o
    jgJ@                     @   sT  d dl mZ d dlmZmZmZmZ d dlmZm	Z	m
Z
mZmZmZ d dlmZ d dlmZmZ d dlmZmZmZ d dlmZ d dlmZmZmZ d d	lmZ d d
lm Z m!Z! d dl"m#Z# d dl$m%Z% d dl&m'Z'm(Z(m)Z)m*Z* d dl+m,Z, d dl-m.Z. dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd Z5dd Z6d d! Z7d d"l8m9Z9m:Z: d d#l;m<Z< d d$lm=Z= d%d& Z>d'd( Z?d)d* Z@d+d, ZAd-d. ZBd/d0 ZCd1d2 ZDd3d4 ZEd5d6 ZFd7d8 ZGd9d: ZHd;d< ZId=d> ZJd?d@ ZKdAdB ZLdCdD ZMdEdF ZNdGdH ZOdIdJ ZPdKdL ZQdMdN ZRdOdP ZSdQdR ZTdSdT ZUdUdV ZVdWdX ZWdYdZ ZXd[d\ ZYd]d^ ZZd_S )`    )N)
DerivativeFunction	PoleErrorSubs)EFloatRationaloopiI)S)Symbolsymbols)LambertWexplog)sqrt)atancossin)gamma)Integral	integrate)Oseries)xynk)raises)
EulerGammac                  C   0   t ttd} tt ttd}| |ksJ d S Nr   )r   r   r   e1e2 r(   V/var/www/html/zoom/venv/lib/python3.10/site-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$J ttdd  ttdd  tt tdttd  t	ttd  
 dksOJ ttj tdd d  fddtd	D tdtd td  gkssJ ttj tdd d
d  fddtd	D tddt td gksJ ttj tdd
dtksJ ttj tdd
dd
 ttt d   tt d d	  d	  ksJ t} | td	 td td	   td	td t dt t ksJ t| ttt | dtksJ | tttj dd| dt| tt | td	 d	 t | td d t ttd  ks+J tttddftdtf tddt  ksCJ dt ttd	   d	ksTJ dt  d u s_J ttdd  td}ttt jtd|dtt| tttt|  t ksJ tdt j ttdddt ddtd    ttd ttf ksJ ttj ttdddtksJ ttj tt dd
dt ksJ tt j ttdddtksJ tt j tt dd
dt ksJ tttt j dddttt  td	 ttd	  d	  ttd ttd   ks#J tddd}tt|d t| j ddd|td t|  t|d t|d   ksTJ ttttt j d	ddttt  ttd	 ttd	   ksyJ d S )N   r   c                   S   s   t tt  S N)r   r   r   r   r(   r(   r(   r)   <lambda>.   s    z!test_issue_5223.<locals>.<lambda>c                   S   s   t jddS )N dir)r   r   r(   r(   r(   r)   r1   /   s    r   c                       g | ]}t  qS r(   next.0ier(   r)   
<listcomp>4       z#test_issue_5223.<locals>.<listcomp>   -)r   r4   c                    r6   r(   r7   r9   r<   r(   r)   r>   6   r?   r3      )r4   r            c                   S   s   dt t t  S Nr/   )r   r   r
   r   r(   r(   r(   r)   r1   G   r?   logx)r   rH      +pTpositivez3/2)r   r   r8   r   Zerolseriesr   r!   
ValueErrorsubsremoveOranger   absr   r   r   r   doitr   r   getnr   r   nseriesr
   r   r   )DrH   rL   r(   r<   r)   test_issue_5223*   sb   42&>$B
0" 
H $"&>
.
NrZ   c                  C   s  t tttd dt   tdtfdd} | tdddtdd   td ttdd d  ttdd  dt	 ttdd    tdt ttd d  ttd d  dt	   dtdd  td ttdd   ttd d  ttdd  ttdd  dt	   dtdd  td ttd	d   ttdd d  ttdd  d
t	   dtdd  td ttdd   ttd d  ttdd  ttdd  dt	   t
td  ksJ d S )NrB   r   none)condsr@   r/   rD   rI   rF         )r   r   r    r   r
   r   r   r   r   r   r   exprr(   r(   r)   test_issue_6350\   s   (`6`R`
rb   c                   C   s  t tttttttksJ ttttjtdd ttjtddks,J ttd ttdtd  ks>J ttd ttdksLJ tttttdksZJ tttttt ksiJ tdtttdtksxJ tt	ttt t	ttksJ dt t	ttt t	ttksJ tt
ttt dt tksJ t t
tttt t
tt t ksJ d S )NrB   r5   r@   r   r/   )r   r   r   r   r   r   rV   as_leading_termr   r   r   rS   r(   r(   r(   r)   test_issue_11313e   s   &2$***8rd   c                     s  ddl m  ttttt} tttt  tt}ttt  t fttf}| t| ks1J ttttttd  d tt ttd d tt ttd  }|  |ksZJ | t|kscJ |  | kslJ | t d tt d ttt d	  tt d	 tt ttttt t d  ksJ |t	 |	 tksJ | 	 ttt ksJ t
t fd
d ttt t t	 t  ksJ d S )Nr   zrB   rD   rI   x   rF      r@   c                      s   t tdt  t  S )Nr@   )r   r   r   r   r(   re   r(   r)   r1      s    z%test_series_of_Subs.<locals>.<lambda>)	sympy.abcrf   r   r   r   r   r   r   r   rV   r!   rQ   )subs1subs2subs3subs1_seriesr(   re   r)   test_series_of_Subsy   s0    
"

 *rn   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   rB   rA   r3   r@   r/   c                   @   s   e Zd ZdS )ztest_issue_3978.<locals>.TestFN)__name__
__module____qualname__r(   r(   r(   r)   TestF   s    rs   )r   r   r   r   r   r   )ro   rs   r(   r(   r)   test_issue_3978   s:    "
 "
00"
rt   )
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]      rF   r@   rI   )
r   roundru   evalfr   rw   rx   r    rv   r   )r=   Ar(   r(   r)   test_acceleration   s
   * ,2r   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   r@   rI   rF   rh   rD   )r   r   r   r   r   r(   r(   r(   r)   test_issue_5852   s
   4
r   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/   r@   r   rI   rB   rD   rF   irh   )r   r   r   r   r   r(   r(   r(   r)   test_issue_4583   s   ."
r   c                  C   s,   dt  tdd } | d t | ksJ d S )Nr/   r@   rB   )r   r	   rc   eqr(   r(   r)   test_issue_6318   s   r   c                  C   s0   t d tdd } |  t tdd ksJ d S )Nr@   rB   rF   )r   r	   r   r   r(   r(   r)   test_x_is_base_detection   s   r   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 )NrB   r]   r@   )r   r   r   r   r   r(   r(   r(   r)   test_issue_7203   s   (r   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, bTrM   r_   r5   r/   r@   rB   rD   rF   rh   rI   rg     r^     )r   r   r   r   )abr   r(   r(   r)   !test_exp_product_positive_factors   s   .r   c                   C   s   t ddddks
J d S )Nr/   r_   r5   r   r(   r(   r(   r)   test_issue_8805   s   r   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 )Nr@   r/   rB   rJ   rF   )r   r   r
   r   r   r(   r(   r)   test_issue_9549   s    Jr   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/   r   r   rB   rF   rI   rD   )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/   r@   rF   r_   r      r5   rD   "      ry   i  rC   i     iC     )r   r   r   r   r   r(   r(   r)   test_issue_12578   s   ,L


r   c                  C   sn  t 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	    d
| t| dt| d	 d   t| tj d | tjf }|| dd |ksJ d S )NbetaTrM   ztheta varphirealr@   r/         ?      ?g      ?g      пg      ?g      ?)r   r   r   r   r   Halfr   trigsimp)r   thetavarphira   solr(   r(   r)   test_issue_12791   s6   $
6$""r   c                     s   t d\ } t |    |  ksJ t d|     d|   ks$J tt| t   t| t  ks9J tt fdd tt fdd tt fdd d S )Nzx ar   c                      s   t  t  S r0   r   r   r(   r   r(   r)   r1      s    z"test_issue_14384.<locals>.<lambda>c                      s   t  td   S rG   r   r(   r   r(   r)   r1      s    c                      s   t ttt   S r0   )r   r   r   r   r(   r   r(   r)   r1      s    )r   r   r   r   r!   r   )r   r(   r   r)   test_issue_14384   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 )Nr   r@   r   r/   rB   rD   rI   rh   r^   rg   	   r      r   )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 )Nr]   rI   r/   rB   r@   r   )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 )
Nr@   rB   r_   rF   }   rI   rh   rD   r5   )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/   r5   )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/   rF   r5   i    rB   r   r@   r_   rE   )r   r   r
   r   r   r   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?r5   l   I l     o )r   r   r   rS   	nsimplifyr   )ro   r(   r(   r)   test_issue_18842  s   r   c                  C   s  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#td'd(d) | d*  td+d(d)| d,   td-d(d)| d.   td/d(d)| d0   td1d(d)| d2   td3d(d)| d4   td3d(d)|   td3d(d) ksJ d S )5N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#@rz   r/   r   r_   z0.00092592592592592596126289F   )	precisionr^   z0.0027777777777777783174695rD   z0.016666666666666656027029rI   z0.083333333333333300951828rF   z0.33333333333333337034077rB   z1.0r@   )r   r   r   r   r   )r   ra   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   )r   r   cr   r(   r(   r)   test_issue_11407W  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   r5   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 )Nr5   c                    r6   r(   r7   r9   r`   r(   r)   r>   c  r?   z$test_issue_20551.<locals>.<listcomp>rB   r/   r@   )r   r   r   rT   )termsr(   r`   r)   test_issue_20551a  s   r   c                  C   s   t d\} }}}}}}| |||t  t  t  d||t  || ||  |d   t |d | || |  ||| |d    |d   t   }|jtdd |td  |t  | ttd  kshJ d S )Nzp_0 p_1 p_2 p_3 b_0 b_1 b_2r/   r@   rB   r5   )r   r   r   ratsimpr   )p_0p_1p_2p_3b_0b_1b_2Qr(   r(   r)   test_issue_20697g  s"   ,>r   c               	   C   s   dt d d } ddt td   td|  d ddt d  dt  dt d t  ttddt d   d tddt d  f dt d dd	t d  d  tt dt  d   ksbJ d S )
Nr/   rI   r@   i4ih  i  i  rz   r   )r   r   r   factorr   )fir(   r(   r)   test_issue_21245o  s   $&,
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/   rh   rF   r@   r   )r   r   r   r   r
   r   r`   r(   r(   r)   test_issue_21938w  s   "Tr   c                  C   s<   dt dtd   } | td}|jrt|jdksJ d S )Nr/   r@   r   r^   )r   r   r   is_Addlenargs)ra   resultr(   r(   r)   test_issue_23432|  s   r   c                  C   s*   t tdtd  td} | jdksJ d S )Nr/   r@   g?T)r   r   r   r   )resr(   r(   r)   test_issue_23727  s   r   c                
   C   s  t t t dt d  tddddt t t  dtd  td   ttd  ks.J t t t dt d  tdt  tdddttdt t    td td  d dtd  d  dt t t    ttd  ksuJ dt t t dt d   tddt td d tt td  ttd t td d tt td   dt t t td d tt td   td    ttd  ksJ dt t dt d   tddt t t td dt t t t t t td  td  ttd  ksJ t	tt dt d   tddt tt tt	 dt t t t tt tt	  tt	  ttd  ksHJ tt	 tt dt d   tddt tt ttt	  dt t t t tt ttt	   ttt	   ttd  ksJ d S )Nr@   r/   r   rB   r]      rC   )
r   r   r   r   r   r   r   r"   r   r   r(   r(   r(   r)   test_issue_24266  s   \D4

D^

ztr   N)[sympy.core.evalfr   sympy.core.functionr   r   r   r   sympy.core.numbersr   r   r	   r
   r   r   sympy.core.singletonr   sympy.core.symbolr   r   &sympy.functions.elementary.exponentialr   r   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   r   sympy.series.orderr   sympy.series.seriesr   ri   r   r   r   r    sympy.testing.pytestr!   
sympy.corer"   r*   r,   r-   r.   rZ   rb   rd   rn   rt   sympy.series.accelerationru   rv   sympy.concrete.summationsrw   rx   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)   <module>   sp     2		
5