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    {þdB- ã                   @   sœ  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„ Z0dhdi„ Z1djdk„ Z2dldm„ Z3dndo„ Z4dpdq„ Z5drds„ Z6dtdu„ Z7dvdw„ Z8dxdy„ Z9dzd{„ Z:ed|d}„ ƒZ;d~d„ Z<d€d„ Z=d‚dƒ„ Z>d„d…„ Z?d†d‡„ Z@dˆd‰„ ZAdŠd‹„ ZBdŒd„ ZCdŽd„ ZDdd‘„ ZEd’d“„ ZFd”d•„ ZGd–d—„ ZHd˜d™„ ZIedšd›„ ƒZJedœd„ ƒZKdždŸ„ ZLd d¡„ ZMd¢d£„ ZNd¤d¥„ ZOd¦d§„ ZPd¨d©„ ZQdªd«„ ZRd¬d­„ ZSd®d¯„ ZTd°d±„ ZUd²d³„ ZVd´dµ„ ZWd¶d·„ ZXd¸d¹„ ZYdºd»„ ZZd¼d½„ Z[dS (¿  é    N)ÚSumÚ	summation)ÚAdd)ÚTuple)ÚExpr)Ú
DerivativeÚFunctionÚLambdaÚdiff)Ú
EulerGamma)ÚEÚFloatÚIÚRationalÚnanÚooÚpiÚzoo)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skipÚON_CIÚ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erb   Úoptions© rj   úm/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/integrals/tests/test_integrals.pyÚNS4   s    rl   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prj   rj   rk   Útest_poly_deprecated8   s     (rs   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   rp   Úprincipal_valuerj   ©Úgrj   rk   Ú<lambda>G   ó    z&test_principal_value.<locals>.<lambda>c                      s   t ˆ ƒ ¡ S ru   )rW   rv   rj   rw   rj   rk   ry   H   rz   é   c                      s   t ˆ tt dfƒ ¡ S ©Nrt   )rW   rp   r   rv   rj   )Úlrj   rk   ry   L   rz   rm   éþÿÿÿé   )rp   rW   r   rv   Úyr   rZ   Ú
ValueErrorÚtogetherr-   r   r"   r1   )ÚdÚvÚsre   rj   )rx   r}   rk   Útest_principal_valueB   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symsr…   rj   rj   rk   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   rt   éÿÿÿÿr~   rm   )rH   r"   rp   r   r    rj   rj   rj   rk   Útest_improper_integrali   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 )Nrt   rm   é
   é   )	rW   rb   Úlimitsr   r   rp   r€   rO   r   )Ús1Ús2Zs3Zs4Zs5Zs6Zs7rj   rj   rk   Útest_constructoro   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   rt   rm   é   r{   rb   F©Zcommutative)rW   rp   r   r   ÚNaNr
   r€   ÚtrH   rˆ   r‰   ÚaZatomsre   ÚZeroÚOner‹   r    Úis_commutativer   ©rh   rb   rj   rj   rk   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›   rj   rj   rj   rk   ÚTest´   s   r¡   rt   rm   r   r{   c                   S   s   t td td ƒS r|   ©rH   rp   rj   rj   rj   rk   ry   ¼   rz   ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfƒS )Nrt   r   r¢   rj   rj   rj   rk   ry   ½   rz   )r   rH   r   rZ   r   )r¡   r—   rj   rj   rk   Útest_diff_wrt³   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 )Nr{   r   rm   rt   )r‹   rW   rp   r€   rj   rj   rj   rk   Útest_basics_multipleÀ   s    2,. $r¤   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ksHJ ‚| ¡  ¡ | ¡  ¡ ksdJ ‚| ¡  ¡ | ¡  ¡ ks€J ‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks¸J ‚| ¡  ¡ | ¡  ¡ ksÔJ ‚| ¡  ¡ | ¡  ¡ ksðJ ‚d S )NzA BFr•   rp   T)Úcomplex©Úreal)r   r   rW   Zadjointrˆ   Ú	conjugateZ	transpose)ÚAÚBrp   rr   rj   rj   rk   Útest_conjugate_transposeÊ   s    r«   c                  C   sD  t dtdtfƒdksJ ‚t dtdtfƒdt ks4J ‚t ttdtfƒtd d ksTJ ‚t dt tdtfƒdtd  d ks|J ‚t dtd  tdtfƒtd ks J ‚t dt tdtfƒttƒksÀJ ‚t dtd  tdtfƒdt d ksèJ ‚t td dt  d tdtfƒtd d dtd  d  dt  ks2J ‚t td tƒtd d ksRJ ‚t dt t d tƒdt d td  d ks†J ‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÀJ ‚t ttd  tdtfƒttd  d ksîJ ‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ks@J ‚d S )Nr   r{   rm   rt   rŒ   r   é   é   ÚbÚcr   )rH   r—   rp   r"   r   r˜   )r®   r¯   rj   rj   rk   Útest_integrationÚ   s     ($ (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 )	Nrm   r   rt   rŒ   é	   r{   r¬   r   )rH   rp   r€   r   r"   r3   rj   rj   rj   rk   Útest_multiple_integrationí   s    06Fÿr²   c                   C   s"   t tt ƒtdtfƒdksJ ‚d S )Nr   rt   )rH   r    rp   r   rj   rj   rj   rk   Útest_issue_3532õ   s    r³   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 )Nr{   rm   r   rt   r~   )rH   r-   rp   rj   rj   rj   rk   Útest_issue_3560ù   s    *&r´   c                   C   s   t tdd„ ƒ d S )Nc                   S   s   t ttfƒS ru   r¢   rj   rj   rj   rk   ry      rz   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorrj   rj   rj   rk   Útest_issue_18038ÿ   s    r¶   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 )Nrm   r{   Fro   Tr   )rK   rp   r€   r^   rW   r_   r`   rH   Ú
isinstanceÚgensÚas_expr)rr   ZqxZqyrj   rj   rk   Útest_integrate_poly  s     (((6rº   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 )	Nrm   r{   r   rt   Fro   Tr   )rK   rp   r€   r^   rW   r_   r`   rH   r   r·   r¸   r¹   r   ÚHalf)rr   ZQxZQyrj   rj   rk   Útest_integrate_poly_definite  s     ...$r¼   c                      sD   t dƒ‰ ttƒtd d ks J ‚ttdd„ ƒ tt‡ fdd„ƒ d S )Nr€   rm   c                   S   s   t dƒS ©Nrm   rG   rj   rj   rj   rk   ry   1  rz   z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS ru   r¢   rj   ©r€   rj   rk   ry   2  rz   )r   rH   rp   rZ   r   rj   rj   r¾   rk   Útest_integrate_omit_var,  s    r¿   c                  C   sd   t dƒ} ttt| ƒ tƒtd t| ƒ d ks2J ‚ttd t| ƒ tƒtd t| ƒ d ks`J ‚d S )Nr€   rm   iè  ié  )r   rH   rp   r3   r¾   rj   rj   rk   Útest_integrate_poly_accurately5  s    *rÀ   c                  C   sN   t dƒ} ttd | ƒtd |  ks&J ‚ttd | ddfƒdtd  ksJJ ‚d S )Nr€   rm   rŒ   rt   )r   rH   rp   r¾   rj   rj   rk   Útest_issue_3635>  s    rÁ   c                  C   sž   t ddd} tt|  tddt| d  | d  ks6J ‚tt| ƒt d|   dt| ƒ  tddt|  ƒt| ƒt d|   dt| ƒ   dt| ƒ  ksšJ ‚d S )Nr€   T©ÚpositiveÚnone©Zcondsrt   rm   )r   rH   rp   r    r3   r¾   rj   rj   rk   Útest_integrate_linearterm_powF  s
    *(4ÿrÆ   c                   C   sˆ   t tttƒ tƒdt ttƒd  d ks.J ‚t tttƒ tttƒd   tƒdt ttƒd  d dt ttƒd  d  ks„J ‚d S )Nrm   r{   r   )rH   r   r-   rp   r   rj   rj   rj   rk   Útest_issue_3618O  s    . .ÿrÇ   c                   C   s$  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 )Nrt   r   T)rH   r2   rb   rp   r.   r3   r   rj   rj   rj   rk   Útest_issue_3623U  s    *ÿ
*ÿ
$..ÿÿrÈ   c                  C   s    t dddd} tdt t| t t d ƒ tddgƒdtt|  ƒ t|   ksRJ ‚ttt| t t d ƒ td	dƒ tddgƒdtt|  ƒ t|   ksœJ ‚d S )
Nrb   T)rd   Únonzerog      à¿rm   r~   r   ç       @rŒ   )r   rH   rp   r3   r   r2   r   ©rb   rj   rj   rk   Útest_issue_3664_  s    &ÿ,ÿrÌ   c                   C   s4   t tdtd dt  d  tddfƒƒdks0J ‚d S )Nrt   rm   r¬   é   r   z1.10714871779409)rl   rW   rp   rj   rj   rj   rk   Útest_issue_3679g  s    rÎ   c                  C   sb   ddl m}  ddlm} | tttd ƒtƒƒtdƒttƒ |tdƒt ttƒ ƒ d ks^J ‚d S )Nr   ©Úexpand_func)Úfresnelsrm   )	Úsympy.core.functionrÐ   Ú'sympy.functions.special.error_functionsrÑ   rH   r3   rp   r-   r   )rÐ   rÑ   rj   rj   rk   Útest_issue_3686l  s
    *ÿrÔ   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ks<J ‚d S )Nrt   r   é   )rY   Úmr…   rH   rp   )rÖ   r…   rj   rj   rk   Útest_integrate_unitss  s    r×   c                   C   s@   t tdt ƒtƒt ttdt ƒ  ttdt ƒ  ks<J ‚d S r½   )rH   r   rp   rj   rj   rj   rk   Útest_transcendental_functionsy  s    $ÿrØ   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 )Nrt   r   rm   r­   rŒ   )rH   r"   rp   r   rj   rj   rj   rk   Útest_log_polylog~  s    .rÙ   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   rm   é*   g»½×Ùß|Û=)r"   rp   r
   rH   ÚabsÚsubsrg   )re   Zfidrj   rj   rk   Útest_issue_3740ƒ  s    rÝ   c                   C   s&   t ddtd   tƒttƒks"J ‚d S ©Nrt   rm   )rH   rp   r1   rj   rj   rj   rk   Útest_issue_3788‰  s    rß   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 r½   r¢   rj   ©re   rj   rk   ry     rz   z!test_issue_3952.<locals>.<lambda>)r3   rp   rH   r2   rZ   r   rj   rj   rà   rk   Útest_issue_3952  s    rá   c                   C   s6   t dt dt  tƒdt tdƒ td  ks2J ‚d S r½   ©rH   rp   r"   rj   rj   rj   rk   Útest_issue_4516“  s    rã   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 )Nrt   r   rŒ   rm   )
rH   r    r   rp   r   r   r   r»   r   r   )Úansrj   rj   rk   Útest_issue_7450—  s    rå   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 )Nrt   rm   r{   r   r   ©rH   r2   rp   r   r-   r1   r5   rV   rj   rj   rj   rk   Útest_issue_8623œ  s    NFÿÿrç   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 ©Nrt   rm   r   r{   ræ   rj   rj   rj   rk   Útest_issue_9569¢  s    ,ré   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 )Nr…   TrÂ   rm   r   )
r   r    Úzr€   r-   r   rH   rp   r   r<   )r…   ZpzZpzgxrj   rj   rk   Útest_issue_13733§  s    2>ÿÿrë   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 rè   ræ   rj   rj   rj   rk   Útest_issue_13749¯  s    ,rì   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 rÞ   )rH   r    rp   rX   rj   rj   rj   rk   Útest_issue_18133´  s    rí   c                  C   sä   t ddd} t ddd}t|t t|  t t t t ƒ t|  t t t t ƒ tt  t	dt t t| t t t t ƒ dƒftt|  t t t t ƒ dfƒ}t
dt t tt tt   d	  }t|tƒ|ksàJ ‚d S )
Nz3999999.9999999995é5   )Z	precisionz2.5000000000000004e-7ç      ð?r   Tr~   gŽíµ ÷Æ >)r   r.   r   r    r   r—   r€   rp   rê   r   r   rH   )r˜   r®   ÚrZfunrj   rj   rk   Útest_issue_21741¸  s    D(ÿ þ$rñ   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 )Nrm   c                 S   s    | | d t | | d t ƒ S r|   )r3   rp   )rŠ   Újrj   rj   rk   ry   Ã  rz   ztest_matrices.<locals>.<lambda>r{   )rJ   rH   rp   r2   )ÚMrj   rj   rk   Útest_matricesÂ  s
    
þrô   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   rt   rm   )rH   re   rp   rW   r
   r"   rj   rj   rj   rk   Útest_integrate_functionsË  s     ,0rö   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 r½   )rH   r   re   rp   r€   rW   rj   rj   rj   rk   Útest_integrate_derivativesÓ  s
     *ÿr÷   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 )Nrm   rt   rŒ   r{   r   éüÿÿÿéýÿÿÿr   c                      s   ˆ   td¡S r|   )Ú	transformrp   rj   ©rŠ   rj   rk   ry   ÷  rz   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S ru   ©rú   rp   r…   r—   rj   rû   rj   rk   ry   ø  rz   c                      s   ˆ   tt ¡S ru   ©rú   rp   r…   rj   rû   rj   rk   ry   ù  rz   c                      s   ˆ   tttf¡S ru   rü   rj   rû   rj   rk   ry   ú  rz   c                      s   ˆ   dt dt ¡S r½   rý   rj   rû   rj   rk   ry   û  rz   c                      s   ˆ   td t¡S r½   rý   rj   rû   rj   rk   ry   þ  rz   r˜   T)Únegativer®   rÂ   )rW   rp   r€   rˆ   rú   r3   r   r    r   rê   r®   r…   rZ   r   r   )r˜   ZfxZfyZ_3ÚamÚbprj   rû   rk   Útest_transformÚ  sZ    0$8ÿ
  ÿ
ÿ
ÿ
ÿ22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sZJ ‚d S rÞ   )	r   r»   r0   rp   r-   rH   r2   r3   r/   rà   rj   rj   rk   Útest_issue_4052
  s    &r  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$}d%|  k rêd&k sðn J ‚t tttƒtd  tdtfƒd'd(d)ksJ ‚t tttt d ƒt tt d*fƒd'd(d+ksRJ ‚t tttƒƒd,ksjJ ‚t ttttfƒƒd-ks†J ‚d S ).Nrm   r   rf   z10.5000000000000z1.77245385090552rt   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r—   r¬   r{   é   r   é   éù   é6   éA   r   é2   é1   é¢   rÕ   z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))é`   zlog(2)/2-1/4T©Úchopzpi/4*log(4*pi**3/gamma(1/4)**4)rÍ   é   é   zsqrt(1-x**2)é   )Úmaxnr  )z0.0Ú0)r  g\Âõ(\ß?gR¸…ëQà?Zosc)Zquadz0.504067061906928rŒ   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rl   rW   rp   r    r   r   r   r   r   r-   r1   r"   r3   r2   rg   r€   )Úgaussr—   r˜   r®   r¯   rƒ   re   rj   rj   rk   Útest_evalf_integrals  s¢    ÿÿÿ4,<,ÿ
0ÿ
4ÿÿÿ
ÿ
ÿÿÿÿ
4ÿ
(ÿÿ
(ÿÿ
(ÿÿ

ÿÿÿ
$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 )	Nrt   r   r   Tr  )z-0.000976138910649103z0.965906660135753z1.93278945918216rm   z0.0144361088886740)rl   rH   rp   rÜ   rW   rj   rj   rj   rk   Útest_evalf_issue_939E  s    $ÿ(ÿÿr  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdks6J ‚| tddƒdtdƒ d  ksXJ ‚t tttt  ƒtddftddfƒtju s†J ‚d S )	Nrt   rm   rŒ   rf   z2.43790283299492rø   r{   r¬   )	rH   r-   rp   r€   rl   r   r3   r   r™   ©Úresrj   rj   rk   Ú(test_double_previously_failing_integralsT  s    $"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 )Nr{   r   rŒ   r   r   rŽ   iúÿÿÿr~   rt   rm   rø   r”   r¬   )
rE   rp   r˜   rH   r€   rU   rW   rˆ   r   re   )	Zin_1Zout_1Zin_2Zout_2Zin_3Zout_3_1Zout_3_2Zin_4Zout_4rj   rj   rk   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   rm   r   rt   rŽ   ée   )	rH   r7   rp   re   r   r€   r    r   r-   rq   rj   rj   rk   Útest_integrate_DiracDelta|  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 )Nrt   rŒ   Tr   rm   ©r   T)rH   rp   r€   r.   r   r"   r    rb   r2   r3   rê   r   r—   r-   rj   rj   rj   rk   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 )Nrp   Tr¦   rm   r   r{   r   r	  rÕ   rt   r~   r¯   )Zextended_real)r   rH   r,   r+   r   r    r.   r   r-   r   r<   )rp   r¯   Zint1Zint2Zint3rj   rj   rk   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$J ‚t	ddd\} }t t| ƒ| ƒt
| d  d | dkf| d d dfƒkspJ ‚t td|  d ƒ| ƒt
| d  d|   | dkf| d d|   d dfƒksÀJ ‚t t| |d  ƒ| ddfƒd|d  td|d ƒ d|d   td|d ƒd  d ksJ ‚t tt| ƒ ƒ| ƒt
t| ƒ| dkfdt|  ƒ dfƒks\J ‚t td|  d ƒ| ƒt
|  | dk f| d dfƒks”J ‚t d|  t| d d ƒ | ƒt
| d | dk f| d  d | dk f| d dfƒksêJ ‚t t| ƒ| |d fƒt
|d |d dkf| d |d dk fdƒks4J ‚d S )Nr~   rt   r   rm   r   r{   r   éñÿÿÿrf   iÓ  rŒ   r  zt sTr¦   r­   é   r  )rH   r   rp   r   r   r»   r   r3   r   r   r.   rÛ   r,   r    )r—   r…   rj   rj   rk   Útest_integrate_Abs_sign½  s<    "&$(&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 ©Nr{   r   rt   rm   r~   )rW   r    rp   r€   rÜ   r	   r   ©rh   re   Úconvrj   rj   rk   Ú
test_subs1Ø  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    rp   r€   r—   rÜ   r	   r   r#  rj   rj   rk   Ú
test_subs2â  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   rt   r{   rm   r~   r&  r#  rj   rj   rk   Ú
test_subs3ì  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#  rj   rj   rk   Ú
test_subs4ô  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 )Nrm   r   rt   r   )rW   r    rp   r   rÜ   r€   rˆ   Úis_zero©rh   rj   rj   rk   Ú
test_subs5ü  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 brt   )r   rW   rp   r€   re   rÜ   )r˜   r®   rh   rj   rj   rk   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 rÞ   )rW   rp   r€   rÜ   r3   r,  rj   rj   rk   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 )Nrm   rt   T)Úforce)rW   re   rp   r€   r‰   r   r,  rj   rj   rk   Útest_expand$  s     8 ÿr1  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 ©Nrm   r{   )rW   r    rp   rj   rj   rj   rk   ry   .  rz   z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  ƒdt tfƒS r2  )rW   r    rp   r   rj   rj   rj   rk   ry   /  rz   )rZ   r   rj   rj   rj   rk   Útest_integration_variable-  s    r3  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 )Nrm   rt   r   )rW   r2   rp   r3   r‰   rj   rj   rj   rk   Útest_expand_integral2  s    *"ÿÿ$ÿÿr4  c                      sN  t ttd d ƒtddfƒ‰ ˆ jddddtdƒ ks:J ‚ˆ jdddd	td
ƒ dtdƒ  ksdJ ‚ˆ jddddtdƒ d dtdƒ d  dtdƒ d  ks¦J ‚ˆ jd	dddtdƒ d	tdƒ  d	tdƒ  dtdƒ  ksèJ ‚tˆ jd	dd ¡ ˆ  ¡  ƒdk sJ ‚t ttd td  ƒtddftddfƒ‰ tt‡ fdd„ƒ d S )Nr{   rt   rm   rŽ   Úmidpoint©Úmethodr¬   éÙ   r   r  rÕ   é9   i	  é   iIÎ  iÚ  r”   éV   r­   é   g      à?r   c                      s
   ˆ   d¡S )Nr   ©Úas_sumrj   r,  rj   rk   ry   F  rz   z'test_as_sum_midpoint1.<locals>.<lambda>)	rW   r-   rp   r>  rÛ   rb   r€   rZ   ÚNotImplementedErrorrj   rj   r,  rk   Útest_as_sum_midpoint1;  s$    *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 )Nrm   r   rt   rb   T©rÃ   rd   r5  r6  r   r   r  r{   é#   él   é   é@   rÕ   )rW   rp   r€   r   r>  r‰   r   rœ   rj   rj   rk   Útest_as_sum_midpoint2I  s    ,,,,$ÿrF  c                  C   sD  t tt d tddfƒ} | jddd ¡ td ks6J ‚| jddd ¡ tddƒtd  td  ksfJ ‚| jddd ¡ tdd	ƒttddƒ  td  ksœJ ‚| jd
dd ¡ tddƒttdd
ƒ  td  ksÒJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks$J ‚| jdddd t¡s@J ‚d S )Nrm   r   rt   Úleftr6  r¬   r{   r   r:  r   r”   é    r­   rŽ   F)r7  Úevaluate)	rW   rp   r€   r>  r‰   r   rb   Úhasr   r,  rj   rj   rk   Útest_as_sum_leftT  s    0668ÿ
rK  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 )Nrm   r   rt   Úrightr6  r   r¬   r{   r<  r:  r   rf   rH  r­   )rW   rp   r€   r>  r‰   r   rb   r,  rj   rj   rk   Útest_as_sum_right_  s    *6668ÿrM  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 )Nrm   r   rt   Z	trapezoidr6  r{   r¬   é   r  r   r  rH  r­   )
rW   rp   r€   r>  r‰   r   r»   r   rb   r   r,  rj   rj   rk   Útest_as_sum_trapezoidi  s    (,,,$ÿ
rO  c                      sr   t tt d tddfƒ‰ tt‡ fdd„ƒ tt‡ fdd„ƒ ttdd„ ƒ tt‡ fdd„ƒ tt‡ fd	d„ƒ d S )
Nrm   r   rt   c                      s
   ˆ   d¡S )NrŒ   r=  rj   r,  rj   rk   ry   v  rz   z$test_as_sum_raises.<locals>.<lambda>c                      s
   ˆ   d¡S ©Nr   r=  rj   r,  rj   rk   ry   w  rz   c                   S   s   t tƒ d¡S )Nr{   )rW   rp   r>  rj   rj   rj   rk   ry   x  rz   c                      s
   ˆ   t¡S ru   )r>  r   rj   r,  rj   rk   ry   y  rz   c                      s   ˆ j dddS )Nr{   Zxxxx2r6  r=  rj   r,  rj   rk   ry   z  rz   )rW   rp   r€   rZ   r   rj   rj   r,  rk   Útest_as_sum_raisest  s    rQ  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ks0J ‚d S ru   )rW   rp   rˆ   ©rh   re   rj   rj   rk   Útest_nested_doit}  s    rS  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 )Nrm   rt   r{   rŒ   zx**2)rp   Ú1N)rW   rp   rˆ   r   r€   rÜ   r—   rH   rR  rj   rj   rk   Útest_issue_4665ƒ  s    44"$rU  c                  C   s*   t td tddfƒ} | t | jŽ ks&J ‚d S )Nrm   rŒ   rt   )rW   rp   Úargsr,  rj   rj   rk   Útest_integral_reconstruct  s    rW  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 )	Nrm   r   rt   r{   F©Údeepre   r   )	rW   rp   rˆ   r   r   r˜   r    ÚlistÚreversed)rh   re   r   rj   rj   rk   Útest_doit_integrals•  s     &"r\  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 )Nrt   rm   r   rf   r   T)rH   r-   rp   r.   r   r   r"   rj   rj   rj   rk   Útest_issue_4884¤  s    Bÿ>ÿÿýÿr]  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 )Nrm   rt   rŒ   T)rH   rp   rb   r"   r.   r   rj   rj   rj   rk   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   ©rp   r€   rê   Frt   Trm   rÊ   r{   )Ú	sympy.abcrp   r€   rê   rW   Z	is_numberrb   r   r3   r2   re   )rp   r€   rê   rŠ   rj   rj   rk   Útest_is_number¶  s0    ((((.ra  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_  rt   rm   )r`  rp   r€   rê   rW   r‡   Úsetre   r_  rj   rj   rk   Útest_free_symbolsÖ  s:     ÿ
ÿ
 ÿ
 ÿ
 ÿ
&rc  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   )rp   rÖ   rt   rm   FT)
r`  rp   rÖ   rW   r+  r€   r    r   r3   r   )rp   rÖ   rŠ   rj   rj   rk   Útest_is_zeroò  s     $rd  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   ©rp   r¬   rË   c                    s   g | ]}t ˆ ƒ‘qS rj   )Únext)Ú.0rò   r,  rj   rk   Ú
<listcomp>	  rz   ztest_series.<locals>.<listcomp>r   )	r`  rp   rW   r2   ZlseriesZnseriesZremoveOr   Úrange)rp   rŠ   rj   r,  rk   Útest_series  s    
rj  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 )Nrp   rt   rm   )r   rH   r3   r"   r;   r2   rJ  r9   re  rj   rj   rk   Ú!test_trig_nonelementary_integrals  s    *rk  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 )
Nrp   r€   rê   TrÂ   rm   r¦   rt   z3/2)r   rH   r-   r$   r"   r   r_  rj   rj   rk   Útest_issue_4403  s    2ÿBÿ ÿrl  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 )Nrm   r   r~   rø   )rH   r-   rp   r1   rj   rj   rj   rk   Útest_issue_4403_2%  s    2ÿrm  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RTrÂ   rm   r   r   )r   rH   r-   rp   r   )rn  rj   rj   rk   Útest_issue_4100*  s    ro  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wrp   r€   rê   re   rm   rt   )r`  rp  rp   r€   rê   r   rW   rV  r   rH   rˆ   )rp  rp   r€   rê   re   rj   rj   rk   Útest_issue_5167/  s(    (",.0ÿ
*,>"":&:ÿrq  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 )Nrê   TrÂ   rm   rt   r   rŒ   )r   rH   r    r"   rp   r-   r   r   r<   r   r»   r>   ©rê   rj   rj   rk   Útest_issue_4890F  s    *ÿ*ÿFÿrs  c                   C   s,   t dttdtd  ƒ  tƒ t¡r(J ‚d S rÞ   )rH   rp   r-   rJ  rW   rj   rj   rj   rk   Útest_issue_4551P  s    rt  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 )Nrb   T©rd   rÃ   rt   r   rm   )r   rQ   rH   rp   r   r»   rË   rj   rj   rk   Útest_issue_4376T  s    "Nÿÿrv  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 )Nr{   rt   r­   r”   r  )rH   r-   rp   r   rj   rj   rj   rk   Útest_issue_4517Z  s    "*ÿrw  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 mTrc   r   rm   r  )
r   rH   r3   rp   r   rQ   r.   r   rI   r2   )ÚkrÖ   rj   rj   rk   Útest_issue_4527_  s$    &($ýÿ \X**ÿÿüry  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€   TrÂ   rm   rÄ   rÅ   )r   rH   r    r   r   rp   r   rW   )Zyposrj   rj   rk   Útest_issue_4199t  s    .*ÿrz  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slJ ‚tt| td  |t  | ƒtƒttƒt|ƒ t|d  d|   ƒ tt| ƒt |dt| ƒ   ƒ dt| ƒ  ksäJ ‚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sLJ ‚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s²J ‚d S )
Nza:dTrÂ   rm   r   r   )Ú
expand_mul)rx  za d)r   rH   r    rp   r   r-   r   r<   r>   rÒ   r{  r`  rx  r   )r˜   r®   r¯   rƒ   r{  rx  rj   rj   rk   Útest_issue_3940{  s     2ÿ Pÿ.ÿ
.ÿr|  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 r½   )rH   r˜   rp   r   r"   rj   rj   rj   rk   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)rÉ   rm   rt   )
r   r   r    r—   r3   rp   r2   r€   rH   r"   )r©   rê   r¯   ZP1ZP2Úh1Úh2rj   rj   rk   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 )Nr{   rm   rÕ   r   )r3   r€   rp   r2   rR   rL   rH   r
   )Úexprrj   rj   rk   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   rm   )rH   r3   rp   re   r€   rê   r   rW   rj   rj   rj   rk   Útest_issue_5178³  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   rŽ   rm   r   é   r­   iÐ  r¬   i€  i _7 r  r   )r3   rp   ZseriesrN   rH   r
   ©re   rx   rj   rj   rk   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heurischrt   )Zsympy.integrals.heurischr‰  rD   rp   rˆ  rj   rj   rk   Útest_atom_bugÂ  s    rŠ  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 )Nrê   F©Zzeror   rm   )
r   rH   r3   rp   r€   r   r‚   r"   r9   r   rr  rj   rj   rk   Útest_limit_bugÇ  s    &*ÿrŒ  c                  C   s,   t dƒ} tttƒ| tƒ tƒ t¡s(J ‚d S )Nrx   )r   rH   r    rp   rJ  rW   rw   rj   rj   rk   Útest_issue_4703Í  s    r  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡s*J ‚d S )Nre   rm   )r   rH   rp   r
   rJ  rW   rà   rj   rj   rk   Útest_issue_1888Ò  s    rŽ  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 )Nrm   r   )rH   r2   rp   r€   r   r;   rj   rj   rj   rk   Útest_issue_3558Ù  s    r  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ks2J ‚d S )Nrt   r  r   rm   )rH   r-   rp   r$   rj   rj   rj   rk   Útest_issue_4422Ý  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 )Nrt   rm   r­   rf   )rQ   rH   rp   r-   rj   rj   rj   rk   Útest_issue_4493á  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 rƒ  )rH   r3   rp   r   r   r;   rj   rj   rj   rk   Útest_issue_4737æ  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   rÏ   r˜   TrÂ   rt   )rÒ   rÐ   r   rQ   rH   r    rp   r"   r   rB   rA   )rÐ   r˜   rj   rj   rk   Útest_issue_4992ì  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
lowergammart   )Ú'sympy.functions.special.gamma_functionsr•  rQ   rH   r    rp   r€   r”  rj   rj   rk   Útest_issue_4487ô  s    r—  c                  C   s,   t dƒ} td| d  | ddfƒtu s(J ‚d S )Nrp   rt   rm   rŒ   )r   rH   r   re  rj   rj   rk   Útest_issue_4215ù  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 )Nrb   Tru  rm   rt   )r   rH   rp   r"   rË   rj   rj   rk   Útest_issue_4400þ  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 )Nrt   rm   T©rD   )rH   r-   rp   rW   rj   rj   rj   rk   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 säJ ‚d S )Nrt   r   iôÿÿÿr{   r­   rm   r¬   r   r”   r   r:  r  é/   ©rH   rp   r€   rê   r"   rj   rj   rj   rk   Útest_issue_4153  s
    .B@*ýrž  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 hrm   )r   rH   rp   r-   rJ  r   rW   )rn  r®   Úhrh   rj   rj   rk   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 r2  râ   rj   rj   rj   rk   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 )Nrt   T)ÚmanualrD   r¢   rj   rj   rj   rk   ry   "  rz   z$test_manual_option.<locals>.<lambda>rt   r   T©r¢  )rZ   r   rH   r"   rp   rJ  rW   rj   rj   rj   rk   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 )Nrt   T)rD   Úrischr¢   rj   rj   rj   rk   ry   (  rz   z%test_meijerg_option.<locals>.<lambda>Trš  )rZ   r   rH   r5   rp   rW   rj   rj   rj   rk   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 )Nrt   r   T©r¥  )rH   r"   rp   r   rj   rj   rj   rk   ry   /  rz   z#test_risch_option.<locals>.<lambda>rm   Tr§  rt   )
rZ   r   rH   r    rp   rX   r"   r€   r<   rW   rj   rj   rj   rk   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 )Nrt   T)r¥  r‰  r¢   rj   rj   rj   rk   ry   8  rz   z&test_heurisch_option.<locals>.<lambda>rm   Trˆ  r{   r   Fi€ÿÿÿrt   i!  éð   r  rÍ   )rZ   r   rH   r    rp   r-   r   r>   rW   r"   r2   r   r3   rj   rj   rj   rk   Útest_heurisch_option6  s    .,*BJÿÿrª  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |dds6J ‚d S )Nrt   gHáz®Gñ?rm   g333333@gê-™—q=)Ztol)rp   rH   r
   ra   r†  rj   rj   rk   Útest_issue_6828C  s    r«  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    rp   r2   r˜   )r¬  rj   rj   rk   Útest_issue_4803I  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 rÞ   )rH   r-   r5   rp   rj   rj   rj   rk   Útest_issue_4234O  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 )
Nrm   r   TrX  rf   r{   é   r¬   iøÿÿÿ)	rQ   rH   rp   r-   rL   r.   r   r#   r0   rj   rj   rj   rk   Útest_issue_4492S  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 )Nrt   rm   r{   g333333ó?r   g333333ó¿)r˜   rê   r"   rX   rW   rˆ   rH   r    rb   r…   r—   rp   )re   Z
integral_frj   rj   rk   Útest_issue_2708\  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      $@gš™™™™™¹?gš™™™™™É?z%1.86831064982608*y + 2.16387491480008)rp   r€   r    rH   Ústr)re   rh   rj   rj   rk   Útest_issue_2884j  s     r³  c                  C   s–  ddl m} m} ttt t ƒttƒ tdtfƒt	t
t	t t
td  d   |td ƒdk fdt
t ddtd     |td ƒdk fttjfdfdtjfdfttƒd ƒdfƒ td dkfttt t ƒttƒ tdtfƒdfƒksìJ ‚ttt t ƒttƒ tdtfƒt	d	td  d dt d  d  t|tƒdk|| tƒƒt
d k || tƒƒt
d kƒfttt t ƒttƒ tdtfƒdfƒks’J ‚d S )
Nr   ©Úargr   rm   rt   r~   )r   r   )r   TrŒ   )Ú$sympy.functions.elementary.complexesrµ  r   rH   r    r…   rp   r%   r   r.   r   rD   r   r»   r   rW   r(   rI   r´  rj   rj   rk   Útest_issue_8368ip  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$J ‚t tdt ƒƒdt dttdt ƒd ƒ  ksXJ ‚t ttƒƒttttƒd ƒ ks|J ‚d S )Nrï   rt   )rH   r(   rp   r%   r)   r"   rj   rj   rj   rk   Útest_issue_8901  s    $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 )Nr{   r   rt   r   rm   )rH   r3   rp   r;   r   r   r2   rj   rj   rj   rk   Útest_issue_8945–  s    >(r¹  c                  C   sd   t rtdƒ tdƒ\} }}}tt|  t | ƒd ||t    t¡}tt|td|fƒj	vs`J ‚d S )NzToo slow for CI.zi L a brm   r   )
r]   r\   r   r2   r   rp   Úrewriter    rH   r‡   )rŠ   ÚLr˜   r®   Ú	integrandrj   rj   rk   Útest_issue_7130  s
    *r½  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 trm   )r   rJ   rH   rW   rˆ   )r˜   r®   r¯   r—   Zvtrj   rj   rk   Útest_issue_10567¦  s    r¾  c                   C   s6   t ttd  dt  d ƒtddfƒdt ks2J ‚d S )Nrm   r¬   é0   r   rÕ   r  )rH   r-   rp   r   rj   rj   rj   rk   Útest_issue_11742­  s    rÀ  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—   rj   rj   rk   Útest_issue_11856±  s    rÁ  c                   C   s0   t ttdt ƒƒtddfƒttƒd ks,J ‚d S ©Nrt   r   rm   )rH   r-   r"   rp   r   rj   rj   rj   rk   Útest_issue_11876¶  s    rÃ  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Àr¬   g      (@r   )rH   r    rp   rj   rj   rj   rk   Útest_issue_4950»  s    ,ÿrÄ  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 )Nrm   r   )rH   r3   r"   rp   r2   rj   rj   rj   rk   Útest_issue_4968À  s    rÅ  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 )Nrt   rm   rŒ   r~   )rH   rp   r   rj   rj   rj   rk   Útest_singularitiesÄ  s
    " $"rÆ  c                  C   s¸   t ddd\} }tt| |  |  ||  ƒ| tt||  ƒ tt||  ƒf|ttƒ ttƒfƒtt| d |d  ƒ| t|d  t ƒ t|d  t ƒf|ttƒ ttƒfƒks´J ‚d S )Nzx yTr¦   r{   rm   )r   rH   r3   r-   r   rW   )rp   r€   rj   rj   rk   Útest_issue_12645Í  s    "þ&þýrÇ  c                   C   s6   t ttƒttƒd  tdtd fƒtddƒks2J ‚d S )Nr{   r   r­   rt   )rH   r3   rp   r2   r   r   rj   rj   rj   rk   Útest_issue_12677×  s    rÈ  c                   C   s6   t tdt ƒttƒ t tdtfƒtdƒ ks2J ‚d S )Nr{   r   )rH   r2   rp   r   r"   rj   rj   rj   rk   Útest_issue_14078Û  s    rÉ  c                   C   s(   t dttƒ tdtfƒtd ks$J ‚d S rÂ  )rH   r%   rp   r   r   rj   rj   rj   rk   Útest_issue_14064ß  s    rÊ  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 r|   )rH   r    rp   r   r»   r"   r   rj   rj   rj   rk   Útest_issue_14027ã  s    &>ÿrË  c                   C   s&   t ttƒtdtd fƒtju s"J ‚d S rƒ  )rH   r5   rp   r   r   ÚInfinityrj   rj   rj   rk   Útest_issue_8170è  s    rÍ  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 )Nrt   rŒ   r~   r{   )rH   rp   r   r–   rj   rj   rj   rk   Útest_issue_8440_14040ì  s    rÎ  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 )
Nrt   rm   r   rŒ   rø   r   r­   r±   r{   r  rj   rj   rj   rk   Útest_issue_14096ñ  s    42"ÿrÏ  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 )Nrt   r{   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rp   rb   rj   rj   rj   rk   Útest_issue_14144÷  s    4rÐ  c                   C   s(   t ttt ƒttƒ tƒ t¡s$J ‚d S ru   )rH   r    r   rp   r"   rJ  r:   rj   rj   rj   rk   Útest_issue_14375ü  s    rÑ  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 )Nre   r   rt   rm   r{   )r   rp   r€   rê   rH   rW   rà   rj   rj   rk   Útest_issue_14437  s    ÿrÒ  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 r|   ©rH   r-   r    rp   r"   rj   rj   rj   rk   Útest_issue_14470  s    rÔ  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 ©Nrt   rm   r{   )r    rp   rH   rà   rj   rj   rk   Útest_issue_14877  s    LHÿrÖ  c                  C   sB   t td  d ƒtd  t  } t| tddgƒt d ks>J ‚d S )Nrm   rt   rŒ   r¬   )r-   rp   rH   r   rà   rj   rj   rk   Útest_issue_14782  s     r×  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 )Nrm   rt   r   r{   r  )r-   rp   rH   r   rš   r   rà   rj   rj   rk   Útest_issue_14782_slow  s     rØ  c                  C   s4   t tddƒ tt  ƒ } t| t dtgƒtu s0J ‚d S )Nrù   rm   r   )rp   r   r    rH   r   rà   rj   rj   rk   Útest_issue_12081  s    rÙ  c                  C   sD   dt  d } d|  td|  ƒ t d  }t|t ddgƒdks@J ‚d S )Nrt   r   r~   rm   r   )rp   r    rH   )r€   re   rj   rj   rk   Útest_issue_15285"  s    rÚ  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   rt   T)rH   rp   rb   r    r"   r   rP   r.   rA   rB   r   rW   rj   rj   rj   rk   Útest_issue_15432(  s    *4(þrÛ  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clsrÄ   rÅ   )rT   r   rS   rH   r    rp   r   )rÜ  rÖ   rr   rj   rj   rk   Útest_issue_15124.  s
    $<ÿrÞ  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 )Nrm   Fro   r   rt   )r^   rW   r   rp   r€   rˆ   r_   r`   rH   r   r»   rj   rj   rj   rk   Útest_issue_152185  s    ,HLL(rß  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 )Nrm   r   r­   )rH   r    rp   r2   r—   r3   r   r·   r.   rP   r-   r   rÜ   r  rj   rj   rk   Útest_issue_15292F  s    >rà  c                   C   s.   t tdt ƒttƒ tƒdttƒ ks*J ‚d S r½   )rH   r3   rp   rj   rj   rj   rk   Útest_issue_4514L  s    rá  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¦   rm   rt   r{   r~   rù   rŒ   r   )r   rH   r    r   rÜ   r   )rp   r˜   r®   ZdefiniteZ
indefiniterj   rj   rk   Útest_issue_15457P  s    "((râ  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 ru   )rH   rp   r    r"   r:   rj   rj   rj   rk   Útest_issue_15431Z  s    *ÿrã  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 )Nrm   r{   r   )rp   r"   r:   rH   r
   r-   r   r=   )re   ÚFrj   rj   rk   Ú"test_issue_15640_log_substitutions_  s     & .rå  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NTrˆ  )Zsympy.vectorræ  rp   rH   r2   r˜   r®   Úx_1Úx_2r.   r3   r   r   )ræ  rç  rp   rj   rj   rk   Útest_issue_15509k  s     Dþrê  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 )
Nrp   Tr¦   r±   rm   r   rù   éQ   r{   )r   rH   rÛ   r.   r   re  rj   rj   rk   Útest_issue_4311_fastt  s    ".ýrì  c               	   C   sæ  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ƒ tt |d  d	|   ƒ td
t |  | | dt| ƒ tt ƒ  ƒ dt| ƒ  ks¼J ‚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slJ ‚tdtt| ƒd  |ƒ| d tttt| ƒd ƒ d  ks²J ‚tdtt| ƒd  |ddt fƒt ksâJ ‚d S )NÚKTrÂ   rp   r¦   rÖ   r—   rm   r   r~   rt   r   )	r   rH   r    r   r-   r   r>   r"   r<   )rí  rp   rÖ   r—   rj   rj   rk   Ú%test_integrate_with_complex_constants|  s"    >ÿ,ÿ
ÿ
>"ÿBFrî  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 )Nrp   rb   TrA  rt   rm   )r   rH   rF   r!   r   r   rA   )rp   rb   rj   rj   rk   Útest_issue_14241‹  s
    :ÿrï  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 )Nrm   r   r   r   )rH   r3   r—   r2   r   rj   rj   rj   rk   Útest_issue_13112’  s    rð  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 )	NrŸ  TrÂ   rt   rm   r   r   r  )r   rH   rp   r/   r   )rŸ  rŠ   rj   rj   rk   Útest_issue_14709b–  s    $rñ  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 )Nrp   r—   r~   r   rm   )r   rH   r    r   r:   r"   )rp   r—   rj   rj   rk   Útest_issue_8614œ  s    &rò  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 )Nr…   TrÂ   rm   gš™™™™™ù?rt   gÏRt?,eÀg:Œ0âŽyE>r¬   r   iöÿÿÿé   r{   )r   r    rH   r   r–   rÛ   rÜ   )r…   r¼  Zsolutionrj   rj   rk   Útest_issue_15494£  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€   rm   r{   r   r  )
r   rW   r@   rp   rˆ   r.   r:   r"   r-   r   r¾   rj   rj   rk   Útest_li_integral³  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 )	Nrp   rb   rt   r{   rm   r   Fr‹  )	r   r   r»   rA   rC   rH   r3   Zxreplacer‰   )rp   rb   rŸ  rä   ÚgotÚ_xZrepsrj   rj   rk   Útest_issue_17473º  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 )Nrm   rt   r{   rŽ   r±   )rH   r"   rp   r   r   rj   rj   rj   rk   Útest_issue_17671Ç  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 )Nrp  ÚCr€   rt   rm   r{   r   )r   rH   r   r-   )rp  rú  r€   rj   rj   rk   Útest_issue_2975Í  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 Mrç  Trc   rt   rm   r   r   r  c                      s   t tˆˆtˆ fƒtƒS ru   ©rH   r   r€   rj   ©rb   rp   rj   rk   ry   à  rz   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS r|   )rH   r   rj   rý  rj   rk   ry   á  rz   c                      s   t tˆ ˆ dtfƒˆ ƒS r|   rü  rj   re  rj   rk   ry   â  rz   )r   r   rH   r   r3   r   r.   r2   r   r   rZ   r   )ró   rç  rj   rý  rk   Útest_issue_7827Ô  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 rÕ  )rp   r-   r"   rH   rà   rj   rj   rk   Útest_issue_4231å  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 rÞ   )r
   rp   r   rH   rà   rj   rj   rk   Útest_issue_17841ê  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 )Nrp   T©r§   rÉ   r   r   rt   rÕ   r­   rm   r{   )
r   r0   r(   r"   r%   r2   rH   r   r-   r1   )rp   Úf1Úf2rj   rj   rk   Útest_issue_21034ï  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 rP  )rH   r"   rp   r    r:   r   r   rj   rj   rj   rk   Útest_issue_4187û  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 )Nr»  rê   Úr0ÚR0rm   r   r   Tr  r   )r   rH   r2   r3   r.   r   r   r   r-   r?   rA   r   rš   )r»  rê   r  r  rp  Zsolrj   rj   rk   Útest_issue_5547   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 )Nrt   rm   r{   r   )rH   rp   r   r   rj   rj   rj   rk   Útest_issue_15810  s    r	  c                  C   sn  t dddd} t| ƒtd|  ƒ td|  tdƒ ƒ }| t| ƒd  | ddtdƒ    d|  d|  tdƒ  t| ƒ  | tdƒd	  td|  tdƒ ƒ  tdƒtd|  tdƒ ƒ d	  }|t|| ƒksÐJ ‚| 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sPJ ‚| 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sàJ ‚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sLJ ‚| 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sÔJ ‚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sŒJ ‚| d  | t  }| d  d t|   tdƒt| t ƒ  }|t|| ƒksÜJ ‚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sxJ ‚| tdƒ| d   }| d d tdƒd| d    }|t|| ƒksÀJ ‚d|  td	ƒ |  }d|  td	ƒt| ƒ  }|t|| ƒks J ‚| 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s–J ‚| | tdƒ| d    |  }| d d | d d  tdƒt| ƒ  }|t|| ƒksîJ ‚| | d
|  tdƒ   }| d d | d
  td
|  tdƒ ƒtdƒ d  }|t|| ƒksNJ ‚| 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sÂJ ‚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sjJ ‚d S )Nrp   Tr  r   r{   rm   rt   r~   r­   r   éûÿÿÿr¬   rŽ   rf   r  r¯  iLÿÿÿéZ   r  rø   )r   r"   r    rH   r)   r(   r   r1   r   r%   r‰   r3   )rp   re   rä  ZF_truerj   rj   rk   Útest_issue_21024  s”    (B"ÿÿ(Dd$@*$$ f(4 <<.nÿ
ÿÿ,r  c                  C   s`   t dƒ} tdtdt|  d    tt tfƒ ¡ tt| ƒd dƒ tt| ƒd dƒ ks\J ‚d S )Nr˜   rt   rm   r   )r   rH   r   rp   r   r‰   r8   r   )r˜   rj   rj   rk   Útest_issue_21721r  s    ($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thetar{   r   r   r   rm   rÕ   r­   )r   rH   r2   r   )r  r¼  rj   rj   rk   Útest_issue_21831x  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 )Nrm   rt   r   rŒ   rH  )rH   rp   r   r-   r   rj   rj   rj   rk   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 )Nrt   rm   rŒ   rø   r{   )rH   rê   rp   r€   r-   r   r   rj   rj   rj   rk   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   rm   r£  )r   r2   rp   r3   rH   rÜ   rW   )r  r  Zres_realrj   rj   rk   Útest_issue_18527Š  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 )Nrt   rm   r   Tza, brÂ   )r®   r2   rp   r˜   r3   r"   r5   r-   r.   r   r   r   rH   r   rÜ   )re   ZFposrä  Zapr   Úreprj   rj   rk   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 )Nrt   rm   r~   rŒ   r{   gC˜qBõ?)rH   r-   rp   r"   ÚmathÚiscloserb   rû   rj   rj   rk   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 )Nrt   rm   T)rH   r-   rp   r   r.   r#   r   r0   rj   rj   rj   rk   Útest_pr_23583®  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 rÞ   )rH   r    rp   r-   r$   rj   rj   rj   rk   Útest_issue_7264³  s    r  c                   C   s.   t ttƒtddfƒdtttjƒƒ ks*J ‚d S rõ   )rH   r*   rp   r1   r)   r   r»   rj   rj   rj   rk   Útest_issue_11254a·  s    r  c                   C   sB   t ttƒtƒtttd ƒƒks"J ‚t ttƒtddfƒtks>J ‚d S )Nrm   r   rt   )rH   r'   rp   r"   r)   r   rj   rj   rj   rk   Útest_issue_11254b»  s    "r  c                   C   sD   t ttƒd  t¡tƒdttd ƒ ttd ƒd d  ks@J ‚d S )Nrm   rt   )rH   r*   rp   rº  r(   r)   rj   rj   rj   rk   Útest_issue_11254dÀ  s    r  c                  C   s   t dtd  td  dt  d ttd dt  d ƒ tddfƒ} | dtdƒ d dtddtdƒ  ƒ d	  ksxJ ‚t |  ¡ d
¡sŒJ ‚d S )Nr{   rm   r   r   rt   i›ÿÿÿr¬   é‡   r  g€2É{¢ÙÀ)rH   rp   r-   r"   r  r  rb   rû   rj   rj   rk   Útest_issue_22863Ä  s    D4r  c                   C   s.  t ttttƒ ƒƒdtttƒt ƒ ttƒd td  tdƒd   tdttƒ dtttƒt ƒ  d ƒd  ksxJ ‚t tdt d tdt d ƒ ƒd ƒtdt tdt d ƒ d ƒdt d	 d
dt d tdƒd   d  tdt d ƒd  dt d d d	  td
ƒd	   d ks*J ‚d S )Nrm   rÕ   r{   rt   r¬   r   r   r±   rŽ   r  é(   ©rH   r-   rp   r   r"   rj   rj   rj   rk   Útest_issue_9723Ê  s    ^ÿ&^ÿÿÿr"  c                   C   sl   t ttƒtd  ttd  tt  t  tddtttƒttd  ttd   ttd    tƒkshJ ‚d S )Nrm   Tr§  r{   r   )rH   r"   rp   r¯   r®   r˜   rX   rj   rj   rj   rk   Útest_issue_23704Ò  s    00ÿr#  c                   C   sd   t dtdtdt ƒ ƒ ƒttdtdt ƒ ƒd ƒd ttdtdt ƒ ƒd ƒd  ks`J ‚d S rÞ   rÓ  rj   rj   rj   rk   Útest_exp_substitutionÚ  s    r$  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 rÞ   )rH   r&   rp   r"   r)   r*   r1   r'   rj   rj   rj   rk   Útest_hyperbolicÞ  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 )Nrm   r   r{   r­   r  rt   rø   r!  rj   rj   rj   rk   Útest_nested_powä  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 )Nrt   r{   rm   r   r   r  rù   rN  r­   r   Tr”   r±   iùÿÿÿrH  ró  r  r¬   r  r  iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rp   r$   r   r0   r"   r»   r˜   r®   r¯   r.   r   rƒ   rh   rj   rj   rj   rk   Útest_sqrt_quadraticë  st    XXnX$hH.þÿ
*Vÿ
*Vÿ
*jÿ
,^Bÿÿ"ýýb"ûÿ
:jÿ
.*ÿÿ
 ^Bÿÿ.ýý,ûÿ
Vÿr'  c                   C   sî   t tttƒ ttƒ ƒtttƒ tttƒttƒ ƒ ks<J ‚t tttƒd  tƒtttƒ tttƒƒ ksnJ ‚t td tttƒtdfƒ ƒtd tttƒtdfƒ dtd  tttƒtdfƒ  dt tttƒtƒ  dttƒ  ksêJ ‚d S )Nrm   r{   r   r­   )rH   rp   r6   r5   r"   r2   r   re   rj   rj   rj   rk   Útest_mul_pow_derivative  s
    <2Xÿr(  )rf   (\  r  Zsympy.concrete.summationsr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.exprr   rÒ   r   r   r	   r
   Z
sympy.corer   Zsympy.core.numbersr   r   r   r   r   r   r   r   Zsympy.core.relationalr   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Zsympy.core.sympifyr   r¶  r   r   r   r   r   Z&sympy.functions.elementary.exponentialr   r    r!   r"   Z%sympy.functions.elementary.hyperbolicr#   r$   r%   r&   r'   r(   r)   r*   Z(sympy.functions.elementary.miscellaneousr+   r,   r-   Z$sympy.functions.elementary.piecewiser.   Z(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Z'sympy.functions.special.delta_functionsr7   r8   rÓ   r9   r:   r;   r<   r=   r>   r?   r@   r–  rA   rB   Zsympy.functions.special.hyperrC   rD   Z-sympy.functions.special.singularity_functionsrE   Z&sympy.functions.special.zeta_functionsrF   Zsympy.integrals.integralsrH   Zsympy.logic.boolalgrI   Zsympy.matrices.denserJ   Zsympy.polys.polytoolsrK   rL   Zsympy.printing.strrM   Zsympy.series.orderrN   Zsympy.sets.setsrO   Zsympy.simplify.gammasimprP   Zsympy.simplify.simplifyrQ   Zsympy.simplify.trigsimprR   Zsympy.tensor.indexedrS   rT   rU   Z#sympy.functions.elementary.integersrV   rW   Zsympy.integrals.rischrX   Zsympy.physicsrY   Zsympy.testing.pytestrZ   r[   r\   r]   r^   r_   Zsympy.utilities.exceptionsr`   Zsympy.core.randomra   rp   r€   rê   r˜   r®   r¯   rƒ   rh   r…   r—   rè  ré  rb   re   rl   rs   r†   r‹   r   r“   r   r£   r¤   r«   r°   r²   r³   r´   r¶   rº   r¼   r¿   rÀ   rÁ   rÆ   rÇ   rÈ   rÌ   rÎ   rÔ   r×   rØ   rÙ   rÝ   rß   rá   rã   rå   rç   ré   rë   rì   rí   rñ   rô   rö   r÷   r  r  r  r  r  r  r  r  r  r!  r%  r'  r)  r*  r-  r.  r/  r1  r3  r4  r@  rF  rK  rM  rO  rQ  rS  rU  rW  r\  r]  r^  ra  rc  rd  rj  rk  rl  rm  ro  rq  rs  rt  rv  rw  ry  rz  r|  r}  r€  r‚  r„  r‡  rŠ  rŒ  r  rŽ  r  r  r‘  r’  r“  r—  r˜  r™  r›  rž  r   r¡  r¤  r¦  r¨  rª  r«  r­  r®  r°  r±  r³  r·  r¸  r¹  r½  r¾  rÀ  rÁ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÔ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÞ  rß  rà  rá  râ  rã  rå  rê  rì  rî  rï  rð  rñ  rò  rô  rõ  rø  rù  rû  rþ  rÿ  r   r  r  r  r	  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r#  r$  r%  r&  r'  r(  rj   rj   rj   rk   Ú<module>   sú  ((((  


.
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	0
3!

			
			 


		 	

	Y	*