t tdt ƒttƒ t tdtfƒtdƒ ks2J ‚d S )Nry   r   )rH   r2   rn   r   r"   rh   rh   rh   ri   Útest_issue_14078×  s    rÈ  c                   C   s(   t dttƒ tdtfƒtd ks$J ‚d S rÁ  )rH   r%   rn   r   r   rh   rh   rh   ri   Útest_issue_14064Û  s    rÉ  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slJ ‚d S rz   )rH   r    rn   r   rº   r"   r   rh   rh   rh   ri   Útest_issue_14027ß  s    &>ÿrÊ  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  s    rÌ  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   rŠ   r|   ry   )rH   rn   r   r”   rh   rh   rh   ri   Útest_issue_8440_14040è  s    rÍ  c                   C   s”   t dtt d  tddfƒdtd  dt  ks4J ‚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sJ ‚d S )
Nrr   rk   r   rŠ   rõ   r}   r«   r¯   ry   rœ  rh   rh   rh   ri   Útest_issue_14096í  s    42"ÿrÎ  c                   C   sh   t tdtdtd  ƒ tddfƒ ¡ d ƒdk s4J ‚t ttdtd  ƒtddfƒ ¡ d ƒdk sdJ ‚d S )Nrr   ry   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rn   r`   rh   rh   rh   ri   Útest_issue_14144ó  s    4rÏ  c                   C   s(   t ttt ƒttƒ tƒ t¡s$J ‚d S rs   )rH   r    r   rn   r"   rG  r:   rh   rh   rh   ri   Útest_issue_14375ø  s    rÐ  c                  C   sX   t dƒtttƒ} t| tddftddftddfƒt| tddftddftddfƒksTJ ‚d S )Nrc   r   rr   rk   ry   )r   rn   r~   ré   rH   rW   rß   rh   rh   ri   Útest_issue_14437þ  s    ÿrÑ  c                   C   sR   t dtttƒd ƒ tƒttttƒd ƒd ƒttttƒd ƒd ƒ ksNJ ‚d S rz   ©rH   r-   r    rn   r"   rh   rh   rh   ri   Útest_issue_14470  s    rÓ  c                  C   s¨   t dt td ƒt  dtd   ƒdtd  t  dt td ƒt  d  } t| tƒt dtd  tt td ƒ  d ƒ tt dtd  ƒ t dtd  ƒ  ks¤J ‚d S ©Nrr   rk   ry   )r    rn   rH   rß   rh   rh   ri   Útest_issue_14877  s    LHÿrÕ  c                  C   sB   t td  d ƒtd  t  } t| tddgƒt d ks>J ‚d S )Nrk   rr   rŠ   rª   )r-   rn   rH   r   rß   rh   rh   ri   Útest_issue_14782  s     rÖ  c                  C   sJ   t td  d ƒtd  t  } t| tddgƒtjd td  ksFJ ‚d S )Nrk   rr   r   ry   r   )r-   rn   rH   r   r˜   r   rß   rh   rh   ri   Útest_issue_14782_slow  s     r×  c                  C   s4   t tddƒ tt  ƒ } t| t dtgƒtu s0J ‚d S )Nrö   rk   r   )rn   r   r    rH   r   rß   rh   rh   ri   Útest_issue_12081  s    rØ  c                  C   sD   dt  d } d|  td|  ƒ t d  }t|t ddgƒdks@J ‚d S )Nrr   r}   r|   rk   r   )rn   r    rH   )r~   rc   rh   rh   ri   Útest_issue_15285  s    rÙ  c                   C   s”   t tt tt ƒ ttƒ tdtfƒ ¡ tttd ƒt	dtƒ ttd ƒt  t
tƒd dkfttt tt ƒ ttƒ tdtfƒdfƒksJ ‚d S )Nr   rr   T)rH   rn   r`   r    r"   r   rP   r.   rA   rB   r   rW   rh   rh   rh   ri   Útest_issue_15432$  s    *4(þrÚ  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clsrÃ   rÄ   )rT   r   rS   rH   r    rn   r   )rÛ  rÕ   rp   rh   rh   ri   Útest_issue_15124*  s
    $<ÿrÝ  c                   C   s†  t ƒ  ttttƒƒ W d   ƒ n1 s*0    Y  t ƒ : ttttƒtƒttttƒtttƒƒksfJ ‚W d   ƒ n1 sz0    Y  t ƒ > ttttƒtƒ ¡ ttd d tt ƒksºJ ‚W d   ƒ n1 sÎ0    Y  ttdd< tttƒ t¡ttd d tt ƒksJ ‚W d   ƒ n1 s(0    Y  ttttƒtddfƒtt	j
tƒksZJ ‚tttƒ tddf¡tt	j
tƒks‚J ‚d S )Nrk   Frm   r   rr   )r\   rW   r   rn   r~   r†   r]   r^   rH   r   rº   rh   rh   rh   ri   Útest_issue_152181  s    ,HLL(rÞ  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sLJ ‚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   r¶   r.   rP   r-   r   rÛ   r  rh   rh   ri   Útest_issue_15292B  s    >rß  c                   C   s.   t tdt ƒttƒ tƒdttƒ ks*J ‚d S r¼   )rH   r3   rn   rh   rh   rh   ri   Útest_issue_4514H  s    rà  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sfJ ‚| | d¡| | d¡ ddt  ksŽJ ‚| |d|d	i¡tdƒ td
ƒ ks¶J ‚| | d	¡| | d¡ tdƒ td
ƒ ksäJ ‚d S )Nzx a bTr¤   rk   rr   ry   r|   rö   rŠ   r   )r   rH   r    r   rÛ   r   )rn   r–   r¬   ZdefiniteZ
indefiniterh   rh   ri   Útest_issue_15457L  s    "((rá  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sJJ ‚d S rs   )rH   rn   r    r"   r:   rh   rh   rh   ri   Útest_issue_15431V  s    *ÿrâ  c                  C   sü   t tt ƒ } tdtt ƒ ƒ}t| t ƒ|kr8| 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r’| t ¡| ks–J ‚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rô| t ¡| ksøJ ‚d S )Nrk   ry   r}   )rn   r"   r:   rH   r
   r-   r   r=   )rc   ÚFrh   rh   ri   Ú"test_issue_15640_log_substitutions[  s     & .rä  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s¤J ‚d S )Nr   )Ú
CoordSys3DÚNTr‡  )Zsympy.vectorrå  rn   rH   r2   r–   r¬   Úx_1Úx_2r.   r3   r   r   )rå  ræ  rn   rh   rh   ri   Útest_issue_15509g  s     Dþré  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sžJ ‚d S )
Nrn   Tr¤   r¯   rk   r}   rö   éQ   ry   )r   rH   rÚ   r.   r   rb  rh   rh   ri   Útest_issue_4311_fastp  s    ".ýrë  c               	   C   sè  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s¾J ‚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snJ ‚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säJ ‚d S )NÚKTrÁ   rn   r¤   rÕ   r•   rk   r}   r|   rr   r   )	r   rH   r    r   r-   r   r>   r"   r<   )rì  rn   rÕ   r•   rh   rh   ri   Ú%test_integrate_with_complex_constantsx  s"    6ÿ,ÿÿ
>"ÿBFrí  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stJ ‚d S )Nrn   r`   Tr>  rr   rk   )r   rH   rF   r!   r   r   rA   )rn   r`   rh   rh   ri   Útest_issue_14241‡  s
    :ÿrî  c                   C   s<   t ttƒd ddttƒ   tddt gƒtd ks8J ‚d S )Nrk   r   r}   r   )rH   r3   r•   r2   r   rh   rh   rh   ri   Útest_issue_13112Ž  s    rï  c                  C   sP   t ddd} tttddt |   ƒ td| fƒ}|d| d  t d ksLJ ‚d S )	Nrž  TrÁ   rr   rk   r   r   r   )r   rH   rn   r/   r   )rž  rˆ   rh   rh   ri   Útest_issue_14709b’  s    $rð  c                  C   sl   t dƒ} t dƒ}tt|ƒ| |t | fƒt| ƒks6J ‚tt|  ƒtd|  ƒ |  | dtfƒtdƒkshJ ‚d S )Nrn   r•   r|   r   rk   )r   rH   r    r   r:   r"   )rn   r•   rh   rh   ri   Útest_issue_8614˜  s    &rñ  c                  C   sò   t ddd} t| d ƒdtd|  ƒ  t| ƒ t| ƒ }t|| ƒ}|tjksPJ ‚t| | d¡d ƒdkslJ ‚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sîJ ‚d S )Nrƒ   TrÁ   rk   gš™™™™™ù?rr   gÏRt?,eÀç:Œ0âŽyE>rª   r   iöÿÿÿé   ry   )r   r    rH   r   r”   rÚ   rÛ   )rƒ   r»  Zsolutionrh   rh   ri   Útest_issue_15494Ÿ  s    ,
4rô  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szJ ‚d S )Nr~   rk   ry   r   r  )
r   rW   r@   rn   r†   r.   r:   r"   r-   r   r½   rh   rh   ri   Útest_li_integral¯  s    ,.ÿþþrõ  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s¤J ‚t ddd}| |i}tt|| ƒ|ƒ| |¡ ¡ ksÜJ ‚d S )	Nrn   r`   rr   ry   rk   r}   FrŠ  )	r   r   rº   rA   rC   rH   r3   Zxreplacer‡   )rn   r`   rž  rã   ÚgotÚ_xZrepsrh   rh   ri   Útest_issue_17473¶  s    (&ÿÿrø  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sdJ ‚t tttƒƒtd  tdtgƒtdƒ d td  ksžJ ‚d S )Nrk   rr   ry   rŒ   r¯   )rH   r"   rn   r   r   rh   rh   rh   ri   Útest_issue_17671Ã  s    *:rù  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szJ ‚d S )Nrm  ÚCr~   rr   rk   ry   r}   )r   rH   r   r-   )rm  rú  r~   rh   rh   ri   Útest_issue_2975É  s    rû  c                     sØ  t dƒ\‰‰ } tddd}ttˆˆ  ˆ d|fƒˆƒˆd |d d |d   ksTJ ‚ttˆtˆ ƒ ˆ d|fƒˆƒtˆd tˆ ƒ d ˆ d|fƒks–J ‚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sæJ ‚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snJ ‚ttˆˆ d| fƒˆƒ| ˆd  d ksšJ ‚t
t‡ ‡fd
d„ƒ t
t‡ ‡fdd„ƒ t
t‡fdd„ƒ d S )Nzx n Mræ  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  rx   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS rz   )rH   r   rh   rý  rh   ri   rw   Ý  rx   c                      s   t tˆ ˆ dtfƒˆ ƒS rz   rü  rh   rb  rh   ri   rw   Þ  rx   )r   r   rH   r   r3   r   r.   r2   r   r   rZ   r   )rð   ræ  rh   rý  ri   Útest_issue_7827Ð  s,    :ÿ,ÿ"2ÿÿÿÿ
,rþ  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s–J ‚d S rÔ  )rn   r-   r"   rH   rß   rh   rh   ri   Útest_issue_4231á  s    Xrÿ  c                  C   s@   t dtd t t  tƒ} t| tƒdtd t t  ks<J ‚d S rÝ   )r
   rn   r   rH   rß   rh   rh   ri   Útest_issue_17841æ  s    r   c                  C   sL  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sðJ ‚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sHJ ‚d S )Nrn   T©r¥   rÈ   r}   r   rr   rÔ   r«   rk   ry   )
r   r0   r(   r"   r%   r2   rH   r   r-   r1   )rn   Úf1Úf2rh   rh   ri   Útest_issue_21034ë  s    6$xÿFÿr  c                   C   sd   t ttƒtt ƒ tƒtt ƒtt ƒttƒ  ks8J ‚t ttƒtt ƒ tdtfƒt ks`J ‚d S rM  )rH   r"   rn   r    r:   r   r   rh   rh   rh   ri   Útest_issue_4187÷  s    8r  c               	   C   s2  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sªJ ‚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sˆJ ‚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 )Nrº  ré   Úr0ÚR0rk   r}   r   Tr   r   )r   rH   r2   r3   r.   r   r   r   r-   r?   rA   r   r˜   )rº  ré   r  r  rm  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s2J ‚d S )Nrr   rk   ry   r   )rH   rn   r   r   rh   rh   rh   ri   Útest_issue_15810  s    r	  c                  C   s`  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sÄJ ‚| tdƒ | d  }t| ƒtdƒ|   }|t|| ƒksþJ ‚| d td	ƒ |  }| d d td	ƒt| ƒ  }|t|| ƒksBJ ‚| d|  tdƒ  }| d td|  tdƒ ƒtdƒ d  }|t|| ƒks’J ‚| tdƒ|   }| d d t| ƒtdƒ  }|t|| ƒksÒJ ‚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sÆJ ‚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s~J ‚| d  | t  }| d  d t|   tdƒt| t ƒ  }|t|| ƒksÎJ ‚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sjJ ‚| tdƒ| d   }| d d tdƒd| d    }|t|| ƒks²J ‚d|  tdƒ |  }d|  tdƒt| ƒ  }|t|| ƒksòJ ‚| 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sˆJ ‚| | tdƒ| d    |  }| d d | d d  tdƒt| ƒ  }|t|| ƒksàJ ‚| | 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s´J ‚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s J ‚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}   ry   rk   rr   r|   r   éûÿÿÿrª   r«   rŒ   rd   r  r®  iLÿÿÿéZ   r  rõ   )r   r"   r    rH   r)   r(   r   r1   r   r%   r‡   r3   )rn   rc   rã  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thetary   r   r}   r   rk   rÔ   r«   )r   rH   r2   r   )r  r»  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}   rŠ   rE  )rH   rn   r   r-   r   rh   rh   rh   ri   Útest_issue_22033_integral{  s    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   rŠ   rõ   ry   )rH   ré   rn   r~   r-   r   r   rh   rh   rh   ri   Útest_issue_21671€  s    ^r  c                  C   sp   t ddd} ttƒdttƒd   }t| t| ¡| dd | t¡}t|tdd|  krft|tƒksln J ‚d S )NÚxrTr¤   r}   rk   r¢  )r   r2   rn   r3   rH   rÛ   rW   )r  r  Zres_realrh   rh   ri   Útest_issue_18527†  s    r  c               	   C   sÄ  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s„J ‚tddd\}}t|t |i}t|  |¡tƒ| |¡ksÀJ ‚d S )Nrr   rk   r   Tza, brÁ   )r¬   r2   rn   r–   r3   r"   r5   r-   r.   r   r   r   rH   r   rÛ   )rc   ZFposrã  Zaprý   Úreprh   rh   ri   Útest_issue_23718  s    FDÿ@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¡sNJ ‚d S )Nrr   rk   r|   rŠ   ry   gC˜qBõ?)rH   r-   rn   r"   ÚmathÚiscloser`   rø   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sXJ ‚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sTJ ‚d S rÝ   )rH   r    rn   r-   r$   rh   rh   rh   ri   Útest_issue_7264¯  s    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 rò   )rH   r*   rn   r1   r)   r   rº   rh   rh   rh   ri   Útest_issue_11254a³  s    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sxJ ‚d S )NrŠ   rk   F©rF  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sxJ ‚t |  ¡ d
¡sŒJ ‚d S )Nry   rk   r}   r   rr   i›ÿÿÿrª   é‡   r   g€2É{¢ÙÀ)rH   rn   r-   r"   r  r  r`   rø   rh   rh   ri   Útest_issue_22863Â  s    D4r!  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sxJ ‚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   rÔ   ry   rr   rª   r}   r   r¯   rŒ   r  é(   ©rH   r-   rn   r   r"   rh   rh   rh   ri   Útest_issue_9723È  s    ^ÿ&^ÿÿÿr$  c                   C   sl   t ttƒtd  ttd  tt  t  tddtttƒttd  ttd   ttd    tƒkshJ ‚d S )Nrk   Tr¦  ry   r}   )rH   r"   rn   r­   r¬   r–   rX   rh   rh   rh   ri   Útest_issue_23704Ð  s    00ÿr%  c                   C   sd   t dtdtdt ƒ ƒ ƒttdtdt ƒ ƒd ƒd ttdtdt ƒ ƒd ƒd  ks`J ‚d S rÝ   rÒ  rh   rh   rh   ri   Útest_exp_substitutionØ  s    r&  c                   C   sx   t ttƒƒttttƒd ƒ tttƒƒ ks0J ‚t ttƒƒdtttd ƒƒ ksTJ ‚t ttƒƒtttd ƒƒkstJ ‚d S rÝ   )rH   r&   rn   r"   r)   r*   r1   r'   rh   rh   rh   ri   Útest_hyperbolicÜ  s    0$r'  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sdJ ‚t dttd ƒ ƒtttƒ ttd ƒ ks”J ‚t tttd ƒ ƒtd ttd ƒ ttƒ ksÈJ ‚d S )Nrk   r   ry   r«   r  rr   rõ   r#  rh   rh   rh   ri   Útest_nested_powâ  s    (<0r(  c                   C   sè  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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tdƒ tdtd  dt  d ƒ  d ƒ d ksJ ‚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svJ ‚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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tdƒ tdtd  dt  d ƒ  d ƒ d  ks6J ‚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sÚJ ‚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sˆJ ‚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s
J ‚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sfJ ‚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säJ ‚d S )Nrr   ry   rk   r}   r   r  rö   rK  r«   r   Tr’   r¯   iùÿÿÿrE  ró  r  rª   r   r   iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rn   r$   r   r0   r"   rº   r–   r¬   r­   r.   r   r   rf   rh   rh   rh   ri   Útest_sqrt_quadraticé  st    XXnX$hH.þÿ
*Vÿ
*Vÿ
*jÿ
,^Bÿÿ"ýýb"ûÿ
:jÿ
.*ÿÿ
 ^Bÿÿ.ýý,ûÿ
Vÿr)  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snJ ‚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sêJ ‚d S )Nrk   ry   r}   r«   )rH   rn   r6   r5   r"   r2   r   rc   rh   rh   rh   ri   Útest_mul_pow_derivative  s
    <2Xÿr*  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sPJ ‚t||ƒdksbJ ‚t|  |ƒdksvJ ‚t| |ƒdksŠJ ‚t||ƒdksœJ ‚t| |ƒdks°J ‚d S )	Nr   g        )rr   Tr·  ÚInfrr   rŠ   g      ð¿)r.   rn   ÚfloatrH   )Zfun1Zfun2Zfun_sumrº  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s`J ‚t| d
ƒt tdƒ t fƒdt  dtd
t ƒ  ks”J ‚d S )Nc                 S   s   t dt| k fdt| kfƒS r±   )r.   rn   r  rh   rh   ri   rw   )  rx   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   *  rx   r+  rr   rk   r·  Fr  r   )rn   r,  rH   r,   r+   )rc   rº  r  rh   r/  ri   Útest_issue_20781(  s    .ÿr1  c                  C   sâ   t dƒ} t| d td| d  ƒ | ddfƒtd ks8J ‚td| d  td| d  ƒ | ddfƒt d ksnJ ‚tdtd| d  ƒ | ddfƒtd ksšJ ‚t| d d| d   d td| d  ƒ | ddfƒdt d ksÞJ ‚d S )	Nrn   r}   rr   rk   rŠ   r   r|   r   )r   rH   r-   r   rb  rh   rh   ri   Útest_issue_194274  s
    06,r2  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sŠJ ‚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   ry   rk   r   rÊ   r}   r   rE  éÁ   iö  i  )rW   r-   r–   rn   ré   r„  rN   )ÚI1ÚI2rh   rh   ri   Útest_issue_23942B  s    0Z0r6  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¡srJ ‚d S )Nrr   y        >ÚÃT¶üí?r·  gÇÅzðñ¿g	
šT8ò?gÇÅzðñ?g>ÚÃT¶üí?)rn   r    r   r~   rH   Zis_samer  r  )rc   ZF_exprã  rh   rh   ri   Útest_issue_25886I  s    ÿþþýr7  c                  C   sÄ   t tttd ƒƒt ƒ} | tttd ƒƒd ks4J ‚t dtd td  tddƒ  tƒ}|ttd ttd td  d ƒ  ks„J ‚t dttƒd  tddt fƒ}|dtdƒ t d ksÀJ ‚d S )Nrk   rr   ry   r   )	rH   r2   r"   rn   r3   r~   r   r-   r   )r4  r5  ZI3rh   rh   ri   Útest_old_issuesT  s    $, r8  c                  C   s‚   t ddd} t dddd}t|| t  ƒd }t|| t t d fƒ}td }d}| ||¡ ¡ }| ¡ }t|| ƒd	ks~J ‚d S )
Nrn   Tr¤   r–   )r¥   rÂ   rk   r}   rr   r   )r   r3   r   rH   rÛ   re   rQ   )rn   r–   Úintegral_exprZsymbolic_resultZcorrect_resultZa_valueZnumeric_symbolic_resultZnumeric_correct_resultrh   rh   ri   Útest_integral_issue_26566`  s    r:  c                  C   sp   t ddd} tdd| d d   ƒ}t|| ddfƒ}| ¡ }td	ƒd
 dt d  }t|| ¡  ƒdk slJ ‚d S )Nrn   Tr¤   rr   g      â?gOUUUUUÕ?rk   rŠ   ry   r«   r}   r¯   rò  )r   r-   rH   re   r   rÚ   )rn   r9  Zresult_symbolicZresult_numericÚexpected_resultrh   rh   ri   Ú.test_definite_integral_with_floats_issue_27231u  s    r<  c                  C   s´   t td td  ƒ} tt|  t dƒ ƒ|  }t|ttƒ tt tt tt  ƒfg¡}dt dƒ t td  ttd  td  d ƒ dt t	ƒ  }t
t|tt tfƒƒ|ks°J ‚d S )Nrk   r|   ry   )r-   rn   ré   r<   r–   r
   rÛ   r¬   r    r   rQ   rH   )rí   ÚuZEcr;  rh   rh   ri   Útest_issue_27374…  s
    (>r>  )rd   (c  r  Zsympy.concrete.summationsr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.exprr   rÑ   r   r   r	   r
   Z
sympy.corer   Zsympy.core.numbersr   r   r   r   r   r   r   r   Zsympy.core.relationalr   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Zsympy.core.sympifyr   rµ  r   r   r   r   r   Z&sympy.functions.elementary.exponentialr   r    r!   r"   Z%sympy.functions.elementary.hyperbolicr#   r$   r%   r&   r'   r(   r)   r*   Z(sympy.functions.elementary.miscellaneousr+   r,   r-   Z$sympy.functions.elementary.piecewiser.   Z(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Z'sympy.functions.special.delta_functionsr7   r8   rÒ   r9   r:   r;   r<   r=   r>   r?   r@   r•  rA   rB   Zsympy.functions.special.hyperrC   rD   Z-sympy.functions.special.singularity_functionsrE   Z&sympy.functions.special.zeta_functionsrF   Zsympy.integrals.integralsrH   Zsympy.logic.boolalgrI   Zsympy.matrices.denserJ   Zsympy.polys.polytoolsrK   rL   Zsympy.printing.strrM   Zsympy.series.orderrN   Zsympy.sets.setsrO   Zsympy.simplify.gammasimprP   Zsympy.simplify.simplifyrQ   Zsympy.simplify.trigsimprR   Zsympy.tensor.indexedrS   rT   rU   Z#sympy.functions.elementary.integersrV   rW   Zsympy.integrals.rischrX   Zsympy.physicsrY   Zsympy.testing.pytestrZ   r[   r\   r]   Zsympy.utilities.exceptionsr^   Zsympy.core.randomr_   rn   r~   ré   r–   r¬   r­   r   rf   rƒ   r•   rç  rè  r`   rc   rj   rq   r„   r‰   r‹   r‘   r›   r¡   r¢   r©   r®   r°   r²   r³   rµ   r¹   r»   r¾   r¿   rÀ   rÅ   rÆ   rÇ   rË   rÍ   rÓ   rÖ   r×   rØ   rÜ   rÞ   rà   râ   rä   ræ   rè   rê   rë   rì   rî   rñ   ró   rô   rþ   rÿ   r  r  r  r  r  r  r  r  r"  r$  r&  r'  r*  r+  r,  r.  r0  r1  r=  rC  rH  rJ  rL  rN  rP  rR  rT  rY  rZ  r[  r^  r`  ra  rg  rh  ri  rj  rl  rn  rp  rq  rs  rt  rv  rw  rz  r{  r~  r€  r‚  r†  r‰  r‹  rŒ  r  rŽ  r  r  r‘  r’  r–  r—  r˜  rš  r  rŸ  r   r£  r¥  r§  r©  rª  r¬  r­  r¯  r°  r²  r¶  r¸  r¹  r¼  r½  r¿  rÀ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÓ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÝ  rÞ  rß  rà  rá  râ  rä  ré  rë  rí  rî  rï  rð  rñ  rô  rõ  rø  rù  rû  rþ  rÿ  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-  r1  r2  r6  r7  r8  r:  r<  r>  rh   rh   rh   ri   Ú<module>   s  (((( 


.
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3!

			
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

		 	

	Y	*