o
    jgï6 ã                   @   sè  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
mZmZmZmZ d dlmZ d dlmZmZmZmZmZmZmZmZ d d	lmZmZ d d
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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_dS (Ë  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)Ú	full_prec)rM   r   Úevalf)Úer`   Úoptions© ri   ú\/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/integrals/tests/test_integrals.pyÚNS3   s   rk   c                  C   s¢   t dt tƒ} |  t¡t td tddksJ ‚ttdd t| tƒ W d   ƒ n1 s-w   Y  ttdd t| tfƒ W d   ƒ d S 1 sJw   Y  d S )Né   ÚQQ)ÚdomainF©Útest_stacklevel)rK   ÚxrH   r]   r^   rW   ©Úpri   ri   rj   Útest_poly_deprecated7   s    ÿ"ÿrt   c                     s,  dt  ‰ tˆ t t tfƒ ¡ dksJ ‚tˆ tt tfƒ ¡ ttdt  ƒ ks(J ‚tt‡ fdd„ƒ tt‡ fdd„ƒ dt d d  ‰tˆt t tfƒ ¡  ¡ t	dƒ t
 d ksZJ ‚tt‡fdd„ƒ dt d d  } t| t t tfƒ ¡ dkszJ ‚t| t d	dfƒ ¡ tdƒ ks‹J ‚t t d d  }t|t t tfƒ ¡ dks¢J ‚t|t d	dfƒ ¡ dks°J ‚t d t d d  }t|t t tfƒ ¡ tu sÉJ ‚t|t d	dfƒ ¡ tdƒ d
 ksÜJ ‚dt d d dt d    }t|t t tfƒ ¡ t
 d ksüJ ‚t|t d	dfƒ ¡ tdƒ tdƒd  ksJ ‚d S )Né   r   c                      s   t ˆ tƒ ¡ S ©N)rW   rq   Úprincipal_valueri   ©Úgri   rj   Ú<lambda>F   ó    z&test_principal_value.<locals>.<lambda>c                      s   t ˆ ƒ ¡ S rv   )rW   rw   ri   rx   ri   rj   rz   G   ó    é   c                      s   t ˆ tt dfƒ ¡ S ©Nru   )rW   rq   r   rw   ri   )Úlri   rj   rz   K   ó    rl   éþÿÿÿé   )rq   rW   r   rw   Úyr   rZ   Ú
ValueErrorÚtogetherr-   r   r"   r1   )ÚdÚvÚsrc   ri   )ry   r   rj   Útest_principal_valueA   s(   *0"&$4r‰   c                 C   s<   | j }|D ]}|  |¡ ¡ |  ¡  |¡  ¡ dksJ ‚q|S )zºReturn the set of symbols, s, which were used in testing that
    i.diff(s) agrees with i.doit().diff(s). If there is an error then
    the assertion will fail, causing the test to fail.r   )Úfree_symbolsr
   ÚdoitÚexpand)ÚiÚsymsrˆ   ri   ri   rj   Ú	diff_test^   s   *r   c                   C   sd   t ttƒtddfƒdksJ ‚t td tdtfƒdksJ ‚t ddttƒ  tdtfƒtdƒks0J ‚d S )Nr   ru   éÿÿÿÿr   rl   )rH   r"   rq   r   r    ri   ri   ri   rj   Útest_improper_integralh   s   ,r‘   c                  C   s  t ttƒ} | jttƒfksJ ‚t ttfƒ}|jttƒfksJ ‚t tttdtfƒƒ}|jttƒfks3J ‚t tttƒƒ}|jttƒfksDJ ‚t tttddƒfƒ}|jttddƒfksZJ ‚t ttdkƒ}|jttdtƒfksmJ ‚t ttdktdk @ ƒ}|jttddƒfks„J ‚d S )Nru   rl   é
   é   )	rW   r`   Úlimitsr   r   rq   rƒ   rO   r   )Ús1Ús2Ús3Ús4Ús5Ús6Ús7ri   ri   rj   Útest_constructorn   s   
rœ   c                  C   sÐ  t dtƒdks	J ‚t ttddfƒdksJ ‚t ttƒtksJ ‚t tjtƒtju s)J ‚tt ttƒtƒdks5J ‚tt ttddfƒtƒdksDJ ‚tt ttƒtƒtksPJ ‚tt ttdtfƒtƒtks_J ‚td d } tt| tdtfƒtƒtt | tdtfƒtƒ 	¡  
¡   krŒdt d  
¡ ksJ ‚ J ‚tt| tdtfƒtƒtt | tdtfƒtƒ  kr¬dks¯J ‚ J ‚tt| tdtfƒtƒtt | tdtfƒtƒ  krÌdksÏJ ‚ J ‚tt| tƒtƒtt | tƒtƒ  krædkséJ ‚ J ‚t| tttfƒ t¡t | tttfƒ t¡ 	¡  
¡ ksJ ‚t | tttfƒ t¡ 	¡ dt d ksJ ‚t| tttfƒ t¡ 	¡ dt d   
¡ ks5J ‚ttd ttdt fƒ t¡dtd  ksMJ ‚t ttƒ ¡ thksZJ ‚t ttƒtddfƒ ¡ tjtjthkspJ ‚tt ttdt fƒƒthksJ ‚tt ttdt fƒƒtthks“J ‚tttttfƒdks J ‚tttt t fƒdks¯J ‚ttt ttƒ tƒtt td d  ttƒ ksËJ ‚t tƒjsÓJ ‚tddd}t |t tƒjdu sæJ ‚d S )	Nr   ru   rl   é   r}   r`   F©Úcommutative)rW   rq   r   r   ÚNaNr
   rƒ   ÚtrH   r‹   rŒ   ÚaÚatomsrc   ÚZeroÚOner   r    Úis_commutativer   ©rg   r`   ri   ri   rj   Útest_basics„   sR   ÿþÿÿÿÿ4
ÿ,20,"$8r¨   c                  C   sz   G dd„ dt ƒ} | ƒ }t|d |ƒ|d d | ksJ ‚t|d |ddfƒtddƒks-J ‚ttdd„ ƒ ttd	d„ ƒ d S )
Nc                   @   s   e Zd ZdZdZdS )ztest_diff_wrt.<locals>.TestTN)Ú__name__Ú
__module__Ú__qualname__Ú	_diff_wrtr¦   ri   ri   ri   rj   ÚTest³   s    r­   ru   rl   r   r}   c                   S   s   t td td ƒS r~   ©rH   rq   ri   ri   ri   rj   rz   »   s    ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfƒS )Nru   r   r®   ri   ri   ri   rj   rz   ¼   ó    )r   rH   r   rZ   r„   )r­   r¡   ri   ri   rj   Útest_diff_wrt²   s   ""r°   c                   C   s  t tttdt dt fttdt fƒƒthksJ ‚t tttdt fttdt fƒƒthks/J ‚t tttdt fttdt fƒƒtthksFJ ‚t ttttƒƒtthksTJ ‚t ttt ttƒƒtthksdJ ‚t ttt ttdtfƒƒthksvJ ‚t ttt tttftttfƒƒtthksŒJ ‚d S )Nr}   r“   rl   ru   )r   rW   rq   rƒ   ri   ri   ri   rj   Útest_basics_multiple¿   s   2,. $0r±   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks$J ‚| ¡  ¡ | ¡  ¡ ks2J ‚| ¡  ¡ | ¡  ¡ ks@J ‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks\J ‚| ¡  ¡ | ¡  ¡ ksjJ ‚| ¡  ¡ | ¡  ¡ ksxJ ‚d S )NzA BFrž   rq   T)Úcomplex©Úreal)r   r   rW   Úadjointr‹   Ú	conjugateÚ	transpose)ÚAÚBrq   rs   ri   ri   rj   Útest_conjugate_transposeÉ   s    rº   c                  C   s:  t dtdtfƒdksJ ‚t dtdtfƒdt ksJ ‚t ttdtfƒtd d ks*J ‚t dt tdtfƒdtd  d ks>J ‚t dtd  tdtfƒtd ksPJ ‚t dt tdtfƒttƒks`J ‚t dtd  tdtfƒdt d kstJ ‚t td dt  d tdtfƒtd d dtd  d  dt  ks˜J ‚t td tƒtd d ks§J ‚t dt t d tƒdt d td  d ksÀJ ‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÜJ ‚t ttd  tdtfƒttd  d ksòJ ‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ksJ ‚d S )Nr   r}   rl   ru   r   r“   é   é   ÚbÚcr‚   )rH   r¡   rq   r"   r   r¢   )r½   r¾   ri   ri   rj   Útest_integrationÙ   s    ($ (H2(,Vr¿   c                   C   s
  t td td  tddftddfƒtdƒksJ ‚t td td  ttƒtddƒtd  td  ks3J ‚t dtd  dt d  tƒtdt ƒtddƒ tdt ƒtddƒ  tddt  dtd     kshJ ‚t ttt ƒt tddftddfƒtdƒ d ksƒJ ‚d S )	Nrl   r   ru   r   é	   r}   r»   r‚   )rH   rq   rƒ   r   r"   r3   ri   ri   ri   rj   Útest_multiple_integrationì   s   06Fÿ:rÁ   c                   C   s"   t tt ƒtdtfƒdksJ ‚d S ©Nr   ru   )rH   r    rq   r   ri   ri   ri   rj   Útest_issue_3532ô   s   "rÃ   c                   C   sz   t ttƒd tƒdttƒd  d ksJ ‚t ttƒtƒdttƒd  d ks(J ‚t dttƒd  tƒdttƒ ks;J ‚d S )Nr}   rl   r“   ru   r   )rH   r-   rq   ri   ri   ri   rj   Útest_issue_3560ø   s   *&*rÄ   c                   C   s   t tdd„ ƒ d S )Nc                   S   s   t ttfƒS rv   r®   ri   ri   ri   rj   rz   ÿ   r|   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorri   ri   ri   rj   Útest_issue_18038þ   s   rÆ   c                  C   sp  t ttd t  td  ttƒ} tƒ  t| tƒ}W d   ƒ n1 s#w   Y  ttdd t| tƒ}W d   ƒ n1 s>w   Y  ttdd t| tƒ}W d   ƒ n1 sYw   Y  t|t ƒdu sgJ ‚t|t ƒdu spJ ‚|j	ttfksyJ ‚|j	ttfks‚J ‚| 
¡ td d td t d  ttd   ksœJ ‚| 
¡ tt td td  d  td d  ks¶J ‚d S )Nrl   r}   Fro   Tr‚   )rK   rq   rƒ   r\   rW   r]   r^   rH   Ú
isinstanceÚgensÚas_expr)rs   ÚqxÚqyri   ri   rj   Útest_integrate_poly  s     ÿÿÿ48rÌ   c                  C   sl  t ttd t  td  ttƒ} tƒ  t| tddfƒ}W d   ƒ n1 s&w   Y  ttdd t| tddfƒ}W d   ƒ n1 sDw   Y  ttdd t| tdtfƒ}W d   ƒ n1 sbw   Y  t	|t ƒdu spJ ‚t	|t ƒdu syJ ‚|j
tfksJ ‚|j
tfks‰J ‚| ¡ tjtd  td  ksšJ ‚| ¡ td d tt  td td  d  ks´J ‚d S )	Nrl   r}   r   ru   Fro   Tr‚   )rK   rq   rƒ   r\   rW   r]   r^   rH   r   rÇ   rÈ   rÉ   r   ÚHalf)rs   ÚQxÚQyri   ri   rj   Útest_integrate_poly_definite  s     ÿÿÿ"8rÐ   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 )Nrƒ   rl   c                   S   s   t dƒS ©Nrl   rG   ri   ri   ri   rj   rz   0  s    z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS rv   r®   ri   ©rƒ   ri   rj   rz   1  r|   )r   rH   rq   rZ   r„   ri   ri   rÒ   rj   Útest_integrate_omit_var+  s   rÓ   c                  C   sd   t dƒ} ttt| ƒ tƒtd t| ƒ d ksJ ‚ttd t| ƒ tƒtd t| ƒ d ks0J ‚d S )Nrƒ   rl   iè  ié  )r   rH   rq   r3   rÒ   ri   ri   rj   Útest_integrate_poly_accurately4  s   *2rÔ   c                  C   sN   t dƒ} ttd | ƒtd |  ksJ ‚ttd | ddfƒdtd  ks%J ‚d S )Nrƒ   rl   r   ru   )r   rH   rq   rÒ   ri   ri   rj   Útest_issue_3635=  s   (rÕ   c                  C   sž   t ddd} tt|  tddt| d  | d  ksJ ‚tt| ƒt d|   dt| ƒ  tddt|  ƒt| ƒt d|   dt| ƒ   dt| ƒ  ksMJ ‚d S )Nrƒ   T©ÚpositiveÚnone©Úcondsru   rl   )r   rH   rq   r    r3   rÒ   ri   ri   rj   Útest_integrate_linearterm_powE  s
   *(4ÿrÛ   c                   C   sˆ   t tttƒ tƒdt ttƒd  d ksJ ‚t tttƒ tttƒd   tƒdt ttƒd  d dt ttƒd  d  ksBJ ‚d S )Nrl   r}   r“   )rH   r   r-   rq   r   ri   ri   ri   rj   Útest_issue_3618N  s   . .ÿrÜ   c                   C   s"  t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒks%J ‚t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒksJJ ‚t ttd t ƒttd t ƒ tƒttttd  ƒtd  ttd dƒftdfƒttttd  ƒtd  ttd dƒftdfƒ ksJ ‚d S )Nru   r   T)rH   r2   r`   rq   r.   r3   r   ri   ri   ri   rj   Útest_issue_3623T  s   *
ÿ*
ÿ$..ÿÿrÝ   c                  C   s    t dddd} tdt t| t t d ƒ tddgƒdtt|  ƒ t|   ks)J ‚ttt| t t d ƒ td	dƒ tddgƒdtt|  ƒ t|   ksNJ ‚d S )
Nr`   T)rb   Únonzerog      à¿rl   r   r   ç       @r   )r   rH   rq   r3   r   r2   r   ©r`   ri   ri   rj   Útest_issue_3664^  s   &ÿ,ÿrá   c                   C   s4   t tdtd dt  d  tddfƒƒdksJ ‚d S )Nru   rl   r»   é   r‚   z1.10714871779409)rk   rW   rq   ri   ri   ri   rj   Útest_issue_3679f  s   4rã   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fresnelsrl   )	Úsympy.core.functionrå   Ú'sympy.functions.special.error_functionsræ   rH   r3   rq   r-   r   )rå   ræ   ri   ri   rj   Útest_issue_3686k  s
   *ÿré   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ksJ ‚d S )Nru   r“   é   )rY   Úmrˆ   rH   rq   )rë   rˆ   ri   ri   rj   Útest_integrate_unitsr  s   4rì   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 rÑ   )rH   r   rq   ri   ri   ri   rj   Útest_transcendental_functionsx  s   $ÿrí   c                   C   sd   t tdt ƒt tddfƒtd  d ksJ ‚t ttƒdt d  tddfƒtd  d ks0J ‚d S )Nru   r   rl   r¼   r   )rH   r"   rq   r   ri   ri   ri   rj   Útest_log_polylog}  s   .6rî   c                  C   s\   dt tƒ dt tƒd   } tt| tƒtƒ}t|  td¡ ¡ | td¡ ¡  ƒdk s,J ‚d S )Nr‚   rl   é*   g»½×Ùß|Û=)r"   rq   r
   rH   ÚabsÚsubsrf   )rc   Úfidri   ri   rj   Útest_issue_3740‚  s   0ró   c                   C   s&   t ddtd   tƒttƒksJ ‚d S ©Nru   rl   )rH   rq   r1   ri   ri   ri   rj   Útest_issue_3788ˆ  ó   &rõ   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 rÑ   r®   ri   ©rc   ri   rj   rz     r{   z!test_issue_3952.<locals>.<lambda>)r3   rq   rH   r2   rZ   r„   ri   ri   r÷   rj   Útest_issue_3952Œ  s   rø   c                   C   s6   t dt dt  tƒdt tdƒ td  ksJ ‚d S rÑ   ©rH   rq   r"   ri   ri   ri   rj   Útest_issue_4516’  ó   6rú   c                  C   sF   t tdt  t ƒtdtfƒ} t| ƒtjkrt| ƒt	ddƒks!J ‚d S )Nru   r   r   rl   )
rH   r    r   rq   r   r   r   rÍ   r   r   )Úansri   ri   rj   Útest_issue_7450–  s   (rý   c                	   C   sÀ   t dtdt ƒ ddtdt ƒ   tdtfƒt d tdƒt d  ks'J ‚t dtdt ƒ ddtdt ƒ   ƒt d tdƒttdƒttƒ ƒttttd  t ƒ   d  ks^J ‚d S )Nru   rl   r}   r   r“   ©rH   r2   rq   r   r-   r1   r5   rV   ri   ri   ri   rj   Útest_issue_8623›  s   NFÿÿrÿ   c                   C   sŒ   t ddttƒ  tdtfƒttdƒ ksJ ‚t ddttƒ  ƒdtdƒ ttdƒttd ƒ ƒtttd td  t ƒ   d ksDJ ‚d S ©Nru   rl   r   r}   rþ   ri   ri   ri   rj   Útest_issue_9569¡  s   ,`r  c                  C   sÀ   t ddd} ttt d  d|  |   ƒtdt |  |  ƒ }t|tttfƒ}t|tdtfƒtdƒ|  ttd  d| d   ƒ dttƒ  tt	tdƒt d|   ƒ d  td  ks^J ‚d S )Nrˆ   TrÖ   rl   r   )
r   r    Úzrƒ   r-   r   rH   rq   r   r<   )rˆ   ÚpzÚpzgxri   ri   rj   Útest_issue_13733¦  s   2>ÿÿr  c                   C   s   t ddttƒ  tdtfƒttdƒ ksJ ‚t ddttƒ  ƒdtdƒ ttdƒttd ƒ d ƒtttd td  t ƒ   d ksFJ ‚d S r   rþ   ri   ri   ri   rj   Útest_issue_13749®  s   ,dr  c                   C   s<   t ttƒdt d  tƒtttƒtd d  tƒksJ ‚d S rô   )rH   r    rq   rX   ri   ri   ri   rj   Útest_issue_18133³  ó   <r  c                  C   s¶   d} d}t |t t|  t t t t ƒ t|  t t t t ƒ tt  ttdƒftt|  t t t t ƒ dfƒ}t	dt t tt tt   d  }t
t|tƒ|ƒsYJ ‚d S )Ng    €„NAgíµ ÷Æ>r   Tr   gŽíµ ÷Æ >)r.   r   r    r   r¡   rƒ   rq   r  r   r   r   rH   )r¢   r½   ÚrÚfunri   ri   rj   Útest_issue_21741·  s   N ÿ$r  c                  C   sZ   t dddd„ ƒ} t| tƒt ttƒ tdt ƒ gtdt ƒ tdt ƒ ggƒks+J ‚d S )Nrl   c                 S   s    | | d t | | d t ƒ S r~   )r3   rq   )r   Újri   ri   rj   rz   Á  s     ztest_matrices.<locals>.<lambda>r}   )rJ   rH   rq   r2   )ÚMri   ri   rj   Útest_matricesÀ  s
   
þr  c                   C   s¬   t ttƒtƒtttƒtƒksJ ‚t ttƒtddfƒtttƒtddfƒks&J ‚t ttƒtttƒtƒ tƒttƒd d ks>J ‚t tttƒtƒttƒ tƒtttƒƒksTJ ‚d S ©Nr   ru   rl   )rH   rc   rq   rW   r
   r"   ri   ri   ri   rj   Útest_integrate_functionsÉ  s    ,00r  c                   C   s‚   t tttƒtƒtƒttƒksJ ‚t tttƒtƒtƒttttƒtƒ ks%J ‚t tttƒtƒd tƒttttƒtƒd tƒks?J ‚d S rÑ   )rH   r   rc   rq   rƒ   rW   ri   ri   ri   rj   Útest_integrate_derivativesÑ  s
    *ÿr  c                     sÞ  t td d tddfƒ} t}dt d }|  ¡ |  ||¡ ¡ ks"J ‚|  ||¡ ||¡| ks0J ‚dt d }t}|  ||¡ ||¡| ksFJ ‚t tdt ƒtddfƒ} |  tdt ¡t ttƒtd  tdtfƒksjJ ‚|  tdt ¡ tdt ¡| ks|J ‚t ttd  ƒtt tfƒ} |  tdt ¡t dtdtd  ƒ tt tfƒks¥J ‚t ttƒ t| t ¡ ¡ t t| d  tƒ ¡ ks¿J ‚tdƒ}t ttd| fƒ tdt ¡ ¡ t dtd  tt d| fƒ ¡ ksçJ ‚t ttd|fƒ tdt ¡t td td| tfƒksJ ‚t tt tddftddfƒ‰ ˆ  ttdt  tf¡ ¡ ˆ  ttdt	  tf¡ ¡   kr7dks:J ‚ J ‚t tt| t
fƒ‰ ˆ  tdt ¡t dt t| d t
d fƒks[J ‚tt‡ fd	d
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ t td tddfƒ‰ tt‡ fdd
„ƒ tddd}tddd}t tt||fƒ‰ ˆ  tdt ¡ ˆ  tdt ¡t dt t|d |d fƒksÐJ ‚t tt| fƒ‰ ˆ  tdt ¡t dt t| d fƒksíJ ‚d S )Nrl   ru   r   r}   r   éüÿÿÿéýÿÿÿr‚   c                      s   ˆ   td¡S r~   )Ú	transformrq   ri   ©r   ri   rj   rz   õ  r|   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S rv   ©r  rq   rˆ   r¡   ri   r  ri   rj   rz   ö  ó    c                      s   ˆ   tt ¡S rv   ©r  rq   rˆ   ri   r  ri   rj   rz   ÷  r{   c                      s   ˆ   tttf¡S rv   r  ri   r  ri   rj   rz   ø  r  c                      s   ˆ   dt dt ¡S rÑ   r  ri   r  ri   rj   rz   ù  ó    c                      s   ˆ   td t¡S rÑ   r  ri   r  ri   rj   rz   ü  r  r¢   T)Únegativer½   rÖ   )rW   rq   rƒ   r‹   r  r3   r   r    r   r  r½   rˆ   rZ   r„   r   )r¢   ÚfxÚfyÚ_3ÚamÚbpri   r  rj   Útest_transformØ  sZ   0$6ÿ  ÿ
ÿ
ÿÿ220r   c                  C   s^   t jttƒ ttdtd  ƒ d  } ttttƒƒtƒ| ks J ‚ttttƒƒtƒ| ks-J ‚d S rô   )	r   rÍ   r0   rq   r-   rH   r2   r3   r/   r÷   ri   ri   rj   Útest_issue_4052  s   &r!  c                  C   sˆ  t tttddfƒdƒdksJ ‚tttd  ƒtt tfƒ} t | dƒdks&J ‚t | d t ttddƒ  dƒdv s:J ‚td	ƒ}d
t	dƒ dd|d    }dt	dƒ d| d  t	d|d  | d ƒd  }d|d  d d|d  d|  d d  }t	dƒd|d  d|  d  d|d  d|  d d  }|||  | }t t||ddfƒdƒt dt	dƒ dt  dt
t	dƒƒ  d dƒksÆJ ‚t tttdt ƒƒdt td   tddfƒdƒt ddƒksæJ ‚t tt
t	td d ƒƒt	td d ƒtd d   tddfƒdƒt dtd  d dƒksJ ‚t ttttt ƒtt t ƒ td d   tdtfƒdƒt ddƒks;J ‚t tttttƒttƒ ƒƒttd td fƒdddt ddƒks^J ‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks~J ‚t dttdttd ƒ ƒtt tfƒ dddt ddƒksžJ ‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks¾J ‚t tdtd tddfƒ  dd!dd"d#v sÕJ ‚tttƒtd  tdtfƒjdd$}d%|  k rôd&k s÷J ‚ J ‚t tttƒtd  tdtfƒd'd(d)ksJ ‚t tttt d ƒt tt d*fƒd'd(d+ks(J ‚t tttƒƒd,ks4J ‚t ttttfƒƒd-ksBJ ‚d S ).Nrl   r“   rd   z10.5000000000000z1.77245385090552ru   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r¡   r»   r}   é   r‚   é   éù   é6   éA   r   é2   é1   é¢   rê   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)râ   é   é   zsqrt(1-x**2)é   )Úmaxnr,  )z0.0Ú0)r0  g\Âõ(\ß?gR¸…ëQà?Úosc)Úquadz0.504067061906928r   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rk   rW   rq   r    r   r   r   r   r   r-   r1   r"   r3   r2   rf   rƒ   )Úgaussr¡   r¢   r½   r¾   r†   rc   ri   ri   rj   Útest_evalf_integrals  s¢   ÿÿÿ4,<,ÿ0ÿ4ÿÿ
ÿÿ
ÿÿÿ
ÿ4
ÿ(ÿ
ÿ(ÿ
ÿ(ÿ
ÿ
ÿÿ
ÿ$ ÿ
ÿÿÿ
ÿ r5  c                   C   s†   t tdtd d  tƒ td¡dddv sJ ‚t tdtd d  tddfƒƒdks+J ‚t tdtd d  tddfƒdddksAJ ‚d S )	Nru   r“   r‚   Tr+  )z-0.000976138910649103z0.965906660135753z1.93278945918216rl   z0.0144361088886740)rk   rH   rq   rñ   rW   ri   ri   ri   rj   Útest_evalf_issue_939C  s   $ÿ(ÿÿr6  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdksJ ‚| tddƒdtdƒ d  ks,J ‚t tttt  ƒtddftddfƒtju sCJ ‚d S )	Nru   rl   r   rd   z2.43790283299492r  r}   r»   )	rH   r-   rq   rƒ   rk   r   r3   r   r¤   ©Úresri   ri   rj   Ú(test_double_previously_failing_integralsR  s   $"2r9  c            	      C   s   t ttdƒt tddƒ } t ttdƒd t tddƒ }t| tƒ|ks#J ‚dt tddƒ dt tddƒ  }dt tdd	ƒ dt tddƒ  }t|tƒ|ksLJ ‚d
td
  t dt tddƒ  d
t tddƒ  }d
td  t d d
t t tddƒ  dt tddƒ d  }td
 td
  dt t tddƒ  d
t tddƒ  }t|tƒ|ks¥J ‚t|tƒ|ks®J ‚tt|tfƒs·J ‚t|tƒt|tfƒksÄJ ‚t|tƒ ¡ |ksÏJ ‚dt tddƒ d
t tddƒ  }dt tddƒ d d
t tddƒ  }t|tt tfƒ|ksþJ ‚tt tddƒtƒt tddƒksJ ‚tt tddƒtt tfƒd	ks"J ‚tdt tddƒ tt tfƒdks6J ‚tt tddƒt	tƒ tt tfƒt	dƒksNJ ‚d S )Nr}   r“   r   r‚   r   r’   iúÿÿÿr   ru   rl   r  r   r»   )
rE   rq   r¢   rH   rƒ   rU   rW   r‹   r   rc   )	Úin_1Úout_1Úin_2Úout_2Úin_3Úout_3_1Úout_3_2Úin_4Úout_4ri   ri   rj   Ú"test_integrate_SingularityFunction]  s*     0<4 $$$(4rC  c                  C   sš  t ttƒttƒ tt tfƒtdƒksJ ‚t ttƒd tt tfƒtdƒks(J ‚t t ddt  tt  dt  ttƒ ttd ƒ tddfƒtddfƒdksPJ ‚ttd td   ƒt } t | ttdt  ƒ tt tftt tfƒt | ttdt  ƒ tt tftt tfƒ  krÈt | tdt t ƒ tt tftt tfƒ  krÈt | tdt t ƒ tt tftt tfƒ  krÈdtdt ƒ ksËJ ‚ J ‚d S )Nr   rl   r‚   ru   r’   ée   )	rH   r7   rq   rc   r   rƒ   r    r   r-   rr   ri   ri   rj   Útest_integrate_DiracDeltaz  s.   *&ÿ
ÿÿÿÿ**ÿ*þ*ýürE  c                	   C   sb  t tt tƒtttd  td  ttdƒfttƒdfƒksJ ‚t tt tƒttt ttƒ tttƒdƒftdfƒks<J ‚t ttt ƒtƒtttt ƒt ttdƒftdfƒksYJ ‚t tttt ƒ tƒttt d ttt ƒ td  ttd dƒftd d dfƒks†J ‚t ttt  tƒtttt d  tt d  ttt dƒfttƒdfƒks­J ‚t ttt  tƒtttt  tttƒ  ttttƒ dƒftdfƒksÒJ ‚t ttt ƒtƒtt	tt ƒt ttdƒftdfƒksïJ ‚t ttt ƒd tƒttt d t	tt ƒttt ƒ d  t ttdƒftdfƒksJ ‚t tttt ƒ tƒttt	tt ƒ t ttt ƒtd   ttdƒftd d dfƒksMJ ‚t t	tt ƒtƒtttt ƒ t ttdƒfdƒksjJ ‚t t	tt ƒd tƒttt d t	tt ƒttt ƒ d  t ttdƒfdƒks–J ‚t tt	tt ƒ tƒtt ttt ƒ t t	tt ƒtd   ttdƒfdƒksÁJ ‚t ttt ƒtdt
fƒtttt
 ƒt dt  tt kttk @ ttdƒ@ ft
dfƒksïJ ‚t ttƒtt ttt ƒ ƒ tƒtttƒ ttt ƒttttt ƒ ƒ ttttt ƒ ƒ  tttd ƒftdfƒks/J ‚d S )Nru   r   Tr   rl   ©r   T)rH   rq   rƒ   r.   r   r"   r    r`   r2   r3   r  r   r¡   r-   ri   ri   ri   rj   Ú test_integrate_returns_piecewise‹  sZ   &
ÿ"
ÿ
ÿ:
ÿ2
ÿ.
ÿ
ÿ:ÿ>ÿÿ6ÿ4ÿ8ÿ$<ÿþrG  c                  C   st  t ddd} tt| dƒ| ddfƒdksJ ‚tt| d | d ƒ| ddfƒtdd	ƒks+J ‚ttt| ƒt|  ƒƒd | ƒttd|  ƒd | dkfd
td|  ƒd  dfƒksUJ ‚t ddd}tt|| ƒt| d  ƒ | t tfƒ}t|t| d  ƒ | t |fƒ}t| t| d  ƒ | |tfƒ}|||   krµtt	ƒ| t
|ƒ d tt	ƒ| d  t|d  ƒd  ks¸J ‚ J ‚d S )Nrq   Tr³   rl   r   r}   r‚   r(  rê   ru   r   r¾   )Úextended_real)r   rH   r,   r+   r   r    r.   r   r-   r   r<   )rq   r¾   Úint1Úint2Úint3ri   ri   rj   Útest_integrate_max_min¬  s   ,,
ÿ& &ÿÿrL  c                  C   s2  t ttƒtddfƒtddƒksJ ‚t ttƒtddfƒtjks J ‚t ttd ƒtddfƒtddƒks3J ‚t ttd d ƒtddfƒdksEJ ‚t ttd dt  ƒtdd	fƒd
ksYJ ‚t ttƒtddfƒdksgJ ‚t ttƒttƒ tt tfƒdkszJ ‚t ttd ƒtd  tddfƒtddƒks‘J ‚t	ddd\} }t t| ƒ| ƒt
| d  d | dkf| d d dfƒks¶J ‚t td|  d ƒ| ƒt
| d  d|   | dkf| d d|   d dfƒksÝJ ‚t t| |d  ƒ| ddfƒd|d  td|d ƒ d|d   td|d ƒd  d ksJ ‚t tt| ƒ ƒ| ƒt
t| ƒ| dkfdt|  ƒ dfƒks+J ‚t td|  d ƒ| ƒt
|  | dk f| d dfƒksGJ ‚t d|  t| d d ƒ | ƒt
| d | dk f| d  d | dk f| d dfƒksrJ ‚t t| ƒ| |d fƒt
|d |d dkf| d |d dk fdƒks—J ‚d S )Nr   ru   r“   rl   r   r}   r‚   éñÿÿÿrd   iÓ  r   r#  zt sTr³   r¼   é   rF  )rH   r   rq   r   r   rÍ   r   r3   r   r   r.   rð   r,   r    )r¡   rˆ   ri   ri   rj   Útest_integrate_Abs_sign»  s<   "&$(&."
ÿ.
ÿ:
ÿÿÿ,ÿ(ÿrO  c                  C   sÞ   t ttt ƒtƒ} |  td¡t ttd ƒtƒksJ ‚t ttt ƒtddfƒ} |  td¡t ttd ƒtddfƒks:J ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfƒ}| tdi¡t tdtd  ƒtt tfƒksmJ ‚d S ©Nr}   r   ru   rl   r   )rW   r    rq   rƒ   rñ   r	   r   ©rg   rc   Úconvri   ri   rj   Ú
test_subs1Ö  s   "("4rS  c                  C   s  t ttt ƒttƒ} |  td¡t ttd ƒttƒksJ ‚t ttt ƒtddftddfƒ} |  td¡t ttd ƒtddftddfƒksDJ ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tftddfƒ}| tdi¡t tdtd  ƒtt tftddfƒksJ ‚d S rP  ©rW   r    rq   rƒ   r¡   rñ   r	   r   rQ  ri   ri   rj   Ú
test_subs2à  s   $ 0*<rU  c                  C   sÊ   t ttt ƒtdtfttdfƒ} |  td¡t ttd ƒtddftddfƒks(J ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒkscJ ‚d S ©Nr   ru   r}   rl   r   rT  rQ  ri   ri   rj   Ú
test_subs3ê  s
    0*<rW  c                  C   s¾   t ttƒtdtfttdfƒ} |  td¡t ttƒtddftddfƒks$J ‚ttttd  ƒƒ}t |tƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒks]J ‚d S rV  rT  rQ  ri   ri   rj   Ú
test_subs4ò  s
   ,&<rX  c                  C   s¸  t ttd  ƒtt tfƒ} |  td¡| ksJ ‚t ttd  t ƒtƒ} |  td¡t ttd  d ƒtƒks8J ‚t ttd  t ƒttfƒ} |  td¡t tttd  ƒtdfƒks[J ‚|  td¡t ttd  d ƒtƒksoJ ‚t ttd  t ƒtt tftt tfƒ} |  td¡| ksŽJ ‚|  td¡| ks˜J ‚t ttd  ƒttfƒ} |  td¡t ttd  ƒtdfƒks¸J ‚t ttƒtƒ} |  td¡|  td¡ t ttƒtddfƒ  ¡ jsÚJ ‚d S )Nrl   r“   ru   r   )rW   r    rq   r   rñ   rƒ   r‹   Úis_zero©rg   ri   ri   rj   Ú
test_subs5ú  s    (*(*(*
ÿr[  c                  C   sŒ  t dƒ\} }ttt tttƒttƒfƒ}| td¡ttt ttdƒttƒfƒks*J ‚| td¡tttttƒtdƒfƒks>J ‚ttt tttƒttƒftttƒttƒfƒ}| td¡ttt ttdƒttƒfttdƒttƒfƒksrJ ‚| td¡ttt tttƒttƒftttƒtdƒfƒksJ ‚ttt tttƒt| ƒftttƒt| ƒfƒ}| | d¡ttt tttƒtdƒftttƒtdƒfƒksÄJ ‚d S )Nza bru   )r   rW   rq   rƒ   rc   rñ   )r¢   r½   rg   ri   ri   rj   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sJ ‚t ttƒttƒ tttƒttƒftddfƒ} |  ttƒd¡| ks;J ‚|  ttƒd¡t ttƒttƒ tdttƒftddfƒksYJ ‚d S rô   )rW   rq   rƒ   rñ   r3   rZ  ri   ri   rj   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s,J ‚t ttƒttd ƒ tdtfƒ} |  ¡ | ksDJ ‚| jddt ttƒtdtfƒt ttd ƒtdtfƒ ksbJ ‚d S )Nrl   ru   T)Úforce)rW   rc   rq   rƒ   rŒ   r   rZ  ri   ri   rj   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 ©Nrl   r}   )rW   r    rq   ri   ri   ri   rj   rz   ,  r  z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  ƒdt tfƒS r`  )rW   r    rq   r   ri   ri   ri   rj   rz   -  ó    )rZ   r„   ri   ri   ri   rj   Útest_integration_variable+  s   rb  c                   C   sÊ   t ttd ƒttd ƒd  tddfƒ ¡ t ttd ƒttd ƒ tddfƒt ttd ƒtddfƒ ks6J ‚t ttd ƒttd ƒd  tƒ ¡ t ttd ƒttd ƒ tƒt ttd ƒtƒ kscJ ‚d S )Nrl   ru   r   )rW   r2   rq   r3   rŒ   ri   ri   ri   rj   Útest_expand_integral0  s   *"ÿÿ$ÿÿrc  c                      sL  t ttd d ƒtddfƒ‰ ˆ jddddtdƒ ksJ ‚ˆ jdddd	td
ƒ dtdƒ  ks2J ‚ˆ jddddtdƒ d dtdƒ d  dtdƒ d  ksSJ ‚ˆ jd	dddtdƒ d	tdƒ  d	tdƒ  dtdƒ  kstJ ‚tˆ jd	dd ¡ ˆ  ¡  ƒdk s‡J ‚t ttd td  ƒtddftddfƒ‰ tt‡ fdd„ƒ d S )Nr}   ru   rl   r’   Úmidpoint©Úmethodr»   éÙ   r‚   r&  rê   é9   i	  é   iIÎ  iÚ  r   éV   r¼   é   g      à?r   c                      ó
   ˆ   d¡S )Nr‚   ©Úas_sumri   rZ  ri   rj   rz   D  ó   
 z'test_as_sum_midpoint1.<locals>.<lambda>)	rW   r-   rq   rn  rð   r`   rƒ   rZ   ÚNotImplementedErrorri   ri   rZ  rj   Útest_as_sum_midpoint19  s$   *ÿ
ÿ
ÿ
ÿ

ÿ&(rq  c                  C   s  t tt d tddfƒ} tdddd}| jddd ¡ tdd	ƒt td  ks)J ‚| jddd ¡ td
dƒt td  ks?J ‚| jddd ¡ tddƒt td  ksUJ ‚| jd	dd ¡ tddƒt td  kskJ ‚| j|dd ¡ td t tddƒ dd|d    ks‰J ‚d S )Nrl   r   ru   r`   T©r×   rb   rd  re  r‚   r“   r"  r}   é#   él   é   é@   rê   )rW   rq   rƒ   r   rn  rŒ   r   r§   ri   ri   rj   Útest_as_sum_midpoint2G  s   ,,,,$ÿrw  c                  C   s@  t tt d tddfƒ} | jddd ¡ td ksJ ‚| jddd ¡ tddƒtd  td  ks3J ‚| jddd ¡ tdd	ƒttddƒ  td  ksNJ ‚| jd
dd ¡ tddƒttdd
ƒ  td  ksiJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks‘J ‚| jdddd t¡sžJ ‚d S )Nrl   r   ru   Úleftre  r»   r}   r“   ri  r‚   r   é    r¼   r’   F)rf  Úevaluate)	rW   rq   rƒ   rn  rŒ   r   r`   Úhasr   rZ  ri   ri   rj   Útest_as_sum_leftR  s   0668ÿr|  c                  C   s8  t tt d tddfƒ} | jddd ¡ ddt  td  ks!J ‚| jddd ¡ tddƒttddƒ  td  ks<J ‚| jddd ¡ td	d
ƒttddƒ  td  ksWJ ‚| jddd ¡ tddƒttddƒ  td  ksrJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ksšJ ‚d S )Nrl   r   ru   Úrightre  r“   r»   r}   rk  ri  r‚   rd   ry  r¼   )rW   rq   rƒ   rn  rŒ   r   r`   rZ  ri   ri   rj   Útest_as_sum_right]  s   *6668ÿr~  c                  C   s*  t tt d tddfƒ} | jddd ¡ td t tj ks J ‚| jddd ¡ td t tddƒ ks6J ‚| jddd ¡ td t tdd	ƒ ksLJ ‚| jd
dd ¡ td t tddƒ ksbJ ‚| jtdd ¡ td t tddƒ ddtd    ks€J ‚t t	tƒtddfƒ dd¡tjks“J ‚d S )Nrl   r   ru   Ú	trapezoidre  r}   r»   é   r%  r‚   r#  ry  r¼   )
rW   rq   rƒ   rn  rŒ   r   rÍ   r   r`   r   rZ  ri   ri   rj   Útest_as_sum_trapezoidg  s   (,,,$ÿ*r  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 )
Nrl   r   ru   c                      rl  )Nr   rm  ri   rZ  ri   rj   rz   t  ro  z$test_as_sum_raises.<locals>.<lambda>c                      rl  ©Nr   rm  ri   rZ  ri   rj   rz   u  ro  c                   S   s   t tƒ d¡S )Nr}   )rW   rq   rn  ri   ri   ri   rj   rz   v  r{   c                      s
   ˆ   t¡S rv   )rn  r   ri   rZ  ri   rj   rz   w  ro  c                      s   ˆ j dddS )Nr}   Úxxxx2re  rm  ri   rZ  ri   rj   rz   x  r{   )rW   rq   rƒ   rZ   r„   ri   ri   rZ  rj   Útest_as_sum_raisesr  s   r„  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ksJ ‚d S rv   )rW   rq   r‹   ©rg   rc   ri   ri   rj   Útest_nested_doit{  s   r†  c                  C   s  t td td dfƒ} t td tdd fƒ}|  ¡ tddƒksJ ‚| ¡ tddƒks*J ‚t tt td tfƒ tt¡t tt td tfƒksDJ ‚t tt ttd fƒ tt¡t tt ttd fƒks^J ‚ttd td dfƒtddƒksoJ ‚ttd tdd fƒtddƒks€J ‚tddƒtddƒksŒJ ‚d S )Nrl   ru   r}   r   zx**2)rq   Ú1N)rW   rq   r‹   r   rƒ   rñ   r¡   rH   r…  ri   ri   rj   Útest_issue_4665  s   44""rˆ  c                  C   s*   t td tddfƒ} | t | jŽ ksJ ‚d S )Nrl   r   ru   )rW   rq   ÚargsrZ  ri   ri   rj   Útest_integral_reconstructŽ  s   rŠ  c                  C   s  t t dt ƒtddfƒ} |  ¡ tddƒksJ ‚| jddtddƒks$J ‚tdƒ}t |tƒtddfƒ ¡ dks8J ‚t dtdt |tƒtƒfƒ ¡ dksKJ ‚t ttdfƒ ¡ dksXJ ‚tdttƒftdff}t tg|¢R Ž  ¡ tddƒkstJ ‚t tgtt|ƒƒ¢R Ž  ¡ dks†J ‚d S )	Nrl   r   ru   r}   F©Údeeprc   r‚   )	rW   rq   r‹   r   r   r¢   r    ÚlistÚreversed)rg   rc   r”   ri   ri   rj   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sdJ ‚t tt dttƒ  ƒtt ksvJ ‚d S )Nru   rl   r“   rd   r‚   T)rH   r-   rq   r.   r   r   r"   ri   ri   ri   rj   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sWJ ‚d S )Nrl   ru   r   T)rH   rq   r`   r"   r.   r   ri   ri   ri   rj   Útest_issue_18153«  s   *&ÿÿþýÿr‘  c               	   C   sˆ  ddl m} m}m} t| ƒjdu sJ ‚td| ƒjdu sJ ‚td| dfƒjdu s)J ‚td| ddfƒjdu s6J ‚td| d|fƒjdu sCJ ‚td| |fƒjdu sOJ ‚t| |ƒjdu sYJ ‚t| |d| fƒjdu sfJ ‚t| |ddfƒjdu ssJ ‚t| | ddfƒjdu s€J ‚t| |ddfƒ}|jdu r“| ¡ dks•J ‚t| |||fƒ}|jdu r¨| ¡ dksªJ ‚td|||d fƒ}|jdu r¿| ¡ dksÁJ ‚t| | | ddf|ddfƒjdu sÔJ ‚t| | | ddf|d|fƒjdu sçJ ‚t| | dfƒjdu sóJ ‚t| | dt||ddfƒfƒjdu sJ ‚tt||ddfƒ| ddfƒjdu sJ ‚tt| ƒd t	| ƒd  d | ƒjdu s2J ‚tt
| ƒ| ddfƒjdu sBJ ‚d S )	Nr   ©rq   rƒ   r  Fru   Trl   rß   r}   )Ú	sympy.abcrq   rƒ   r  rW   Ú	is_numberr`   r   r3   r2   rc   )rq   rƒ   r  r   ri   ri   rj   Útest_is_number´  s0   &&((.$r•  c                  C   s\  ddl m} m}m} td| ƒj| hksJ ‚t| ƒj| hksJ ‚t| | d |fƒj|hks-J ‚t| | |d fƒj|hks;J ‚t| | d|fƒj|hksIJ ‚t| | |dfƒj|hksWJ ‚t| | | |fƒj| |hksfJ ‚t| | |ƒj| |hkssJ ‚t| | ddfƒjtƒ ksJ ‚t| |ddfƒj| hksJ ‚t| |||fƒj| |hksžJ ‚t| |ddf|d d fƒj| |hks±J ‚t| |ddf| d|fƒj|hksÃJ ‚td|ddf|d| f| ddfƒjtƒ ksÙJ ‚td|| df|d| f| ddfƒjtƒ ksïJ ‚td| ddf|| df|ddfƒj| hksJ ‚tt| ƒt| ƒd|fƒj|hksJ ‚tt| ƒt| ƒd| fƒj| hks,J ‚d S )Nr   r’  ru   rl   )r“  rq   rƒ   r  rW   rŠ   Úsetrc   r’  ri   ri   rj   Útest_free_symbolsÔ  s:   ÿÿÿÿ
ÿ&*r—  c                  C   s.  ddl m} m} td| d| fƒjsJ ‚td| ddfƒjsJ ‚td| ddftdfƒjdu s.J ‚t| |dfƒjs8J ‚t| | |dfƒjd u sFJ ‚t||dt| ƒf| dfƒ}|jd u sZJ ‚t|| df|dt| ƒfƒjdu slJ ‚t| | ttfƒjswJ ‚t| | t t fƒjs„J ‚tt| ƒ| ddt	 fƒjd u s•J ‚d S )Nr   )rq   rë   ru   rl   FT)
r“  rq   rë   rW   rY  rƒ   r    r   r3   r   )rq   rë   r   ri   ri   rj   Útest_is_zeroð  s    $&r˜  c                     s\   ddl m}  tt| ƒ| | fƒ}| | ¡‰ |j| dd ¡ t‡ fdd„tdƒD ƒŽ ks,J ‚d S )Nr   ©rq   r»   rà   c                    s   g | ]}t ˆ ƒ‘qS ri   )Únext)Ú.0r  rZ  ri   rj   Ú
<listcomp>  r  ztest_series.<locals>.<listcomp>r‚   )	r“  rq   rW   r2   ÚlseriesÚnseriesÚremoveOr   Úrange)rq   r   ri   rZ  rj   Útest_series  s   
4r¡  c                  C   sV   t dƒ} tdt| ƒ |  | ƒt| ƒt| ƒ ksJ ‚tt| ƒd |  | ƒ t¡s)J ‚d S )Nrq   ru   rl   )r   rH   r3   r"   r;   r2   r{  r9   r™  ri   ri   rj   Ú!test_trig_nonelementary_integrals
  s   *$r¢  c               	   C   s2  t dƒ} t dƒ}t ddd}tt| d |d  ƒ| ƒ|d t| | ƒ d | t| d |d  ƒ d  ks7J ‚tt| d |d  ƒ| ƒ| t| d |d  ƒ d |d t| t| d |d  ƒ ƒ d  kshJ ‚t ddd} t ddd}td| d |d  td	ƒ  | ƒ| |d t| d |d  ƒ  ks—J ‚d S )
Nrq   rƒ   r  TrÖ   rl   r³   ru   z3/2)r   rH   r-   r$   r"   r   r’  ri   ri   rj   Útest_issue_4403  s   2ÿBÿ ÿr£  c                   C   sT   t ttd  d ƒtƒdtttdtd  ƒ ƒ ttdtd  ƒ d  ks(J ‚d S )Nrl   r‚   r   r  )rH   r-   rq   r1   ri   ri   ri   rj   Útest_issue_4403_2#  s   2ÿr¤  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RTrÖ   rl   r   r‚   )r   rH   r-   rq   r   )r¥  ri   ri   rj   Útest_issue_4100(  s   8r¦  c                  C   sÄ  ddl m} m}m}m} tdƒ}tt||ƒ|ƒ|ƒt||ƒ||ƒks$J ‚t||ƒƒj||ƒt|ƒfks5J ‚tt||ƒƒƒj||ƒt|ƒt|ƒfksKJ ‚tt||ƒƒ|ƒj||ƒt|ƒt|ƒfksbJ ‚tt||ƒ|ƒ|ƒj||ƒt|ƒt|ƒfkszJ ‚ttt||ƒ|ƒ|ƒ|ƒj||ƒt|ƒt|ƒt|ƒfks˜J ‚t	t||ƒ|ƒ|ƒt||ƒ||ƒks¬J ‚t	t||ƒ|ƒ|ƒ|t||ƒ|ƒ ksÁJ ‚t	t||ƒ|ƒ|ƒt|||ƒ |ƒ|t||ƒ|ƒ fv sßJ ‚t	td|ƒ|ƒ|d ksíJ ‚t	td|ƒ|ƒd| | ksýJ ‚td||ƒjtd||ƒjksJ ‚t||ƒ||||ƒ 
¡ |d t||ƒ||ƒ d ks+J ‚t||ƒ|ddf| d|f|d|fƒ 
¡ ||d  t||ƒ|ddfƒ |d t||ƒ|ddfƒ  ks`J ‚d S )Nr   )Úwrq   rƒ   r  rc   rl   ru   )r“  r§  rq   rƒ   r  r   rW   r‰  r   rH   r‹   )r§  rq   rƒ   r  rc   ri   ri   rj   Útest_issue_5167-  s(   (",.0ÿ(*< ":&:ÿr¨  c                  C   s  t ddd} ttttƒd  ƒtƒttƒttddƒƒ tttƒt	j
 ƒ d ks*J ‚ttttƒd ƒtƒttƒttddƒƒ tttƒt	j
 ƒ d ksMJ ‚tt|  ttƒd  ƒtƒttƒtdd|   ƒ tt| ƒttƒ ddt| ƒ   ƒ dt| ƒ  ksJ ‚d S )Nr  TrÖ   rl   ru   r‚   r   )r   rH   r    r"   rq   r-   r   r   r<   r   rÍ   r>   ©r  ri   ri   rj   Útest_issue_4890D  s   *ÿ*ÿFÿrª  c                   C   s,   t dttdtd  ƒ  tƒ t¡rJ ‚d S rô   )rH   rq   r-   r{  rW   ri   ri   ri   rj   Útest_issue_4551N  s   ,r«  c               	   C   s   t dddd} tt| td|   d  tdtjfƒ| d dd|   | d   | dd|     ddd|    | ddd|        ƒdksFJ ‚d S )Nr`   T©rb   r×   ru   r   rl   )r   rQ   rH   rq   r   rÍ   rà   ri   ri   rj   Útest_issue_4376R  s   "Nÿÿr­  c                   C   sX   t ttƒtd  ttddƒ  tƒdttddƒ  d dttddƒ  d  ks*J ‚d S )Nr}   ru   r¼   r   r#  )rH   r-   rq   r   ri   ri   ri   rj   Útest_issue_4517X  s   "*ÿr®  c               
   C   sú  t ddd\} }tt| t ƒt|t ƒ tdtfƒ ¡ tdt| dƒt|dƒB ft d t| | ƒt| dƒt|dƒ@ B ftd t| |ƒt| dƒt|dƒ@ B fdƒksSJ ‚tt| t ƒt|t ƒ tfƒtdtt| dƒt|dƒƒft t|t ƒd  d tt	|t ƒd  d  t|t ƒt	|t ƒ d|   t| | ƒftt|t ƒd  d tt	|t ƒd  d  t|t ƒt	|t ƒ d|   t| |ƒf|t| t ƒ t	|t ƒ | d |d   | t|t ƒ t	| t ƒ | d |d    dfƒksûJ ‚d S )Nzk mTra   r   rl   rF  )
r   rH   r3   rq   r   rQ   r.   r   rI   r2   )Úkrë   ri   ri   rj   Útest_issue_4527]  s$   &($ýÿ \X**ÿÿür°  c                  C   sp   t ddd} ttt d t |  t ƒt tt tfddttt d t |  t ƒt tt tfƒks6J ‚d S )Nrƒ   TrÖ   rl   rØ   rÙ   )r   rH   r    r   r   rq   r   rW   )Úyposri   ri   rj   Útest_issue_4199r  s   .*ÿr²  c                  C   s®  t ddd\} }}}tttd  t| t  ƒtƒttƒ t|d  d ƒ tt| d t ƒ d ks6J ‚tt| td  |t  | ƒtƒ ttƒt||d d|    ƒ t	d|  t | dt| ƒ  ƒ dt| ƒ  ¡spJ ‚ddl
m} ddlm} |tttd  ƒtt| t ƒ tt tfƒƒttƒt|d  d ƒ ks£J ‚t d	dd\} }|tt|  td  d| t  ƒtt tfƒƒttƒt|d |  ƒ t| ƒ ksÕJ ‚d S )
Nza:dTrÖ   rl   r‚   r   )Ú
expand_mul)r¯  za d)r   rH   r    rq   r   r-   r   r<   Úequalsr>   rç   r³  r“  r¯  r   )r¢   r½   r¾   r†   r³  r¯  ri   ri   rj   Útest_issue_3940y  s    2ÿ"Jÿ.ÿ.ÿrµ  c                   C   sV   t t td td   tƒttt t t ƒ d tttt t ƒ d  ks)J ‚d S rÑ   )rH   r¢   rq   r   r"   ri   ri   ri   rj   Útest_issue_5413‰  s   Vr¶  c               
   C   s¸  t dƒ\} }tddd}|  t| ƒ }|  |t  ttƒd ttƒd   }ttƒd  ttƒd  }ttƒd  ttƒd  d }t|||  tƒ||  |  t	|t ƒ | | t t| ƒ   ||  |  t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   | | t | |  t	tƒ t|ƒ  t| ƒ | | t | |  t	tƒ t|ƒ  t| ƒ fv sÚJ ‚d S )NzA zr¾   T)rÞ   rl   ru   )
r   r   r    r¡   r3   rq   r2   rƒ   rH   r"   )r¸   r  r¾   ÚP1ÚP2Úh1Úh2ri   ri   rj   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s,J ‚d S )Nr}   rl   rê   r   )r3   rƒ   rq   r2   rR   rL   rH   r
   )Úexprri   ri   rj   Útest_issue_4892b¤  s   4	(r½  c                   C   sX   t ttƒtttƒ tdtftdtftdtfƒdttttƒtdtftdtfƒ ks*J ‚d S ©Nr   rl   )rH   r3   rq   rc   rƒ   r  r   rW   ri   ri   ri   rj   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s6J ‚tt| tƒtƒ| ksBJ ‚tttd ƒtƒttd ƒksSJ ‚d S )Nr   r’   rl   r‚   é   r¼   iÐ  r»   i€  i _7 r#  r“   )r3   rq   ÚseriesrN   rH   r
   ©rc   ry   ri   ri   rj   Útest_integrate_series¶  s
   H&rÃ  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heurischru   )Úsympy.integrals.heurischrÅ  rD   rq   rÄ  ri   ri   rj   Útest_atom_bugÀ  s   $rÇ  c                  C   sh   t ddd} tttt |  ƒtdtftdtfƒ ¡ t| ƒttd |  ƒ t	 dttƒ  |  ks2J ‚d S )Nr  F©Úzeror   rl   )
r   rH   r3   rq   rƒ   r   r…   r"   r9   r   r©  ri   ri   rj   Útest_limit_bugÅ  s   &*ÿrÊ  c                  C   s,   t dƒ} tttƒ| tƒ tƒ t¡sJ ‚d S )Nry   )r   rH   r    rq   r{  rW   rx   ri   ri   rj   Útest_issue_4703Ë  ó   $rË  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡sJ ‚d S )Nrc   rl   )r   rH   rq   r
   r{  rW   r÷   ri   ri   rj   Útest_issue_1888Ð  s   &rÍ  c                   C   sF   t ttt ƒtt d td ftdtfƒdttd d ƒ ks!J ‚d S )Nrl   r   )rH   r2   rq   rƒ   r   r;   ri   ri   ri   rj   Útest_issue_3558×  s   FrÎ  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ksJ ‚d S )Nru   r"  r‚   rl   )rH   r-   rq   r$   ri   ri   ri   rj   Útest_issue_4422Û  rû   rÏ  c                   C   sN   t tttddt  ƒ tƒƒtdt d ƒdtd  t d  d ks%J ‚d S )Nru   rl   r¼   rd   )rQ   rH   rq   r-   ri   ri   ri   rj   Útest_issue_4493ß  s   &ÿrÐ  c                   C   sh   t ttƒt tt tfƒtksJ ‚t ttƒt tdtfƒtd ks#J ‚t ttƒt tƒttƒks2J ‚d S r¾  )rH   r3   rq   r   r   r;   ri   ri   ri   rj   Útest_issue_4737ä  s   "$"rÑ  c                  C   sh   ddl m}  tddd}t| ttt ƒttƒ t|  tdtfƒƒƒ|t	d|ƒ d t
|ƒ ks2J ‚d S )Nr   rä   r¢   TrÖ   ru   )rç   rå   r   rQ   rH   r    rq   r"   r   rB   rA   )rå   r¢   ri   ri   rj   Útest_issue_4992ê  s
   ,ÿrÒ  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
lowergammaru   )Ú'sympy.functions.special.gamma_functionsrÔ  rQ   rH   r    rq   rƒ   rÓ  ri   ri   rj   Útest_issue_4487ò  s   2rÖ  c                  C   s,   t dƒ} td| d  | ddfƒtu sJ ‚d S )Nrq   ru   rl   r   )r   rH   r   r™  ri   ri   rj   Útest_issue_4215÷  rÌ  r×  c                  C   s    t dddd} tt|  ttƒ tƒ| t t|   ttƒ | d d|   d  tt|   ttƒ | d d|   d   tt|   | d d|   d   ksNJ ‚d S )Nr`   Tr¬  rl   ru   )r   rH   rq   r"   rà   ri   ri   rj   Útest_issue_4400ü  s   RÿÿrØ  c                   C   sZ   t tdt ƒtdt ƒ d t tddttt d ƒttd ƒ d t tƒks+J ‚d S )Nru   rl   T©rD   )rH   r-   rq   rW   ri   ri   ri   rj   Útest_issue_6253  s   (&ÿrÚ  c                   C   sè   t ddt t t  tddftddftddfƒdtdƒ dtdƒ d  dtdƒ d  dtdƒ  d	td
ƒ  dtdƒ dtd
ƒ  dtdƒ d  dtdƒ dtdƒ d  dtdƒ dtdƒ d  dtdƒ d  fv srJ ‚d S )Nru   r   iôÿÿÿr}   r¼   rl   r»   r“   r   r‚   ri  r.  é/   ©rH   rq   rƒ   r  r"   ri   ri   ri   rj   Útest_issue_4153
  s
   .B@*ýrÝ  c                  C   sf   t dƒ\} }}t|t|  |  | t| d td  ƒ t| | | fƒ}| t¡r*J ‚| t¡r1J ‚d S )NzR b hrl   )r   rH   rq   r-   r{  r   rW   )r¥  r½   Úhrg   ri   ri   rj   Útest_issue_4326  s   8rß  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`  rù   ri   ri   ri   rj   Útest_powers  s   >rà  c                   C   s<   t tdd„ ƒ ttdt ƒt tddfdd t¡sJ ‚d S )Nc                   S   ó   t dt tdddS )Nru   T)ÚmanualrD   r®   ri   ri   ri   rj   rz      r  z$test_manual_option.<locals>.<lambda>ru   r   T©râ  )rZ   r„   rH   r"   rq   r{  rW   ri   ri   ri   rj   Útest_manual_option  s   .rä  c                   C   s6   t tdd„ ƒ tttƒtddtttƒtƒksJ ‚d S )Nc                   S   rá  )Nru   T)rD   Úrischr®   ri   ri   ri   rj   rz   &  r  z%test_meijerg_option.<locals>.<lambda>TrÙ  )rZ   r„   rH   r5   rq   rW   ri   ri   ri   rj   Útest_meijerg_option%  s   (ræ  c                   C   sª   t tdd„ ƒ tttd  ƒtddtttd  ƒtƒksJ ‚ttdt ƒt ttddtd ttdt ƒ d td   ksAJ ‚tttƒtddt	ttƒtƒksSJ ‚d S )Nc                   S   s   t dttƒ tdtfddS )Nru   r   T©rå  )rH   r"   rq   r   ri   ri   ri   rj   rz   -  ra  z#test_risch_option.<locals>.<lambda>rl   Trç  ru   )
rZ   r„   rH   r    rq   rX   r"   rƒ   r<   rW   ri   ri   ri   rj   Útest_risch_option+  s   0D(rè  c                   C   s,  t tdd„ ƒ tttd ƒtddttƒttƒ d ksJ ‚tttƒt tddtttƒt tƒks4J ‚tt	tƒt
t	tƒƒ ttddƒ  tddd	ttd
dƒ  tt	tƒƒ d dttd
dƒ  t
t	tƒƒ d  dttd
dƒ  tt	tƒƒ d dttd
dƒ  t
t	tƒƒ d  t	tƒ  ks”J ‚d S )Nc                   S   rá  )Nru   T)rå  rÅ  r®   ri   ri   ri   rj   rz   6  r  z&test_heurisch_option.<locals>.<lambda>rl   TrÄ  r}   r‚   Fi€ÿÿÿru   i!  éð   r"  râ   )rZ   r„   rH   r    rq   r-   r   r>   rW   r"   r2   r   r3   ri   ri   ri   rj   Útest_heurisch_option4  s   .,*BJÿÿrê  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |ddsJ ‚d S )Nru   gHáz®Gñ?rl   g333333@gê-™—q=)Útol)rq   rH   r
   r_   rÂ  ri   ri   rj   Útest_issue_6828A  s   rì  c                  C   sX   t dƒ} ttt t| t  ttƒ ƒ tƒttt|  ttƒ ƒ ttƒ t ks*J ‚d S )NÚx_max)r   rH   rƒ   r   r    rq   r2   r¢   )rí  ri   ri   rj   Útest_issue_4803G  s   ""ÿrî  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 rô   )rH   r-   r5   rq   ri   ri   ri   rj   Útest_issue_4234M  s   @rï  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 )
Nrl   r“   Tr‹  rd   r}   é   r»   iøÿÿÿ)	rQ   rH   rq   r-   rL   r.   r   r#   r0   ri   ri   ri   rj   Útest_issue_4492Q  s    "ÿJÿÿFÿÿýÿrñ  c                  C   s  dt t ttƒ  } t| tddfƒ}t| tddfƒ ¡ |ks J ‚t| ttƒ tddfƒ|tdƒ tdƒ ks8J ‚td|  ttƒ tddfƒd| tdƒ tdƒ ksTJ ‚ttdt t	 t t
 t  t
 ƒtdtfƒttdt t	 t ƒtdt t	 td  t
 ƒ tdtfƒks‹J ‚d S )Nru   rl   r}   g333333ó?r   g333333ó¿)r¢   r  r"   rX   rW   r‹   rH   r    r`   rˆ   r¡   rq   )rc   Ú
integral_fri   ri   rj   Útest_issue_2708Z  s   0ÿ,0ÿÿró  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      $@gš™™™™™¹?gš™™™™™É?z%1.86831064982608*y + 2.16387491480008)rq   rƒ   r    rH   Ústr)rc   rg   ri   ri   rj   Útest_issue_2884h  s    rõ  c                  C   s”  ddl m} m} ttt t ƒttƒ tdtfƒt	t
t	t t
td  d   |td ƒdk fdt
t ddtd     |td ƒdk fttjfdfdtjfdfttƒd ƒdfƒ td dkfttt t ƒttƒ tdtfƒdfƒksvJ ‚ttt t ƒttƒ tdtfƒt	d	td  d dt d  d  t|tƒdk|| tƒƒt
d k || tƒƒt
d kƒfttt t ƒttƒ tdtfƒdfƒksÈJ ‚d S )
Nr   ©Úargr   rl   ru   r   )r   r   )r   Tr   )Ú$sympy.functions.elementary.complexesr÷  r   rH   r    rˆ   rq   r%   r   r.   r   rD   r   rÍ   r   rW   r(   rI   rö  ri   ri   rj   Útest_issue_8368in  sN    ÿÿ

ýüû
õ þòÿ  
ýÿ ÿùÿrù  c                   C   s€   t tdt ƒƒdtdt ƒ ksJ ‚t tdt ƒƒdt dttdt ƒd ƒ  ks,J ‚t ttƒƒttttƒd ƒ ks>J ‚d S )Nç      ð?ru   )rH   r(   rq   r%   r)   r"   ri   ri   ri   rj   Útest_issue_8901Ž  s   $4(rû  c                   C   s¶   t ttƒd t tddfƒtdƒ d dtdƒ d  ksJ ‚t ttƒd t tdtfƒtd ks3J ‚t ttƒd td  tƒtdt ƒ tdt ƒdt   ddt   ksYJ ‚d S )Nr}   r   ru   r‚   rl   )rH   r3   rq   r;   r   r   r2   ri   ri   ri   rj   Útest_issue_8945”  s   >(Prü  c                  C   sX   t dƒ\} }}}tt|  t | ƒd ||t    t¡}tt|td|fƒjvs*J ‚d S )Nzi L a brl   r   )r   r2   r   rq   Úrewriter    rH   rŠ   )r   ÚLr¢   r½   Ú	integrandri   ri   rj   Útest_issue_7130›  s   *r   c                  C   sx   t dƒ\} }}}t| | ||gƒ}t||ƒt||ƒ ¡ ksJ ‚t||ƒt| |d  d g|| g|| ggƒks:J ‚d S )Nza b c trl   )r   rJ   rH   rW   r‹   )r¢   r½   r¾   r¡   Úvtri   ri   rj   Útest_issue_10567¢  s   :r  c                   C   s6   t ttd  dt  d ƒtddfƒdt ksJ ‚d S )Nrl   r»   é0   r‚   rê   r"  )rH   r-   rq   r   ri   ri   ri   rj   Útest_issue_11742©  rû   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¡   ri   ri   rj   Útest_issue_11856­  s   *r  c                   C   s0   t ttdt ƒƒtddfƒttƒd ksJ ‚d S ©Nru   r   rl   )rH   r-   r"   rq   r   ri   ri   ri   rj   Útest_issue_11876²  s   0r  c                   C   sV   t dttƒ dtdt ƒ  tdt ƒ tƒdtdt ƒ dtdt ƒ  ks)J ‚d S )NiÄÿÿÿg3333333@r‚   g333333Àr»   g      (@r“   )rH   r    rq   ri   ri   ri   rj   Útest_issue_4950·  s   ,ÿr  c                   C   sP   t tttd ƒƒƒttttd ƒƒ d dt tttd ƒƒ d  ks&J ‚d S )Nrl   r“   )rH   r3   r"   rq   r2   ri   ri   ri   rj   Útest_issue_4968¼  s   Pr	  c                   C   s²   t dtd  tt tfƒtu sJ ‚t dtd  tddfƒtu s!J ‚t dtd d  tddfƒtu s3J ‚t dtd  tddfƒt u sDJ ‚t dtd d  tddfƒt u sWJ ‚d S )Nru   rl   r   r   )rH   rq   r   ri   ri   ri   rj   Útest_singularitiesÀ  s
   " $"*r
  c                  C   s¸   t ddd\} }tt| |  |  ||  ƒ| tt||  ƒ tt||  ƒf|ttƒ ttƒfƒtt| d |d  ƒ| t|d  t ƒ t|d  t ƒf|ttƒ ttƒfƒksZJ ‚d S )Nzx yTr³   r}   rl   )r   rH   r3   r-   r   rW   )rq   rƒ   ri   ri   rj   Útest_issue_12645É  s   "þ&þýr  c                   C   s6   t ttƒttƒd  tdtd fƒtddƒksJ ‚d S )Nr}   r   r¼   ru   )rH   r3   rq   r2   r   r   ri   ri   ri   rj   Útest_issue_12677Ó  rû   r  c                   C   s6   t tdt ƒttƒ t tdtfƒtdƒ ksJ ‚d S )Nr}   r   )rH   r2   rq   r   r"   ri   ri   ri   rj   Útest_issue_14078×  rû   r  c                   C   s(   t dttƒ tdtfƒtd ksJ ‚d S r  )rH   r%   rq   r   r   ri   ri   ri   rj   Útest_issue_14064Û  s   (r  c                	   C   sp   t ddtttj ƒdttƒ    tƒtttjƒtttƒttjƒdttjƒ   ƒ ttjƒt   ks6J ‚d S r~   )rH   r    rq   r   rÍ   r"   r   ri   ri   ri   rj   Útest_issue_14027ß  s   &>ÿr  c                   C   s&   t ttƒtdtd fƒtju sJ ‚d S r¾  )rH   r5   rq   r   r   ÚInfinityri   ri   ri   rj   Útest_issue_8170ä  rö   r  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 )Nru   r   r   r}   )rH   rq   r   r    ri   ri   ri   rj   Útest_issue_8440_14040è  s   &r  c                   C   s”   t dtt d  tddfƒdtd  dt  ksJ ‚t ddt t t d  tddftddftddfƒdtdƒ dtdƒ  dtd	ƒ  ksHJ ‚d S )
Nru   rl   r   r   r  r‚   r¼   rÀ   r}   rÜ  ri   ri   ri   rj   Útest_issue_14096í  s   42"ÿr  c                   C   sh   t tdtdtd  ƒ tddfƒ ¡ d ƒdk sJ ‚t ttdtd  ƒtddfƒ ¡ d ƒdk s2J ‚d S )Nru   r}   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rq   r`   ri   ri   ri   rj   Útest_issue_14144ó  s   44r  c                   C   s(   t ttt ƒttƒ tƒ t¡sJ ‚d S rv   )rH   r    r   rq   r"   r{  r:   ri   ri   ri   rj   Útest_issue_14375ø  s   (r  c                  C   sX   t dƒtttƒ} t| tddftddftddfƒt| tddftddftddfƒks*J ‚d S )Nrc   r   ru   rl   r}   )r   rq   rƒ   r  rH   rW   r÷   ri   ri   rj   Útest_issue_14437þ  s   ÿr  c                   C   sR   t dtttƒd ƒ tƒttttƒd ƒd ƒttttƒd ƒd ƒ ks'J ‚d S r~   ©rH   r-   r    rq   r"   ri   ri   ri   rj   Útest_issue_14470  s   Rr  c                  C   s¨   t dt td ƒt  dtd   ƒdtd  t  dt td ƒt  d  } t| tƒt dtd  tt td ƒ  d ƒ tt dtd  ƒ t dtd  ƒ  ksRJ ‚d S ©Nru   rl   r}   )r    rq   rH   r÷   ri   ri   rj   Útest_issue_14877  s   LHÿr  c                  C   sB   t td  d ƒtd  t  } t| tddgƒt d ksJ ‚d S )Nrl   ru   r   r»   )r-   rq   rH   r   r÷   ri   ri   rj   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s#J ‚d S )Nrl   ru   r   r}   r"  )r-   rq   rH   r   r¥   r   r÷   ri   ri   rj   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 sJ ‚d S )Nr  rl   r   )rq   r   r    rH   r   r÷   ri   ri   rj   Útest_issue_12081  s   r  c                  C   sD   dt  d } d|  td|  ƒ t d  }t|t ddgƒdks J ‚d S )Nru   r‚   r   rl   r   )rq   r    rH   )rƒ   rc   ri   ri   rj   Útest_issue_15285  s   r  c                   C   s”   t tt tt ƒ ttƒ tdtfƒ ¡ tttd ƒt	dtƒ ttd ƒt  t
tƒd dkfttt tt ƒ ttƒ tdtfƒdfƒksHJ ‚d S )Nr   ru   T)rH   rq   r`   r    r"   r   rP   r.   rA   rB   r   rW   ri   ri   ri   rj   Útest_issue_15432$  s   *4(þr  c                  C   s„   t dƒ} tdtd\}}tttt | | | |   ƒtddt ttt | |  ƒ ttt | |  ƒ | | | |   ks@J ‚d S )NÚomegazm p)ÚclsrØ   rÙ   )rT   r   rS   rH   r    rq   r   )r   rë   rs   ri   ri   rj   Útest_issue_15124*  s
   $<ÿr"  c                   C   s~  t ƒ  ttttƒƒ W d   ƒ n1 sw   Y  t ƒ  ttttƒtƒttttƒtttƒƒks3J ‚W d   ƒ n1 s=w   Y  t ƒ  ttttƒtƒ ¡ ttd d tt ƒks]J ‚W d   ƒ n1 sgw   Y  ttdd tttƒ t¡ttd d tt ƒksˆJ ‚W d   ƒ n1 s’w   Y  ttttƒtddfƒtt	j
tƒksªJ ‚tttƒ tddf¡tt	j
tƒks½J ‚d S )Nrl   Fro   r   ru   )r\   rW   r   rq   rƒ   r‹   r]   r^   rH   r   rÍ   ri   ri   ri   rj   Útest_issue_152181  s   ÿ,ÿ0ÿ,ý&*r#  c                  C   s€   t ttd  tdt ƒ ƒttd tdt ƒ ƒ tdtfƒ} t| tƒs&J ‚t	| t
tƒd ttƒ   ttd ¡ƒdks>J ‚d S )Nrl   r   r¼   )rH   r    rq   r2   r¡   r3   r   rÇ   r.   rP   r-   r   rñ   r7  ri   ri   rj   Útest_issue_15292B  s   >4r$  c                   C   s.   t tdt ƒttƒ tƒdttƒ ksJ ‚d S rÑ   )rH   r3   rq   ri   ri   ri   rj   Útest_issue_4514H  ó   .r%  c                  C   sè   t ddd\} }}ttt| d ƒƒ| ||fƒ}ttt| d ƒƒ| ƒ}| |d|di¡ddt  ks3J ‚| | d¡| | d¡ ddt  ksGJ ‚| |d|d	i¡tdƒ td
ƒ ks[J ‚| | d	¡| | d¡ tdƒ td
ƒ ksrJ ‚d S )Nzx a bTr³   rl   ru   r}   r   r  r   r“   )r   rH   r    r   rñ   r   )rq   r¢   r½   ÚdefiniteÚ
indefiniteri   ri   rj   Útest_issue_15457L  s   "((2r)  c                   C   sN   t tttƒ ttƒ tƒtttƒ ttƒ ttƒ ttƒ ttƒ ks%J ‚d S rv   )rH   rq   r    r"   r:   ri   ri   ri   rj   Útest_issue_15431V  s   *ÿr*  c                  C   sü   t tt ƒ } tdtt ƒ ƒ}t| t ƒ|kr| t ¡| ksJ ‚t d tt ƒd  } t d  tt ƒ dtdtt ƒ ƒ  }t| t ƒ|krI| t ¡| ksKJ ‚ttt ƒƒt d  } ttƒ tttt ƒƒƒ d ttt ƒƒt   }t| t ƒ|krz| t ¡| ks|J ‚d S )Nrl   r}   r‚   )rq   r"   r:   rH   r
   r-   r   r=   )rc   ÚFri   ri   rj   Ú"test_issue_15640_log_substitutions[  s    & .$r,  c                  C   s¨   ddl m}  | dƒ}|j}ttt| t ƒ|ttfddt	t
tt t ƒ t t
tt t ƒt  tt kttk @ ttdƒ@ ft ttƒ tttƒ  dfƒksRJ ‚d S )Nr   )Ú
CoordSys3DÚNTrÄ  )Úsympy.vectorr-  rq   rH   r2   r¢   r½   Úx_1Úx_2r.   r3   r   r   )r-  r.  rq   ri   ri   rj   Útest_issue_15509g  s    Dþr2  c                  C   s¢   t ddd} t| td| d  ƒ | ƒt| d d d| d  d  | dkf| d  d d| d  d  tddƒ | d	kf| d d d| d  d  dfƒksOJ ‚d S )
Nrq   Tr³   rÀ   rl   r‚   r  éQ   r}   )r   rH   rð   r.   r   r™  ri   ri   rj   Útest_issue_4311_fastp  s   ".ýr4  c               	   C   sà  t ddd} t ddd}t ddd}t ddd}ttt |  |d  ||  ƒ|ƒttƒtt |d  d	|   ƒ td
t |  | | dt| ƒ tt ƒ  ƒ dt| ƒ tt ƒ  ks_J ‚tddt|d    |ƒt tt ƒt|ttt ƒ  ƒ d tt ƒt|ttt ƒ  ƒ d   ks•J ‚ttt |d  ƒ|ƒttƒtttƒ| ƒ dttƒ  ksµJ ‚tdtt| ƒd  |ƒ| d tttt| ƒd ƒ d  ks×J ‚tdtt| ƒd  |ddt fƒt ksîJ ‚d S )NÚKTrÖ   rq   r³   rë   r¡   rl   r‚   r   ru   r   )	r   rH   r    r   r-   r   r>   r"   r<   )r5  rq   rë   r¡   ri   ri   rj   Ú%test_integrate_with_complex_constantsx  s"   6ÿ,ÿ
ÿ>"ÿ@D2r6  c                  C   sx   t dƒ} t dddd}t|| |d   | d  | ƒ|d | |  t| ttt ƒ d|ƒ t|ƒ t|d ƒ ks:J ‚d S )Nrq   r`   Trr  ru   rl   )r   rH   rF   r!   r   r   rA   )rq   r`   ri   ri   rj   Útest_issue_14241‡  s
   :ÿr7  c                   C   s<   t ttƒd ddttƒ   tddt gƒtd ksJ ‚d S )Nrl   r“   r‚   r   )rH   r3   r¡   r2   r   ri   ri   ri   rj   Útest_issue_13112Ž  r  r8  c                  C   sP   t ddd} tttddt |   ƒ td| fƒ}|d| d  t d ks&J ‚d S )	NrÞ  TrÖ   ru   rl   r   r“   r"  )r   rH   rq   r/   r   )rÞ  r   ri   ri   rj   Útest_issue_14709b’  s   $ r9  c                  C   sl   t dƒ} t dƒ}tt|ƒ| |t | fƒt| ƒksJ ‚tt|  ƒtd|  ƒ |  | dtfƒtdƒks4J ‚d S )Nrq   r¡   r   r   rl   )r   rH   r    r   r:   r"   )rq   r¡   ri   ri   rj   Útest_issue_8614˜  s   &6r:  c                  C   sò   t ddd} t| d ƒdtd|  ƒ  t| ƒ t| ƒ }t|| ƒ}|tjks(J ‚t| | d¡d ƒdks6J ‚t| d ƒdttd	ƒd
 |  ƒ  t| ƒ t| ƒ }t|| ƒdtd|  d
 ƒ d dtd|  d ƒ d  td|  ƒd  kswJ ‚d S )Nrˆ   TrÖ   rl   gš™™™™™ù?ru   gÏRt?,eÀg:Œ0âŽyE>r»   r“   iöÿÿÿé   r}   )r   r    rH   r   r    rð   rñ   )rˆ   rÿ  Úsolutionri   ri   rj   Útest_issue_15494Ÿ  s   ,
4Rr=  c               	   C   s~   t dƒ} tt| td  ƒtƒ ¡ ttttd |  ƒ ttdttd |  ƒ d ƒ ttd |  ƒ  t	| dƒfdƒks=J ‚d S )Nrƒ   rl   r}   r   rF  )
r   rW   r@   rq   r‹   r.   r:   r"   r-   r   rÒ   ri   ri   rj   Útest_li_integral¯  s   ,.ÿþþr>  c                  C   sà   t dƒ} t dƒ}tj}| |d  t|||  ƒ t|||  fd| d| ||  f| d|   d ƒ d| td| ||  ƒ  }tt| | ƒ| ƒ}||ksRJ ‚t ddd}| |i}tt|| ƒ|ƒ| |¡ ¡ ksnJ ‚d S )	Nrq   r`   ru   r}   rl   r‚   FrÈ  )	r   r   rÍ   rA   rC   rH   r3   ÚxreplacerŒ   )rq   r`   rÞ  rü   ÚgotÚ_xÚrepsri   ri   rj   Útest_issue_17473¶  s   (&ÿÿ(rC  c                   C   s¢   t tttƒƒtd  tdtgƒt ksJ ‚t tttƒƒtd  tdtgƒtdƒ d td  ks2J ‚t tttƒƒtd  tdtgƒtdƒ d td  ksOJ ‚d S )Nrl   ru   r}   r’   rÀ   )rH   r"   rq   r   r   ri   ri   ri   rj   Útest_issue_17671Ã  s   *:>rD  c                  C   s~   t dƒ} t dƒ}t dƒ}td|d | tdƒd   ||  d | d fƒ| |tdƒd  td| d d|   ƒ  ks=J ‚d S )Nr§  ÚCrƒ   ru   rl   r}   r‚   )r   rH   r   r-   )r§  rE  rƒ   ri   ri   rj   Útest_issue_2975É  s   frF  c                     sÔ  t dƒ\‰‰ } tddd}ttˆˆ  ˆ d|fƒˆƒˆd |d d |d   ks*J ‚ttˆtˆ ƒ ˆ d|fƒˆƒtˆd tˆ ƒ d ˆ d|fƒksKJ ‚tttˆ ˆ ƒˆ d|fƒˆƒtttˆ ˆ ƒ ˆ  tˆ dƒfd	ƒˆ d|fƒkssJ ‚ttttˆ ˆ ƒˆ d|fƒˆƒˆƒttttˆ ˆ ƒ ˆ d  tˆ dƒfˆ ˆ  dfƒˆ d|fƒˆ t	 kˆ t	k @ tˆ dƒ@ fd	ƒks¶J ‚ttˆˆ d| fƒˆƒ| ˆd  d ksËJ ‚t
t‡ ‡fd
d„ƒ t
t‡ ‡fdd„ƒ t
t‡fdd„ƒ d S )Nzx n Mr.  Tra   ru   rl   r‚   r   rF  c                      s   t tˆˆtˆ fƒtƒS rv   ©rH   r   rƒ   ri   ©r`   rq   ri   rj   rz   Ü  r€   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS r~   )rH   r   ri   rH  ri   rj   rz   Ý  r€   c                      s   t tˆ ˆ dtfƒˆ ƒS r~   rG  ri   r™  ri   rj   rz   Þ  r€   )r   r   rH   r   r3   r   r.   r2   r   r   rZ   r„   )r  r.  ri   rH  rj   Útest_issue_7827Ð  s,   :ÿ,ÿ"2ÿÿÿÿ*rI  c               	   C   sš   ddt   tt tt ƒ ƒddt     t d  t t tt tt ƒ ƒ  tt tt ƒ ƒ  } t| t ƒdtt tt ƒ ƒ dtt tt tt ƒ ƒ ƒ  ksKJ ‚d S r  )rq   r-   r"   rH   r÷   ri   ri   rj   Útest_issue_4231á  s   XBrJ  c                  C   s@   t dtd t t  tƒ} t| tƒdtd t t  ksJ ‚d S rô   )r
   rq   r   rH   r÷   ri   ri   rj   Útest_issue_17841æ  s   &rK  c                  C   sJ  t dddd} | | d  tdƒd  | t| ttdƒƒ ƒ  d  }| ttdƒƒ | | dd|      }t|| ƒ| d  dtdƒd   | d	 t| ttdƒƒ ƒ  d| d	  d	  d	|  t| ttdƒƒ ƒ  d	t| ttdƒƒ ƒ  ksxJ ‚t|| ƒt| d	 tdƒd  ƒd	 d	td
ƒ ttdƒƒ t	d	td
ƒ |  ƒ  ks£J ‚d S )Nrq   T©r´   rÞ   r‚   r“   ru   rê   r¼   rl   r}   )
r   r0   r(   r"   r%   r2   rH   r   r-   r1   )rq   Úf1Úf2ri   ri   rj   Útest_issue_21034ë  s   6$xÿFÿrO  c                   C   sd   t ttƒtt ƒ tƒtt ƒtt ƒttƒ  ksJ ‚t ttƒtt ƒ tdtfƒt ks0J ‚d S r‚  )rH   r"   rq   r    r:   r   r   ri   ri   ri   rj   Útest_issue_4187÷  s   8,rP  c               	   C   s0  t dƒ} t dƒ}t dƒ}t dƒ}t|d t|ƒd  ||  d | d fƒ|d  |  d t| d ƒt| d ƒ d   |d | d t| d ƒt| d ƒ d    ksUJ ‚t|d t|| ƒd  ||  d | d fƒt|d  |  | d t| | d ƒt| | d ƒ d   | |d | | d t| | d ƒt| | d ƒ d   |  |t k|tk @ t|dƒ@ f| |d  dfƒksÃJ ‚dt | |  }tdƒt| ƒ |d  t	tdƒt| ƒ ƒ t
tjd ƒ d	t
td
ƒd ƒ  | |d  d  }t|d t|| ƒd  ||  d | d fƒ|ksJ ‚d S )Nrþ  r  Úr0ÚR0rl   r‚   r   Tr"  r“   )r   rH   r2   r3   r.   r   r   r   r-   r?   rA   r   r¥   )rþ  r  rQ  rR  r§  Úsolri   ri   rj   Útest_issue_5547ü  s(   8ÿ*
ÿ.>:ÿÿ
ý^<rT  c                   C   s6   t dddt d  d  tdtfƒtddƒksJ ‚d S )Nru   rl   r}   r   )rH   rq   r   r   ri   ri   ri   rj   Útest_issue_15810  rû   rU  c                  C   sf  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shJ ‚| tdƒ | d  }t| ƒtdƒ|   }|t|| ƒks…J ‚| d td
ƒ |  }| d d td
ƒt| ƒ  }|t|| ƒks¦J ‚| d|  tdƒ  }| d td|  tdƒ ƒtdƒ d  }|t|| ƒksÍJ ‚| tdƒ|   }| d d t| ƒtdƒ  }|t|| ƒksìJ ‚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sfJ ‚d|  | td
ƒ  }d|  dt| td
ƒ ƒ td
ƒ  }|t|| ƒksŒJ ‚| 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sÂJ ‚| d  | t  }| d  d t|   tdƒt| t ƒ  }|t|| ƒksêJ ‚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s8J ‚| tdƒ| d   }| d d tdƒd| d    }|t|| ƒks\J ‚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sÇJ ‚| | tdƒ| d    |  }| d d | d d  tdƒt| ƒ  }|t|| ƒksóJ ‚| | 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sJ ‚|  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s1J ‚d S )Nrq   TrL  r‚   r}   rl   ru   r   r¼   r“   éûÿÿÿr»   r’   rd   r-  rð  iLÿÿÿéZ   rM  r  )r   r"   r    rH   r)   r(   r   r1   r   r%   rŒ   r3   )rq   rc   r+  ÚF_trueri   ri   rj   Útest_issue_21024  s”   (B"ÿÿ(Dd$@*$$ f(4 <<.nÿ
ÿÿ,rY  c                  C   s`   t dƒ} tdtdt|  d    tt tfƒ ¡ tt| ƒd dƒ tt| ƒd dƒ ks.J ‚d S )Nr¢   ru   rl   r   )r   rH   r   rq   r   rŒ   r8   r   ©r¢   ri   ri   rj   Útest_issue_21721n  s   ($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thetar}   r“   r‚   r   rl   rê   r¼   )r   rH   r2   r   )r\  rÿ  ri   ri   rj   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 )Nrl   ru   r‚   r   ry  )rH   rq   r   r-   r   ri   ri   ri   rj   Útest_issue_22033_integral{  s   Br^  c                	   C   sº   t dttd td  dtd  td  fttdtd  ƒ tdtd  ƒftddfƒtks/J ‚t ddtd  tdƒd   d dtdtd  ƒ ddtd     tddfƒtks[J ‚d S )Nru   rl   r   r  r}   )rH   r  rq   rƒ   r-   r   r   ri   ri   ri   rj   Útest_issue_21671€  s   ^\r_  c                  C   sr   t ddd} ttƒdttƒd   }t| t| ¡| dd | t¡}t|tdd|  kr4t|tƒks7J ‚ J ‚d S )NÚxrTr³   r‚   rl   rã  )r   r2   rq   r3   rH   rñ   rW   )r`  r¼  Úres_realri   ri   rj   Útest_issue_18527†  s   0rb  c               	   C   sÀ  dt ttƒ tttƒ   } tt t  ttd ƒ ttd t d  ƒt   ƒ ttd t d  ƒ tt t  ttd ƒ ttd t d  ƒt   ƒttd t d  ƒ  }tt	tttd ƒd ƒ tttd ƒd ƒ  t
tdƒt
t dƒ@ ftttd ƒƒt t
t dƒft t t  ttƒ t ttƒ   t
tt t  ƒfttt  ttƒ t ttƒ   t
ttt  ƒf|dfƒ}t| tƒ|ksÁJ ‚tddd\}}t|t |i}t|  |¡tƒ| |¡ksÞJ ‚d S )Nru   rl   r   Tza, brÖ   )r½   r2   rq   r¢   r3   r"   r5   r-   r.   r   r   r   rH   r   rñ   )rc   ÚFposr+  Úapr  Úrepri   ri   rj   Útest_issue_23718  s   FDÿ@2,ø
"rf  c                  C   sR   t dttd d ƒ tddfƒ} | tdtdƒ ƒ ksJ ‚t |  ¡ d¡s'J ‚d S )Nru   rl   r   r   r}   gC˜qBõ?)rH   r-   rq   r"   ÚmathÚiscloser`   r  ri   ri   rj   Útest_issue_23566¤  s    ri  c                   C   s\   t dttt d d ƒ ƒtttt ƒttt d ƒdkft ttt ƒ dfƒks,J ‚d S )Nru   rl   T)rH   r-   rq   r   r.   r#   r   r0   ri   ri   ri   rj   Útest_pr_23583ª  s   \rj  c                   C   sX   t ttƒtdtdt ƒ ƒ ƒttdt ƒd ƒttƒ d tttƒƒd  ks*J ‚d S rô   )rH   r    rq   r-   r$   ri   ri   ri   rj   Útest_issue_7264¯  s   Xrk  c                   C   s.   t ttƒtddfƒdtttjƒƒ ksJ ‚d S r  )rH   r*   rq   r1   r)   r   rÍ   ri   ri   ri   rj   Útest_issue_11254a³  r&  rl  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 )Nrl   r   ru   )rH   r'   rq   r"   r)   r   ri   ri   ri   rj   Útest_issue_11254b·  s   " rm  c                   C   s|   t dtttt d  ddd  tƒdtdt ƒd  ksJ ‚t ttƒd tƒdttd ƒ ttd ƒd d  ks<J ‚d S )Nr   rl   F©rz  r   ru   )rH   r(   rq   r   r   r    r%   r)   ri   ri   ri   rj   Útest_issue_11254d¼  s   >>ro  c                  C   s   t dtd  td  dt  d ttd dt  d ƒ tddfƒ} | dtdƒ d dtddtdƒ  ƒ d	  ks<J ‚t |  ¡ d
¡sFJ ‚d S )Nr}   rl   r‚   r   ru   i›ÿÿÿr»   é‡   r"  g€2É{¢ÙÀ)rH   rq   r-   r"   rg  rh  r`   r  ri   ri   rj   Útest_issue_22863Â  s   D4rq  c                   C   s,  t ttttƒ ƒƒdtttƒt ƒ ttƒd td  tdƒd   tdttƒ dtttƒt ƒ  d ƒd  ks<J ‚t tdt d tdt d ƒ ƒd ƒtdt tdt d ƒ d ƒdt d	 d
dt d tdƒd   d  tdt d ƒd  dt d d d	  td
ƒd	   d ks”J ‚d S )Nrl   rê   r}   ru   r»   r‚   r“   rÀ   r’   r#  é(   ©rH   r-   rq   r   r"   ri   ri   ri   rj   Útest_issue_9723È  s   ^ÿ&^ÿÿÿrt  c                   C   sl   t ttƒtd  ttd  tt  t  tddtttƒttd  ttd   ttd    tƒks4J ‚d S )Nrl   Trç  r}   r‚   )rH   r"   rq   r¾   r½   r¢   rX   ri   ri   ri   rj   Útest_issue_23704Ð  s   00ÿru  c                   C   sd   t dtdtdt ƒ ƒ ƒttdtdt ƒ ƒd ƒd ttdtdt ƒ ƒd ƒd  ks0J ‚d S rô   r  ri   ri   ri   rj   Útest_exp_substitutionØ  s   drv  c                   C   sx   t ttƒƒttttƒd ƒ tttƒƒ ksJ ‚t ttƒƒdtttd ƒƒ ks*J ‚t ttƒƒtttd ƒƒks:J ‚d S rô   )rH   r&   rq   r"   r)   r*   r1   r'   ri   ri   ri   rj   Útest_hyperbolicÜ  s   0$$rw  c                   C   sÌ   t ttd ƒƒtttd ƒ d ksJ ‚t tttdƒd  ƒƒdt tttdƒd  ƒ d ks2J ‚t dttd ƒ ƒtttƒ ttd ƒ ksJJ ‚t tttd ƒ ƒtd ttd ƒ ttƒ ksdJ ‚d S )Nrl   r“   r}   r¼   r#  ru   r  rs  ri   ri   ri   rj   Útest_nested_powâ  s   (<08rx  c                   C   sä  t dtdtd  dt  d ƒ ƒtdƒtdtdƒ ttdƒd   d ƒ d ks,J ‚t dtdtd  dt  d ƒ ƒtdƒtdtdƒ ttdƒd   d ƒ d ksXJ ‚t dtdtd  dt  d ƒ ƒtdƒtd	t dtdƒ tdtd  dt  d ƒ  d ƒ d ksŽJ ‚t dtdtd  dt  d ƒ ƒttj tttj ƒ dtttj d ƒ  ks¹J ‚t dttt	t  t
td   ƒ tƒttt	dtt
ƒ ttt	t  t
td   ƒ  dt
 t  ƒtt
ƒ tt
d
ƒttt	d dt
   d
ƒ@ ft	dt
  t tt	dt
  t ƒ tt
t	dt
  t d  ƒ tt
d
ƒfdttt	t  ƒ t	 tt	d
ƒftttƒ dfƒks@J ‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ tdtdƒ ttdƒd   d ƒ d  ks…J ‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ tdtdƒ ttdƒd   d ƒ d  ksÊJ ‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ td	t dtdƒ tdtd  dt  d ƒ  d ƒ d  ksJ ‚t ttt  ttt	t  t
td   ƒ tƒtt	 t dt
  t ttt	dtt
ƒ ttt	t  t
td   ƒ  dt
 t  ƒtt
ƒ ttt	d dt
   d
ƒft	dt
  t tt	dt
  t ƒ tt
t	dt
  t d  ƒ dfƒ tttt	t  t
td   ƒ t
  tt
d
ƒfdt ttt	t  ƒ dt t ttt	t  ƒ tt	t  tdƒd  d   t	  t	 tt	d
ƒftt ttd  d  ttƒ dfƒksëJ ‚t dtd  td  dt  d ttd dt  d ƒ ƒttd dt  d ƒtd dt d  tdƒd   dtdt dttd dt  d ƒ  d ƒ d  ksBJ ‚t tdtd  dt  d ƒƒtd tdƒd  tdtd  dt  d ƒ dtdƒ tdt d tdƒd  ƒ d  ksƒJ ‚t ttt	t  t
td   ƒtƒttd t	d dt
   ttt	dtt
ƒ ttt	t  t
td   ƒ  dt
 t  ƒtt
ƒ ttt	d dt
   d
ƒft	dt
  t tt	dt
  t ƒ tt
t	dt
  t d  ƒ dfƒ t	dt
  td  ttt	t  t
td   ƒ  tt
d
ƒfdtt	t  tdƒd   dt	  tt	d
ƒfttƒt dfƒks1J ‚t tttd dt  d ƒ ƒtd d td	  tdƒd	  ttd dt  d ƒ dttdƒtd  d ƒ d  kspJ ‚d S )Nru   r}   rl   r‚   r“   r#  r  r€  r¼   r   Tr   rÀ   iùÿÿÿry  r;  rD  r»   rp  r"  iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rq   r$   r   r0   r"   rÍ   r¢   r½   r¾   r.   r   r†   rg   ri   ri   ri   rj   Útest_sqrt_quadraticé  st   XXlV$hH.þ
ÿ*V
ÿ*V
ÿ*j
ÿ,^Bÿÿ"ýýb"û
ÿ:j
ÿ.*ÿ
ÿ ^Bÿÿ.ýý,û
ÿVÿry  c                   C   sî   t tttƒ ttƒ ƒtttƒ tttƒttƒ ƒ ksJ ‚t tttƒd  tƒtttƒ tttƒƒ ks7J ‚t td tttƒtdfƒ ƒtd tttƒtdfƒ dtd  tttƒtdfƒ  dt tttƒtƒ  dttƒ  ksuJ ‚d S )Nrl   r}   r‚   r¼   )rH   rq   r6   r5   r"   r2   r   rc   ri   ri   ri   rj   Útest_mul_pow_derivative  s
   <2Xÿrz  c                  C   s´   t dtdk fdƒ} t dtdk fdƒ }| | }ttdƒ df}t| |ƒdks(J ‚t||ƒdks1J ‚t|  |ƒdks;J ‚t| |ƒdksEJ ‚t||ƒdksNJ ‚t| |ƒdksXJ ‚d S )	Nr   g        )ru   Trú  ÚInfru   r   g      ð¿)r.   rq   ÚfloatrH   )Úfun1Úfun2Úfun_sumrþ  ri   ri   rj   Útest_issue_20782  s   r€  c               	      s˜   dd„ ‰ ‡ fdd„} t tdƒ t f}t| dƒ|ƒ}|dt  tdt ƒ tt tdddd	ƒ ks0J ‚t| d
ƒt tdƒ t fƒdt  dtd
t ƒ  ksJJ ‚d S )Nc                 S   s   t dt| k fdt| kfƒS rÂ   )r.   rq   rZ  ri   ri   rj   rz   )  s    z"test_issue_20781.<locals>.<lambda>c                    s   ˆ t | ƒƒˆ t| ƒƒ S rv   )Úintr|  rZ  ©ÚPri   rj   rz   *  r¯   r{  ru   rl   rú  Frn  r   )rq   r|  rH   r,   r+   )rc   rþ  rM  ri   r‚  rj   Útest_issue_20781(  s   .ÿr„  c                  C   sâ   t dƒ} t| d td| d  ƒ | ddfƒtd ksJ ‚td| d  td| d  ƒ | ddfƒt d ks7J ‚tdtd| d  ƒ | ddfƒtd ksMJ ‚t| d d| d   d td| d  ƒ | ddfƒdt d ksoJ ‚d S )	Nrq   r‚   ru   rl   r   r"  r   r“   )r   rH   r-   r   r™  ri   ri   rj   Útest_issue_194274  s
   06,Hr…  c                  C   s(  t dttdt d  dt d  ƒ tdtfƒ} | jtdddt dttd dtd   dt  d ƒ tdtfƒttd tdfƒ ksEJ ‚t dttdt d  dt d  ƒ tdtfƒ}|jtdddt dtdtd  dtd   d	td   d
t  d ƒ tdtfƒttd tdfƒ ks’J ‚d S )Nru   r}   rl   r   rà   r‚   r“   ry  éÁ   iö  i  )rW   r-   r¢   rq   r  rÁ  rN   )ÚI1ÚI2ri   ri   rj   Útest_issue_23942B  s   0Z0nr‰  c                  C   sv   dt  tdt  ƒ } ddt t d dt   tdt t ƒ dtdt ƒ  }t| t tdfƒ}| |tj¡s9J ‚d S )Nru   y        >ÚÃT¶üí?rú  gÇÅzðñ¿g	
šT8ò?gÇÅzðñ?g>ÚÃT¶üí?)rq   r    r   rƒ   rH   Úis_samerg  rh  )rc   ÚF_expr+  ri   ri   rj   Útest_issue_25886I  s   ÿþþýrŒ  c                  C   sÄ   t tttd ƒƒt ƒ} | tttd ƒƒd ksJ ‚t dtd td  tddƒ  tƒ}|ttd ttd td  d ƒ  ksBJ ‚t dttƒd  tddt fƒ}|dtdƒ t d ks`J ‚d S )Nrl   ru   r}   r   )	rH   r2   r"   rq   r3   rƒ   r   r-   r   )r‡  rˆ  ÚI3ri   ri   rj   Útest_old_issuesT  s   $,  rŽ  )rd   (`  rg  Úsympy.concrete.summationsr   r   Úsympy.core.addr   Úsympy.core.containersr   Úsympy.core.exprr   rç   r   r   r	   r
   Ú
sympy.corer   Úsympy.core.numbersr   r   r   r   r   r   r   r   Úsympy.core.relationalr   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   Úsympy.core.sympifyr   rø  r   r   r   r   r   Ú&sympy.functions.elementary.exponentialr   r    r!   r"   Ú%sympy.functions.elementary.hyperbolicr#   r$   r%   r&   r'   r(   r)   r*   Ú(sympy.functions.elementary.miscellaneousr+   r,   r-   Ú$sympy.functions.elementary.piecewiser.   Ú(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Ú'sympy.functions.special.delta_functionsr7   r8   rè   r9   r:   r;   r<   r=   r>   r?   r@   rÕ  rA   rB   Úsympy.functions.special.hyperrC   rD   Ú-sympy.functions.special.singularity_functionsrE   Ú&sympy.functions.special.zeta_functionsrF   Úsympy.integrals.integralsrH   Úsympy.logic.boolalgrI   Úsympy.matrices.denserJ   Úsympy.polys.polytoolsrK   rL   Úsympy.printing.strrM   Úsympy.series.orderrN   Úsympy.sets.setsrO   Úsympy.simplify.gammasimprP   Úsympy.simplify.simplifyrQ   Úsympy.simplify.trigsimprR   Úsympy.tensor.indexedrS   rT   rU   Ú#sympy.functions.elementary.integersrV   rW   Úsympy.integrals.rischrX   Úsympy.physicsrY   Úsympy.testing.pytestrZ   r[   r\   r]   Úsympy.utilities.exceptionsr^   Úsympy.core.randomr_   rq   rƒ   r  r¢   r½   r¾   r†   rg   rˆ   r¡   r0  r1  r`   rc   rk   rt   r‰   r   r‘   rœ   r¨   r°   r±   rº   r¿   rÁ   rÃ   rÄ   rÆ   rÌ   rÐ   rÓ   rÔ   rÕ   rÛ   rÜ   rÝ   rá   rã   ré   rì   rí   rî   ró   rõ   rø   rú   rý   rÿ   r  r  r  r  r  r  r  r  r   r!  r5  r6  r9  rC  rE  rG  rL  rO  rS  rU  rW  rX  r[  r\  r]  r_  rb  rc  rq  rw  r|  r~  r  r„  r†  rˆ  rŠ  r  r  r‘  r•  r—  r˜  r¡  r¢  r£  r¤  r¦  r¨  rª  r«  r­  r®  r°  r²  rµ  r¶  r»  r½  r¿  rÃ  rÇ  rÊ  rË  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÖ  r×  rØ  rÚ  rÝ  rß  rà  rä  ræ  rè  rê  rì  rî  rï  rñ  ró  rõ  rù  rû  rü  r   r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r#  r$  r%  r)  r*  r,  r2  r4  r6  r7  r8  r9  r:  r=  r>  rC  rD  rF  rI  rJ  rK  rO  rP  rT  rU  rY  r[  r]  r^  r_  rb  rf  ri  rj  rk  rl  rm  ro  rq  rt  ru  rv  rw  rx  ry  rz  r€  r„  r…  r‰  rŒ  rŽ  ri   ri   ri   rj   Ú<module>   s
   (((( 


.
			
		0
3!

			
			 


		 	

	Y	*