o
    ev<                     @   s@  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$m%Z% d dl&m'Z'm(Z(m)Z)m*Z* d dl+m,Z, dd Z-dd Z.dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd  Z5d d!l6m7Z7m8Z8 d d"l9m:Z: d d#lm;Z; d$d% Z<d&d' Z=d(d) Z>d*d+ Z?d,d- Z@d.d/ ZAd0d1 ZBd2d3 ZCd4d5 ZDd6d7 ZEd8d9 ZFd:d; ZGd<d= ZHd>d? ZId@dA ZJdBdC ZKdDdE ZLdFdG ZMdHdI ZNdJdK ZOdLdM ZPdNdO ZQdPdQ ZRdRdS ZSdTdU ZTdVdW ZUdXdY ZVdZd[ ZWd\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)raisesc                  C   0   t ttd} tt ttd}| |ksJ d S Nr   )r   r   r   e1e2 r'   ND:\Projects\ConvertPro\env\Lib\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(   r/   .   s    r   c                       g | ]}t  qS r'   next.0ier'   r(   
<listcomp>3       z#test_issue_5223.<locals>.<listcomp>   -)r   r2   c                    r4   r'   r5   r7   r:   r'   r(   r<   5   r=   r1      )r2   r            c                   S   s   dt t t  S )Nr.   )r   r   r
   r   r'   r'   r'   r(   r/   F   r=   logx)r   rE      +pTZpositivez3/2)r   r   r6   r   ZZeroZlseriesr   r!   
ValueErrorsubsremoveOranger   absr   r   r   r   doitr   r   Zgetnr   r   Znseriesr
   r   r   )DrE   rI   r'   r:   r(   test_issue_5223)   sb   42&>$B
0" 
H $"&>
.
NrR   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 )Nr@   r   none)Zcondsr>   r.   rB   rF   rD         )r   r   r    r   r
   r   r   r   r   r   r   exprr'   r'   r(   test_issue_6350[   s   (`6`R`
rY   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@   r3   r>   r   r.   )r   r   r   r   r   r   rP   as_leading_termr   r   r   rM   r'   r'   r'   r(   test_issue_11313d   s   &2$***8r[   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   zr@   rB   rF   x   rD      r>   c                      s   t tdt  t  S )Nr>   )r   r   r   r   r'   r\   r'   r(   r/      s    z%test_series_of_Subs.<locals>.<lambda>)	sympy.abcr]   r   r   r   r   r   r   r   rP   r!   rK   )Zsubs1Zsubs2Zsubs3Zsubs1_seriesr'   r\   r(   test_series_of_Subsx   s0    
"

 *ra   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@   r?   r1   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    rf   )r   r   r   r   r   r   )rb   rf   r'   r'   r(   test_issue_3978   s:    "
 "
00"
rg   )
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.   
      rT      rD   r>   rF   )
r   roundrh   Zevalfr   rj   rk   r    ri   r   )r;   Ar'   r'   r(   test_acceleration   s
   * ,2rq   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>   rF   rD   r_   rB   )r   r   r   r   r   r'   r'   r'   r(   test_issue_5852   s
   4
rr   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   rF   r@   rB   rD   ir_   )r   r   r   r   r   r'   r'   r'   r(   test_issue_4583   s   ."
rs   c                  C   s,   dt  tdd } | d t | ksJ d S )Nr.   r>   r@   )r   r	   rZ   eqr'   r'   r(   test_issue_6318   s   rv   c                  C   s0   t d tdd } |  t tdd ksJ d S )Nr>   r@   rD   )r   r	   r   rt   r'   r'   r(   test_x_is_base_detection   s   rw   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@   rT   r>   )r   r   r   r   r   r'   r'   r'   r(   test_issue_7203   s   (rx   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, bTrJ   rV   r3   r.   r>   r@   rB   rD   r_   rF   r^     rU     )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.   rV   r3   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.   r@   rG   rD   )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   r@   rD   rF   rB   )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>   rD   rV   r      r3   rB   "      rl   i  rA   i     iC     )r   r   r   r   r   r'   r'   r(   test_issue_12578   s   ,L


r   c                  C   s^  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t| d	 d   t| tj d | tjf }|| dd |ksJ d S )NbetaTrJ   ztheta varphirealr>   r.         ?      ?g      ?g      пg      ?g      ?r@   )r   r   r   r   r   ZHalfr   Ztrigsimp)r   thetaZvarphirX   Zsolr'   r'   r(   test_issue_12791   s>   $
*$"r   c                  C   s   t d\} }t| | | | | ksJ t| d|  | | d|  ks$J tt|t|  | t|t|  ks9J t| t | | t ksFJ t| td  | | dt  ksWJ tttt|  | ttt|  kslJ d S )Nzx ar   r.   )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.   r@   rB   rF   r_   rU   r^   	   ry      rz   )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 )NrT   rF   r.   r@   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>   r@   rV   rD   }   rF   r_   rB   r3   )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.   r3   )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.   rD   r3   i    r@   r   r>   rV   rC   )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?r3   l   I l     o )r   r   r   rM   Z	nsimplifyr   )rb   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$ }t|| d%d&d#td'd(d) | d*  td+d(d)| d,   td-d(d)| d.   td/d(d)| d0   td1d(d)| d2   td3d(d)| d4   td3d(d)|   td3d(d) ksJ d S )5NdtTr   r   g      ?g       @r   g      ?-   1   gPFvBgI?gwkN?gh/?gh/?g	%?gIp?r      r      gaAοgi?gi/?gϥ;} @gvQ?go?gUUUUUU?g@g?br@gF)7^@g~j`?g~?g#@rm   r.   r   rV   z0.00092592592592592596126289F   )	precisionrU   z0.0027777777777777783174695rB   z0.016666666666666656027029rF   z0.083333333333333300951828rD   z0.33333333333333337034077r@   z1.0r>   )r   r   r   r   r   )r   rX   r'   r'   r(   test_issue_19534   s"  *&&&&&&



&&&&
&&&&

%%'
r   c                  C   s   t d\} }}}tt| | ||  |ddt| | t| ks#J tt| | | ||  |ddt| | | t| ksBJ d S )Nza b c xr   r.   )r   r   r   r   )r{   r|   cr   r'   r'   r(   test_issue_11407U  s   6Br   c                   C   s8   t td td  jtdddt tdt ksJ d S )N2   3   r   r3   r.   )r   r   r   r   r'   r'   r'   r(   test_issue_14037[  s   8r   c                     sJ   t tt jtd d  fddtdD } | dt dtd gks#J d S )Nr3   c                    r4   r'   r5   r7   rW   r'   r(   r<   a  r=   z$test_issue_20551.<locals>.<listcomp>r@   r.   r>   )r   r   r   rN   )Ztermsr'   rW   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.   r>   r@   r3   )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_20697e  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.   rF   r>   i4ih  i  i  rm   r   )r   r   r   factorr   )fir'   r'   r(   test_issue_21245m  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.   r_   rD   r>   r   )r   r   r   r   r
   r   rW   r'   r'   r(   test_issue_21938u  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   rU   )r   r   r   is_Addlenargs)rX   resultr'   r'   r(   test_issue_23432z  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   N)XZsympy.core.evalfr   Zsympy.core.functionr   r   r   r   Zsympy.core.numbersr   r   r	   r
   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z&sympy.functions.elementary.exponentialr   r   r   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   r   Z'sympy.functions.special.gamma_functionsr   Zsympy.integrals.integralsr   r   Zsympy.series.orderr   Zsympy.series.seriesr   r`   r   r   r   r    Zsympy.testing.pytestr!   r)   r+   r,   r-   rR   rY   r[   ra   rg   Zsympy.series.accelerationrh   ri   Zsympy.concrete.summationsrj   rk   rq   rr   rs   rv   rw   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(   <module>   sl     2		
5