o
    8Va5                     @   s  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 d dlmZmZmZmZ d dlmZ d dlmZ dd Z dd Z!d	d
 Z"dd Z#dd Z$dd Z%dd Z&dd Z'd dl(m)Z)m*Z* d dl m+Z+m,Z, dd Z-dd Z.dd Z/dd Z0dd  Z1d!d" Z2d#d$ Z3d%d& Z4d'd( Z5d)d* Z6d+d, Z7d-d. Z8d/d0 Z9d1d2 Z:d3d4 Z;d5d6 Z<d7d8 Z=d9d: Z>d;d< Z?d=d> Z@d?d@ ZAdAdB ZBdCdD ZCdEdF ZDdGdH ZEdIdJ ZFdKS )L    )sincosexpEseriesooS
DerivativeOIntegralFunction	PoleErrorlogsqrtNSymbolSubspisymbolsatanLambertWRational)xynk)raises)calculate_seriesc                  C   0   t ttd} tt ttd}| |ksJ d S Nr   )r   r   r   Ze1Ze2 r!   @/usr/lib/python3/dist-packages/sympy/series/tests/test_series.pytest_sin      r#   c                  C   r   r   )r   r   r   r    r!   r!   r"   test_cos   r$   r%   c                  C   r   r   )r   r   r   r    r!   r!   r"   test_exp   r$   r&   c                  C   s8   t tttd} tt tttd}| |ksJ d S r   )r   r   r   r   r    r!   r!   r"   	test_exp2   s   r'   c                     s  t dtdks	J ttjtdksJ tt  tt tks$J ttdd  ttdd  tt tdttd  t	ttd  
 dksOJ ttj tdd d  fddtd	D tdtd td  gkssJ ttj tdd d
d  fddtd	D tddt td gksJ ttj tdd
dtksJ ttj tdd
dd
 ttt d   tt d d	  d	  ksJ t} | td	 td td	   td	td t dt t ksJ t| ttt | dtksJ | tttj dd| dt| tt | td	 d	 t | td d t ttd  ks+J tttddftdtf tddt  ksCJ dt ttd	   d	ksTJ dt  d u s_J ttdd  td}ttt jtd|dtt| tttt|  t ksJ tdt j ttdddt ddtd    ttd ttf ksJ ttj ttdddtksJ ttj tt dd
dt ksJ tt j ttdddtksJ tt j tt dd
dt ksJ tttt j dddttt  td	 ttd	  d	  ttd ttd   ks#J tddd}tt|d t| j ddd|td t|  t|d t|d   ksTJ ttttt j d	ddttt  ttd	 ttd	   ksyJ d S )N   r   c                   S   s   t tt  S )N)r   r   r   r   r!   r!   r!   r"   <lambda>$   s    z!test_issue_5223.<locals>.<lambda>c                   S   s   t jddS )N dir)r   r   r!   r!   r!   r"   r)   %   s    r   c                       g | ]}t  qS r!   next.0ier!   r"   
<listcomp>*       z#test_issue_5223.<locals>.<listcomp>   -)r   r,   c                    r.   r!   r/   r1   r4   r!   r"   r6   ,   r7   r+      )r,   r            c                   S   s   dt t t  S )Nr(   )r   r   r   r   r!   r!   r!   r"   r)   =   r7   logx)r   r?      +pTpositivez3/2)r   r   r0   r   ZZeroZlseriesr   r   
ValueErrorZsubsremoveOranger   absr   r   r	   r   doitr
   r   Zgetnr   r   Znseriesr   r   r   )Dr?   rC   r!   r4   r"   test_issue_5223    sb   42&>$B
0" 
H $"&>
.
NrL   c                   C   s  t tttttttksJ ttttjtdd ttjtddks,J ttd ttdtd  ks>J ttd ttdksLJ tttttdksZJ tttttt ksiJ tdtttdtksxJ tt	ttt t	ttksJ dt t	ttt t	ttksJ tt
ttt dt tksJ t t
tttt t
tt t ksJ d S )Nr:   r-   r8   r   r(   )r   r   r   r   r   r	   rJ   as_leading_termr   r   r   rG   r!   r!   r!   r"   test_issue_11313R   s   &2$***8rN   c                     s  ddl m mm tt  } tt t  }tt   f f}|  | ks5J t  t d  d   t d d   td  }|  |ks^J | |ksgJ | | kspJ |td t  d  td	  t  d	   tt   td  ksJ | 	 |	  ksJ |	 t  ksJ t
t fd
d t   	   ksJ d S )Nr   r   r   zr:   r<   r@   x   r>      r8   c                      s   t  d   S )Nr8   )r   r   r!   rO   r!   r"   r)   x   s    z%test_series_of_Subs.<locals>.<lambda>)	sympy.abcr   r   rP   r   r   r   r   r
   rJ   r   rF   )Zsubs1Zsubs2Zsubs3Zsubs1_seriesr!   rO   r"   test_series_of_Subsf   s0    
"

 *rT   c                  C   s  t d} | tjtdddd| dttt| tttd  td tt| ttttd d  ttd  ks:J | ttdd| dttt| tttd  td tt| ttttd d  ttd  ksnJ | td tdd| dtd tt| tttd  ttd  ksJ | td d tdd| dtd tt| tttd  ttd  ksJ G dd	 d	t }|ttdd|dttt|tttd  td tt|ttttd d  ttd  ksJ d S )
Nfr   r:   r9   r+   r8   r(   c                   @   s   e Zd ZdS )ztest_issue_3978.<locals>.TestFN)__name__
__module____qualname__r!   r!   r!   r"   TestF   s    rY   )r   r   r   r   r	   r
   )rU   rY   r!   r!   r"   test_issue_3978|   s:    "
 "
00"
rZ   )
richardsonshanks)SumIntegerc                  C   s   ddt   t  } tt| t dd dtt dksJ ttdtd  t tdt f}tt|t d dtt	d dksCJ tt|t dd dtt	d dksZJ d S )	Nr(   
         r>   r8   r@   )
r   roundr[   Zevalfr   r]   r^   r   r\   r   )r5   Ar!   r!   r"   test_acceleration   s
   * ,2re   c                   C   sh   t dtttt  tddtd dttd    dtd  dttd    ttd  ks2J d S )Nr(   r   r8   r@   r>   rR   r<   )r   r   r   r   r
   r!   r!   r!   r"   test_issue_5852   s
   4
rf   c                   C   s   t dt td  tddt dttd  td td t dd    td t d tdd    td dt d d	 tdd    ttd  ksQJ d S )
Nr(   r8   r   r@   r:   r<   r>   irR   )r   r   r   r   r
   r!   r!   r!   r"   test_issue_4583   s   ."
rg   c                  C   s,   dt  tdd } | d t | ksJ d S )Nr(   r8   r:   )r   r   rM   eqr!   r!   r"   test_issue_6318   s   rj   c                  C   s0   t d tdd } |  t tdd ksJ d S )Nr8   r:   r>   )r   r   r   rh   r!   r!   r"   test_x_is_base_detection   s   rk   c                  C   s&   t td } t| ttd ksJ d S )Ng333333?)r   r   r   r4   r!   r!   r"   test_sin_power   s   rl   c                   C   sD   t ttttddtt d d  ttt d ttf ks J d S )Nr:   ra   r8   )r   r   r   r   r
   r!   r!   r!   r"   test_issue_7203   s   (rm   c                  C   s   t ddd\} }| | }tt||ddd| |  | d |d  d  | d |d  d	  | d
 |d
  d  | d |d  d  | d	 |d	  d  | d |d  d  t| d |d  | | kseJ d S )Nza, bTrD      r-   r(   r8   r:   r<   r>   rR   r@   rQ          )r   r   r   r
   )abr   r!   r!   r"   !test_exp_product_positive_factors   s   .rt   c                   C   s   t ddddks
J d S )Nr(   rn   r-   )r   r!   r!   r!   r"   test_issue_8805   s   ru   c                  C   sj   t d t  d t d t d   } t| t tt d dt d   t d  dt   tt d t tf ks3J d S )Nr8   r(   r:   rA   r>   )r   r   r   r
   r   r!   r!   r"   test_issue_9549   s    Jry   c                   C   sH   t dtd td   tdtd td  td  ttd  ks"J d S )	Nr(   rv   r   r:   r>   r@   r<   )r   r   r
   r!   r!   r!   r"   test_issue_10761   s   Hr{   c                  C   s   ddt d ddt    d   tdd  } | jt dddddt d   dt d   d	t d   d
t d   dt d   dt d   dt d   tt d  ksRJ d S )Nr(   r8   r>   rn   r      r-   r<   "      r_   i  r;   i     iC     )r   r   r   r
   rx   r!   r!   r"   test_issue_12578   s   ,L


r   c                  C   s\  t dddd} t ddd\}}| d  | t| | d t|  | | t|  | t|  |  d | t| d d  }ddt| d	 d  d
t| dt| d	 d   | d d| td|  dt|  d
td|   d  dt| d	 d   d
| t| dt| d	 d   t| d d | df }|| dd |ksJ d S )NbetaT)realrE   ztheta varphir   r8   r(         ?      ?g      ?g      пg      ?g      ?r:   )r   r   r   r
   r   Ztrigsimp)r   ZthetaZvarphiexprZsolr!   r!   r"   test_issue_12791   s>   $
*$"r   c                   C   s   t ttdd tt tdttdd dtt  ttd  ttdd d  ttdd d  ttd	d d
  ttdd d  ttdd d  ttd  ksWJ d S )Nrv   r8   r   r(   r:   r<   r@   rR   rp   rQ   	   ro      rq   )r   r   r   r   r   r
   r!   r!   r!   r"   test_issue_14885   s   4

r   c                   C   s   t tttt ddtd   ddtd    dt  td  ttd tt f ks-J t ttttddtd   ddtd    dt  td  ttd ttf ksXJ d S )Nra   r@   r(   r:   r8   rw   )r   r   r   r   r   r
   r!   r!   r!   r"   test_issue_15539   s   >
<r   c                   C   s   t tttttd  dtd  d  dtd  d  dtd  d  ttd  ks-J t ttd tdd	td td  dtd  d  ttd  ksPJ t ttttdd	ttd  dtd  d  ttd  ksqJ d S )
Nr8   r:   rn   r>   }   r@   rR   r<   r-   )r   r   r   r
   r   r!   r!   r!   r"   test_issue_7259   s   ZFFr   c                   C   s6   t tjtdddt dttd tdf ksJ d S )Nr(   r-   )r   r   r   r
   r!   r!   r!   r"   test_issue_11884   s   6r   c                  C   s   t dt dt     dt dt    dt  dt     } | jt tddddt d   ddt d    dd	t    tdd  t d  tt d
 t tf ksMJ d S )Nr(   r>   r-   i    r:   r   r8   rn   r=   )r   r   r   r   r
   rx   r!   r!   r"   test_issue_18008   s   4Lr   c                  C   s>   t tdt  } | jtddd  td d ksJ d S )Nr(   gCl?r-   l   I l     o )r   r   r   rG   Z	nsimplifyr   )rU   r!   r!   r"   test_issue_18842  s   r   c                  C   sF  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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|  d|  d|  d  d|  d|  d|  d  d|   d   d|   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|  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|  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$ }t|| d%d&d#d'| d(  d)| d*   d+| d,   d-| d.   d/| d0   d| d1   d|   d ksJ d S )2NdtTr   r   g      ?g       @r   g      ?-   1   gPFvBgI?gwkN?gh/?gh/?g	%?gIp?r      r      gaAοgi?gi/?gϥ;} @gvQ?go?gUUUUUU?g@g?br@gF)7^@g~j`?g~?g#@r`   r(   r   rn   gt:WNrp   gllf?r<   g?r@   gSUUUUU?r>   gVUUUUU?r:   r8   )r   r   r   r   )r   r   r!   r!   r"   test_issue_19534  s  *&&&&&&



&&&&
&&&&

%%('



r   c                  C   s   t d\} }}}tt| | ||  |ddt| | t| ks#J tt| | | ||  |ddt| | | t| ksBJ d S )Nza b c xr   r(   )r   r   r   r
   )rr   rs   cr   r!   r!   r"   test_issue_114076  s   6Br   c                   C   s8   t td td  jtdddt tdt ksJ d S )N2   3   r   r-   r(   )r   r   r   r
   r!   r!   r!   r"   test_issue_14037<  s   8r   c                     sJ   t tt jtd d  fddtdD } | dt dtd gks#J d S )Nr-   c                    r.   r!   r/   r1   r   r!   r"   r6   B  r7   z$test_issue_20551.<locals>.<listcomp>r:   r(   r8   )r   r   r   rH   )Ztermsr!   r   r"   test_issue_20551@  s   r   c                  C   s   t d\} }}}}}}| |||t  t  t  d||t  || ||  |d   t |d | || |  ||| |d    |d   t   }|jtdd |td  |t  | ttd  kshJ d S )Nzp_0 p_1 p_2 p_3 b_0 b_1 b_2r(   r8   r:   r-   )r   r   r   Zratsimpr
   )Zp_0Zp_1Zp_2Zp_3Zb_0Zb_1Zb_2Qr!   r!   r"   test_issue_20697F  s"   ,>r   c               	   C   s   dt d d } ddt td   td|  d dt d d dt d t  dt  ttddt d   d tddt d  f dt d d dd	t d  d  tt dt  d   ksdJ d S )
Nr(   r@   r8   ii<  i	  iP  r`   r   )r   r   r   Zfactorr
   )fir!   r!   r"   test_issue_21245N  s   $&,r   c                  C   sv   t dt tt  t dt  } | ttddtd   ddtd    d ttd ttf tt  ks9J d S )Nr(   rR   r>   r8   rw   )r   r   r   r   r   r
   r   r!   r!   r"   test_issue_21938V  s   "Tr   N)GZsympyr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   rS   r   r   r   r   Zsympy.testing.pytestr   Zsympy.series.gruntzr   r#   r%   r&   r'   rL   rN   rT   rZ   Zsympy.series.accelerationr[   r\   r]   r^   re   rf   rg   rj   rk   rl   rm   rt   ru   ry   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r!   r!   r!   r"   <module>   sP   ` 2	.