o
    *Î®c‚) 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
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
lmZ d dlm Z m!Z! d dl"m#Z# d dl$m%Z%m&Z&m'Z'm(Z(m)Z) d dl*m+Z+m,Z,m-Z-m.Z. d dl/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7 d dl8m9Z9m:Z:m;Z; d dl<m=Z= d dl>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZF d dlGmHZHmIZI d dlJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZR d dlSmTZTmUZU d dlVmWZWmXZX d dlYmZZZ d dl[m\Z\ d dl]m^Z^ d dl_m`Z` d dlambZb d dlcmdZdmeZe d dlfmgZg d dlhmiZi d dljmkZk d d llmmZm d d!lnmoZo d d"lpmqZq d d#lrmsZsmtZt d d$lmuZu d d%lvmwZw d d&l]mxZx d d'lymzZz d d(l{m|Z| d d)l}m~Z~mZm€Z€mZm‚Z‚mƒZƒ d d*l„m…Z… d d+l†m‡Z‡ e!d,ƒ\ZˆZ‰ZŠZ‹ZŒZZŽZZZ‘Z’Z“e d-d.d/Z”ed0ƒZ•d¾d2d3„Z–d4d5„ Z—ed6d7„ ƒZ˜d8d9„ Z™d:d;„ Zšd<d=„ Z›d>d?„ Zœd@dA„ ZdBdC„ ZždDdE„ ZŸdFdG„ Z dHdI„ Z¡dJdK„ Z¢dLdM„ Z£dNdO„ Z¤dPdQ„ Z¥dRdS„ Z¦dTdU„ Z§dVdW„ Z¨dXdY„ Z©dZd[„ Zªd\d]„ Z«d^d_„ Z¬d`da„ Z­dbdc„ Z®ddde„ Z¯dfdg„ Z°dhdi„ Z±djdk„ Z²dldm„ Z³dndo„ Z´dpdq„ Zµdrds„ Z¶dtdu„ Z·dvdw„ Z¸dxdy„ Z¹dzd{„ Zºd|d}„ Z»d~d„ Z¼d€d„ Z½d‚dƒ„ Z¾d„d…„ Z¿d†d‡„ ZÀdˆd‰„ ZÁdŠd‹„ ZÂedŒd„ ƒZÃdŽd„ ZÄdd‘„ ZÅd’d“„ ZÆd”d•„ ZÇd–d—„ ZÈd˜d™„ ZÉdšd›„ ZÊdœd„ ZËdždŸ„ ZÌd d¡„ ZÍd¢d£„ ZÎd¤d¥„ ZÏd¦d§„ ZÐd¨d©„ ZÑdªd«„ ZÒd¬d­„ ZÓd®d¯„ ZÔd°d±„ ZÕd²d³„ ZÖd´dµ„ Z×d¶d·„ ZØd¸d¹„ ZÙdºd»„ ZÚd¼d½„ ZÛd¾d¿„ ZÜdÀdÁ„ ZÝdÂdÃ„ ZÞdÄdÅ„ ZßdÆdÇ„ ZàdÈdÉ„ ZádÊdË„ ZâdÌdÍ„ ZãdÎdÏ„ ZädÐdÑ„ ZådÒdÓ„ ZædÔdÕ„ ZçdÖd×„ ZèdØdÙ„ ZédÚdÛ„ ZêdÜdÝ„ ZëdÞdß„ Zìdàdá„ Zídâdã„ Zîdädå„ Zïdædç„ Zðdèdé„ Zñdêdë„ Zòdìdí„ Zódîdï„ Zôdðdñ„ Zõdòdó„ Zödôdõ„ Z÷död÷„ Zødødù„ Zùdúdû„ Zúdüdý„ Zûdþdÿ„ Züd d„ Zýdd„ Zþdd„ Zÿdd„ 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	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_TRAVISÚ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erb   Úoptions© rk   úK/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/tests/test_integrals.pyÚNS4   s   rm   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prk   rk   rl   Útest_poly_deprecated8   s    ÿ"ÿrv   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   rs   Úprincipal_valuerk   ©Úgrk   rl   Ú<lambda>G   ó    z&test_principal_value.<locals>.<lambda>c                      s   t ˆ ƒ ¡ S rx   )rW   ry   rk   rz   rk   rl   r|   H   ó    é   c                      s   t ˆ tt dfƒ ¡ S ©Nrw   )rW   rs   r   ry   rk   )Úlrk   rl   r|   L   ó    rn   éþÿÿÿé   )rs   rW   r   ry   Úyr   rZ   Ú
ValueErrorÚtogetherr-   r   r"   r1   )ÚdÚvÚsre   rk   )r{   r   rl   Útest_principal_valueB   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symsrŠ   rk   rk   rl   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   rw   éÿÿÿÿrƒ   rn   )rH   r"   rs   r   r    rk   rk   rk   rl   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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 )Nrw   rn   é
   é   )	rW   rb   Úlimitsr   r   rs   r…   rO   r   )Ús1Ús2Ús3Ús4Ús5Ús6Ús7rk   rk   rl   Útest_constructoro   s   
rž   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   rw   rn   é   r   rb   F©Úcommutative)rW   rs   r   r   ÚNaNr
   r…   ÚtrH   r   rŽ   ÚaÚatomsre   ÚZeroÚOner‘   r    Úis_commutativer   ©ri   rb   rk   rk   rl   Útest_basics…   sR   ÿþÿÿÿÿ4
ÿ,20,"$8rª   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¨   rk   rk   rk   rl   ÚTest´   s    r¯   rw   rn   r   r   c                   S   s   t td td ƒS r€   ©rH   rs   rk   rk   rk   rl   r|   ¼   s    ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfƒS )Nrw   r   r°   rk   rk   rk   rl   r|   ½   s    )r   rH   r   rZ   r†   )r¯   r£   rk   rk   rl   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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•   rn   rw   )r‘   rW   rs   r…   rk   rk   rk   rl   Útest_basics_multipleÀ   s   2,. $0r²   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks$J ‚| ¡  ¡ | ¡  ¡ ks2J ‚| ¡  ¡ | ¡  ¡ ks@J ‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks\J ‚| ¡  ¡ | ¡  ¡ ksjJ ‚| ¡  ¡ | ¡  ¡ ksxJ ‚d S )NzA BFr    rs   T)Úcomplex©Úreal)r   r   rW   Úadjointr   Ú	conjugateÚ	transpose)ÚAÚBrs   ru   rk   rk   rl   Útest_conjugate_transposeÊ   s    r»   c                  C   s:  t dtdtfƒdksJ ‚t dtdtfƒdt ksJ ‚t ttdtfƒtd d ks*J ‚t dt tdtfƒdtd  d ks>J ‚t dtd  tdtfƒtd ksPJ ‚t dt tdtfƒttƒks`J ‚t dtd  tdtfƒdt d kstJ ‚t td dt  d tdtfƒtd d dtd  d  dt  ks˜J ‚t td tƒtd d ks§J ‚t dt t d tƒdt d td  d ksÀJ ‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÜJ ‚t ttd  tdtfƒttd  d ksòJ ‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ksJ ‚d S )Nr   r   rn   rw   r’   r•   é   é   ÚbÚcr„   )rH   r£   rs   r"   r   r¤   )r¾   r¿   rk   rk   rl   Útest_integrationÚ   s    ($ (H2(,VrÀ   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 )	Nrn   r   rw   r’   é	   r   r¼   r„   )rH   rs   r…   r   r"   r3   rk   rk   rk   rl   Útest_multiple_integrationí   s   06Fÿ:rÂ   c                   C   s"   t tt ƒtdtfƒdksJ ‚d S )Nr   rw   )rH   r    rs   r   rk   rk   rk   rl   Útest_issue_3532õ   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   rn   r•   rw   rƒ   ©rH   r-   rs   rk   rk   rk   rl   Útest_issue_3560ù   s   *&*rÅ   c                   C   s   t tdd„ ƒ d S )Nc                   S   s   t ttfƒS rx   r°   rk   rk   rk   rl   r|      r~   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorrk   rk   rk   rl   Útest_issue_18038ÿ   s   rÇ   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 )Nrn   r   Frq   Tr„   )rK   rs   r…   r^   rW   r_   r`   rH   Ú
isinstanceÚgensÚas_expr)ru   ÚqxÚqyrk   rk   rl   Útest_integrate_poly  s     ÿÿÿ48rÍ   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 )	Nrn   r   r   rw   Frq   Tr„   )rK   rs   r…   r^   rW   r_   r`   rH   r   rÈ   rÉ   rÊ   r   ÚHalf)ru   ÚQxÚQyrk   rk   rl   Útest_integrate_poly_definite  s     ÿÿÿ"8rÑ   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…   rn   c                   S   s   t dƒS ©Nrn   rG   rk   rk   rk   rl   r|   1  s    z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS rx   r°   rk   ©r…   rk   rl   r|   2  r~   )r   rH   rs   rZ   r†   rk   rk   rÓ   rl   Útest_integrate_omit_var,  s   rÔ   c                  C   sd   t dƒ} ttt| ƒ tƒtd t| ƒ d ksJ ‚ttd t| ƒ tƒtd t| ƒ d ks0J ‚d S )Nr…   rn   iè  ié  )r   rH   rs   r3   rÓ   rk   rk   rl   Útest_integrate_poly_accurately5  s   *2rÕ   c                  C   sN   t dƒ} ttd | ƒtd |  ksJ ‚ttd | ddfƒdtd  ks%J ‚d S )Nr…   rn   r’   rw   )r   rH   rs   rÓ   rk   rk   rl   Útest_issue_3635>  s   (rÖ   c                  C   sž   t ddd} tt|  tddt| d  | d  ksJ ‚tt| ƒt d|   dt| ƒ  tddt|  ƒt| ƒt d|   dt| ƒ   dt| ƒ  ksMJ ‚d S )Nr…   T©ÚpositiveÚnone©Úcondsrw   rn   )r   rH   rs   r    r3   rÓ   rk   rk   rl   Útest_integrate_linearterm_powF  s
   *(4ÿrÜ   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 )Nrn   r   r•   )rH   r   r-   rs   r   rk   rk   rk   rl   Útest_issue_3618O  s   . .ÿrÝ   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 )Nrw   r   T)rH   r2   rb   rs   r.   r3   r   rk   rk   rk   rl   Útest_issue_3623U  s   *
ÿ*
ÿ$..ÿÿrÞ   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 )
Nrb   T)rd   Únonzerog      à¿rn   rƒ   r   g       @r’   )r   rH   rs   r3   r   r2   r   ©rb   rk   rk   rl   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 )Nrw   rn   r¼   é   r„   z1.10714871779409)rm   rW   rs   rk   rk   rk   rl   Útest_issue_3679g  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fresnelsrn   )	Úsympy.core.functionrå   Ú'sympy.functions.special.error_functionsræ   rH   r3   rs   r-   r   )rå   ræ   rk   rk   rl   Útest_issue_3686l  s
   *ÿré   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ksJ ‚d S )Nrw   r•   é   )rY   ÚmrŠ   rH   rs   )rë   rŠ   rk   rk   rl   Útest_integrate_unitss  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 rÒ   )rH   r   rs   rk   rk   rk   rl   Útest_transcendental_functionsy  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 )Nrw   r   rn   r½   r’   )rH   r"   rs   r   rk   rk   rk   rl   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„   rn   é*   g»½×Ùß|Û=)r"   rs   r
   rH   ÚabsÚsubsrh   )re   Úfidrk   rk   rl   Útest_issue_3740ƒ  s   0ró   c                   C   s&   t ddtd   tƒttƒksJ ‚d S ©Nrw   rn   )rH   rs   r1   rk   rk   rk   rl   Útest_issue_3788‰  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 rÒ   r°   rk   ©re   rk   rl   r|     r}   z!test_issue_3952.<locals>.<lambda>)r3   rs   rH   r2   rZ   r†   rk   rk   r÷   rl   Útest_issue_3952  s   rø   c                   C   s6   t dt dt  tƒdt tdƒ td  ksJ ‚d S rÒ   ©rH   rs   r"   rk   rk   rk   rl   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 )Nrw   r   r’   rn   )
rH   r    r   rs   r   r   r   rÎ   r   r   )Úansrk   rk   rl   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 )Nrw   rn   r   r   r•   ©rH   r2   rs   r   r-   r1   r5   rV   rk   rk   rk   rl   Útest_issue_8623œ  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 ©Nrw   rn   r   r   rþ   rk   rk   rk   rl   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 )NrŠ   Tr×   rn   r   )
r   r    Úzr…   r-   r   rH   rs   r   r<   )rŠ   ÚpzÚpzgxrk   rk   rl   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   rk   rk   rk   rl   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    rs   rX   rk   rk   rk   rl   Útest_issue_18133´  ó   <r  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spJ ‚d S )
Nz3999999.9999999995é5   )Ú	precisionz2.5000000000000004e-7ç      ð?r   Trƒ   gŽíµ ÷Æ >)r   r.   r   r    r   r£   r…   rs   r  r   r   rH   )r¤   r¾   ÚrÚfunrk   rk   rl   Útest_issue_21741¸  s   D(ÿ þ$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 )Nrn   c                 S   s    | | d t | | d t ƒ S r€   )r3   rs   )r   Újrk   rk   rl   r|   Ã  s     ztest_matrices.<locals>.<lambda>r   )rJ   rH   rs   r2   )ÚMrk   rk   rl   Útest_matricesÂ  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   rw   rn   )rH   re   rs   rW   r
   r"   rk   rk   rk   rl   Útest_integrate_functionsË  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 rÒ   )rH   r   re   rs   r…   rW   rk   rk   rk   rl   Útest_integrate_derivativesÓ  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 )Nrn   rw   r’   r   r   éüÿÿÿéýÿÿÿr„   c                      s   ˆ   td¡S r€   )Ú	transformrs   rk   ©r   rk   rl   r|   ÷  r~   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S rx   ©r  rs   rŠ   r£   rk   r  rk   rl   r|   ø  ó    c                      s   ˆ   tt ¡S rx   ©r  rs   rŠ   rk   r  rk   rl   r|   ù  r}   c                      s   ˆ   tttf¡S rx   r  rk   r  rk   rl   r|   ú  r  c                      s   ˆ   dt dt ¡S rÒ   r  rk   r  rk   rl   r|   û  ó    c                      s   ˆ   td t¡S rÒ   r  rk   r  rk   rl   r|   þ  r  r¤   T)Únegativer¾   r×   )rW   rs   r…   r   r  r3   r   r    r   r  r¾   rŠ   rZ   r†   r   )r¤   ÚfxÚfyÚ_3ÚamÚbprk   r  rl   Útest_transformÚ  sZ   0$6ÿ  ÿ
ÿ
ÿÿ220r#  c                  C   s^   t jttƒ ttdtd  ƒ d  } ttttƒƒtƒ| ks J ‚ttttƒƒtƒ| ks-J ‚d S rô   )	r   rÎ   r0   rs   r-   rH   r2   r3   r/   r÷   rk   rk   rl   Útest_issue_4052
  s   &r$  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$}d%|  k rôd&k s÷J ‚ J ‚t tttƒtd  tdtfƒd'd(d)ksJ ‚t tttt d ƒt tt d*fƒd'd(d+ks(J ‚t tttƒƒd,ks4J ‚t ttttfƒƒd-ksBJ ‚d S ).Nrn   r•   rf   z10.5000000000000z1.77245385090552rw   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r£   r¼   r   é   r„   é   éù   é6   éA   r   é2   é1   é¢   rê   z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))é`   zlog(2)/2-1/4T©Úchopzpi/4*log(4*pi**3/gamma(1/4)**4)râ   é   é   zsqrt(1-x**2)é   )Úmaxnr/  )z0.0Ú0)r3  g\Âõ(\ß?gR¸…ëQà?Úosc)Úquadz0.504067061906928r’   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rm   rW   rs   r    r   r   r   r   r   r-   r1   r"   r3   r2   rh   r…   )Úgaussr£   r¤   r¾   r¿   rˆ   re   rk   rk   rl   Útest_evalf_integrals  s¢   ÿÿÿ4,<,ÿ0ÿ4ÿÿ
ÿÿ
ÿÿÿ
ÿ4
ÿ(ÿ
ÿ(ÿ
ÿ(ÿ
ÿ
ÿÿ
ÿ$ ÿ
ÿÿÿ
ÿ r8  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 )	Nrw   r•   r„   Tr.  )z-0.000976138910649103z0.965906660135753z1.93278945918216rn   z0.0144361088886740)rm   rH   rs   rñ   rW   rk   rk   rk   rl   Útest_evalf_issue_939E  s   $ÿ(ÿÿr9  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdksJ ‚| tddƒdtdƒ d  ks,J ‚t tttt  ƒtddftddfƒtju sCJ ‚d S )	Nrw   rn   r’   rf   z2.43790283299492r  r   r¼   )	rH   r-   rs   r…   rm   r   r3   r   r¦   ©Úresrk   rk   rl   Ú(test_double_previously_failing_integralsT  s   $"2r<  c            	      C   s   t ttdƒt tddƒ } t ttdƒd t tddƒ }t| tƒ|ks#J ‚dt tddƒ dt tddƒ  }dt tdd	ƒ dt tddƒ  }t|tƒ|ksLJ ‚d
td
  t dt tddƒ  d
t tddƒ  }d
td  t d d
t t tddƒ  dt tddƒ d  }td
 td
  dt t tddƒ  d
t tddƒ  }t|tƒ|ks¥J ‚t|tƒ|ks®J ‚tt|tfƒs·J ‚t|tƒt|tfƒksÄJ ‚t|tƒ ¡ |ksÏJ ‚dt tddƒ d
t tddƒ  }dt tddƒ d d
t tddƒ  }t|tt tfƒ|ksþJ ‚tt tddƒtƒt tddƒksJ ‚tt tddƒtt tfƒd	ks"J ‚tdt tddƒ tt tfƒdks6J ‚tt tddƒt	tƒ tt tfƒt	dƒksNJ ‚d S )Nr   r•   r’   r„   r   r”   iúÿÿÿrƒ   rw   rn   r  rŸ   r¼   )
rE   rs   r¤   rH   r…   rU   rW   r   r   re   )	Úin_1Úout_1Úin_2Úout_2Úin_3Úout_3_1Úout_3_2Úin_4Úout_4rk   rk   rl   Ú"test_integrate_SingularityFunction_  s*     0<4 $$$(4rF  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   rn   r„   rw   r”   ée   )	rH   r7   rs   re   r   r…   r    r   r-   rt   rk   rk   rl   Útest_integrate_DiracDelta|  s.   *&ÿ
ÿÿÿÿ**ÿ*þ*ýürH  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 )Nrw   r’   Tr   rn   ©r   T)rH   rs   r…   r.   r   r"   r    rb   r2   r3   r  r   r£   r-   rk   rk   rk   rl   Ú test_integrate_returns_piecewise  sZ   &
ÿ"
ÿ
ÿ:
ÿ2
ÿ.
ÿ
ÿ:ÿ>ÿÿ6ÿ4ÿ8ÿ$<ÿþrJ  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 )Nrs   Tr´   rn   r   r   r„   r+  rê   rw   rƒ   r¿   )Úextended_real)r   rH   r,   r+   r   r    r.   r   r-   r   r<   )rs   r¿   Úint1Úint2Úint3rk   rk   rl   Útest_integrate_max_min®  s   ,,
ÿ& &ÿÿrO  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 )Nrƒ   rw   r•   rn   r   r   r„   éñÿÿÿrf   iÓ  r’   r&  zt sTr´   r½   é   rI  )rH   r   rs   r   r   rÎ   r   r3   r   r   r.   rð   r,   r    )r£   rŠ   rk   rk   rl   Útest_integrate_Abs_sign½  s<   "&$(&."
ÿ.
ÿ:
ÿÿÿ,ÿ(ÿrR  c                  C   sÞ   t ttt ƒtƒ} |  td¡t ttd ƒtƒksJ ‚t ttt ƒtddfƒ} |  td¡t ttd ƒtddfƒks:J ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfƒ}| tdi¡t tdtd  ƒtt tfƒksmJ ‚d S ©Nr   r   rw   rn   rƒ   )rW   r    rs   r…   rñ   r	   r   ©ri   re   Úconvrk   rk   rl   Ú
test_subs1Ø  s   "("4rV  c                  C   s  t ttt ƒttƒ} |  td¡t ttd ƒttƒksJ ‚t ttt ƒtddftddfƒ} |  td¡t ttd ƒtddftddfƒksDJ ‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tftddfƒ}| tdi¡t tdtd  ƒtt tftddfƒksJ ‚d S rS  ©rW   r    rs   r…   r£   rñ   r	   r   rT  rk   rk   rl   Ú
test_subs2â  s   $ 0*<rX  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   rw   r   rn   rƒ   rW  rT  rk   rk   rl   Ú
test_subs3ì  s
    0*<rZ  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$J ‚ttttd  ƒƒ}t |tƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒks]J ‚d S rY  rW  rT  rk   rk   rl   Ú
test_subs4ô  s
   ,&<r[  c                  C   s¸  t ttd  ƒtt tfƒ} |  td¡| ksJ ‚t ttd  t ƒtƒ} |  td¡t ttd  d ƒtƒks8J ‚t ttd  t ƒttfƒ} |  td¡t tttd  ƒtdfƒks[J ‚|  td¡t ttd  d ƒtƒksoJ ‚t ttd  t ƒtt tftt tfƒ} |  td¡| ksŽJ ‚|  td¡| ks˜J ‚t ttd  ƒttfƒ} |  td¡t ttd  ƒtdfƒks¸J ‚t ttƒtƒ} |  td¡|  td¡ t ttƒtddfƒ  ¡ jsÚJ ‚d S )Nrn   r•   rw   r   )rW   r    rs   r   rñ   r…   r   Úis_zero©ri   rk   rk   rl   Ú
test_subs5ü  s    (*(*(*
ÿr^  c                  C   sŒ  t dƒ\} }ttt tttƒttƒfƒ}| td¡ttt ttdƒttƒfƒks*J ‚| td¡tttttƒtdƒfƒks>J ‚ttt tttƒttƒftttƒttƒfƒ}| td¡ttt ttdƒttƒfttdƒttƒfƒksrJ ‚| td¡ttt tttƒttƒftttƒtdƒfƒksJ ‚ttt tttƒt| ƒftttƒt| ƒfƒ}| | d¡ttt tttƒtdƒftttƒtdƒfƒksÄJ ‚d S )Nza brw   )r   rW   rs   r…   re   rñ   )r¤   r¾   ri   rk   rk   rl   Ú
test_subs6  s   ,(,<<,@r_  c                  C   s¶   t ttdtftddfƒ} |  tdtdi¡| ksJ ‚t ttƒttƒ tttƒttƒftddfƒ} |  ttƒd¡| ks;J ‚|  ttƒd¡t ttƒttƒ tdttƒftddfƒksYJ ‚d S rô   )rW   rs   r…   rñ   r3   r]  rk   rk   rl   Ú
test_subs7  s    ÿ*ÿr`  c                  C   s\   t ttƒttd ƒ tdtfƒ} |  ¡ t ttƒtdtfƒt ttd ƒtdtfƒ ks,J ‚d S ©Nrn   rw   )rW   re   rs   r…   rŽ   r]  rk   rk   rl   Útest_expand$  s    <rb  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 ©Nrn   r   )rW   r    rs   rk   rk   rk   rl   r|   *  r  z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  ƒdt tfƒS rc  )rW   r    rs   r   rk   rk   rk   rl   r|   +  ó    )rZ   r†   rk   rk   rk   rl   Útest_integration_variable)  s   re  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 )Nrn   rw   r   )rW   r2   rs   r3   rŽ   rk   rk   rk   rl   Útest_expand_integral.  s   *"ÿÿ$ÿÿrf  c                      sL  t ttd d ƒtddfƒ‰ ˆ jddddtdƒ ksJ ‚ˆ jdddd	td
ƒ dtdƒ  ks2J ‚ˆ jddddtdƒ d dtdƒ d  dtdƒ d  ksSJ ‚ˆ jd	dddtdƒ d	tdƒ  d	tdƒ  dtdƒ  kstJ ‚tˆ jd	dd ¡ ˆ  ¡  ƒdk s‡J ‚t ttd td  ƒtddftddfƒ‰ tt‡ fdd„ƒ d S )Nr   rw   rn   r”   Úmidpoint©Úmethodr¼   éÙ   r„   r)  rê   é9   i	  é   iIÎ  iÚ  rŸ   éV   r½   é   g      à?r   c                      ó
   ˆ   d¡S )Nr„   ©Úas_sumrk   r]  rk   rl   r|   B  ó   
 z'test_as_sum_midpoint1.<locals>.<lambda>)	rW   r-   rs   rq  rð   rb   r…   rZ   ÚNotImplementedErrorrk   rk   r]  rl   Útest_as_sum_midpoint17  s$   *ÿ
ÿ
ÿ
ÿ

ÿ&(rt  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 )Nrn   r   rw   rb   T©rØ   rd   rg  rh  r„   r•   r%  r   é#   él   é   é@   rê   )rW   rs   r…   r   rq  rŽ   r   r©   rk   rk   rl   Útest_as_sum_midpoint2E  s   ,,,,$ÿrz  c                  C   s@  t tt d tddfƒ} | jddd ¡ td ksJ ‚| jddd ¡ tddƒtd  td  ks3J ‚| jddd ¡ tdd	ƒttddƒ  td  ksNJ ‚| jd
dd ¡ tddƒttdd
ƒ  td  ksiJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks‘J ‚| jdddd t¡sžJ ‚d S )Nrn   r   rw   Úleftrh  r¼   r   r•   rl  r„   rŸ   é    r½   r”   F)ri  Úevaluate)	rW   rs   r…   rq  rŽ   r   rb   Úhasr   r]  rk   rk   rl   Útest_as_sum_leftP  s   0668ÿr  c                  C   s8  t tt d tddfƒ} | jddd ¡ ddt  td  ks!J ‚| jddd ¡ tddƒttddƒ  td  ks<J ‚| jddd ¡ td	d
ƒttddƒ  td  ksWJ ‚| jddd ¡ tddƒttddƒ  td  ksrJ ‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ksšJ ‚d S )Nrn   r   rw   Úrightrh  r•   r¼   r   rn  rl  r„   rf   r|  r½   )rW   rs   r…   rq  rŽ   r   rb   r]  rk   rk   rl   Útest_as_sum_right[  s   *6668ÿr  c                  C   s*  t tt d tddfƒ} | jddd ¡ td t tj ks J ‚| jddd ¡ td t tddƒ ks6J ‚| jddd ¡ td t tdd	ƒ ksLJ ‚| jd
dd ¡ td t tddƒ ksbJ ‚| jtdd ¡ td t tddƒ ddtd    ks€J ‚t t	tƒtddfƒ dd¡tjks“J ‚d S )Nrn   r   rw   Ú	trapezoidrh  r   r¼   é   r(  r„   r&  r|  r½   )
rW   rs   r…   rq  rŽ   r   rÎ   r   rb   r   r]  rk   rk   rl   Útest_as_sum_trapezoide  s   (,,,$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 )
Nrn   r   rw   c                      ro  )Nr’   rp  rk   r]  rk   rl   r|   r  rr  z$test_as_sum_raises.<locals>.<lambda>c                      ro  ©Nr   rp  rk   r]  rk   rl   r|   s  rr  c                   S   s   t tƒ d¡S )Nr   )rW   rs   rq  rk   rk   rk   rl   r|   t  r}   c                      s
   ˆ   t¡S rx   )rq  r   rk   r]  rk   rl   r|   u  rr  c                      s   ˆ j dddS )Nr   Úxxxx2rh  rp  rk   r]  rk   rl   r|   v  r}   )rW   rs   r…   rZ   r†   rk   rk   r]  rl   Útest_as_sum_raisesp  s   r‡  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ksJ ‚d S rx   )rW   rs   r   ©ri   re   rk   rk   rl   Útest_nested_doity  s   r‰  c                  C   s  t td td dfƒ} t td tdd fƒ}|  ¡ tddƒksJ ‚| ¡ tddƒks*J ‚t tt td tfƒ tt¡t tt td tfƒksDJ ‚t tt ttd fƒ tt¡t tt ttd fƒks^J ‚ttd td dfƒtddƒksoJ ‚ttd tdd fƒtddƒks€J ‚tddƒtddƒksŒJ ‚d S )Nrn   rw   r   r’   zx**2)rs   Ú1N)rW   rs   r   r   r…   rñ   r£   rH   rˆ  rk   rk   rl   Útest_issue_4665  s   44""r‹  c                  C   s*   t td tddfƒ} | t | jŽ ksJ ‚d S )Nrn   r’   rw   )rW   rs   Úargsr]  rk   rk   rl   Útest_integral_reconstructŒ  s   r  c                  C   s  t t dt ƒtddfƒ} |  ¡ tddƒksJ ‚| jddtddƒks$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 )	Nrn   r   rw   r   F©Údeepre   r„   )	rW   rs   r   r   r   r¤   r    ÚlistÚreversed)ri   re   r–   rk   rk   rl   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 )Nrw   rn   r•   rf   r„   T)rH   r-   rs   r.   r   r   r"   rk   rk   rk   rl   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 )Nrn   rw   r’   T)rH   rs   rb   r"   r.   r   rk   rk   rk   rl   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   ©rs   r…   r  Frw   Trn   r   )Ú	sympy.abcrs   r…   r  rW   Ú	is_numberrb   r   r3   r2   re   )rs   r…   r  r   rk   rk   rl   Útest_is_number³  s0   &&((.$r˜  c                  C   s\  ddl m} m}m} td| ƒj| hksJ ‚t| ƒj| hksJ ‚t| | d |fƒj|hks-J ‚t| | |d fƒj|hks;J ‚t| | d|fƒj|hksIJ ‚t| | |dfƒj|hksWJ ‚t| | | |fƒj| |hksfJ ‚t| | |ƒj| |hkssJ ‚t| | ddfƒjtƒ ksJ ‚t| |ddfƒj| hksJ ‚t| |||fƒj| |hksžJ ‚t| |ddf|d d fƒj| |hks±J ‚t| |ddf| d|fƒj|hksÃJ ‚td|ddf|d| f| ddfƒjtƒ ksÙJ ‚td|| df|d| f| ddfƒjtƒ ksïJ ‚td| ddf|| df|ddfƒj| hksJ ‚tt| ƒt| ƒd|fƒj|hksJ ‚tt| ƒt| ƒd| fƒj| hks,J ‚d S )Nr   r•  rw   rn   )r–  rs   r…   r  rW   rŒ   Úsetre   r•  rk   rk   rl   Útest_free_symbolsÓ  s:   ÿÿÿÿ
ÿ&*rš  c                  C   s.  ddl m} m} td| d| fƒjsJ ‚td| ddfƒjsJ ‚td| ddftdfƒjdu s.J ‚t| |dfƒjs8J ‚t| | |dfƒjd u sFJ ‚t||dt| ƒf| dfƒ}|jd u sZJ ‚t|| df|dt| ƒfƒjdu slJ ‚t| | ttfƒjswJ ‚t| | t t fƒjs„J ‚tt| ƒ| ddt	 fƒjd u s•J ‚d S )Nr   )rs   rë   rw   rn   FT)
r–  rs   rë   rW   r\  r…   r    r   r3   r   )rs   rë   r   rk   rk   rl   Útest_is_zeroï  s    $&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   ©rs   r¼   rà   c                    s   g | ]}t ˆ ƒ‘qS rk   )Únext)Ú.0r  r]  rk   rl   Ú
<listcomp>  r  ztest_series.<locals>.<listcomp>r„   )	r–  rs   rW   r2   ÚlseriesÚnseriesÚremoveOr   Úrange)rs   r   rk   r]  rl   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 )Nrs   rw   rn   )r   rH   r3   r"   r;   r2   r~  r9   rœ  rk   rk   rl   Ú!test_trig_nonelementary_integrals	  s   *$r¥  c               	   C   s2  t dƒ} t dƒ}t ddd}tt| d |d  ƒ| ƒ|d t| | ƒ d | t| d |d  ƒ d  ks7J ‚tt| d |d  ƒ| ƒ| t| d |d  ƒ d |d t| t| d |d  ƒ ƒ d  kshJ ‚t ddd} t ddd}td| d |d  td	ƒ  | ƒ| |d t| d |d  ƒ  ks—J ‚d S )
Nrs   r…   r  Tr×   rn   r´   rw   z3/2)r   rH   r-   r$   r"   r   r•  rk   rk   rl   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 )Nrn   r„   rƒ   r  )rH   r-   rs   r1   rk   rk   rk   rl   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RTr×   rn   r   r„   )r   rH   r-   rs   r   )r¨  rk   rk   rl   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wrs   r…   r  re   rn   rw   )r–  rª  rs   r…   r  r   rW   rŒ  r   rH   r   )rª  rs   r…   r  re   rk   rk   rl   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  Tr×   rn   rw   r„   r’   )r   rH   r    r"   rs   r-   r   r   r<   r   rÎ   r>   ©r  rk   rk   rl   Útest_issue_4890C  s   *ÿ*ÿFÿr­  c                   C   s,   t dttdtd  ƒ  tƒ t¡rJ ‚d S rô   )rH   rs   r-   r~  rW   rk   rk   rk   rl   Útest_issue_4551M  ó   ,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 )Nrb   T©rd   rØ   rw   r   rn   )r   rQ   rH   rs   r   rÎ   rà   rk   rk   rl   Útest_issue_4376Q  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   rw   r½   rŸ   r&  )rH   r-   rs   r   rk   rk   rk   rl   Útest_issue_4517W  s   "*ÿr²  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 mTrc   r   rn   rI  )
r   rH   r3   rs   r   rQ   r.   r   rI   r2   )Úkrë   rk   rk   rl   Útest_issue_4527\  s$   &($ýÿ \X**ÿÿür´  c                  C   sp   t ddd} ttt d t |  t ƒt tt tfddttt d t |  t ƒt tt tfƒks6J ‚d S )Nr…   Tr×   rn   rÙ   rÚ   )r   rH   r    r   r   rs   r   rW   )Úyposrk   rk   rl   Útest_issue_4199q  s   .*ÿr¶  c                  C   s²  t ddd\} }}}tttd  t| t  ƒtƒttƒ t|d  d ƒ tt| d t ƒ d ks6J ‚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srJ ‚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s×J ‚d S )
Nza:dTr×   rn   r„   r   )Ú
expand_mul)r³  za d)r   rH   r    rs   r   r-   r   r<   r>   rç   r·  r–  r³  r   )r¤   r¾   r¿   rˆ   r·  r³  rk   rk   rl   Útest_issue_3940x  s    2ÿ Pÿ.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s)J ‚d S rÒ   )rH   r¤   rs   r   r"   rk   rk   rk   rl   Útest_issue_5413ˆ  s   Vr¹  c               
   C   s¸  t dƒ\} }tddd}|  t| ƒ }|  |t  ttƒd ttƒd   }ttƒd  ttƒd  }ttƒd  ttƒd  d }t|||  tƒ||  |  t	|t ƒ | | t t| ƒ   ||  |  t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   | | t | |  t	tƒ t|ƒ  t| ƒ | | t | |  t	tƒ t|ƒ  t| ƒ fv sÚJ ‚d S )NzA zr¿   T)rß   rn   rw   )
r   r   r    r£   r3   rs   r2   r…   rH   r"   )r¹   r  r¿   ÚP1ÚP2Úh1Úh2rk   rk   rl   Útest_issue_4892aŽ  s   &00,,..úr¾  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   rn   rê   r   )r3   r…   rs   r2   rR   rL   rH   r
   )Úexprrk   rk   rl   Útest_issue_4892b£  s   4	(rÀ  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   rn   )rH   r3   rs   re   r…   r  r   rW   rk   rk   rk   rl   Útest_issue_5178°  s   , ÿrÂ  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”   rn   r„   é   r½   iÐ  r¼   i€  i _7 r&  r•   )r3   rs   ÚseriesrN   rH   r
   ©re   r{   rk   rk   rl   Útest_integrate_seriesµ  s
   H&rÆ  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heurischrw   )Úsympy.integrals.heurischrÈ  rD   rs   rÇ  rk   rk   rl   Útest_atom_bug¿  s   $rÊ  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   rn   )
r   rH   r3   rs   r…   r   r‡   r"   r9   r   r¬  rk   rk   rl   Útest_limit_bugÄ  s   &*ÿrÌ  c                  C   s,   t dƒ} tttƒ| tƒ tƒ t¡sJ ‚d S )Nr{   )r   rH   r    rs   r~  rW   rz   rk   rk   rl   Útest_issue_4703Ê  ó   $rÍ  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡sJ ‚d S )Nre   rn   )r   rH   rs   r
   r~  rW   r÷   rk   rk   rl   Útest_issue_1888Ï  s   &rÏ  c                   C   sF   t ttt ƒtt d td ftdtfƒdttd d ƒ ks!J ‚d S )Nrn   r   )rH   r2   rs   r…   r   r;   rk   rk   rk   rl   Útest_issue_3558Ö  s   FrÐ  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ksJ ‚d S )Nrw   r%  r„   rn   )rH   r-   rs   r$   rk   rk   rk   rl   Útest_issue_4422Ú  rû   rÑ  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 )Nrw   rn   r½   rf   )rQ   rH   rs   r-   rk   rk   rk   rl   Útest_issue_4493Þ  s   &ÿrÒ  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 rÁ  )rH   r3   rs   r   r   r;   rk   rk   rk   rl   Útest_issue_4737ã  s   "$"rÓ  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¤   Tr×   rw   )rç   rå   r   rQ   rH   r    rs   r"   r   rB   rA   )rå   r¤   rk   rk   rl   Útest_issue_4992é  s
   ,ÿrÔ  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
lowergammarw   )Ú'sympy.functions.special.gamma_functionsrÖ  rQ   rH   r    rs   r…   rÕ  rk   rk   rl   Útest_issue_4487ñ  s   2rØ  c                  C   s,   t dƒ} td| d  | ddfƒtu sJ ‚d S )Nrs   rw   rn   r’   )r   rH   r   rœ  rk   rk   rl   Útest_issue_4215ö  rÎ  rÙ  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 )Nrb   Tr°  rn   rw   )r   rH   rs   r"   rà   rk   rk   rl   Útest_issue_4400û  s   RÿÿrÚ  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 )Nrw   rn   T©rD   )rH   r-   rs   rW   rk   rk   rk   rl   Útest_issue_6253  s   (&ÿrÜ  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 )Nrw   r   iôÿÿÿr   r½   rn   r¼   r•   rŸ   r„   rl  r1  é/   ©rH   rs   r…   r  r"   rk   rk   rk   rl   Útest_issue_4153	  s
   .B@*ýrß  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 hrn   )r   rH   rs   r-   r~  r   rW   )r¨  r¾   Úhri   rk   rk   rl   Útest_issue_4326  s   8rá  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 rc  rù   rk   rk   rk   rl   Útest_powers  s   >râ  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 )Nrw   T)ÚmanualrD   r°   rk   rk   rk   rl   r|     r  z$test_manual_option.<locals>.<lambda>rw   r   T©rä  )rZ   r†   rH   r"   rs   r~  rW   rk   rk   rk   rl   Útest_manual_option  s   .ræ  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   rã  )Nrw   T)rD   Úrischr°   rk   rk   rk   rl   r|   %  r  z%test_meijerg_option.<locals>.<lambda>TrÛ  )rZ   r†   rH   r5   rs   rW   rk   rk   rk   rl   Útest_meijerg_option$  s   (rè  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 )Nrw   r   T©rç  )rH   r"   rs   r   rk   rk   rk   rl   r|   ,  rd  z#test_risch_option.<locals>.<lambda>rn   Tré  rw   )
rZ   r†   rH   r    rs   rX   r"   r…   r<   rW   rk   rk   rk   rl   Útest_risch_option*  s   0D(rê  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   rã  )Nrw   T)rç  rÈ  r°   rk   rk   rk   rl   r|   5  r  z&test_heurisch_option.<locals>.<lambda>rn   TrÇ  r   r„   Fi€ÿÿÿrw   i!  éð   r%  râ   )rZ   r†   rH   r    rs   r-   r   r>   rW   r"   r2   r   r3   rk   rk   rk   rl   Útest_heurisch_option3  s   .,*BJÿÿrì  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |ddsJ ‚d S )Nrw   gHáz®Gñ?rn   g333333@gê-™—q=)Útol)rs   rH   r
   ra   rÅ  rk   rk   rl   Útest_issue_6828@  s   rî  c                  C   sX   t dƒ} ttt t| t  ttƒ ƒ tƒttt|  ttƒ ƒ ttƒ t ks*J ‚d S )NÚx_max)r   rH   r…   r   r    rs   r2   r¤   )rï  rk   rk   rl   Útest_issue_4803F  s   ""ÿrð  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   rs   rk   rk   rk   rl   Útest_issue_4234L  s   @rñ  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 )
Nrn   r•   TrŽ  rf   r   é   r¼   iøÿÿÿ)	rQ   rH   rs   r-   rL   r.   r   r#   r0   rk   rk   rk   rl   Útest_issue_4492P  s    "ÿJÿÿFÿÿýÿró  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 )Nrw   rn   r   g333333ó?r   g333333ó¿)r¤   r  r"   rX   rW   r   rH   r    rb   rŠ   r£   rs   )re   Ú
integral_frk   rk   rl   Útest_issue_2708Y  s   0ÿ,0ÿÿrõ  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)rs   r…   r    rH   Ústr)re   ri   rk   rk   rl   Útest_issue_2884g  s    r÷  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   rn   rw   rƒ   )r   r   )r   Tr’   )Ú$sympy.functions.elementary.complexesrù  r   rH   r    rŠ   rs   r%   r   r.   r   rD   r   rÎ   r   rW   r(   rI   rø  rk   rk   rl   Útest_issue_8368im  sN    ÿÿ

ýüû
õ þòÿ  
ýÿ ÿùÿrû  c                   C   s€   t tdt ƒƒdtdt ƒ ksJ ‚t tdt ƒƒdt dttdt ƒd ƒ  ks,J ‚t ttƒƒttttƒd ƒ ks>J ‚d S )Nr  rw   )rH   r(   rs   r%   r)   r"   rk   rk   rk   rl   Útest_issue_8901  s   $4(rü  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   rw   r„   rn   )rH   r3   rs   r;   r   r   r2   rk   rk   rk   rl   Útest_issue_8945“  s   >(Prý  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s0J ‚d S )NzToo slow for travis.zi L a brn   r   )
r]   r\   r   r2   r   rs   Úrewriter    rH   rŒ   )r   ÚLr¤   r¾   Ú	integrandrk   rk   rl   Útest_issue_7130š  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 trn   )r   rJ   rH   rW   r   )r¤   r¾   r¿   r£   Úvtrk   rk   rl   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 )Nrn   r¼   é0   r„   rê   r%  )rH   r-   rs   r   rk   rk   rk   rl   Útest_issue_11742ª  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£   rk   rk   rl   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 ©Nrw   r   rn   )rH   r-   r"   rs   r   rk   rk   rk   rl   Útest_issue_11876³  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Àr¼   g      (@r•   )rH   r    rs   rk   rk   rk   rl   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 )Nrn   r•   )rH   r3   r"   rs   r2   rk   rk   rk   rl   Útest_issue_4968½  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 )Nrw   rn   r’   rƒ   )rH   rs   r   rk   rk   rk   rl   Útest_singularitiesÁ  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 yTr´   r   rn   )r   rH   r3   r-   r   rW   )rs   r…   rk   rk   rl   Útest_issue_12645Ê  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   r½   rw   )rH   r3   rs   r2   r   r   rk   rk   rk   rl   Útest_issue_12677Ô  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   rs   r   r"   rk   rk   rk   rl   Útest_issue_14078Ø  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%   rs   r   r   rk   rk   rk   rl   Útest_issue_14064Ü  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    rs   r   rÎ   r"   r   rk   rk   rk   rl   Útest_issue_14027à  s   &>ÿr  c                   C   s&   t ttƒtdtd fƒtju sJ ‚d S rÁ  )rH   r5   rs   r   r   ÚInfinityrk   rk   rk   rl   Útest_issue_8170å  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 )Nrw   r’   rƒ   r   )rH   rs   r   r¢   rk   rk   rk   rl   Útest_issue_8440_14040é  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 )
Nrw   rn   r   r’   r  r„   r½   rÁ   r   rÞ  rk   rk   rk   rl   Útest_issue_14096î  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 )Nrw   r   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rs   rb   rk   rk   rk   rl   Útest_issue_14144ô  s   44r  c                   C   s(   t ttt ƒttƒ tƒ t¡sJ ‚d S rx   )rH   r    r   rs   r"   r~  r:   rk   rk   rk   rl   Útest_issue_14375ù  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 )Nre   r   rw   rn   r   )r   rs   r…   r  rH   rW   r÷   rk   rk   rl   Útest_issue_14437ÿ  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    rs   r"   rk   rk   rk   rl   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 ©Nrw   rn   r   )r    rs   rH   r÷   rk   rk   rl   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 )Nrn   rw   r’   r¼   )r-   rs   rH   r   r÷   rk   rk   rl   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 )Nrn   rw   r   r   r%  )r-   rs   rH   r   r§   r   r÷   rk   rk   rl   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  rn   r   )rs   r   r    rH   r   r÷   rk   rk   rl   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 )Nrw   r„   rƒ   rn   r   )rs   r    rH   )r…   re   rk   rk   rl   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   rw   T)rH   rs   rb   r    r"   r   rP   r.   rA   rB   r   rW   rk   rk   rk   rl   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clsrÙ   rÚ   )rT   r   rS   rH   r    rs   r   )r!  rë   ru   rk   rk   rl   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 )Nrn   Frq   r   rw   )r^   rW   r   rs   r…   r   r_   r`   rH   r   rÎ   rk   rk   rk   rl   Útest_issue_152182  s   ÿ,ÿ0ÿ,ý&*r$  c                  C   s€   t ttd  tdt ƒ ƒttd tdt ƒ ƒ tdtfƒ} t| tƒs&J ‚t	| t
tƒd ttƒ   ttd ¡ƒdks>J ‚d S )Nrn   r   r½   )rH   r    rs   r2   r£   r3   r   rÈ   r.   rP   r-   r   rñ   r:  rk   rk   rl   Útest_issue_15292C  s   >4r%  c                   C   s.   t tdt ƒttƒ tƒdttƒ ksJ ‚d S rÒ   )rH   r3   rs   rk   rk   rk   rl   Útest_issue_4514I  ó   .r&  c                  C   sè   t ddd\} }}ttt| d ƒƒ| ||fƒ}ttt| d ƒƒ| ƒ}| |d|di¡ddt  ks3J ‚| | d¡| | d¡ ddt  ksGJ ‚| |d|d	i¡tdƒ td
ƒ ks[J ‚| | d	¡| | d¡ tdƒ td
ƒ ksrJ ‚d S )Nzx a bTr´   rn   rw   r   rƒ   r  r’   r•   )r   rH   r    r   rñ   r   )rs   r¤   r¾   ÚdefiniteÚ
indefiniterk   rk   rl   Útest_issue_15457M  s   "((2r*  c                   C   sN   t tttƒ ttƒ tƒtttƒ ttƒ ttƒ ttƒ ttƒ ks%J ‚d S rx   )rH   rs   r    r"   r:   rk   rk   rk   rl   Útest_issue_15431W  s   *ÿr+  c                  C   sü   t tt ƒ } tdtt ƒ ƒ}t| t ƒ|kr| t ¡| ksJ ‚t d tt ƒd  } t d  tt ƒ dtdtt ƒ ƒ  }t| t ƒ|krI| t ¡| ksKJ ‚ttt ƒƒt d  } ttƒ tttt ƒƒƒ d ttt ƒƒt   }t| t ƒ|krz| t ¡| ks|J ‚d S )Nrn   r   r„   )rs   r"   r:   rH   r
   r-   r   r=   )re   ÚFrk   rk   rl   Ú"test_issue_15640_log_substitutions\  s    & .$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NTrÇ  )Úsympy.vectorr.  rs   rH   r2   r¤   r¾   Úx_1Úx_2r.   r3   r   r   )r.  r/  rs   rk   rk   rl   Útest_issue_15509h  s    Dþr3  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 )
Nrs   Tr´   rÁ   rn   r„   r  éQ   r   )r   rH   rð   r.   r   rœ  rk   rk   rl   Útest_issue_4311_fastq  s   ".ýr5  c               	   C   sÞ  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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s´J ‚tdtt| ƒd  |ƒ| d tttt| ƒd ƒ d  ksÖJ ‚tdtt| ƒd  |ddt fƒt ksíJ ‚d S )NÚKTr×   rs   r´   rë   r£   rn   r„   rƒ   rw   r   )	r   rH   r    r   r-   r   r>   r"   r<   )r6  rs   rë   r£   rk   rk   rl   Ú%test_integrate_with_complex_constantsy  s"   >ÿ,ÿ

ÿ>"ÿ@D2r7  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 )Nrs   rb   Tru  rw   rn   )r   rH   rF   r!   r   r   rA   ©rs   rb   rk   rk   rl   Útest_issue_14241ˆ  s
   :ÿr9  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 )Nrn   r•   r„   r   )rH   r3   r£   r2   r   rk   rk   rk   rl   Útest_issue_13112  r  r:  c                  C   sP   t ddd} tttddt |   ƒ td| fƒ}|d| d  t d ks&J ‚d S )	Nrà  Tr×   rw   rn   r   r•   r%  )r   rH   rs   r/   r   )rà  r   rk   rk   rl   Útest_issue_14709b“  s   $ r;  c                  C   sl   t dƒ} t dƒ}tt|ƒ| |t | fƒt| ƒksJ ‚tt|  ƒtd|  ƒ |  | dtfƒtdƒks4J ‚d S )Nrs   r£   rƒ   r   rn   )r   rH   r    r   r:   r"   )rs   r£   rk   rk   rl   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 )NrŠ   Tr×   rn   gš™™™™™ù?rw   gÏRt?,eÀg:Œ0âŽyE>r¼   r•   iöÿÿÿé   r   )r   r    rH   r   r¢   rð   rñ   )rŠ   r   Úsolutionrk   rk   rl   Útest_issue_15494   s   ,
4Rr?  c               	   C   s~   t dƒ} tt| td  ƒtƒ ¡ ttttd |  ƒ ttdttd |  ƒ d ƒ ttd |  ƒ  t	| dƒfdƒks=J ‚d S )Nr…   rn   r   r   rI  )
r   rW   r@   rs   r   r.   r:   r"   r-   r   rÓ   rk   rk   rl   Útest_li_integral°  s   ,.ÿþþr@  c               	   C   sÆ   t dƒ} t dƒ}tt| | ƒ| ƒ| | |  ttdƒd dd|   ƒ ttdƒd dd|   ftdƒd tdƒd dd|   f| d|   d ƒ d| ttdƒd dd|   ƒ  ksaJ ‚d S )Nrs   rb   rw   rn   r   r„   )r   rH   r3   rA   r   rC   r8  rk   rk   rl   Útest_issue_17473·  s   @"þ"þÿrA  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 )Nrn   rw   r   r”   rÁ   )rH   r"   rs   r   r   rk   rk   rk   rl   Útest_issue_17671À  s   *:>rB  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 )Nrª  ÚCr…   rw   rn   r   r„   )r   rH   r   r-   )rª  rC  r…   rk   rk   rl   Útest_issue_2975Æ  s   frD  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/  Trc   rw   rn   r„   r   rI  c                      s   t tˆˆtˆ fƒtƒS rx   ©rH   r   r…   rk   ©rb   rs   rk   rl   r|   Ù  r‚   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS r€   )rH   r   rk   rF  rk   rl   r|   Ú  r‚   c                      s   t tˆ ˆ dtfƒˆ ƒS r€   rE  rk   rœ  rk   rl   r|   Û  r‚   )r   r   rH   r   r3   r   r.   r2   r   r   rZ   r†   )r  r/  rk   rF  rl   Útest_issue_7827Í  s,   :ÿ,ÿ"2ÿÿÿÿ*rG  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  )rs   r-   r"   rH   r÷   rk   rk   rl   Útest_issue_4231Þ  s   XBrH  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
   rs   r   rH   r÷   rk   rk   rl   Útest_issue_17841ã  s   &rI  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 )Nrs   T©rµ   rß   r„   r•   rw   rê   r½   rn   r   )
r   r0   r(   r"   r%   r2   rH   r   r-   r1   )rs   Úf1Úf2rk   rk   rl   Útest_issue_21034è  s   6$xÿFÿrM  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"   rs   r    r:   r   r   rk   rk   rk   rl   Útest_issue_4187ô  s   8,rN  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 )Nrÿ  r  Úr0ÚR0rn   r„   r   Tr%  r•   )r   rH   r2   r3   r.   r   r   r   r-   r?   rA   r   r§   )rÿ  r  rO  rP  rª  Úsolrk   rk   rl   Útest_issue_5547ù  s(   8ÿ*
ÿ.>:ÿÿ
ý^<rR  c                   C   s6   t dddt d  d  tdtfƒtddƒksJ ‚d S )Nrw   rn   r   r   )rH   rs   r   r   rk   rk   rk   rl   Útest_issue_15810  rû   rS  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 )Nrs   TrJ  r„   r   rn   rw   rƒ   r½   r•   éûÿÿÿr¼   r”   rf   r0  rò  iLÿÿÿéZ   rP  r  )r   r"   r    rH   r)   r(   r   r1   r   r%   rŽ   r3   )rs   re   r,  ÚF_truerk   rk   rl   Útest_issue_21024  s”   (B"ÿÿ(Dd$@*$$ f(4 <<.nÿ
ÿÿ,rW  c                  C   s`   t dƒ} tdtdt|  d    tt tfƒ ¡ tt| ƒd dƒ tt| ƒd dƒ ks.J ‚d S )Nr¤   rw   rn   r   )r   rH   r   rs   r   rŽ   r8   r   )r¤   rk   rk   rl   Útest_issue_21721k  s   ($ÿrX  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   rn   rê   r½   )r   rH   r2   r   )rY  r   rk   rk   rl   Útest_issue_21831q  s   8$rZ  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 )Nrn   rw   r„   r’   r|  )rH   rs   r   r-   r   rk   rk   rk   rl   Útest_issue_22033_integralx  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 )Nrw   rn   r’   r  r   )rH   r  rs   r…   r-   r   r   rk   rk   rk   rl   Útest_issue_21671}  s   ^\r\  c                  C   sr   t ddd} ttƒdttƒd   }t| t| ¡| dd | t¡}t|tdd|  kr4t|tƒks7J ‚ J ‚d S )NÚxrTr´   r„   rn   rå  )r   r2   rs   r3   rH   rñ   rW   )r]  r¿  Úres_realrk   rk   rl   Útest_issue_18527ƒ  s   0r_  c               	   C   sÀ  dt ttƒ tttƒ   } tt t  ttd ƒ ttd t d  ƒt   ƒ ttd t d  ƒ tt t  ttd ƒ ttd t d  ƒt   ƒttd t d  ƒ  }tt	tttd ƒd ƒ tttd ƒd ƒ  t
tdƒt
t dƒ@ ftttd ƒƒt t
t dƒft t t  ttƒ t ttƒ   t
tt t  ƒfttt  ttƒ t ttƒ   t
ttt  ƒf|dfƒ}t| tƒ|ksÁJ ‚tddd\}}t|t |i}t|  |¡tƒ| |¡ksÞJ ‚d S )Nrw   rn   r   Tza, br×   )r¾   r2   rs   r¤   r3   r"   r5   r-   r.   r   r   r   rH   r   rñ   )re   ÚFposr,  Úapr"  Úreprk   rk   rl   Útest_issue_23718Œ  s   FDÿ@2,ø
"rc  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 )Nrw   rn   rƒ   r’   r   gC˜qBõ?)rH   r-   rs   r"   ÚmathÚiscloserb   r  rk   rk   rl   Útest_issue_23566¡  s    rf  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 )Nrw   rn   T)rH   r-   rs   r   r.   r#   r   r0   rk   rk   rk   rl   Útest_pr_23583§  s   \rg  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    rs   r-   r$   rk   rk   rk   rl   Útest_issue_7264¬  s   Xrh  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*   rs   r1   r)   r   rÎ   rk   rk   rk   rl   Útest_issue_11254a°  r'  ri  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 )Nrn   r   rw   )rH   r'   rs   r"   r)   r   rk   rk   rk   rl   Útest_issue_11254b´  s   " rj  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 ra  )rH   r*   rs   rþ  r(   r)   rk   rk   rk   rl   Útest_issue_11254d¹  s   Drk  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   rn   r„   r   rw   i›ÿÿÿr¼   é‡   r%  g€2É{¢ÙÀ)rH   rs   r-   r"   rd  re  rb   r  rk   rk   rl   Útest_issue_22863½  s   D4rm  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 )Nrn   rê   r   rw   r¼   r„   r•   rÁ   r”   r&  é(   )rH   r-   rs   r   r"   rk   rk   rk   rl   Útest_issue_9723Ã  s   ^ÿ&^ÿÿÿro  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 )Nrn   Tré  r   r„   )rH   r"   rs   r¿   r¾   r¤   rX   rk   rk   rk   rl   Útest_issue_23704Ë  s   00ÿrp  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  rk   rk   rk   rl   Útest_exp_substitutionÓ  s   drq  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&   rs   r"   r)   r*   r1   r'   rk   rk   rk   rl   Útest_hyperbolic×  s   0$$rr  c                   C   s,   t ttd ƒƒtttd ƒ d ksJ ‚d S rÒ   rÄ   rk   rk   rk   rl   Útest_nested_powÝ  r¯  rs  c                   C   sj  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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fdtttt  ƒ t ttd
ƒftttƒ dfƒksãJ ‚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smJ ‚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s¼J ‚t ttt  tttt  t	td   ƒ tƒt
ttttt  t	td   ƒ t	 t t 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	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s^J ‚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sµJ ‚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söJ ‚t tttt  t	td   ƒtƒt
td tdt	   tttt  t	td   ƒ td td d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fdttt  tdƒd   dt  ttd
ƒfttƒt dfƒkstJ ‚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s³J ‚d S )Nrw   r   rn   r„   r•   r&  r  rƒ  r½   r   TrŸ   rÁ   iùÿÿÿr|  r=  rG  r¼   rl  r%  iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rs   r$   r   r0   r"   r¤   r¾   r¿   r.   r   rˆ   ri   rk   rk   rk   rl   Útest_sqrt_quadraticá  s`   XXl$N.ÿÿ*V
ÿ*V
ÿ*j
ÿ,$Xÿÿb"ý
ÿ:j
ÿ.*ÿ
ÿ 0Zÿÿ,ý
ÿVÿrt  c                   C   sî   t tttƒ ttƒ ƒtttƒ tttƒttƒ ƒ ksJ ‚t tttƒd  tƒtttƒ tttƒƒ ks7J ‚t td tttƒtdfƒ ƒtd tttƒtdfƒ dtd  tttƒtdfƒ  dt tttƒtƒ  dttƒ  ksuJ ‚d S )Nrn   r   r„   r½   )rH   rs   r6   r5   r"   r2   r   re   rk   rk   rk   rl   Útest_mul_pow_derivative  s
   <2Xÿru  )rf   (\  rd  Úsympy.concrete.summationsr   r   Úsympy.core.addr   Úsympy.core.containersr   Úsympy.core.exprr   rç   r   r   r	   r
   Ú
sympy.corer   Úsympy.core.numbersr   r   r   r   r   r   r   r   Úsympy.core.relationalr   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   Úsympy.core.sympifyr   rú  r   r   r   r   r   Ú&sympy.functions.elementary.exponentialr   r    r!   r"   Ú%sympy.functions.elementary.hyperbolicr#   r$   r%   r&   r'   r(   r)   r*   Ú(sympy.functions.elementary.miscellaneousr+   r,   r-   Ú$sympy.functions.elementary.piecewiser.   Ú(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Ú'sympy.functions.special.delta_functionsr7   r8   rè   r9   r:   r;   r<   r=   r>   r?   r@   r×  rA   rB   Úsympy.functions.special.hyperrC   rD   Ú-sympy.functions.special.singularity_functionsrE   Ú&sympy.functions.special.zeta_functionsrF   Úsympy.integrals.integralsrH   Úsympy.logic.boolalgrI   Úsympy.matrices.denserJ   Úsympy.polys.polytoolsrK   rL   Úsympy.printing.strrM   Úsympy.series.orderrN   Úsympy.sets.setsrO   Úsympy.simplify.gammasimprP   Úsympy.simplify.simplifyrQ   Úsympy.simplify.trigsimprR   Úsympy.tensor.indexedrS   rT   rU   Ú#sympy.functions.elementary.integersrV   rW   Úsympy.integrals.rischrX   Úsympy.physicsrY   Úsympy.testing.pytestrZ   r[   r\   r]   r^   r_   Úsympy.utilities.exceptionsr`   Úsympy.core.randomra   rs   r…   r  r¤   r¾   r¿   rˆ   ri   rŠ   r£   r1  r2  rb   re   rm   rv   r‹   r‘   r“   rž   rª   r±   r²   r»   rÀ   rÂ   rÃ   rÅ   rÇ   rÍ   rÑ   rÔ   rÕ   rÖ   rÜ   rÝ   rÞ   rá   rã   ré   rì   rí   rî   ró   rõ   rø   rú   rý   rÿ   r  r  r  r  r  r  r  r  r#  r$  r8  r9  r<  rF  rH  rJ  rO  rR  rV  rX  rZ  r[  r^  r_  r`  rb  re  rf  rt  rz  r  r  r„  r‡  r‰  r‹  r  r’  r“  r”  r˜  rš  r›  r¤  r¥  r¦  r§  r©  r«  r­  r®  r±  r²  r´  r¶  r¸  r¹  r¾  rÀ  rÂ  rÆ  rÊ  rÌ  rÍ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rØ  rÙ  rÚ  rÜ  rß  rá  râ  ræ  rè  rê  rì  rî  rð  rñ  ró  rõ  r÷  rû  rü  rý  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-  r3  r5  r7  r9  r:  r;  r<  r?  r@  rA  rB  rD  rG  rH  rI  rM  rN  rR  rS  rW  rX  rZ  r[  r\  r_  rc  rf  rg  rh  ri  rj  rk  rm  ro  rp  rq  rr  rs  rt  ru  rk   rk   rk   rl   Ú<module>   sü   ((((  

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