o
    ÜÓhŃ{  ć                   @   sx  d dl mZmZ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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- d dl.m/Z/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@ d dlAmBZBmCZC d d	lDmEZEmFZF d
d ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQd d! ZRd"d# ZSd$d% ZTd&d' ZUd(d) ZVd*d+ ZWd,d- ZXd.d/ ZYd0d1 ZZd2d3 Z[d4d5 Z\d6d7 Z]d8d9 Z^d:d; Z_d<d= Z`d>d? Zad@dA ZbdBdC ZcdDdE ZddFdG ZedHdI ZfdJdK ZgdLdM ZhdNdO Zie0dPdQ ZjdRdS ZkdTdU ZldVS )Wé    )ŚZZŚQQŚEXŚRR)Śring)Śpuiseux_ring)$Ś_invert_monomsŚrs_integrateŚrs_truncŚrs_mulŚ	rs_squareŚrs_powŚ_has_constant_termŚrs_hadamard_expŚrs_series_from_listŚrs_expŚrs_logŚ	rs_newtonŚrs_series_inversionŚrs_compose_addŚrs_asinŚ_atanŚrs_atanŚ_atanhŚrs_atanhŚrs_asinhŚrs_tanŚrs_cotŚrs_sinŚrs_cosŚ
rs_cos_sinŚrs_sinhŚrs_coshŚrs_cosh_sinhŚrs_tanhŚ_tan1Śrs_funŚrs_nth_rootŚrs_LambertWŚrs_series_reversionŚrs_is_puiseuxŚ	rs_series)ŚraisesŚslow)Śsymbols)ŚsinŚcosŚexpŚtanŚcotŚsinhŚcoshŚatanŚatanhŚasinhŚtanhŚlogŚsqrt)ŚRationalŚpi)ŚexpandŚSc                 C   s   d}t | | |k sJ d S )Ng»½×Łß|Ū=)Śabs)ŚaŚbŚtol© rD   śX/var/www/html/ai/venv/lib/python3.10/site-packages/sympy/polys/tests/test_ring_series.pyŚis_close   s   rF   c                  C   s  t dt\} }|d d|d   d|  d }t|d|d  d|d   d|  d ks/J t||d d |d d  d|  d ksGJ t dt\} }|d d|d   d|  d }t|||d d |d d  d|d  d  d|  ks}J t dt\} }}|d |d  | d }t|||d |d  d |d d  | ksŖJ t|||d |d  d ||  | ksĮJ d S )	NŚxé   é   é   é   é   é   śx, y)r   r   r   r   r	   )ŚRrG   ŚpŚyrD   rD   rE   Śtest_ring_series1   s    00 >22rR   c                  C   sr   t dt\} }}}|||  d }t||d}||d d|d  | |  d|d  |d  |d   ks7J d S )Nśx, y, trH   rJ   é   rI   )r   r   r
   )rO   rG   rQ   ŚtrP   Śp1rD   rD   rE   Ś
test_trunc%   s   DrW   c                     sz  t dt\} }}d|  ||   tdD ]	}t  |d q dd  |d  d | |d   d|d  |d   d |  d| |  d ksQJ d|  ||  |d  |   t  |d}|dd|   d| |  ks|J t dt\}tt fd	d
 dd  dd   }dd  }t||ddd  dd   d  d ks»J d S )NrS   rK   rI   rJ   rT   é   rH   Śzc                      s   t  dS )NrI   )r   rD   ©rP   rG   rY   rD   rE   Ś<lambda>7   s    z test_mul_trunc.<locals>.<lambda>é   )r   r   Śranger   r,   Ś
ValueError)rO   rQ   rU   ŚirV   ŚR1Śp2rD   rZ   rE   Śtest_mul_trunc,   s   `$$:rb   c                  C   s    t dt\} }}}d||  ||  d }t|||d}t||d}||ks(J d| |d  |d  }t||dd|d  d|d   d|  d ksNJ d S )NrS   rK   rI   rJ   rH   )r   r   r   r   )rO   rG   rQ   rU   rP   rV   ra   rD   rD   rE   Śtest_square_trunc>   s   8rc   c            	      C   sJ  t dt\} }}}|||  }|d }|||fD ]}t||d}t|d|d}||ks-J qd| }t|d|d}|dd|  ksCJ t|d|ddksNJ t|d|ddd|  ks]J || }t|d|d|d d|d  |  d| |d   ks~J td| tdd|d	d	|d  d
 |d d  |tdd  d ks£J d S )Nśx, y, zé   é   rK   rJ   rI   r   éž’’’rH   éQ   é	   )r   r   r
   r   r<   )	rO   rG   rQ   rY   Śp0rP   ŚxxrV   ra   rD   rD   rE   Śtest_pow_truncH   s   :Nrl   c                  C   sx   t dt\} }}}|||  }t||sJ ||d  }t||r#J d| |d  }t||s2J || ||  }d S )Nrd   rH   rK   )r   r   r   )rO   rG   rQ   rY   rP   rD   rD   rE   Śtest_has_constant_term[   s   rm   c                     s  t dt\} d dd    d}t |}t | |dks%J t dt\} }d dd   |  d |   t |}t | |dksSJ t dt\} }d |  tt fdd | j tt fdd t dt\} d  tt	 fd	d d S )
NrG   rI   rM   rK   rN   c                      ó   t  dS )NrH   ©r   rD   ©rP   rG   rD   rE   r[   s   ó    z test_inversion.<locals>.<lambda>c                      rn   ©NrJ   ro   rD   rp   rD   rE   r[   u   rq   c                      rn   rr   ro   rD   rp   rD   rE   r[   y   rq   )
r   r   r   r
   r,   ŚNotImplementedErrorŚzeroŚZeroDivisionErrorr   r^   )rO   ŚnrV   rQ   rD   rp   rE   Śtest_inversionf   s"   (rw   c                  C   s   t dt\} }}t||d}t||d|t||dksJ t||d}t||d|d|d  d d|d  d  |d d	  | ksDJ d S )
NrN   é
   rf   rM   é   ép   rJ   é(   rT   )r   r   r   r)   r   r   ©rO   rG   rQ   rP   rD   rD   rE   Śtest_series_reversion|   s   *
’’r}   c                  C   sT  t dt\} }dd|  |d  d|d   }g d¢}t|||d}|  tt|”}t| ||”|d}||ks;J t dt\} }}g d¢}t|| ||dd	d
}tdd||   d|| d   d|| d   |d}	||	kstJ t dt\} }d}
t|||
d }t||||
}d	}	t	|D ]\}}|	|t
||||
 7 }	q||	ksØJ d S )NrG   rK   rI   rJ   )rK   rI   r   rH   rH   rM   rN   )rK   rJ   rM   ry   r   )Śconcurry   é   )r   r   r   Ś	from_listŚlistŚreversedr
   Ścomposer   Ś	enumerater   )rO   rG   rP   ŚcŚrŚpcŚr1rQ   rV   ra   Śhr_   ŚcxrD   rD   rE   Śtest_series_from_list   s(    8r   c                  C   s`  t dt\} }d| }t||d||d d  |d d  ks!J d| d|d  d  }t||d}|d|d  d	 d
|d  d  d|d  d  |d d  d|d  d  |d d  |d d  | kskJ t||d}t||d}|| ks~J t dt\} }}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  | ksźJ td}t dt\} }}t|| |dtdd|d    |d  tdd|d   |d   tdd|d   |d   td| |  tt| ks:J t||d |  | |dt|d  |d  | tdd|d   |d   td| |d  |  tdd|d   |d   td| |  tt| ksJ ||d  d }t||d |d”ttdtdd ks®J d S )NrG   rK   rH   rI   rJ   ri   iļ’’’rf   i  é   ry   é½   r\   rT   é¢   rM   é-   é$   rN   rA   rg   rx   l   K)z ič^ )	r   r   r   r   r.   r   r:   r   r<   )rO   rG   rP   rV   ra   Śp3rQ   rA   rD   rD   rE   Śtest_log   sn   ,<’
’
’
’T
’’
’’
’
’F’’
’2’’’ž
ž4r   c            
      C   s  t dt\} }||d  }dD ]}td| ||d }t|||}t|||}||ks-J qt||d}| |d ”tddksBJ d	}td| ||}t|||}||d ksZJ td
}t dtt||f \} }}	t|| |dt||d  d t||d  d  t||d  d  t||  t| ksJ t||d |	  | |dt||d  |	d  d t||d  |	 d  t||d  d  t||d  |	  t||d  d  t||d  |	  t||d  d  t||  t| ksJ t dt\} }}	t|| |dtt|d |d  tt|d |d   tt|d |d   tt||  tt| ksJJ t||d |	  | |dtt|d |d  |	d  tt|d |d  |	  tt|d |d   tt||d  |	  tt|d |d   tt||d  |	  tt|d |d   tt||  tt| ksĆJ d S )NrG   rH   )rx   é   rK   r   é   l   ŃOÄ$o¢bļ®l      LÉeFS«Xé   rA   rN   rM   rL   rJ   rT   rI   )	r   r   r   r   r   Ścoeffr.   r1   r   )
rO   rG   rP   r   ŚqrV   Śq1ŚprecrA   rQ   rD   rD   rE   Śtest_exp¾   s   4’
’
’4’’’žžž
žž<’’
’8’’’žžžż
żr   c                  C   sN   t dt\} }|d d }t||d}|d|d  d|d   d ks%J d S )NrG   rI   rH   rf   )r   r   r   )rO   rG   rP   r   rD   rD   rE   Śtest_newtonß   s   (r   c                  C   sp   t dt\} }|d d }|d d }t|||d d|d   d|d   d|d   d|  d ks6J d S )	NrG   rJ   rK   rI   rT   rH   rX   ry   )r   r   r   )rO   rG   rV   ra   rD   rD   rE   Śtest_compose_addę   s   Jr   c                  C   st   t dt\} }}|| |d |d   |d |  }t|t|dt||dks)J t|t|dt||dks8J d S )NrN   rI   rJ   rM   rx   )r   r   r&   r   r%   r|   rD   rD   rE   Śtest_funķ   s   $"r   c               	   C   sņ  t dt\} }}td|d |  d|dd|d  |d  d d	|d
  |d  d  d|d  |d  d  |d | d  d ksEJ 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 ks±J td| d|dd|tdd  ksÅJ td| |d  |d  d|d|tdd d d|tdd   ksźJ td| |d |  |d  d|d}||td	d  |d  d |td	d d  |tdd | d  d|tdd   ks-J td}t dt\} }}t|t| d|dtdd|tdd   |d  tdd|tdd   |d   tdd|tdd   |  t|tdd  ksJ t|tdd |d |  d d|dttdd  |tdd  | ttdd |tdd   ttdd |d  |  ttdd |d   ttdd |tdd   ttdd |tdd   ttd ks÷J d S )NrN   rK   rI   rH   rx   i³’’’rf   i   ry   rT   rJ   é   é    rM   ri   é   éó   rh   rX   i   rA   éd   i>  iŠ  éČ   )r   r   r'   r.   r   r;   )rO   rG   rQ   r   rA   rD   rD   rE   Śtest_nth_rootō   sr   .’’’
’8’’’’žž
ž
ž(J&`4 ’’’6’’’’žžż
żr¤   c                  C   sĘ  t dt\} }}t||d|d  d |d d  |d d  | ks%J 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   ||  ksJ td}t dt\} }}t|| |dt|d | |d d
|d	   d	|d
   d
|d   d   |d
  td|d  d d|d	  d|d
   d|d   d  |d   t||d
 d|d   d  |d   td|d d  |  tt| ks#J t||d |  | |d
td| |d
 d|d   d   |d  | td|d  d d|d	  d|d
   d|d   d  |d   td|d d  |d  |  t||d
 d|d   d  |d   td|d d  |  tt| ks„J t dt\} }|d d|  }t||dt||dksĆJ t dt\} }|d d|  }t||dt||dksįJ d S )NrN   ri   ry   rM   rJ   rI   rf   r\   rT   rH   rA   rK   rG   )r   r   r   r.   r   r6   r   ©rO   rG   rQ   rA   rP   rD   rD   rE   Ś	test_atan  s   :@’’’’’žžžž
ž8
’’’&
’’’’&žż
ż>’’B’ž&ž
’’ž
ż"r¦   c                  C   s  t dt\} }}t|||  |d|d |d  d |d |d  d  |d | d  |d d  ||  | ks<J t|| |d |d   |d|d |d  d d|d  |d  d  |d |d  d  |d |d  d  |d |d   ||  ksJ d S )	NrN   rM   rJ   rT   rI   ry   r{   rH   )r   r   r   ©rO   rG   rQ   rD   rD   rE   Ś	test_asin(  s"   H
’’
’H’’’’rØ   c                  C   s$  t dt\} }}t||d||d d  tdd|d   tdd|d	   ks*J 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   ||  ks“J td}t dtt||f \} }}t|| |dt|d dt|d  d  dt| d  |d
  t|d
 d
t|d  d  tdd |d   t|d t| |d   t|d d |  t| ks"J t||d |  | |d
dt|d  dt|  |d  | t|d
 td
dt|d   tdd |d   t|d d |d  |  t|d t| |d   t|d d |  t| ksJ t dt\} }}t|| |dtt|d dt|d  d  dt| d  |d
  tt|d
 d
t|d  d  tdd  |d   tt|d t| |d   tt|d d |  tt| ksśJ t||d |  | |d
tdt|d  dt|  |d  | tt|d
 d
t|d  d  tdd  |d   tt|d d |d  |  tt|d t| |d   tt|d d |  tt| ksoJ ||d  d }t||d |d”tt	dt
dd  ksJ d S )NrN   ri   rJ   rI   é   rM   é   é;  ry   rH   rf   r\   r   rT   rA   rK   rx   l   PH]ųl   Įn)r   r   r   r.   r2   r<   r   r   r   r6   r?   r„   rD   rD   rE   Śtest_tan0  sØ   DL’’’’žžžžž
ž,’’0’žžž@2’’žžž.’’6’žž
ž*
’’’6’žžż
ż ’r¬   c                  C   sB  t dt\} }}t|d |d  |d|d |d  |d  |d  |d	  |d
  d | |d  |d  |d  |d  d|d  d  d|d  d  ksRJ t||d |  |d|d  |d  |d | d  |d |d   |d d  |d |d   |d | d  ||d   |d  | |d
  ksJ d S )NrN   rT   ry   rf   iś’’’éū’’’éü’’’éż’’’rg   é’’’’rK   rI   rJ   rH   rM   r©   r   )r   r   r   r§   rD   rD   rE   Śtest_cotO  sN   ,’’’’’’’’’ž
žF
’’’
’’’’r±   c                  C   s,  t dt\} }}t||d||d d  |d d  |d d  ks$J 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   ||  ks¦J td}t dtt|t||f \} }}t|| |dt||d  d t||d  d  t||d	  d	  t||  t| ksķJ t||d	 |  | |dt| |d  |d	  d	 t||d  | d	  t||d  d  t||d  |  t||d  d  t||d	  |  t||d	  d	  t||  t| ksUJ t dt\} }}t|| |dtt|d |d  tt|d |d   tt|d	 |d	   tt||  tt| ksJ t||d	 |  | |dtt|d	  |d  |d	  tt|d	 |d  |  tt|d |d   tt||d  |  tt|d |d   tt||d	  |  tt|d	 |d	   tt||  tt| ksJ d S )NrN   ri   rJ   rT   rM   éx   ry   é°  rI   rf   r\   rX   éŠ  rL   rH   rA   )r   r   r   r.   r/   r0   r   ©rO   rG   rQ   rA   rD   rD   rE   Śtest_sinX  s   80’’’’žžžžżż
ż"4’
’
’6’’’’žž
žž<’’
’:’’’žžžż
żr¶   c                  C   sH  t dt\} }}t||dd|d d  |d d  |d d  |d	 d
  ks*J 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 ks“J td}t dtt|t||f \} }}t|| |dt||d  d t||d  d  t||d  d  t||  t| ksūJ t||d |  | |dt| |d  |d  d t||d  | d  t||d  d  t||d  |  t||d  d  t||d  |  t||d  d  t||  t| kscJ t dt\} }}t|| |dtt|d |d  tt|d |d   tt|d |d   tt||  tt| ksØJ t||d |  | |dtt|d  |d  |d  tt|d |d  |  tt|d |d   tt||d  |  tt|d |d   tt||d  |  tt|d |d   tt||  tt| ks"J d S )NrN   ri   rK   rI   rH   rL   rT   r“   rf   é  rJ   rX   rx   é0   ry   r²   rM   rA   )r   r   r   r.   r/   r0   r   rµ   rD   rD   rE   Śtest_cosr  s   D0’’’žžžžżżżż
ż"4’
’
’6’’’’žž
žž<’’
’:’’’žžžż
żr¹   c                  C   sŗ  t dt\} }}t||d\}}|t||dksJ |t||dks$J t|||  |d\}}|t|||  |dks>J |t|||  |dksLJ td| |d  |d\}}|td| |d  |dksjJ |td| |d  |dkszJ td}t dtt|t||f \} }}t|| |d\}}|t|| |dks„J |t|| |dks±J t dt\} }}t|| |d\}}|t|| |dksĻJ |t|| |dksŪJ d S ©NrN   ri   rM   rK   rI   rA   )	r   r   r    r   r   r.   r/   r0   r   )rO   rG   rQ   r   ŚsrA   rD   rD   rE   Śtest_cos_sin  s&     "r¼   c                  C   s   t dt\} }}t||d||d d  |d d  |d d  ks$J t|| |d |d   |dd|d  |d  |d |d   d|d  |d   |d |d  d  |d	 |d  d  |d	 |d   |d |d   |d |d  d  |d
 |d   |d |d  d  |d |d   ||  ksJ td}t dt\} }}t|| |dt|d | |d d
|d	   d	|d
   d
|d   d  |d
  td|d  d d|d	  d|d
   d|d   d  |d   t||d
 d|d   d  |d   td|d d  |  tt| ks!J t||d |  | |d
td| |d
 d|d   d  |d  | td|d  d d|d	  d|d
   d|d   d  |d   td|d d  |d  |  t||d
 d|d   d  |d   td|d d  |  tt| ks¢J ||d  d }t||d |d”ttddtd ksĀJ t dt\} }|d d|  }t||dt||dksąJ t dt\} }|d d|  }t||dt||dksžJ d S )NrN   ri   rJ   rM   ry   rI   rf   r\   rT   rH   rA   rK   rx   lü’’’×y«Y?l l    P{] rG   )	r   r   r   r.   r   r7   r   r<   r   r„   rD   rD   rE   Ś
test_atanh¦  s   8@’’’’’žžžž
ž8
’’’&
’’’’&ž
’’ž
ż4’’’B’ž&žż
ż’"r½   c               	   C   sŚ  t dt\} }}t||dd|d  d|d   d|d   | ks$J 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   ||  ks¦J td}t dt\} }}t|| |dt|d	|d	  t|d	 d  d	t|d	 d     |d	  tdt|d	 d  |  tt| ksńJ t||d	 |  | |dtdt|d	 d  |d	  | t|d	|d	  t|d	 d  d	t|d	 d    |d	   tdt|d	 d  |  tt| ksHJ ||d	  d }t||d |d”ttddtd d  kskJ d S )NrN   ri   g·mŪ¶mŪ¦æry   g333333³?rM   ēUUUUUUÅ?rJ   rI   g      č?rf   r\   g      Ō?g·mŪ¶mŪ¦?rT   g      Ų?ē      ą?rH   rA   rK   rx   l   Ó](~ é   l   |`'9æ )r   r   r   r.   r   r;   r8   r   r„   rD   rD   rE   Ś
test_asinhĒ  sf   8D’’’’’’’žžžž
žF’’

’J’’’’
’$’rĮ   c                  C   s(  t dt\} }}t||d||d d  |d d  |d d  ks$J 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   ||  ks¦J td}t dtt|t||f \} }}t|| |dd|d  t| d|d  t|  d|d	  t|  |t|  t| ksķJ t||d	 |  | |ddt| |d  |d	  dt| |d  |  dt| |d   t||d  |  dt| |d   t||d	  |  dt| |d	   t||  t| ksTJ t dt\} }}t|| |dtt|d |d  tt|d |d   tt|d	 |d	   tt||  tt| ksJ t||d	 |  | |dtt|d	 |d  |d	  tt|d	 |d  |  tt|d |d   tt||d  |  tt|d |d   tt||d	  |  tt|d	 |d	   tt||  tt| ksJ d S )NrN   ri   rJ   rT   rM   r²   ry   r³   rI   rf   r\   rX   r“   rL   rH   rA   ēUUUUUU„?r¾   ræ   )r   r   r!   r.   r4   r5   r   rµ   rD   rD   rE   Ś	test_sinhŪ  sØ   80’’’’žžžžżż
ż"6’’
’
’>’’’’’žž
žž<’’
’@’’’’’’žžž
žrĆ   c                  C   sD  t dt\} }}t||dd|d d  |d d  |d d  |d	 d
  ks*J 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 ks“J td}t dtt|t||f \} }}t|| |ddt| |d  dt| |d   dt| |d   t||  t| ksūJ t||d |  | |ddt| |d  |d  dt| |d  |  dt| |d   t||d  |  dt| |d   t||d  |  dt| |d   t||  t| ksbJ t dt\} }}t|| |dtt|d |d  tt|d |d   tt|d |d   tt||  tt| ks§J t||d |  | |dtt|d |d  |d  tt|d |d  |  tt|d |d   tt||d  |  tt|d |d   tt||d  |  tt|d |d   tt||  tt| ks J d S )NrN   ri   rK   rI   rH   rL   rT   r“   rf   r·   rJ   rX   rx   rø   ry   r²   rM   rA   rĀ   r¾   ræ   )r   r   r"   r.   r4   r5   r   rµ   rD   rD   rE   Ś	test_coshō  sØ   D0’’’žžžžżżżż
ż"4’
’
’>’’’’’žž
žž<’’
’@’’’’’’žžž
žrÄ   c                  C   sŗ  t dt\} }}t||d\}}|t||dksJ |t||dks$J t|||  |d\}}|t|||  |dks>J |t|||  |dksLJ td| |d  |d\}}|td| |d  |dksjJ |td| |d  |dkszJ td}t dtt|t||f \} }}t|| |d\}}|t|| |dks„J |t|| |dks±J t dt\} }}t|| |d\}}|t|| |dksĻJ |t|| |dksŪJ d S rŗ   )	r   r   r#   r"   r!   r.   r4   r5   r   )rO   rG   rQ   ŚchŚshr   r»   rA   rD   rD   rE   Śtest_cosh_sinh  s&     "rĒ   c                  C   sŽ  t dt\} }}t||d|tdd|d   tdd|d   tdd	|d
   ks-J t|| |d |d   |dd|d  |d  d d|d  |d  d  d|d
  |d  d  d|d
  |d
  d	  |d |d  d  d|d  |d
  d  |d |d
   d|d  |d  d  |d |d   |d |d  d  |d |d   ||  ks·J td}t dt\} }}t|| |dtt|d dt|d  d  dt| d  |d  tt|d  dt|d  d  tdd |d   tt|d t| |d   tt|d  d |  tt| ks+J t||d |  | |d}| |d” |d”tdt|d  dt|d   dt|d  d  dt|  tdd ksmJ d S )NrN   ri   rK   rJ   rI   r©   rM   rŖ   r«   ry   rH   rf   r\   r   rT   rA   rx   iü’’it'  i¦	  is'  i  )r   r   r$   r.   r   r9   r   r„   rD   rD   rE   Ś	test_tanh%  sd   J4’’’’žžžžżż
ż.’’6’žž
ž"’’
’’rČ   c            
      C   sš   t tttttg} tttt	t
tg}tdt\}}}td}t| |D ]*\}}|d| |d |d”}|d|  |dd” ” }	t| ” |	 |d” ”  q!td| d|d |d”}d| tdd  |dd” ” }	t| ” |	 |d” ”  d S )NrN   rA   rI   rM   r   rK   )r   r   r   r   r   r$   r/   r0   r2   r3   r6   r9   r   r   r.   Śzipr   ŚseriesŚremoveOrF   Śas_exprŚsubsrv   r'   r   )
Śrs_funcsŚsympy_funcsrO   rG   rQ   rA   Śrs_funcŚ
sympy_funcrP   r   rD   rD   rE   Śtest_RR9  s    rŅ   c                  C   s    t dt\} }}dd|  |d  d|d   }t||rJ ||tdd |  }t||s1J t||r8J ||d |tdd  |  }t||rNJ d S )NrN   rK   rI   rJ   rM   )r   r   r*   r|   rD   rD   rE   Śtest_is_regularH  s    rÓ   c                  C   sś
  t dt\} }}|tdd |tdd  | }t||d}|tdd  |tdd  d|td	d   |tdd  d|td
d   |tdd  |tdd  |tdd  |tdd  |tdd  }||ksoJ td| d|d}||tdd  d |tdd d  |tdd d  d ksJ td| |d}||tdd  d |tdd  |tdd  ks¾J t||d}||tdd  |tdd  |tdd  ksŽJ ||tdd |  }t||d}||tdd |d  d |tdd |d  d  |tdd |d  d  |tdd |  d ks&J t||d}||tdd  |tdd  |tdd  |tdd d  | |tdd  |tdd  ks`J t||d}||tdd |d  d |tdd |d   |td
d |d
  d
  |td
d |d   ||d  d  | |tdd |d  d  |tdd |  ks»J t||d}||tdd |tdd  | tdd|tdd   |tdd  |tdd  |tdd  ks÷J t	||d}||tdd |tdd  | tdd|tdd   tdd|tdd   tdd|tdd   tdd|tdd   ksBJ t
||d}|dtdd|tdd   |tdd  tdd|tdd   |td
d  tdd|tdd   |tdd  tdd|tdd   ksJ t||d}||tdd d |tdd d  |tdd d  |tdd d  | |tdd  |tdd  ksÓJ t||d}||tdd  |tdd  d|td	d   d|tdd  d  d|td
d   d|tdd  d  |tdd  |tdd  |tdd  |tdd  ks1J t||d}|d |tdd d |tdd  |tdd d  |td
d  |tdd d  |tdd  |tdd d  d ksyJ |d |tdd  d |tdd d  |tdd d  |tdd d  | |tdd  |tdd  ksµJ t||d}||tdd |tdd  |tdd  |tdd d  | |tdd  |tdd  ksīJ t||d}||tdd |tdd  | tdd|tdd   tdd|tdd   tdd|tdd   tdd|tdd   ks9J t||d}||tdd d |tdd  |tdd d  |td
d  |tdd d  |tdd  |tdd d  d ksJ t||d}||tdd d |tdd d  |tdd d  |tdd d  | |tdd  |tdd  ks¾J t||d}|d |tdd d |tdd  |tdd d  |td
d  |tdd d  |tdd  |tdd d  d ksJ |d |tdd d |tdd d  |tdd d  |tdd d  | |tdd  |tdd  ksAJ t||d}||tdd  |tdd  |tdd  |tdd d  | |tdd  |tdd  ks{J d S )NrN   rI   rM   rJ   rK   é   r©   rH   r\   ry   rg   ri   rL   rT   rĄ   é   re   rf   é   r   )r   r   r   r'   r   r(   r   r   r   r   r   r   r   r    r   r   r"   r!   r#   r$   )rO   rG   rQ   rP   r   r   rV   rD   rD   rE   Śtest_puiseuxU  sh   <’’’’’žD84N’’>’’’J’’’’’F’’B’’’B’’’’6’’’’0’’’’žžžD’’’’<’’’’@’’B’’’@’’’’6’’’’D’’’’:’’’’>’’’r×   c                  C   sģ   t  td”} |  td”}td\}}t||g| \}}}d| |t dd  d| |t dd   }| ” t ddt dfd| t dt ddfd| iksRJ | ” dtd |tdd   dtd |tdd    kstJ d S )NrI   rN   rK   rJ   r   )	r   Śalgebraic_fieldr;   Ś
from_sympyr.   r   Śto_dictrĢ   r?   )ŚKŚsqrt2rG   rQ   rO   ŚxrŚyrrP   rD   rD   rE   Śtest_puiseux_algebraic«  s   ,<Hrß   c                  C   sĘ  t dt\} }t||d|d  }||d d |d d  |d d	  |d
 d  tdd |d d  |d  ks<J t||d}t|d
|d}|d|tdd
  d |tdd
 d  |tdd
 d  |tdd
 d  |tdd
  kszJ t||d}t|d|d}t|d|d}|d|tdd  d |tdd d  d |td!d  d"  d|td#d  d$  |tdd  ksĆJ t|tdd
 |d}||td#d
 d% |d d&  |tdd
 d'  |d d(  |tdd
 d)  |d d*  |tdd
 d  |d d+  |td d
 d  |d d,  |tdd
 d	  |d d-  |tdd
 d  |d. d/  |tdd
 d  |d
 d0  |td.d
 d  |d
  |tdd
  d ksaJ d S )1NrG   r©   r­   rf   l    LQf rT   i arH   i rI   r³   rK   r²   rg   r®   rx   i½’’’rŖ   i ųŗr   i^  ri   i   rM   rX   ry   i’’’é=   i:ké/   iP@  r\   é!   iČ  é   é*   l     L.l     ę³{µ l     ]ū
 l     ėnLl    XīnĮl    (vQ i üi _7 r·   rJ   r“   rL   )r   r   r   r'   r   r   )rO   rG   r   rP   rD   rD   rE   Śtest1·  s   0’
’
’(’’
’(’’
’’
’ž
žż
żż
üü
üü
ūū
ūūūśśrå   c                  C   s&  t dt\} }td|  ” \}}||tdd |  }t||d}||d d |d  d|d   |tdd  |d	 d	 |d
  | |td	d   |d d |d  |tdd   |d d |d  |tdd   |d d d |  |d |tdd  d  ||tdd   ksJ d S )NrQ   rG   rK   rM   rJ   r   rf   rI   r\   rT   ri   rH   ry   )r   r   r   Ś	to_domainr   )rO   rQ   r?   rG   rP   r   rD   rD   rE   Śtest_puiseux2Ņ  s.   @’’ ’
’’’žžžrē   c                  C   s  t d\} }}}t||d ” |ksJ tt||d ” t| |dd” ” ks+J tt|t| |d ” t|t|  |dd” ” ksJJ tt|t| |d ” t|t|  |dd” ” ksiJ t|| t|d |d d   }tt||d ” t| |dd” ” ksJ t|d d |d  t|d t|d d   }tt||d ” t| |dd” ” ksĆJ t| d | t| d d | |d   }tt||d ” t| |dd” ” ksšJ t|d |d  d d t|d |d   }tt||d ” t| |dd” ” ks J t|| | }tt||d ” t| |dd” ” ks@J t	t|d d | | }tt||d	 ” t| |dd	” ” ksfJ |t
dd |t
dd  | }tt	||d}| ” |t
d
d |t
dd  |t
dd  |t
d	d d  | |t
dd  |t
dd  ks³J tt||d}| ” |t
dd d |t
dd  |t
dd  d ksŪJ tt||d}| ” |t
d
d  d |t
dd d  |t
dd d  |t
d	d d	  | |t
dd  |t
dd  ksJ tt||d}| ” |t
dd d	 |t
dd  |t
dd d  |t
dd  |t
dd d  |t
dd  |t
dd d  d ksiJ tt|d |d ” t|d  |dd” ” ksJ d S )Nz
x, a, b, crM   r   rI   rH   rx   rJ   rK   rT   ri   rĄ   r©   rÕ   rÖ   rf   rL   ry   re   )r.   r+   rĢ   r/   rŹ   rĖ   r0   r>   r1   r2   r   )rG   rA   rB   r   rP   r   rD   rD   rE   Śtest_rs_seriesŻ  s²   ’’ ’’ ’’$’
’4’
’,’
’0’’’’’’ @’’’@<’’’’D’’’’&’’rč   c                  C   sØ  t d\} }ttd|  | d ” | d  d | d d  | d d  |  ks)J ttdd|   | d ” d| d  d| d  d  d	| d   d|   ksQJ ttd|  | d  | d
 ” d| d  d | d	 d	  | d d  | d d  | d d  | d d  d| d  d  | d d  |  ksJ ttd| |d   | d ” | d  |d  d | d |d
  d  | d |d	  d  | d |d  d  | d |d  d  | |d   ksäJ ttd|  | d ” | d  d | d d  | d d  | d d  | d d  | d  td  ksJ ttd|  | d  | d ” d| d  d | d d  d| d  d  d| d  d  | d d  | d  td  ksYJ ttd| |  | d ” |d  | d  d |d | d  d  |d | d  d  |d | d  d  |d | d  d  ||  d  td  ks§J ttd|  | d ” d| d  tdd  d | d tdd   d| d  td d  | d tdd   | d d  d| d  tdd  d  | d td  | d tdd   | tdd   |  td ksJ ttd| |  | d ” |d  | d  td |d | d  tdd   ||  tdd   ||   td ksVJ ttd|  | d ” | d td d | d td d  | d td d  | td  td ksJ ttd| |  | d ” |d | d  td d |d | d  td d  |d | d  td d  ||  td  td ksŌJ ttd|  | d ” | d td d | d td d  | d td d  | td  td ksJ ttd| |  | d ” |d | d  td d |d | d  td d  |d | d  td d  ||  td  td ksRJ d S )Nzx arK   rM   rH   rJ   rI   iĄ’’’é@   rf   rx   rg   ri   ry   rT   rX   rz   rø   r{   iń’’’r­   rL   )	r.   r+   r:   rĢ   r6   r=   r9   r4   r5   )rG   rA   rD   rD   rE   Śtest_rs_series_ConstantInExpr  s  .
’
’4
’
’,
’
’
’
’
’’
’
’2’’’’

’:
’
’’’8’’
’’’B’’’
’’6
’’’
’’’’žžžžž:’
’’’’<’
’’4’’’’<’
’’4’’’’rź   c                  C   s¬   t d\} }tt| tdd t| |tdd   | d ” | tdd t|tdd  | tdd t|tdd  d  | tdd t|tdd   ksTJ d S )Nza brJ   ry   rT   rI   rx   ri   )r.   r+   r/   r   r1   rĢ   )rA   rB   rD   rD   rE   Ś
test_issue9  s   2b’rė   N)mŚsympy.polys.domainsr   r   r   r   Śsympy.polys.ringsr   Śsympy.polys.puiseuxr   Śsympy.polys.ring_seriesr   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+   Śsympy.testing.pytestr,   r-   Śsympy.core.symbolr.   Śsympy.functionsr/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   Śsympy.core.numbersr<   r=   Ś
sympy.corer>   r?   rF   rR   rW   rb   rc   rl   rm   rw   r}   r   r   r   r   r   r   r¤   r¦   rØ   r¬   r±   r¶   r¹   r¼   r½   rĮ   rĆ   rÄ   rĒ   rČ   rŅ   rÓ   r×   rß   rå   rē   rč   rź   rė   rD   rD   rD   rE   Ś<module>   s`    <
!	!V
8#