o
    ŗ„gV`  ć                   @   s(  d dl mZmZ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& d dl'm(Z(m)Z) d dl*m+Z+ d dl,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z; d	d
 Z<dd Z=dd Z>dd Z?dd Z@dd ZAdd ZBdd ZCdd ZDdd ZEdd ZFdd  ZGd!d" ZHd#d$ ZId%d& ZJd'd( ZKd)d* ZLd+d, ZMd-d. ZNd/d0 ZOd1d2 ZPd3d4 ZQd5d6 ZRd7d8 ZSd9d: ZTd;d< ZUd=d> ZVd?d@ ZWdAdB ZXdCdD ZYdEdF ZZdGdH Z[dIdJ Z\e)dKdL Z]dMS )Né    )ŚQQŚEXŚRR)Ś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rs_atanŚrs_atanhŚrs_tanŚrs_cotŚrs_sinŚrs_cosŚ
rs_cos_sinŚrs_sinhŚrs_coshŚ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atanŚatanhŚtanhŚlogŚsqrt)ŚRational)ŚexpandŚSc                 C   s   d}t | | |k sJ d S )Ng»½×Łß|Ū=)Śabs)ŚaŚbŚtol© r:   śY/var/www/visachat/venv/lib/python3.10/site-packages/sympy/polys/tests/test_ring_series.pyŚis_close   s   r<   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Rr=   ŚpŚyr:   r:   r;   Śtest_ring_series1   s    00 >22rH   c                  C   sr   t dt\} }}}|||  d }t||d}||d d|d  | |  d|d  |d  |d   ks7J d S )Nśx, y, tr>   r@   é   r?   )r   r   r   )rE   r=   rG   ŚtrF   Śp1r:   r:   r;   Ś
test_trunc!   s   DrM   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 )NrI   rA   r?   r@   rJ   é   r>   Śzc                      s   t  dS )Nr?   )r	   r:   ©rF   r=   rO   r:   r;   Ś<lambda>2   s    z test_mul_trunc.<locals>.<lambda>é   )r   r   Śranger	   r&   Ś
ValueError)rE   rG   rK   ŚirL   ŚR1Śp2r:   rP   r;   Śtest_mul_trunc'   s   `$$:rX   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 )NrI   rA   r?   r@   r>   )r   r   r	   r
   )rE   r=   rG   rK   rF   rL   rW   r:   r:   r;   Śtest_square_trunc8   s   8rY   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   rA   r@   r?   r   éž’’’r>   éQ   é	   )r   r   r   r   r3   )	rE   r=   rG   rO   Śp0rF   ŚxxrL   rW   r:   r:   r;   Śtest_pow_truncA   s   :Nrb   c                  C   sx   t dt\} }}}|||  }t||sJ ||d  }t||r#J d| |d  }t||s2J || ||  }d S )NrZ   r>   rA   )r   r   r   )rE   r=   rG   rO   rF   r:   r:   r;   Śtest_has_constant_termS   s   rc   c                     sō   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 d S )	Nr=   r?   rC   rA   rD   c                      ó   t  dS )Nr>   ©r   r:   ©rF   r=   r:   r;   rQ   j   ó    z test_inversion.<locals>.<lambda>c                      rd   )Nr@   re   r:   rf   r:   r;   rQ   l   rg   )r   r   r   r   r&   ŚNotImplementedErrorŚzeroŚZeroDivisionError)rE   ŚnrL   rG   r:   rf   r;   Śtest_inversion]   s   (rl   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 )
NrD   é
   r\   rC   é   ép   r@   é(   rJ   )r   r   r   r#   r   r   ©rE   r=   rG   rF   r:   r:   r;   Śtest_series_reversiono   s   *
’’rr   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 )Nr=   rA   r?   r@   )rA   r?   r   r>   r>   rC   rD   )rA   r@   rC   rn   r   )Śconcurrn   é   )r   r   r   Ś	from_listŚlistŚreversedr   Ścomposer   Ś	enumerater   )rE   r=   rF   ŚcŚrŚpcŚr1rG   rL   rW   ŚhrU   Ścxr:   r:   r;   Śtest_series_from_listy   s(    8r   c                  C   sl  t dt\} }d| }t||d|d  }|tdd| tj |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sqJ 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sšJ 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 )Nr=   rA   r>   r?   r@   é’’’’r_   éļ’’’r\   i  é   rn   é½   rR   rJ   é¢   rC   é-   é$   rD   r7   r]   rm   l   K)z ič^ )r   r   r   r3   r5   ŚHalfr   r(   r   r1   rx   )rE   r=   rF   rL   rW   Śp3rG   r7   r:   r:   r;   Śtest_log   sp   $<’
’
’
’T
’’
’’
’
’F’’
’2’’’ž
ž4r   c            
      C   s  t dt\} }||d  }dD ]}td| ||d }t|||}t|||}||ks-J qt||d}| |d ”tddksBJ d	}td| ||}t|||}||d ksZJ td
}t dtt||f \} }}	t|| |dt||d  d t||d  d  t||d  d  t||  t| ksJ t||d |	  | |dt||d  |	d  d t||d  |	 d  t||d  d  t||d  |	  t||d  d  t||d  |	  t||d  d  t||  t| ksJ t dt\} }}	t|| |dtt|d |d  tt|d |d   tt|d |d   tt||  tt| ksJJ t||d |	  | |dtt|d |d  |	d  tt|d |d  |	  tt|d |d   tt||d  |	  tt|d |d   tt||d  |	  tt|d |d   tt||  tt| ksĆJ d S )Nr=   r>   )rm   é   rA   r   é   l   ŃOÄ$o¢bļ®l      LÉeFS«Xé   r7   rD   rC   rB   r@   rJ   r?   )	r   r   r   r   r   Ścoeffr(   r+   r   )
rE   r=   rF   r~   ŚqrL   Śq1Śprecr7   rG   r:   r:   r;   Śtest_expÆ   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 )Nr=   r?   r>   r\   )r   r   r   )rE   r=   rF   r{   r:   r:   r;   Śtest_newtonĻ   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 )	Nr=   r@   rA   r?   rJ   r>   rN   rn   )r   r   r   )rE   r=   rL   rW   r:   r:   r;   Śtest_compose_addÕ   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 )NrD   r?   r@   rC   rm   )r   r   r    r   r   rq   r:   r:   r;   Śtest_funŪ   s   $"r   c               	   C   sī  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|| 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sõJ d S )NrD   rA   r?   r>   rm   i³’’’r\   i   rn   rJ   r@   é   é    rC   r_   é   éó   r^   rN   i   r7   éd   i>  iŠ  éČ   )r   r   r!   r(   r   r2   )rE   r=   rG   r{   r7   r:   r:   r;   Śtest_nth_rootį   sr   .’’’
’8’’’’žž
ž
ž(J&`0 ’’’6’’’’žžż
żr   c                  C   sN  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 S )NrD   r_   rn   rC   r@   r?   r\   rR   rJ   r>   r7   rA   )r   r   r   r(   r   r.   ©rE   r=   rG   r7   r:   r:   r;   Ś	test_atan÷   s   :@’’’’’žžžž
ž8
’’’&
’’’’&žż
ż>’’B’ž&ž
’’ž
żr   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 )	NrD   rC   r@   rJ   r?   rn   rp   r>   )r   r   r   ©rE   r=   rG   r:   r:   r;   Ś	test_asin
  s"   H
’’
’H’’’’r    c                  C   s.  t dt\} }}t||d|d  tdd|d  tdd t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s¹J 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s’J 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stJ ||d  d }t||d |d”tt	dt
dd  ksJ d S )NrD   r_   rC   é   é;  r?   é   rA   r@   r]   éü’’’r>   r\   rR   r   rn   rJ   r7   rm   l   PH]ųl   Įn)r   r   r   r3   r(   r,   r   r   rx   r.   r5   ©rE   r=   rG   r7   rF   r:   r:   r;   Śtest_tan  s¬   4’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 )NrD   rJ   rn   r\   iś’’’éū’’’r¤   éż’’’r]   r   rA   r?   r@   r>   rC   r£   r   )r   r   r   r   r:   r:   r;   Śtest_cot0  sN   ,’’’’’’’’’ž
žF
’’’
’’’’r©   c                  C   sB  t dt\} }}t||d|d  tdd|d  tdd t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sųJ 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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 )NrD   r_   rC   r   é°  r?   rA   éx   rJ   r]   r¤   r@   r\   rR   rN   éŠ  rn   rB   r>   r7   )r   r   r   r3   r(   r)   r*   r   r   r:   r:   r;   Śtest_sin8  s   4’0’’’’žžžžżż
ż"4’
’
’6’’’’žž
žž<’’
’:’’’žžžż
żr­   c                  C   sf  t dt\} }}t||d|d  tdd|d  tdd|  tdd|d	   tj|d
   |d  ks8J 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sĀJ td}t dt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srJ 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s1J d S )NrD   r_   rC   rA   é  r@   r¬   rB   r   rØ   r§   r?   r\   rN   rm   é0   rn   rJ   r«   r>   r7   )
r   r   r   r3   r5   r   r(   r)   r*   r   r   r:   r:   r;   Śtest_cosR  s    F’0’’’žžžžżżżż
ż"4’
’’6’’’’žž
žž<’’
’:’’’žžžż
żr°   c                  C   s   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 d S )NrD   r_   rC   )r   r   r   r   r   )rE   r=   rG   r*   r)   r:   r:   r;   Śtest_cos_sinl  s    r±   c                  C   s  t dt\} }}t||d|d  tdd|d  tdd t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s­J ||d  d }t||d |d”ttddtd ksĶJ d S )NrD   r_   rC   rA   rn   r?   r@   r]   r¤   r\   rR   rJ   r>   r7   rm   lü’’’×y«Y?l l    P{] )r   r   r   r3   r(   r   r/   rx   r„   r:   r:   r;   Ś
test_atanhu  s   N@’’’’’žžžž
ž8
’’’&
’’’’&ž
’’ž
ż4’’’B’ž&žż
ż’r²   c                  C   sf  t dt\} }}t||d|d  tdd|d  tdd t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 d S )NrD   r_   rC   rA   rŖ   r?   r«   rJ   r]   r¤   r@   r\   rR   rN   r¬   rn   rB   r>   )r   r   r   r3   r   r:   r:   r;   Ś	test_sinh  s2   N0’’’’žžžžżżżr³   c                  C   s  t dt\} }}t||d|d  tdd|d  tdd|  tdd|d	   tj|d
   |d  ks8J 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sĀJ d S )NrD   r_   rC   rA   r®   r@   r¬   rB   r   rØ   r§   r?   r\   rN   rm   rÆ   rn   rJ   r«   r>   )r   r   r   r3   r5   r   r   r:   r:   r;   Ś	test_cosh  s>   B’
’0’’’žžžžżżżżżr“   c                  C   sā  t dt\} }}t||d|d  tdd|d  tdd t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s¹J 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soJ d S )NrD   r_   rC   r   r¢   r?   r£   rA   r@   r]   r¤   r>   r\   rR   r”   r   rn   rJ   r7   rm   iü’’it'  i¦	  is'  i  )r   r   r   r3   r(   r   r0   rx   r„   r:   r:   r;   Ś	test_tanh  sd   N4’’’’žžžžżż
ż.’’6’žž
ž"’’
’’rµ   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 )NrD   r7   r?   rC   r   rA   )r   r   r   r   r   r   r)   r*   r,   r-   r.   r0   r   r   r(   Śziprx   ŚseriesŚremoveOr<   Śas_exprŚsubsrk   r!   r   )
Śrs_funcsŚsympy_funcsrE   r=   rG   r7   Śrs_funcŚ
sympy_funcrF   r   r:   r:   r;   Śtest_RR°  s    ræ   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 )NrD   rA   r?   r@   rC   )r   r   r$   rq   r:   r:   r;   Śtest_is_regular¾  s    rĄ   c                  C   s¬  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 d |tdd d  |tdd d  |tdd d  | |tdd  |tdd  ksśJ 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sXJ 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sÜJ 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 |tdd d  |tdd d  |tdd d  | |tdd  |tdd  ksTJ 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  |tdd  |tdd  |tdd d  | |tdd  |tdd  ksŌJ d S )NrD   r?   rC   r@   rA   é   r£   r>   rR   rn   r]   r_   rB   rJ   é   é   r   é   r\   r[   )r   r   r   r!   r   r"   r   r   r   r   r   r   r   r   r   )rE   r=   rG   rF   r{   r}   rL   r:   r:   r;   Śtest_puiseuxŹ  s   <’’’’’žD84N’’>’’’J’’’’’6’’’’0’’’’žžžD’’’’<’’’’@’’6’’’’@’’’’>’’’rÅ   c                  C   sģ   t  td”} |  td”}td\}}t||g| \}}}d| |t dd  d| |t dd   }t|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 )Nr?   rD   rA   r@   r   )	r   Śalgebraic_fieldr2   Ś
from_sympyr(   r   Śdictr¹   r5   )ŚKŚsqrt2r=   rG   rE   ŚxrŚyrrF   r:   r:   r;   Śtest_puiseux_algebraic	  s   ,<HrĶ   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 )1Nr=   r£   r§   r\   l    LQf rJ   i ar>   i r?   rŖ   rA   r«   r]   r¤   rm   i½’’’r”   i ųŗr   i^  r_   i   rC   rN   rn   i’’’é=   i:ké/   iP@  rR   é!   iČ  é   é*   l     L.l     ę³{µ l     ]ū
 l     ėnLl    XīnĮl    (vQ i üi _7 r®   r@   r¬   rB   )r   r   r   r!   r   r   )rE   r=   r{   rF   r:   r:   r;   Śtest1  s   0’
’
’(’’
’(’’
’’
’ž
žż
żż
üü
üü
ūū
ūūūśśrÓ   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 )NrG   r=   rA   rC   r@   r   r\   r?   rR   rJ   r_   r>   rn   )r   r   r   )rE   rG   r5   r=   rF   r{   r:   r:   r;   Śtest_puiseux2/  s.   @’’ ’
’’’žžžrŌ   c                  C   sŅ  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 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sŅJ 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sgJ d S )Nz
x, a, b, crC   r   r?   r>   rm   r@   rA   rJ   r_   rĀ   r£   rĆ   rÄ   r\   rB   rn   r[   iĄ’’’é@   r]   rN   )r(   r%   r¹   r)   r·   rø   r*   r4   r+   r,   r   r1   )r=   r7   r8   rz   rF   r{   r:   r:   r;   Śtest_rs_series:  sž   ’’ ’’ ’’$’
’4’
’,’
’0’’’’’’ @’’’@<’’’’D’’’’&’
’.
’’4
’’,
’
’
’
’
’’
žž2’’’ž
žrÖ   N)^Śsympy.polys.domainsr   r   r   Śsympy.polys.ringsr   Śsympy.polys.ring_seriesr   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   Śsympy.testing.pytestr&   r'   Śsympy.core.symbolr(   Śsympy.functionsr)   r*   r+   r,   r-   r.   r/   r0   r1   r2   Śsympy.core.numbersr3   Ś
sympy.corer4   r5   r<   rH   rM   rX   rY   rb   rc   rl   rr   r   r   r   r   r   r   r   r   r    r¦   r©   r­   r°   r±   r²   r³   r“   rµ   ræ   rĄ   rÅ   rĶ   rÓ   rŌ   rÖ   r:   r:   r:   r;   Ś<module>   sV    0	

 		?