a
    khnB                     @   sd  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_d` Z[dadb Z\dcS )d    )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   s0   t ttd} tt ttd}| |ks,J d S Nr   )r   r   r   e1e2 r'   L/var/www/auris/lib/python3.9/site-packages/sympy/series/tests/test_series.pytest_sin   s    r)   c                  C   s0   t ttd} tt ttd}| |ks,J d S r#   )r   r   r   r$   r'   r'   r(   test_cos   s    r*   c                  C   s0   t ttd} tt ttd}| |ks,J d S r#   )r   r   r   r$   r'   r'   r(   test_exp   s    r+   c                  C   s8   t tttd} tt tttd}| |ks4J 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sHJ ttdd  ttdd  tt tdttd  t	ttd  
 dksJ ttj tdd d  fddtd	D tdtd td  gksJ ttj tdd d
d  fddtd	D tddt td gks0J ttj tdd
dtksNJ 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s J | 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sJ dt ttd	   d	ksJ dt  d u sJ ttdd  td}ttt jtd|dtt| tttt|  t ksJ tdt j ttdddt ddtd    ttd ttf ksfJ 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sPJ tddd}tt|d t| j ddd|td t|  t|d t|d   ksJ ttttt j d	ddttt  ttd	 ttd	   ksJ d S )N   r   c                   S   s   t tt  S N)r   r   r   r   r'   r'   r'   r(   <lambda>.       z!test_issue_5223.<locals>.<lambda>c                   S   s   t jddS )N dir)r   r   r'   r'   r'   r(   r/   /   r0   r   c                    s   g | ]}t  qS r'   next.0ier'   r(   
<listcomp>4   r0   z#test_issue_5223.<locals>.<listcomp>   -)r   r3   c                    s   g | ]}t  qS r'   r5   r7   r:   r'   r(   r<   6   r0   r2      )r3   r            c                   S   s   dt t t  S Nr-   )r   r   r
   r   r'   r'   r'   r(   r/   G   r0   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4&
@&B
0" 
H $"&>
.
rR   c                  C   s  t tttd dt   tdtfdd} | tdddtdd   td ttdd d  ttdd  dt	 ttdd    tdt ttd d  ttd d  dt	   dtdd  td ttdd   ttd d  ttdd  ttdd  dt	   dtdd  td ttd	d   ttdd d  ttdd  d
t	   dtdd  td ttdd   ttd d  ttdd  ttdd  dt	   t
td  ksJ d S )Nr?   r   none)Zcondsr=   r-   rA   rF   rC         )r   r   r    r   r
   r   r   r   r   r   r   exprr'   r'   r(   test_issue_6350\   s    (`6`R`
rY   c                   C   s  t tttttttks&J ttttjtdd ttjtddksXJ ttd ttdtd  ks|J ttd ttdksJ tttttdksJ tttttt ksJ tdtttdtksJ tt	ttt t	ttksJ dt t	ttt t	ttksHJ tt
ttt dt tkstJ t t
tttt t
tt t ksJ d S )Nr?   r4   r=   r   r-   )r   r   r   r   r   r   rP   as_leading_termr   r   r   rM   r'   r'   r'   r(   test_issue_11313e   s    &2$,,,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sbJ ttttttd  d tt ttd d tt ttd  }|  |ksJ | t|ksJ |  | ksJ | t d tt d ttt d	  tt d	 tt ttttt t d  ks>J |t	 |	 tks`J | 	 ttt ksJ t
t fd
d ttt t t	 t  ksJ d S )Nr   zr?   rA   rF   x   rC      r=   c                      s   t tdt  t  S )Nr=   )r   r   r   r   r'   r\   r'   r(   r/      r0   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_Subsy   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stJ | 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 | td tdd| dtd tt| tttd  ttd  ks*J | td d tdd| dtd tt| tttd  ttd  ks|J 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>   r2   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sJ tt|t dd dtt	d dksJ d S )	Nr-   
      rT      rC   r=   rF   )
r   roundrh   Zevalfr   rj   rk   r    ri   r   )r;   Ar'   r'   r(   test_acceleration   s
    * ,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sdJ d S )Nr-   r   r=   rF   rC   r_   rA   )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sJ d S )
Nr-   r=   r   rF   r?   rA   rC   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?   rC   )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sJ d S )Nza, bTrJ   rV   r4   r-   r=   r?   rA   rC   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   r4   r   r'   r'   r'   r(   test_issue_8805   s    r~   c            	   	   C   s  t d\} }}}}}}| |||t  t  t  d||t  || ||  |d   t |d | || |  ||| |d    |d   t   }|jtdd}|t|| | || | ||     td || | || | | ||   |  || | || ||  d  || ||   ||  |d |d       | ttd  ks`J | |td  |t  | ttd  ksJ d S )Nzp0 p1 p2 p3 b0 b1 b2r-   r=   r?   r4   )r   r   r   r   Zsimplify)	Zp0p1p2Zp3Zb0b1b2Qr   r'   r'   r(   test_issue_9173   s.    B2<.
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sfJ d S )Nr=   r-   r?   rG   rC   )r   r   r
   r   r   r'   r'   r(   test_issue_9549   s     r   c                   C   sH   t dtd td   tdtd td  td  ttd  ksDJ d S )	Nr-   r   r   r?   rC   rF   rA   )r   r   r   r'   r'   r'   r(   test_issue_10761   s    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sJ d S )Nr-   r=   rC   rV   r      r4   rA   "      rl   i  r@   i     iC     )r   r   r   r   r   r'   r'   r(   test_issue_12578   s    ,L


r   c                  C   sp  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slJ d S )NbetaTrJ   ztheta varphirealr=   r-         ?      ?g      ?g      пg      ?g      ?)r   r   r   r   r   ZHalfr   Ztrigsimp)r   thetaZvarphirX   Zsolr'   r'   r(   test_issue_12791   s6    $
6$""r   c                     s   t d\ } t |    |  ks&J t d|     d|   ksHJ tt| t   t| t  ksrJ 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 r.   r   r   r'   r   r'   r(   r/     r0   z"test_issue_14384.<locals>.<lambda>c                      s   t  td   S rD   r   r'   r   r'   r(   r/   	  r0   c                      s   t ttt   S r.   )r   r   r   r   r'   r   r'   r(   r/   
  r0   )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sJ d S )Nr   r=   r   r-   r?   rA   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sZJ t ttttddtd   ddtd    dt  td  ttd ttf ksJ 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sZJ t ttd tdd	td td  dtd  d  ttd  ksJ t ttttdd	ttd  dtd  d  ttd  ksJ d S )
Nr=   r?   rV   rC   }   rF   r_   rA   r4   )r   r   r   r   r   r'   r'   r'   r(   test_issue_7259  s    ZFr   c                   C   s6   t tjtdddt dttd tdf ks2J d S )Nr-   r4   )r   r   r   r   r'   r'   r'   r(   test_issue_11884  s    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sJ d S )Nr-   rC   r4   i    r?   r   r=   rV   rB   )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?r4   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$ }t|| d%d&d#td'd(d) | d*  td+d(d)| d,   td-d(d)| d.   td/d(d)| d0   td1d(d)| d2   td3d(d)| d4   td3d(d)|   td3d(d) ksJ d S )5NdtTr   r   g      ?g       @r   g      ?-   1   gPFvBgI?gwkN?gh/?gh/?g	%?gIp?r      r      gaAοgi?gi/?gϥ;} @gvQ?go?gUUUUUU?g@g?br@gF)7^@g~j`?g~?g#@rm   r-   r   rV   z0.00092592592592592596126289F   )Z	precisionrU   z0.0027777777777777783174695rA   z0.016666666666666656027029rF   z0.083333333333333300951828rC   z0.33333333333333337034077r?   z1.0r=   )r   r   r   r   r   )r   rX   r'   r'   r(   test_issue_19534/  s"   *&&&&&&



&&&&
&&&&

%%'
r   c                  C   s   t d\} }}}tt| | ||  |ddt| | t| ksFJ tt| | | ||  |ddt| | | t| ksJ d S )Nza b c xr   r-   )r   r   r   r   )r{   r|   cr   r'   r'   r(   test_issue_11407d  s    6r   c                   C   s8   t td td  jtdddt tdt ks4J d S )N2   3   r   r4   r-   )r   r   r   r   r'   r'   r'   r(   test_issue_14037j  s    r   c                     sJ   t tt jtd d  fddtdD } | dt dtd gksFJ d S )Nr4   c                    s   g | ]}t  qS r'   r5   r7   rW   r'   r(   r<   p  r0   z$test_issue_20551.<locals>.<listcomp>r?   r-   r=   )r   r   r   rN   )Ztermsr'   rW   r(   test_issue_20551n  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sJ d S )Nzp_0 p_1 p_2 p_3 b_0 b_1 b_2r-   r=   r?   r4   )r   r   r   Zratsimpr   )Zp_0Zp_1Zp_2Zp_3Zb_0Zb_1Zb_2r   r'   r'   r(   test_issue_20697t  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 tt dt  d   ksJ d S )Nr-   rF   r=   iS         )r   r   r   Zfactorr   )fir'   r'   r(   test_issue_21245|  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srJ d S )Nr-   r_   rC   r=   r   )r   r   r   r   r
   r   rW   r'   r'   r(   test_issue_21938  s    "r   c                  C   s<   dt dtd   } | td}|jr4t|jdks8J d S )Nr-   r=   r   rU   )r   r   r   is_Addlenargs)rX   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sJ 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sJ 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sJ d S )Nr=   r-   r   r?   rT      r@   )
r   r   r   r   r   r   r   r"   r   r   r'   r'   r'   r(   test_issue_24266  s    \D4

D^
ztr   c                   C   s   t tdd  d S )Nc                   S   s   dt  t tdS )Nr=   rT   )r   r   r
   r'   r'   r'   r(   r/     r0   z"test_issue_26856.<locals>.<lambda>)r!   rK   r'   r'   r'   r(   test_issue_26856  s    r   N)]Z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!   Z
sympy.corer"   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'   r'   r'   r(   <module>   sr    2		
5