o
    8Va                     @   s  d dl mZ d dlmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z= d dl>m?Z? d dl@mAZA d dlBmCZC d dlDmEZE d dlFmGZGmHZH d dlImJZJmKZKmLZLmMZM ed	d
d
dZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXd d! ZYd"d# ZZd$d% Z[d&d' Z\d(d) Z]d*d+ Z^d,d- Z_d.d/ Z`d0d1 Zad2d3 Zbd4d5 ZceGd6d7 Zdd8d9 Zed:d; Zfd<d= Zgd>d? Zhd@dA ZidBdC ZjdDdE ZkdFdG ZldHdI ZmdJdK ZndLdM ZodNdO ZpdPdQ ZqdRdS ZrdTdU ZsdVdW ZteGdXdY ZudZd[ Zvd\d] Zwd^d_ Zxd`da Zydbdc Zzddde Z{dfdg Z|dhdi Z}eGdjdk Z~dldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ Zddń ZddǄ ZeGddɄ Zdd˄ Zdd̈́ Zddτ Zddф Zddӄ ZddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZȐd d Zɐdd Zʐdd Zːdd Z̐dd	 Z͐d
d Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd ZԐdd ZՐdd Z֐dd Zאdd Zؐd d! Zِd"S (#      )product):limitexpoologsqrtLimitsinfloorcosceilingsinhatanAbsgammaSymbolSpiIntegralRationalIEbesseljtancot	integrateSumsignFunctionsubfactorialsymbolsbinomialsimplifyfracFloatseczoofresnelcfresnels	real_rootacoserferfcerfiLambertW	factorialdigamma
uppergammareEi
EulerGammaasinatanhacotacothasecacsccbrtbesselk)AccumBounds)Mul)
heuristics)Order)XFAILraises)xyzknTintegerpositivec                   C   s  t ttttu s
J t ttt t u sJ t t ttt u s"J t td tt tu s/J t td  ttt u s=J t ttt tddddksMJ t dt ttdksYJ t tttttu seJ t tt ttt u ssJ t ttt tttu sJ t dt tt  ttdksJ t tdt  tttu sJ t ttd  ttt u sJ t dt dtd  tddksJ t dt t tdttd t tdksJ t dt t tdddttd t tdddksJ t dt t t tdddtdt t t tdddksJ t tt tt tdt tt ks&J t t	tt t tdtt	tt ks=J t t
dt d ttdksNJ t tjtt tju s\J t tdt ttjtju smJ t dtd  tdddtu s~J t dtd  tdddt u sJ t ddt d  tdddt u sJ t ddt d  tdddtu sJ t dtt ttddt u sJ t dtt ttddtu sJ t dt	t ttd ddt u sJ t dt	t ttd ddtu sJ t dttd  tdt tdd ddtu sJ t dttd  tdt tdd ddt u s6J t dttd  tttdd ddt u sOJ t dttd  tttdd ddtu sgJ t ttt tdd	ddksxJ t td tdd	ddksJ t dtd  tdd	dtu sJ t dt tdd	dtu sJ t ddt  tdtu sJ t ddt  tdddt u sJ t td
 tdddtu sJ t td tdddt u sJ t dtt tdddt t ksJ t td tddddks
J t tttddddksJ t tt  tdddt ddt   ks0J t dt	t t tdtt	td t tdksKJ d S )N   r   +dir   -      +-)r   rC   r   r   r   r   r   rD   r   r   r   r   NaNr@   r	   r   r   r   r   r&   r    rX   rX   @/usr/lib/python3/dist-packages/sympy/series/tests/test_limits.pytest_basic1   s^    "$,4>,."""$(&$"(&4620""$ (.:rZ   c                   C   s  t tt tddddksJ t ttd t tddksJ t ddt  ttdks,J t tdt  ttdks;J t ttt  tttu sJJ t tttd   tttu s[J t tttt  tttu slJ t ddt  tt  ttdksJ d S )Nr   rL   rM   rO   rV   rK      r   rC   r   r   rX   rX   rX   rY   test_basic2P   s    ""*r]   c                   C   s>   t dt tdddtu sJ t dt tdddt u sJ d S )NrO   r   rL   rM   rP   r   rC   r   rX   rX   rX   rY   test_basic3[   s   "r_   c                   C   s   t dt tt  tddksJ t dt tt  tddt ks"J t dtd  ttd   tddtd  ks:J t ttd tt ttdksLJ tdtd d  tdtfdt td d	 ksfJ d S )
NrK   r   rO      rU   rT   i   rQ   	   )r   rC   rD   r   r   r   r   rX   rX   rX   rY   test_basic4`   s
    $0$8rb   c                  C   s.  t ddd\} }}t| | t| t|  }|| tdks!J || | tdks-J t ddd\}}|d |d |d  t|d  |d d d  d|d d |d    d| t||  |d d d	 t|d |d    |d d d    }t||tt|d
  |d d d  ksJ d S )Nza b cTrJ   r   ztau xrK   rO   rT         ?rQ   )r    r   r   r   r   r   )abcAZtaurC   exprrX   rX   rY   test_logh   s"   8(0rj   c                   C   s6   t ttd dd td  tddtddksJ d S )N   rQ   rK   rT   rL   rO      )r   r)   rC   r   rX   rX   rX   rY   test_piecewisew   s   6rm   c                  C   s8   G dd dt } t| tttt| tttksJ d S )Nc                   @   s   e Zd Zedd ZdS )ztest_basic5.<locals>.myc                 S   s   |t ju rt jS d S N)r   ZInfinityrW   )clsargrX   rX   rY   eval~   s   
ztest_basic5.<locals>.my.evalN)__name__
__module____qualname__classmethodrq   rX   rX   rX   rY   my}   s    rv   )r   r   rC   r   r   )rv   rX   rX   rY   test_basic5|   s   (rw   c                   C   s0   t tt tt  tdtt dt  ksJ d S NrK   )r   rC   rD   rE   rX   rX   rX   rY   test_issue_3885      0ry   c                   C   sf   t ttt tddksJ t ttt td dksJ t ttdddjttdtdfks1J d S )Nr   rO   rS   rM   )r   r	   rC   doitargsr   rX   rX   rX   rY   
test_Limit   s    *r}   c                   C   s  t tttdddksJ t tttdddksJ t tttdddks'J t tttdddks4J t tttdddksAJ t tttdddksNJ t tttdddks[J t tttdddkshJ t tttdddksuJ t tttdddksJ t tttd	dd	ksJ t tttd	dd
ksJ t ttdt  d tddtddksJ t ttd tt tttddksJ d S )NrT   rL   rP   rU   rV   r   rO   rK         rQ   rd               ?)r   r
   rC   r   r   r=   rX   rX   rX   rY   
test_floor      ,.r   c                   C   s  t ttttdddksJ t ttttdddksJ t ttttdddks-J t ttttdddks<J t tdtt tdddksMJ t tdtt tdddks^J t tdtt tdddksoJ t tdtt tdddksJ d S )Nr   rL   rP   rV   rR      )r   r
   r	   rC   r   rX   rX   rX   rY   &test_floor_requires_robust_assumptions      """&r   c                   C   s  t tttdddksJ t tttdddksJ t tttdddks'J t tttdddks4J t tttdddksAJ t tttdddksNJ t tttdddks[J t tttdddkshJ t tttdddksuJ t tttdddksJ t tttd	dd
ksJ t tttd	dd	ksJ t ttdt  d tddtddksJ t ttd tt tttddksJ d S )NrT   rL   rV   rP   r   rO   rK   rQ   r~      rd   r   r   )r   r   rC   r   r   r=   rX   rX   rX   rY   test_ceiling   r   r   c                   C   s  t ttttdddksJ t ttttdddksJ t ttttdddks-J t ttttdddks<J t tdtt tdddksMJ t tdtt tdddks^J t tdtt tdddksoJ t tdtt tdddksJ d S )Nr   rL   rO   rP   rR   rk   )r   r   r	   rC   r   rX   rX   rX   rY   (test_ceiling_requires_robust_assumptions   r   r   c                  C   sd   t ddd} tt| td|   | ddksJ tt| t| d  t|  | ttd ks0J d S )NrC   TrealrO   r   rK   )r   r   r   r	   r   r   r   rC   rX   rX   rY   	test_atan   s   $4r   c                  C   s  t tttddksJ t ttttddksJ t ttttddks(J t tttd tdtdks:J t ttt ttt  dt  tdttksTJ t ttttd  tt	dksfJ t tttttd  tttd td d   d  tt	dksJ t tttd d d tddt	ksJ t ttttdt	ksJ t tttttdt	ksJ t
ddd} t tt| d t|  | t	dksJ t | td|  t ttd|     d | ddksJ t t| t|  | td	d
ksJ d S )Nr   rO   rK   rQ   rL   rE   Trc   rP   rV   )r   absrC   r	   r   r   rD   r   r   r   r   r   rE   rX   rX   rY   test_set_signs   s   $4$H* (8(r   c                  C   st   t ddd} ttd|  t|  | ddtddksJ ttdtt| ttd|    | dtdks8J d S )	NrC   Tr   rO   r   rL   rV   rK   )r   r?   r	   r   r=   r   r   r   r   rX   rX   rY   test_heuristic   s   ,<r   c                  C   sN   t ddd} d|  t|  t  }t|ttdksJ |ttdks%J d S )NrE   Trc   rV   r   )r   r   rC   r   r   )rE   frX   rX   rY   test_issue_3871   s   r   c                  C   s  t d} t ddd}td||   |  | tt|ksJ td|d|    |  | tt|d ks2J td|d|  d   |  | tt|d ksJJ t|d |d  | |ttdks^J tddd|  |  |tdtj kssJ tdd|  | d| |  |tttd	ksJ d S )
NrG   rC   Tr   rO   rK   rT   rk   z1/3)r   r   r   r   r   Exp1)rG   rC   rX   rX   rY   test_exponential   s   $,0(*8r   c                  C   s8   t d} tdt| t|    |  | tttksJ d S )NrG   rO   )r   r   rC   r	   r   r   )rG   rX   rX   rY   test_exponential2  s   0r   c                  C   s.   t dt t} t| tt}| tu sJ d S rx   r   rC   r   r   r{   r   lrX   rX   rY   	test_doit  s   r   c                  C   s  t ttttd  tttddksJ t ttttd  d tttddks,J t tttttt  tttddksCJ tttd d tdd  tdd tj ddtd  } t t	t
ttttdtf ttt| ksJ ttdtdd  tdd d ddtd  }t t	t
ttttdtf ttt|ksJ t ttt tttdtksJ t ttd d t tttdtksJ d S )NrO   rT   rK   rV   rQ   r   )r   r	   rF   r   r=   r   r>   r   Halfr"   r   rG   Zrewriter   r{   r#   rC   )t1t2rX   rX   rY   test_series_AccumBounds  s   *..@848".r   c                  C   s2   t dt t} t| tt}|jdd|ksJ d S )NrK   FZdeepr   r   rX   rX   rY   
test_doit2%  s   r   c                   C   s.   t ttt ttd  tt dksJ d S NrO   r   r\   rX   rX   rX   rY   test_issue_2929-     .r   c                   C   s   t dtt td  ttjddttj  ksJ t tttd d tdtdtd ks2J t tttd d tddtd ksHJ d S )NrO   rK   r   r   )r   r   rC   r   r   r	   r   rX   rX   rX   rY   test_issue_37921  s   400r   c                   C   s   t dtd  tdtddksJ t dtt  tdtjdt  ks$J t tttd d  tdtdd ks:J t tttd t  tdtddt  ksRJ d S )NrO   rQ   rK   rR      r   )r   rC   r   r   r   Oner   rX   rX   rX   rY   test_issue_40907  s   "&,4r   c                   C   s@   t tttdddtu sJ t ttttd dddksJ d S )Nr   rL   rM   rK   )r   r   rC   r   r   rX   rX   rX   rY   test_issue_4547>  s   $r   c                   C   s   t td tttd   krtu sJ  J t td tdtdd ks&J t td tddks2J t td ttdks>J t td tdtdd ksNJ d S )Nrd      r   r   r   )r   rC   r   r   rX   rX   rX   rY   test_issue_5164C  s
   , $r   c                  C   s0   ddt   dt   } t| t dt ksJ d S )N      ?r   )rC   r   r   rG   )funcrX   rX   rY   test_issue_5383K  s   r   c                  C   sp   t tdd  tt  t  tdt d  ttt  tddt    t d  } t| t ttdd ks6J d S )NrO   rK   rl   rQ   ih  )rC   r   r   r   r/   r   r   ri   rX   rX   rY   test_issue_14793P  s   *
 r   c            
   
   C   sb  t ttt gddgddtjtddgddg} g ttt tt t tt dtdd  tddddddddtttt tt t tt dtdd  ddddddddR }t| t|ks}J t	t
| |D ]*\}\}}|\}}}}|||  }	zt|	td|d|ksJ W q ty   	 J w d S )	NrV   rO   rK   rQ   rP   rL   r   rM   )listcartesrC   r   r   r   r   r   len	enumeratezipr   AssertionErrorprint)
testsresultsir|   resrD   sedeqrX   rX   rY   test_issue_5183V  s   :r   c                  C   s   t ttt ttdksJ t tttttd ksJ t tttttu s(J t ttt ttdks6J t ttttj	t
tksEJ tddd} t | td|   | ddks[J d S )Nr   rK   rTr   rO   )r   r	   rC   r   r   r   r   r   r   r   r   r   r   rX   rX   rY   test_issue_5184n  s   $r   c                   C   s*   t dt dt  tj tddksJ d S r   )r   rD   r   r   rX   rX   rX   rY   test_issue_5229y     *r   c            	      C   s   t tttgt d dtd tttdd gddg} ddt tddt tddtt ddtt ddtt f}t| t|ks@J tt	| |D ]'\}\}}|\}}}|t
}zt|t
||d|kscJ W qG tyn   	 J w d S )NrK   r   rQ   rP   rL   rM   )r   r   r   r   r   r   r   r   r   r   rC   r   r   r   )	r   r   r   r|   r   r   r   r   r   rX   rX   rY   test_issue_4546}  s$   
 
r   c                   C   sX   t dttd  dt  tddksJ t ddt  ddt   t tddks*J d S )NrO   rQ   r   rR   )r   rC   r   rX   rX   rX   rY   test_issue_3934  s   (0r   c                   C   sX   t ttdd dttdd   ttdksJ t td dtd   ttdks*J d S )NM   rQ   rO   gfffffFY@)r   rC   r   r   rX   rX   rX   rY   test_calculate_series  s   0(r   c                   C   s   t td dtd   ttdksJ t td dtd   ttdks$J t td dtd   ttdks6J t td td d tt   ttdksMJ d S )Nr   rO   d   i]    r   rC   r   r   rX   rX   rX   rY   test_issue_5955  s   $$$2r   c                   C   s0   t tdtt ttt tddksJ d S r   )r   r   r	   rC   r   rX   rX   rX   rY   test_newissue  rz   r   c                   C   s   t tt ttttt ttksJ t dttt  t tdtdttt  t tdks0J t tt ttttt ttksBJ t tt dt  ttttt dt  ttks\J d S r   )r   rC   r   r   r	   rX   rX   rX   rY   test_extended_real_line  s   $<$8r   c                  C   sJ   t ddd} t| t td| ksJ tt| d d  | ttu s#J d S )NrC   Trc   rO   rK   r   )r   r@   r   r   r   rX   rX   rY   test_order_oo  s   $r   c                   C       t tdd  t tdd  d S )Nc                   S   s   t ttt ttS rn   r   r   rC   rD   r   rX   rX   rX   rY   <lambda>      z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ttS rn   r   rX   rX   rX   rY   r     s    rB   NotImplementedErrorrX   rX   rX   rY   test_issue_5436     r   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttdddS )Nr   rM   r   rC   rX   rX   rX   rY   r         z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   0rM   r   rX   rX   rX   rY   r     r   )rB   	TypeError
ValueErrorrX   rX   rX   rY   test_Limit_dir  r   r   c                   C   s^   t td d td d d  ttdksJ t td d td d d  tt dks-J d S )NrO   r   r^   rX   rX   rX   rY   test_polynomial  s   ,2r   c                   C   s   t dt dtt  ttt  t  t  tttd tt  ks"J t dt dtt  ttt  t  t  tt td tt  ksEJ d S NrO   )r   rD   rC   rE   r   rX   rX   rX   rY   test_rational  s   DJr   c                   C   s<   t ttt tdt t  tdtttt  ksJ d S )NrK   r   )r   r   rC   rE   rD   r   r   rX   rX   rX   rY   test_issue_5740     <r   c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|td | d ks-J d S )NrG   TrH   rO   rK   )r   rC   r   Zcancel)rG   r   rX   rX   rY   test_issue_6366  s   0 r   c                  C   s   ddl m} m} | t}t|tttu sJ tt| ttdks"J t|tdt t t| t   ttdks:J t|tt | t ksHJ d S )Nr   )r/   r   rK   rO   )sympyr/   r   rC   r   r   r   r   )r/   r   r   rX   rX   rY   test_factorial  s   0 r   c                  C   s   dt d  d t tdd  tdt d  d tj  dt d  d  dt d  d  tdd dtd    } t| ttdt d  d dt d  d  dt  d  tdd ksZJ d S )	NrR   rQ   r   rK   #   r`      rO   )rC   r   rD   r   r   r   r   r   rX   rX   rY   test_issue_6560  s   4
Jr   c                     s$  t dt ddd} t d}t ddd}t ddd}d	 |  d
  | |  d
    | | d
 |  d	  | |  d
    |    |     ||d
  tt fdd t ||td
kspJ t ||t d	|d
  |  d
 | d
 |d
   ksJ d S )NrG   r   Trc   rg   pm)negativerK   rO   c                      s   t  tS rn   )r   r   rX   ri   rG   rX   rY   r     s    z!test_issue_5172.<locals>.<lambda>)r   subsrB   r   r   r   r"   )r   rg   r   r   rX   r   rY   test_issue_5172  s$   *.
"r   c                  C   s,   t d} tttt|   ttdksJ d S )Nre   rO   )r   r   r   rC   r   re   rX   rX   rY   test_issue_7088  s   $r   c                   C   s  t ttt d tdttd ksJ t ttt d tddtdks'J t ttt d tdtd ks:J t ttt d tddt td ksPJ t ttt d tdtd kscJ t ttt d tddtdksvJ t ttt d tdtdksJ t ttt d tdddt td ksJ t ttdt  tdttd ksJ t ttdt  tddt ttd  ksJ t ttdt  tdtttd  ksJ t ttdt  tddt td ksJ t tdt tdtd ksJ t tdt tddt d ksJ t tttttd ks*J t tttt t d ks;J t t	tt
dd t  tdtttt
dd   ksZJ t t	tt
dd t  tddt tt
dd  ksyJ t t	tt
dd t  tdttt
dd  ksJ t t	tt
dd t  tddt ttt
dd   ksJ t t	ttdtd ksJ t t	ttddt d ksJ t ttt t
dd  tdtt
dd ksJ t ttt t
dd  tddtt
dd  ksJ t ttt t
dd  tddt tt
d d  ks/J t ttt t
dd  tddtt
d d ksLJ t ttt t
dd  tdtt
dd ksgJ t ttt t
dd  tddttt
dd  ksJ t ttt t
dd  tdt tt
dd  ksJ t ttt t
dd  tddtt
dd  ksJ t ttt d tdtt ksJ t ttt d tddt t ksJ t tt t d tdt t ksJ t tt t d tddtt ksJ t ttt d tdtks#J t ttt d tddt ks6J t tt t d tdt ksIJ t tt t d tddtks\J t ttt d tddt
dd  kssJ t ttt d tdddt
dd   ksJ t tt t d tddt
dd   ksJ t tt t d tdddt
dd  ksJ d S )NrK   r   rP   rT   rO   rV   rQ   )r   r5   r   rC   r   r*   r   r6   r   r7   r   r8   r9   r:   r   r   r;   rX   rX   rX   rY   test_branch_cuts  sT   (&&,&&$.(0,,"&">>:B"6:@:6<<:&***"&&&.226r   c                  C   sj   t d} tdtdt t| d   tdt t| d    }t|tddt| d tj  ks3J d S )Nre   rO   rK   r   )r   rE   r   r	   r   r   r   r   )re   r   rX   rX   rY   test_issue_6364*  s   8*r   c                  C   s   t d} t| t tdtt|  ksJ t|  t tdt t|  ks&J t|  t ttt t|  ks8J t| t tttt|  ksHJ d S )Nre   r   )r   r   rC   r   r   r   rX   rX   rY   test_issue_40990  s
    $$$r   c                  C   s\   t d} ttdtt|   tdtt  |  | dttdtttd   ks,J d S )NdxrO   r   rK   )r   r   r   r   rC   )r   rX   rX   rY   test_issue_45038  s   .r   c                   C   s&   t ttddd  ttdksJ d S )NrO   g    eAr   )r   rG   r   r   rX   rX   rX   rY   test_issue_8208>     &r   c                   C   s<   t ttdd d ttd tdd  tddksJ d S )NrO   r   rK   rQ   r   r   )r   rC   r   r   rX   rX   rX   rY   test_issue_8229B  r   r   c                  C   s4   t ddd\} }ttd||   |tdksJ d S )Nzd tTrc   rO   rV   )r    r   r+   r   )r   trX   rX   rY   test_issue_8433F  s   $r   c                  C   sF   t dddd} t dddd}t||  t|  t|  | tdk d S )NrF   T)rI   Znonnegativelamda)r   rJ   r   )r   r   r   r/   r   )rF   r   rX   rX   rY   test_issue_8481K  s   *r   c                   C   s   t tttttu sJ d S rn   )r   r   rC   r   rX   rX   rX   rY   test_issue_8730Q     r   c                      s`   t dddt ddd ttt  d    tdks$J tt fdd	 d S )
NrG   T)rI   rg   rc   rO   r   c                      s$   t tt     tS rn   )r   r   r   rX   rg   rG   rX   rY   r   Z  s   $ z!test_issue_9252.<locals>.<lambda>)r   r   r   r   rB   r   rX   rX   r   rY   test_issue_9252U  s   0r  c                   C   s"   t ttd tdddksJ d S )Nr   r   rP   )r   r	   rC   rX   rX   rX   rY   test_issue_9558]  s   "r  c                   C   s2   t dt ttdt td   tttksJ d S )Nr   rK   )r   rF   r!   r   r   rX   rX   rX   rY   test_issue_10801a  s   2r  c                  C   s8   t ddd\} }tt| | t|  | d|ksJ d S )Nzs xTr   r   )r    r   r+   )r   rC   rX   rX   rY   test_issue_10976f  s   (r  c                   C   s<   t ttttd t tdt t   ttdksJ d S NrO   rK   )r   r/   rG   r   r   r   r   rX   rX   rX   rY   test_issue_9041k  r   r  c                  C   s   t d\} }}t| | |j|hksJ t| | |dj|hks J t| | | | |j|hks0J t| d  | | d |j||hksDJ d S )Nzx, y, arP   rK   )r    r   Zfree_symbols)rC   rD   re   rX   rX   rY   test_issue_9205o  s
    ,r  c                   C   sT   t dttd td  ttdksJ t dttdd  td  ttdks(J d S )N   rQ   rO   )r   r   rG   r   rX   rX   rX   rY   test_issue_9471w  s   &.r	  c                   C   s$   t ttdt ttdksJ d S r  )r   r,   r   rC   r   rX   rX   rX   rY   test_issue_11496|     $r
  c                   C   s<   t ttt t tt  t tdtttd   ksJ d S )Nr   rO   )r"   r   rC   rD   rG   rX   rX   rX   rY   test_issue_11879  r   r  c                  C   sD   t d} td|  | tdksJ tdd|   | ttdks J d S )NrF   r   rO   g333333?)r    r   r   r$   )rF   rX   rX   rY   test_limit_with_Float  s   $r  c                   C   sD   t dt dt d   td d  td  tttddks J d S NrQ   rO   rK   )r   rC   r   r   rX   rX   rX   rY   test_issue_10610     Dr  c                   C   s$   t ttt t ttdksJ d S r   )r   rG   r   r   rX   rX   rX   rY   test_issue_6599  r  r  c                   C   sn   t dt dtd   td tt  tt dksJ t dt dtd   td tt  tttu s5J d S )NrQ   rK   
   r\   rX   rX   rX   rY   test_issue_12555  s   68r  c                  C   s  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d    ||  | |  d  }
|
||jddt|
||jddksJ d S )	Nzr z xTr   za b s0 K F0 s T)rJ   r   rK   rO   r   )r    r   r   Zfactorr   )r   rE   rC   re   rf   Zs0KZF0r   TZfxrX   rX   rY   test_issue_12769  s$   :":::*0r  c                   C   sz   t tdddt d   dt t  dt d dt dtj    dt d dt dtj    tttd	d
ks;J d S )N   rR   rO   i@  rK   rk   i   $   )r   r   rC   r   r   r   r   rX   rX   rX   rY   test_issue_13332  s   Br  c                   C   s   t td ttt  tt tt tu sJ t td ttt  tt tttu s-J t ttt d  tttu s?J t ttt d  tttu sQJ t ttt d  tt tu sdJ t ttt d  tt tu swJ d S rx   )r   rC   r	   r   r   expandrX   rX   rX   rY   test_issue_12564  s   .,$$&*r  c                   C   r   )Nc                   S   s   t tttt S rn   )r   r   rC   r&   r{   rX   rX   rX   rY   r     r   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  tt S )NrK   rO   )r   rC   r&   r{   rX   rX   rX   rY   r     s    r   rX   rX   rX   rY   test_issue_14456  r   r  c                   C   sB   t dtdt t td   tdt dt d  t u sJ d S )NrQ   r      rK   )r   r%   r   rC   r   rX   rX   rX   rY   test_issue_14411  s   Br   c                   C   s8   t ttd d d td d  d  ttdksJ d S r  r^   rX   rX   rX   rY   test_issue_13382  s   8r!  c                   C   s<   t tdtttd  d ttt    ttdksJ d S )NrV   rO   r   rC   r   r   rX   rX   rX   rY   test_issue_13403  r   r#  c                   C   sb   t td  ttd  td td d  ttd d   td ttd   ttdks/J d S r  r"  rX   rX   rX   rY   test_issue_13416  s   br$  c                   C   sx   t td dt dddt   t  d  t td  d td  t   tttd d td d  td  ks:J d S )NrK   rO   r   rQ   r  r`   rl   )r   rG   rC   r   rX   rX   rX   rY   test_issue_13462  s   xr%  c                  C   sH   t d} tt| t ttdksJ ttttt ttdks"J d S )Nre   rV   )r   r   r+   rC   r   r   r   rX   rX   rY   test_issue_13750  s   $r&  c                   C   s0   t dtttt  dt  ttdksJ d S r   )r   r   rC   r   rX   rX   rX   rY   test_issue_14514  rz   r'  c                   C   s4   t tttttd   td  ttdksJ d S )NrK   rO   r   )r   r   rC   r   r   rX   rX   rX   rY   test_issue_14574  s   4r(  c                   C   s   t tttttjksJ t dtt ttdtj ksJ t dtt tttddks/J t tttttjks<J t tttt tddksLJ t dtt tt dks[J d S )NrQ   rR   rK   rV   r   rT   )r   r(   rC   r   r   r   r   r'   rX   rX   rX   rY   test_issue_10102  s   "" "r)  c                   C   s   t tdd  d S )Nc                   S   s    t ttt ttt  ttS rn   )r   r   r   rC   r	   r   r   rX   rX   rX   rY   r     s     z"test_issue_14377.<locals>.<lambda>r   rX   rX   rX   rY   test_issue_14377  s   r*  c                  C   s   t d dt d  dt d d  t d  tt d d   dt d d  t d  tt d t  d   t  d  } t| t ttdd ksFJ d S )NrK   rT   rQ   rO   )rC   r0   r   r   r   r   rX   rX   rY   test_issue_15146  s   8* r+  c                  C   s   dt  ddt   ddt   t  d    t d  t d  } t| t ttdks)J tt dd dt  tt   dt   tt d dtt   dt    } t| t tdksVJ d S )NrK   rT   rO   r   r  rR   rQ   )rC   r   r   r   r   r/   r   rX   rX   rY   test_issue_15202  s   :Fr,  c                   C   s0   t td td d  td  ttdksJ d S )Ni  rO   i  i0r^   rX   rX   rX   rY   test_issue_15282  rz   r-  c                   C   s2   t t tttd  t ttdddksJ d S )NrO   rP   rM   r   )r   rC   r   r   r   rX   rX   rX   rY   test_issue_15984     2r.  c                   C   s&   t ttdtt ttdksJ d S r   )r   r1   rC   r   r   rX   rX   rX   rY   test_issue_13571  r   r0  c                   C   s*   t ttttdtttjksJ d S r   )r   r*   r-   rC   r   r   rX   rX   rX   rY   test_issue_13575  r   r1  c                   C   s   t ttt tddd dksJ t td tddd dks"J t dtd  tddd tu s4J t dt tddd tu sDJ d S )Nr   rS   rM   rO   rK   )r   r	   rC   r{   r   r&   rX   rX   rX   rY   test_issue_17325  s   $ $$r2  c                   C   s   t ttddksJ d S Nr   )r.   rC   r   rX   rX   rX   rY   test_issue_10978
  r   r4  c                   C   s    t ttd tttu sJ d S rx   )r   r
   rG   r   rX   rX   rX   rY   test_issue_14313_comment      r5  c                  C   s2   ddt   t  t } t| t ddddksJ d S )NrO   rL   rM   )rC   Zdiffr   )r   rX   rX   rY   test_issue_15323  s   r7  c                   C   s,   t ttt  tt tddksJ d S r   )r   r.   r   rC   rX   rX   rX   rY   test_issue_12571     ,r8  c                   C   sH   t td td t t  td td  td   tttdks"J d S r  r   rX   rX   rX   rY   test_issue_14590     Hr:  c                  C   sR   t d\} }tt| t|  t|  t|    tt|t|  |   |  ks'J d S )Na b)r    r   rC   rD   re   rf   rX   rX   rY   test_issue_14393   s   Fr>  c                   C   s@   t ttd dtd   ttdt   tttdksJ d S )NrO   rV   )r   r/   rG   r   r   rX   rX   rX   rY   test_issue_14556%     @r?  c                   C   sL   t dtdd td   dt  dtdd td    tttks$J d S )NrO   rK   rQ   r   r   r   rC   r   rX   rX   rX   rY   test_issue_14811)  s   LrB  c                   C   s   t tdtttdksJ d S r3  )r   r<   rC   r   rX   rX   rX   rY   test_issue_14874-  s   rC  c                   C   s    t tttdtdksJ d S )Ni ʚ;)r   r   rC   rX   rX   rX   rY   test_issue_162221  r6  rD  c                   C   sD   t ttd  td t  ttd   t ttttdks J d S r   r   rX   rX   rX   rY   test_issue_167145  r  rE  c                  C   s   t ddd} ttt|  tt|    ttdt| d  ks J t dddd} ttt|  tt|    ttdt| d  ksAJ d S )NrE   Trc   rO   )rJ   rI   )r    r   r!   rG   r   r   r   rX   rX   rY   test_issue_167229  s   48rF  c                   C   s   t td d td d ttd   td  tt td  ttdks&J t td d tt td td  ttd   ttdksFJ t td tt tttd   ttdks^J d S )NrO   rK   r   rQ   )r   rG   r/   r   rX   rX   rX   rY   test_issue_17431@  s"   $04rG  c                   C   s2   t ttt tttt  tdtksJ d S r   )r   r3   r   rC   r4   rX   rX   rX   rY   test_issue_17671H  r/  rH  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  |  |t| d|  d  ks1J d S )Nza b c xTrc   rO   rK   )r    r   r   r   )re   rf   rg   rC   rX   rX   rY   test_issue_17751L  s   RrI  c                   C   s@   t tttt tdt t  tttdtt ksJ d S r  )r   r/   rG   r   r   r   r   rX   rX   rX   rY   test_issue_17792Q  r@  rJ  c                   C   s@   t ttttdddksJ t ttttdddksJ d S )Nr   rP   rV   rL   rO   )r   r   r	   rC   rX   rX   rX   rY   test_issue_18118U  s   "rK  c                   C   s.   t tttttt tdddksJ d S )Nr   rL   rO   )r   r	   r   rC   rX   rX   rX   rY   test_issue_18306Z  r   rL  c                   C   s<   t ttdt t ttttd   ttdksJ d S )NrQ   r   )r   r   r   rC   r   rX   rX   rX   rY   test_issue_18378^  r   rM  c                   C   sJ   t dtdd t  dt  tttu sJ t t t tttu s#J d S )NrO   rK   rQ   )r   r   rC   r   r&   rX   rX   rX   rY   test_issue_18399b  s   ,rN  c                   C   sH   t ttdtt  ttddtttdtt  ttddks"J d S )NrK   rP   rM   )r   r   rC   r   r   r   r   rX   rX   rX   rY   test_issue_18442g  r;  rO  c                   C   sF   t tttt tddksJ t tttt tdddks!J d S )Nr   rO   rP   )r   r   r   rC   rX   rX   rX   rY   test_issue_18452k  s    &rP  c                   C   s@   t dtdt  tdt d  dt  tttdksJ d S NrK   rQ   rO   )r   r   rC   r   rX   rX   rX   rY   test_issue_18482p  r@  rR  c                   C   s   t tttdtt  tdtdksJ t tttdtt  tdddtdks.J t tttdtt  tdddtd ksGJ d S )NrO   r   rK   rL   rM   rP   )r   r	   rC   r   r   rX   rX   rX   rY   test_issue_18508t  s   ,06rS  c                  C   sT   t ddd\} }tt| | |t|ksJ ttt| | |tt|ks(J d S )Nr<  Trc   )r    r   r.   r   r=  rX   rX   rY   test_issue_18969z  s   (rT  c                   C   s,   t tttdt   tttdksJ d S r   )r   rG   r/   r   r   rX   rX   rX   rY   test_issue_18992  r9  rU  c                  C   s<   t d} tt| t| d t| d   | ddksJ d S )NrC   rO   rK   r   rV   )r   r   r   r   rX   rX   rY   test_issue_19067  s   4rV  c                   C   s*   t tdt dt    ttdksJ d S rQ  r^   rX   rX   rX   rY   test_issue_19586  r   rW  c                  C   s0   t d} t ddd}t| | | ddksJ d S )NrG   r   T)Zzeror   )r   r   )rG   r   rX   rX   rY   test_issue_13715  s   rX  c                   C   sT   t td t d tdt  td tdtd     t d  ttdks(J d S r  )r   rG   r	   r   rX   rX   rX   rY   test_issue_15055  s   TrY  c                  C   s   t ddd\} }t d\}}}t|| | t| td| | | | |d     | |  ||  |d|||  | ks?J d S )Nzm viTrc   zB ti drT   rK   r   )r    r   r   )r   viBZtir   rX   rX   rY   test_issue_16708  s   dr\  c                   C   s&   t td d t ttdksJ d S )NrO   r   r   rA  rX   rX   rX   rY   test_issue_19739  r   r]  c                   C   s2   t dt  tdtd  d  ttdksJ d S )NrK   r   rO   )r   rC   r   r   rX   rX   rX   rY   test_issue_19766  r/  r^  c                  C   s   t d} tt| t t tttt| t t ttddks J t ddd} tt| t t tttt| t t ttddksBJ t ddd} tt| t tttddksYJ tt| t t ttd	ksiJ d S )
Nr   rP   rM   Tr   )ZnonzerorV   rO   r   )r   r   r   rC   r   r   r=   )r   rX   rX   rY   test_issue_19770  s   88"$r_  c                   C   s  t ttttt ttd tttttt ttd ddks$J t ttttt ttd ddtttttt ttd ddksJJ t ttttt ttd ddtttttt ttd ddkspJ t tttttd tddksJ t dtt   tt tksJ tdtt  tt tksJ tdtt   tt tksJ t dtt  tt tksJ d S )NrK   rL   rM   rP   rS   rV   rO   )r   r   rC   r	   r   r   r=   r   rX   rX   rX   rY   test_issue_7535  s   HLL&$ "&r`  c                   C   s2   t td dt  t t tdt d ksJ d S )NrO   r   rK   )r   rC   r   rX   rX   rX   rY   test_issue_20365  r/  ra  c                   C   sH   t dt dt  ddt  ddt    tt tdtd ks"J d S )NrO   rK   r   )r   rC   r5   r   rX   rX   rX   rY   test_issue_21031  r;  rb  c                   C   s0   t ttt dt d  tdtd ksJ d S )NrQ   rl   r   )r   r	   r   rC   rX   rX   rX   rY   test_issue_21038  rz   rc  c                  C   sZ   t ttdt  } t| tdddksJ t| tdddks J t| tdddks+J d S )NrO   r   rL   rP   rS   )r   rC   r	   r   r   rX   rX   rY   test_issue_20578  s   rd  c                  C   sH   t d tdt d   } | t ddksJ |  t ddks"J d S r   )rC   r   r   r  )r   rX   rX   rY   test_issue_21415  s   re  c                   C   s(   t ttd tt tttksJ d S r   )r   r   rG   r   r   rX   rX   rX   rY   test_issue_21530  s   (rf  c                  C   sD   t dd d } tt|  td t d  t| t dd ks J d S )NrR   rO   rK   )r   r   rC   r   rX   rX   rY   test_issue_21550  s   4rg  c                  C   sL   t ttd  ttd  d t td} | tdd dtd  ks$J d S )NrO      l   qjl   S[	)r   rC   r   r   )outrX   rX   rY   test_issue_21661  s   ($rj  c                   C   s6   t ttttt  tdtdtdd ksJ d S )Nr   r   rO   i 	 )r   r   rE   rC   r   r   rX   rX   rX   rY   test_issue_21701  s   6rk  c                  C   sD   t ddd} tdtdt|  d    t}|tttjks J d S )Nre   Tr   rO   rK   )r   r   r   rC   r   r   r   r   )re   r   rX   rX   rY   test_issue_21721  s   rl  c                  C   sd   dt dt t t  dt dt t t d   } | tddks$J t| tddks0J d S )NrO   rT   rR   r   )r   r   r   rE   r   r2   )ZtermrX   rX   rY   test_issue_21756  s   4rm  c                  C   s@   t d} t| d  td  dtd   | ddtksJ d S )Nre   rK   rO   rP   )r   r   rC   r   r   r   rX   rX   rY   test_issue_21785  s   8rn  N)	itertoolsr   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!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   Zsympy.calculus.utilr=   Zsympy.core.mulr>   Zsympy.series.limitsr?   Zsympy.series.orderr@   Zsympy.testing.pytestrA   rB   Z	sympy.abcrC   rD   rE   rF   rG   rZ   r]   r_   rb   rj   rm   rw   ry   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r   r!  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r0  r1  r2  r4  r5  r7  r8  r:  r>  r?  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rR  rS  rT  rU  rV  rW  rX  rY  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rj  rk  rl  rm  rn  rX   rX   rX   rY   <module>   s0   ;	


0		
